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\begin{document}

\title{The Influence of Microstructure on the Fatigue Crack Growth Rate in
ferrite-pearlite Steels in the Paris Region}



\author[1]{Victor Igwemezie}%
\author[2]{Feargal Brennan}%
\affil[1]{Cranfield University}%
\affil[2]{University of Strathclyde}%


\vspace{-1em}



  
  \date{June 16, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
This paper presents a study on the effect of microstructure on the
fatigue crack growth rate (FCGR) in advanced normalised-rolled (NR) and
thermomechanical control process (TMCP) S355 steels in the Paris Region
of the da/dN vs. \selectlanguage{greek}Δ\selectlanguage{english}K log-log plot. The environments of study were air and
seawater (SW), under constant amplitude sinewave fatigue loading.
Discussions were based mainly on the comparison between the crack path
in the TMCP and NR steels. Fundamentally, three phenomena: crack-tip
diversion, crack-front bifurcation and metal crumb formation were
observed to influence the rate of fatigue crack growth (FCG). The
prevalence of these phenomena appears to be a function of the nature of
the material microstructure, environment and crack-tip loading
conditions. The three factors appear to retard the crack growth by
reducing or re-distributing the effective driving force at the main
active crack tip. A crack path containing extensively the three
phenomena was observed to offer strong resistance to FCG. Increase in
the FCGR was observed with decrease in the crack-tip diversion angle,
branched-crack length and metal crumbs formed. In SW, the degree of the
electrochemical dissolution of the microplastic zone (or crack-tip
blunting) appears to be an additional factor influencing crack growth in
ferrite-pearlite (\selectlanguage{greek}α-\selectlanguage{english}P) steel. This study, generally tends to present
microstructural features that strongly influenced FCGR in \selectlanguage{greek}α-\selectlanguage{english}P steels in
the Paris Region both in air and SW. This work is very important in the
design of fatigue resistant steel.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

Understanding how a crack propagates in a given material is fundamental
to all forms of theoretical postulations, modelling, analytical and
numerical analyses. If the premise of crack growth path is wrong, no
matter how elegant the mathematical or numerical expression may appear,
the result will not represent reality. The knowledge of corrosion
fatigue and its mechanism is of immense value in preventing failure in
marine environment. Understanding the influence of microstructure on
fatigue mechanism is fundamental because it supports: fatigue life
prediction of structures, design of fatigue resistant materials and
realistic fatigue modelling attempts. Fatigue is a complex problem and
there have been several numbers of publications on the problem of
fatigue, each presenting similar or different ideas or trying to modify
existing theories -- using from simple to complex analytical and
numerical approaches. Generally, fatigue crack growth (\emph{FCG} ) in
metallic materials is divided into three regions. Each region has been
reported to exhibit different mechanisms and characteristics. These
regions are the threshold region (or early stages of fatigue crack
development), the Paris Region (or the linear and steady crack growth
stage) and region of final failure (or unstable/accelerated crack growth
stage). The Paris Region is of interest in this study because it is the
part commonly used and recommended in ASTM E647-15 {[}1{]} and BS EN ISO
11782-2:2008 {[}2{]} for engineering design.

In many reports {[}3{]}{[}4{]}{[}5{]}{[}6{]}{[}7{]}{[}8{]},
microstructure, mean stress, mechanical properties and initial crack
length were said to have large influence on the threshold and final
failure regions. In addition, the accelerated region is said to be
influenced by sample thickness. These factors were reported to have
little or negligible effects when the propagating crack has grown to a
considerable length or beyond few grains, usually in the Paris Region
{[}5{]}{[}9{]}{[}10{]}{[}11{]}{[}12{]}{[}13{]}{[}14{]}. In the threshold
region, non-continuum or single shear mechanism is said to operate and
the nature of the fractured surface is seen to be faceted. The crack tip
was under both tensile and shear forces. The crack closure phenomenon
was reported to be high and the plastic zone size is equal or less than
the microstructural grain diameter. In the final or accelerated failure
region, fatigue and additional static loading modes are said to operate.
And, microvoid coalescence, intergranular or additional cleavage failure
mechanism have been found on the fractured surface and the crack tip was
under tensile loading. The plastic zone size in this final region was
reported to be very much bigger than the grain diameter.

Many researchers have reported that fatigue failure in the Paris Region
is generally by transgranular ductile striation mechanism
{[}10{]}{[}15{]}{[}16{]}. The crack path is generally taken to be across
the grains (or transcrystalline), although they may also propagate along
the grain boundaries or intergranular depending on the material
properties, loading and environmental conditions {[}17{]}. In this
linear crack growth region, the crack tip is under tensile loading and
the plastic zone size is reported to be greater than a grain diameter.
The crack closure is low and mechanism of growth is by striation --
alternating or simultaneous shear on two slip systems {[}16{]}. The
conclusions {[}3{]}{[}5{]}{[}6{]}{[}18{]} that microstructure has little
or no influence on the fatigue crack growth rate (\emph{FCGR} ) of
metallic materials is often based on the frequent observation of ductile
striation mechanism in the Paris Region in fractographs. One thing that
must be noted is that most of the fatigue theories existing today --
including that of crack extension {[}16{]}, crack path {[}15{]} and
crack closure {[}19{]}{[}20{]} were propounded from experiments
performed on non-ferrous materials. For example, two other phenomena
which are associated with crack retardation across metallic materials in
the literature are crack closure and interlocking. It is pertinent to
note that crack closure effect may be more important for non-ferrous
ductile metals. It is a common knowledge that the concept of crack
closure and the use of effective stress intensity factor range
(\emph{SIFR} ) was proposed by Elber {[}19{]}{[}20{]}. This theory is
based on the fact that plastically deformed surface wake is left behind
as the crack propagates. He argued that there is a premature contact of
the crack faces during unloading from tension in a fatigue test. This
effect reduces the effective stress at the crack tip. Elber proposed the
use of effective \emph{SIFR} instead of the conventional \emph{SIFR} in
plotting fatigue curve. The mechanisms such as the plasticity-induced
and the roughness-induced crack closure can cause retardation of
the\emph{FCGR} . However, it is pertinent to note that Elber's theory is
based on his study of 2024-T3 aerospace aluminium alloy of a moderate
ductility. The validity of this theory to steel will vary since; (a)
steel can have high ductility in annealed or fine-grained condition to
`near-brittle' ductility in martensitic or very low temperature
condition, and (b) the thickness effect in steel material. As sample
thickness of steel is increased, the plain stress region at the outer
surface tends to be eliminated leaving only plain strain condition where
plastic zone becomes little or almost negligible. Hence, the concept of
crack closure may not be rigorously applied to steel at all conditions,
coupled with the fatigue test condition under plain strain condition --
i.e. with little or negligible plastic zone at the crack tip. In other
words, when the plastic zone is little, the effect of crack closure can
then be ignored, or its consequences will be insignificant.

None of these studies in practical terms showed vividly how the crack
propagated through the phases in the microstructure of the materials
studied. There are many variables, e.g. alloying elements and their
concentrations, forming process and the mode of deformation, heat
treatment - involving temperature range, heating time, cooling time,
etc. which can be combined in so many ways to obtain varieties of steel
properties, e.g., ranging from high ductility to almost completely
brittle steel. The primary goal of this paper, therefore, is to present
some observed microstructural influence on the \emph{FCG} phenomenon in
the Paris Region of ferrite-pearlite (\selectlanguage{greek}\emph{α-P)}\selectlanguage{english} steels produced by
Normalized-rolled (\emph{NR} ) and Thermo-mechanical control process
(\emph{TMCP} ) in air and seawater (\emph{SW} ).

\section*{Metallurgy and characterisation of phase constituents of
experimental
steels}

{\label{metallurgy-and-characterisation-of-phase-constituents-of-experimental-steels}}

The increasing demand for economic steels with higher toughness, better
weldability and less expensive alloying elements has resulted to
modern\emph{TMCP} steels. These materials are increasingly being used in
the design of offshore support structures. Some of the advance
structural steels are shown in Table 1(a) and conventional steels in
Table 1(b). The \emph{TMCP} steel grades have been manufactured
specifically for offshore pipelines, platforms, pressure vessels, and
modern wind turbine installations {[}21{]}. Currently they are replacing
the more traditional ones in Table 1(b). The BS4360 Grade 50D is
equivalent to S355J2+N hot rolled normalized steel.

Table 1: (a) Advanced S355 steel subgrades for marine applications
{[}22{]} (b) Conventional S355 structural steel grades
{[}23{]}{[}24{]}{[}25{]}{[}26{]}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Offshore Structural Steel Plates & Offshore Structural Steel Plates &
Offshore Structural Steel Plates\tabularnewline
\midrule
\endhead
(a) & (a) & (b)\tabularnewline
European & Typical offshore application & European\tabularnewline
EN10225 & & EN10025 Part 2: 2004\tabularnewline
S355G7+N & Primary Structure & S355\tabularnewline
S355G7+M & Primary Structure & S355JR\tabularnewline
S355G8+N & Critical Joints & S355JO\tabularnewline
S355G8+M & Critical Joints & S355J2\tabularnewline
S355G9+N & Primary Structure & S355J2+N\tabularnewline
S355G9+M & Primary Structure & S355K2\tabularnewline
S355G10+N & Critical Joints & S355K2+N\tabularnewline
S355G10+M & Critical Joints & S355NL\tabularnewline
\bottomrule
\end{longtable}

Fig. 1(a) is common \emph{Fe-C} phase diagram showing important regions
in the heat treatment of marine steels. \selectlanguage{greek}γ \selectlanguage{english}denotes austenite,
\selectlanguage{greek}\emph{α}\selectlanguage{english}ferrite and \emph{P} pearlite. A\textsubscript{1} is an
equilibrium lower transformation temperature. Eutectoid reaction occurs
at A\textsubscript{1} which is 723*C in the binary diagram. The
Ar\textsubscript{1} temperature depicts the lower transformation
temperature upon cooling. Ac\textsubscript{1} temperature depicts the
start point of the transformation between the \selectlanguage{greek}α-\selectlanguage{english}ferrite and the
austenite \selectlanguage{greek}γ \selectlanguage{english}upon heating. A\textsubscript{3} is an equilibrium upper
transformation temperature where alpha iron (\selectlanguage{greek}\emph{α-Fe}\selectlanguage{english} ) transforms to
gamma iron (\selectlanguage{greek}γ-\selectlanguage{english}Fe) and it is 910\selectlanguage{ngerman}°C for pure iron and it is lowered with
addition of carbon. Ar\textsubscript{3} is the temperature at which
austenite \selectlanguage{greek}γ \selectlanguage{english}starts transforming to ferrite \selectlanguage{greek}α \selectlanguage{english}during cooling.
Ac\textsubscript{3} temperature depicts the upper transformation
temperatures upon heating. The line in Fig. 1(a) are straight - in fact
in the case above they are drawn arbitrarily. In reality, the shape and
position of the lines -- straight or curved, depend on the steel
chemistry, cooling rate and rolling or deformation variables.
Austenitization is the first operation in many of the most important
deformation and heat treatment processes. After austenitization, upon
cooling the austenite decomposes into various morphologies. From the
austenite region, the bcc \selectlanguage{greek}α-\selectlanguage{english}ferrite is reported to be the first to
nucleate at the austenite grain surfaces. Other microstructures that
form as the transformation temperature is lowered are pearlite (\emph{P}
), bainite, and martensite.

The nature of \selectlanguage{greek}\emph{α-P}\selectlanguage{english}microstructure due to heat treatment can be
explained by the type of heat treatment process -- commonly referred to
as as-rolled (\emph{AR} ), normalized (\emph{N} ), normalized-rolled
(\emph{NR} ), quenched and tempered (\emph{Q\&T} ) and thermomechanical
control process (\emph{TMCP} ). The common phases in these steels are
ferrite (\selectlanguage{greek}\emph{α} \selectlanguage{english}) and pearlite (\selectlanguage{greek}\emph{α+Fe\textsubscript{3}C}\selectlanguage{english} ). Fig.
1(b - f) are schematic of heat treatment of modern steel. The heat
treatments of interest in this study are \emph{AR} , \emph{N} ,
\emph{NR} and\emph{TMCP} . \emph{Normalizing} involves cooling of
austenitized steel, usually in air, to a temperature substantially below
the transformation range {[}27{]}. The austenitizing temperature for
normalizing is typically 30--80\selectlanguage{ngerman}ºC above the Ac\textsubscript{3}
transformation temperature (the upper critical temperature, 800 -- 925)
for hypoeutectoid steels. As-rolled is obtained by austenitizing at say
about 1250 °C, holding for specified time and then deforming at roughing
and finishing mills within the austenite range. The finishing rolling
may, for example, be at some temperature above Ac\textsubscript{3} and
the steel is allowed to cool naturally to room temperature as shown in
Fig. 1(b).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Fig. 1: Heat treatments of modern steel. (a) a schematic phase diagram
of carbon composition range and phases expected in the microstructure of
marine steel, (b \& c) rolling and normalization (d) TMCP route
involving reheating, accelerated cooling and self-temper or tempering at
temperature below Ac\textsubscript{1} (e) rolling, accelerated cooling
and (f) rolling, direct-quenching and tempering at temperature below
Ac\textsubscript{1} {[}28{]}{[}29{]}.

Normalized steel (\emph{N} -steel) is commonly obtained when the
as-rolled steel is reheated to about 900\selectlanguage{ngerman}°C or very little above
Ac\textsubscript{3,} held for a desired period and allowed to cool
naturally back to room temperature as shown in Fig. 1(c). When the
finishing rolling operation is done at a temperature above about 900°C
before cooling naturally to room temperature, a\emph{NR} -steel is
obtained. Here no reheating is necessary. Normalized and \emph{NR}
steels have practically the same properties and so are designated
`\emph{N} '. The strength or other properties of the steel can be
increased by addition of small amount of alloying elements and then
quenched or accelerated-cooled and tempered as shown in Fig. 1(d). The
tempering is then done below Ac\textsubscript{1}. \emph{TMCP} is a
microstructural control technique combining controlled rolling
(\emph{CR} ) and accelerated cooling to obtain exceptional
strength-toughness combinations in low-alloy steels by grain refinement
{[}29{]}{[}30{]}{[}31{]}{[}32{]}. In general, controlled-rolling,
controlled-cooling, accelerated cooling and direct-quenching are typical
examples of thermomechanical processing {[}29{]}. Controlled rolling
involves carrying out of the finishing deformation at temperature
sufficiently low to prevent grain growth of the recrystallized austenite
during cooling. The property obtained may not be different from those
obtained after normalization {[}28{]}{[}29{]}. The \emph{TMCP} route is
illustrated in Fig. 1(e \& f) {[}28{]}. Traditional marine steels shown
in Table 1(b) are produced by\emph{AR} , \emph{N} or \emph{NR} . The
\emph{TMCP} steels production route is proprietary and so processing
conditions and number of deformations are slightly different, producing
what may appear as variation in the \selectlanguage{greek}\emph{α} \selectlanguage{english}and \emph{P} sizes and
morphologies.

Ideally, most common marine steels have microstructures consisting of
very small volume fraction of \emph{P} in a \selectlanguage{greek}\emph{α} \selectlanguage{english}matrix. It may be
called \selectlanguage{greek}\emph{α-P}\selectlanguage{english} steels where volume fraction of \emph{P} phase is
significant. The common \selectlanguage{greek}\emph{α} \selectlanguage{english}morphologies are grain boundary
allotriomorphic \selectlanguage{greek}\emph{α} , \selectlanguage{english}idiomorphic \selectlanguage{greek}\emph{α} , \selectlanguage{english}Widmanst\selectlanguage{ngerman}ätten \selectlanguage{greek}\emph{α}
, \selectlanguage{english}and intragranular \selectlanguage{greek}\emph{α} \selectlanguage{english}or acicular \selectlanguage{greek}\emph{α}\selectlanguage{english} {[}33{]}. The
\selectlanguage{greek}\emph{α}\selectlanguage{english}morphologies commonly encountered or that dominate in marine
steels are the allotriomorphic and idiomorphic \selectlanguage{greek}\emph{α} . \selectlanguage{english}In this study
they will collectively be referred to as \selectlanguage{greek}\emph{α} . \selectlanguage{english}The microstructure
shown in Fig. 2(a) is air-cooled of medium carbon steel and the
relatively rapid method of cooling, limited the \selectlanguage{greek}\emph{α} \selectlanguage{english}grain growth.
The \selectlanguage{greek}\emph{α} \selectlanguage{english}then appears to form layers which followed the austenite
grain boundary contours. The prior austenite grain boundaries are
completely covered by the \selectlanguage{greek}\emph{α} \selectlanguage{english}allotriomorphs and the residual
austenite has transformed into \emph{P} upon reaching the temperature,
723 \textsuperscript{o}C, of eutectoid reaction. The \selectlanguage{greek}\emph{α} \selectlanguage{english}phase is
soft and ductile, while the\emph{P} is hard and brittle. \emph{P} grows
in colonies and each colony consists of a thin lamellar, alternating
mixture of \selectlanguage{greek}\emph{α} \selectlanguage{english}(iron) and cementite, \selectlanguage{greek}\emph{θ} \selectlanguage{english}(iron carbide) or
(\selectlanguage{greek}\emph{α+Fe\textsubscript{3}C}\selectlanguage{english} ). Fig. 2(b) shows a situation where the
Fe - 0.4C steel is slowly cooled to room temperature, producing equiaxed
grains. Several distinct\emph{P} colonies can be seen (dark etching).
The \selectlanguage{greek}\emph{α} \selectlanguage{english}phase (light etching) is soft and ductile, while the
\emph{P} is hard and brittle. As the volume fraction of \emph{P}
increases the bulk strength increases and ductility decreases. If the
carbon content of the steel is decreased, the volume fraction of
\emph{P} in the microstructure will decrease while that of \selectlanguage{greek}\emph{α}
\selectlanguage{english}increases as can be seen in Fig. 2(c). The morphology or shape of the
\selectlanguage{greek}\emph{α-P}\selectlanguage{english} phases therefore depends on the processing route discussed
above and electrochemical composition. These two phases are of major
interest in this study. Any other phase that might be present for the
purposes of clarity is neglected.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\par\null

Fig. 2: Ferrite and pearlite morphologies: (a) ferrite in Fe-0.46 steel
that forms layer tracing the austenite grain boundary contours {[}34{]},
(b) equiaxed ferrite in a Fe-0.4C steel {[}33{]}, (c) ferrite in low
carbon steel {[}33{]} (\selectlanguage{greek}\emph{α} \selectlanguage{english}= ferrite, \emph{P} = pearlite). The
white etching is ferrite while the dark-etching is\emph{P}.

The steels for this study are S355J2+N (J2N), S355G10+M (G10) and
S355G8+M (G8) with compositions as given in Table 2. The composition of
J2N was extracted from {[}35{]}. They are marine steels having low
carbon contents with the microstructures consisting of very small volume
fraction of \emph{P} in a \selectlanguage{greek}\emph{α} \selectlanguage{english}matrix {[}36{]}. Fig. 3 shows the
phase morphologies of the microstructure of the J2N.

Table 2: Chemical compositions and mechanical properties of test
materials (see {[}36{]})

(CE = carbon equivalent)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Fig. 3: Photomicrographs of \selectlanguage{greek}\emph{α-P}\selectlanguage{english} steels - NR - S355J2+N

In Fig. 3(a), the optical micrograph shows that the microstructure is
composed of \emph{P} (dark etching) and the rest \selectlanguage{greek}\emph{α} \selectlanguage{english}(light
etching). Microstructural examination of S355J2+N shows that, 80\% of
the microstructure is allotriomorphic \selectlanguage{greek}\emph{α} \selectlanguage{english}and others \emph{P} ,
with traces of acicular or Widmanst\selectlanguage{ngerman}ätten \selectlanguage{greek}\emph{α}\selectlanguage{english} {[}37{]}. The \emph{P}
colonies in the J2N- steel are large, blocky and dense. This is a
consequence of its chemical composition, heat-treatment and deformation
or manufacturing method. Fig. 3(b) is the SEM micrograph of the
microstructure. The blocky\emph{P} and the proeutectoid \selectlanguage{greek}\emph{α} , \selectlanguage{english}are
noted accordingly. The proeutectoid \selectlanguage{greek}\emph{α} \selectlanguage{english}is the \selectlanguage{greek}\emph{α} \selectlanguage{english}phase that
formed before the formation of \emph{P} at the eutectoid temperature
(723\textsuperscript{o}C). Fig. 3(c) is the part denoted with a yellow
box in Fig. 3(b) and the micrograph shows differently oriented
\emph{P}colonies as demarcated by the yellow lines. Fig. 3(d) shows what
would have been the image of the part in the yellow box in Fig. 3(c) on
a typical transmission electron microscopy (TEM) micrograph. The
structure that appears as parallel rods in that colony is the cementite
(\selectlanguage{greek}\emph{θ} \selectlanguage{english}). Note that the \selectlanguage{greek}\emph{θ} \selectlanguage{english}plates are not generally continuous.
The \selectlanguage{greek}\emph{α} \selectlanguage{english}that formed in between the \selectlanguage{greek}\emph{θ} \selectlanguage{english}rods are referred to as
eutectoid \selectlanguage{greek}\emph{α} -- \selectlanguage{english}because they are produced during the
\emph{P}formation at the eutectoid temperature. Fig. 3(d), is extracted
from Ref {[}33{]}. Fig. 4 shows the microstructures of G10, G8. These
microstructures are found to be similar, but it is evident that they are
distinct from that of J2N in Fig. 3. Fig. 4(a) is the optical image of
G10 while Fig. 4 (b) is the SEM image. Similarly, Fig. 4(c) is the
optical image of G8 while Fig. 4(d) is the SEM image. It is evident that
the SEM image shows more details of the microconstituents. In both
microstructures, the \emph{P} nodules are very small compared to that of
J2N and the volume fraction of the \emph{P} is also less than that of
J2N.

Fig. 5 shows the morphologies of the phases present in J2N in the
rolling direction. The ferrite phase tends to have three forms -- high
relief (\emph{HR} ), low relief (\emph{LR} ) and ribbon like structure
(\emph{HA} ) as shown in Fig. 5(a). Note that the low and high
relief\selectlanguage{greek}\emph{α} \selectlanguage{english}phase variants could not be distinguished under optical
micrographs (see Fig. 3(a)). These features are important in analysing
the work presented in this paper. For the purposes of description,
let\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} denotes\selectlanguage{greek}\emph{α} \selectlanguage{english}with high relief and
\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} is low relief while the ferrite ribbon is
denoted \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} . The yellow arrow shows the \emph{P}
, the blue arrow indicates the\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} , the red arrow
is the\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} and the black arrow is
the\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} . To the extent of information available
to the authors, the \selectlanguage{greek}\emph{α} \selectlanguage{english}phase morphology observed in Fig. 5(a) is
novel and has not been described in any literature elsewhere. Fig. 5(b
to d) show the Energy-Dispersive X-ray (EDX) analyses of the chemical
composition of the phases present in the J2N at locations 1 to 31 and
the results are shown in Table 3.

\par\null\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Fig. 4: Optical and SEM micrographs of \selectlanguage{greek}\emph{α-P}\selectlanguage{english} \emph{TMCP} steels (a)
TMCP - S355G10+M

\par\null\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Fig. 5: EDX analysis of phase composition in S355J2+N steel

Table 3: EDX compositional average results of \selectlanguage{greek}\emph{α} \selectlanguage{english}and \emph{P}
phases in Fig. 5

(\emph{HR} = high relief \selectlanguage{greek}α, \selectlanguage{english}\emph{LR} = low relief \selectlanguage{greek}α, \selectlanguage{english}\emph{HA} = \selectlanguage{greek}α
\selectlanguage{english}ribbon, EDX= Energy-dispersive X-ray analysis)\selectlanguage{english}
\begin{longtable}[]{@{}llllllllllllll@{}}
\toprule
Spect. Label & C & Mn & Ni & Si & Cu & Cr & Mo & Al & Co & P & S & O &
Fe\tabularnewline
\midrule
\endhead
\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} Average & 5.50 & 1.41 & 0.09 & 0.37 & 0.02 &
0.02 & 0.01 & 0.12 & 0.41 & 0.02 & 0.01 & 0.10 & 91.79\tabularnewline
\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} Average & 5.59 & 1.36 & 0.08 & 0.37 & 0.02 &
0.02 & 0.01 & 0.12 & 0.40 & 0.02 & 0.01 & 0.07 & 91.79\tabularnewline
\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} Average & 9.86 & 1.41 & 0.09 & 0.46 & 0.04 &
0.02 & 0.01 & 0.17 & 0.39 & 0.03 & 0.01 & 0.45 & 88.12\tabularnewline
\emph{P} Average & 9.33 & 1.50 & 0.08 & 0.40 & 0.06 & 0.02 & 0.01 & 0.11
& 0.38 & 0.02 & 0.02 & 1.38 & 86.59\tabularnewline
\bottomrule
\end{longtable}

The relative abundance of the alloying elements in the phases is in
wt\%. Note that the EDX composition simply shows the relative abundance
of the alloying elements within an area in the phase and has no direct
relationship with the steel overall composition shown in Table 2. In
Fig. 5(b to d), locations 1, 3, 4, 16, 21, 30, etc., are areas of
analyses on the \selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} , while 2, 5, 17, 25, 28,
etc. are areas on the \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} . The light etching is
the\emph{P} , e.g. locations 6, 7, 8, 13, 26 etc. In Table 3, simple
observation of the EDX results show that the alloying compositions of
\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} and\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} are almost the
same. But for the\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} , all other alloy
compositions are generally the same with that of
\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} and\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} except that the
amount of C, Si, Al and O are higher. The Fe content of
\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} and \emph{P} are close, but lower than those
of \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} and\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} . This tends
to suggest that\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} is a ferrite phase with the
highest concentration of alloying solutes. The \emph{P} is found to have
generally the same composition with the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} , but
with higher oxygen content. An important note here is that the
concentration of these solutes may weaken this phase, making it an easy
path for \emph{FCG} . General observed phase morphologies of J2N, G8 and
G10 are shown in Fig. 6. Fig. 6 (a \& b) are that of J2N obtained in the
through thickness direction. The same basic microstructural features as
presented in Fig. 5(a) were also observed in Fig. 6 (a \& b). Fig. 6(c
to i) present microstructural features in the \emph{TMCP} steels which
are basically the same as that found in the J2N steel. For the
\emph{TMCP} , the \(P\) formed mainly between boundaries of
the ferrite grains and with width that is relatively small. In the
\emph{NR} steel, \(P\) forms as dense and blocky phase in
the \selectlanguage{greek}\emph{α}\selectlanguage{english}matrix.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

Fig. 6: Phase morphologies of J2N, G8 and G10 S355 steel subgrades
showing\selectlanguage{greek}\emph{α} \selectlanguage{english}and \emph{P} phases

\section*{FCGRs in NR and TMCP S355 steels in
air}

{\label{fcgrs-in-nr-and-tmcp-s355-steels-in-air}}

The formation of the microstructural phase morphologies described in
Section 2 created different local microstructural properties. The
presence of a hard phase (\emph{P} ) in a soft matrix (\selectlanguage{greek}\emph{α} \selectlanguage{english}) is
expected to influence local\emph{FCG} behaviour in steel {[}38{]}. The
crack paths in these microstructures are also expected to vary. Steel
microstructure influences fatigue crack propagation primarily by
changing the mode of crack propagation. The mode can change from ductile
striation to cleavage mode and the combination of the two modes
increases crack propagation rates. There are many studies that claimed
that microstructure has negligible effect at intermediate \emph{FCGR} s
(Paris Region) {[}3{]}{[}5{]}{[}6{]}{[}11{]}{[}12{]}
{[}13{]}{[}14{]}{[}18{]}. Some other study concluded that grain size
affected sub-critical crack growth to the extent to which it affected
fracture toughness,\emph{K} \textsubscript{Ic} and the onset of rapid
fracture, and that grain size did not affect the \emph{FCG}
threshold,\selectlanguage{greek}\emph{ΔK}\selectlanguage{english} \textsubscript{th} {[}4{]}. Zerbst {[}6{]} in his
recent publication reported, I quote, `\ldots{} \emph{Perhaps the most
astonishing observation is that the curve, in the Paris Region, is only
slightly influenced by the microstructure of the material within whole
material classes such as steels or aluminium alloys} .' In fact, it is
commonly reported that microstructure has little or no influence in the
Paris Region of the da/dN sigmoidal curve in air. Part of the
presentation in this paper is to show what appears to be an influence of
the \emph{FCGR} by microstructural phase morphologies in the Paris
Region of the da/dN vs. \selectlanguage{greek}Δ\selectlanguage{english}K curve.

In the recent studies, the authors evaluated the resistance of the
\emph{NR} and \emph{TMCP} steels given in Table 2 to \emph{FCG} . The
details of the experimental methods have been discussed in Refs
{[}22{]}{[}36{]}{[}39{]}. The results of that experiment - for
\emph{FCGR} tests in air are shown in Fig. 7. Shown also are the
microstructures of the J2N and \emph{TMCP}(G10 \& G8) steels examined.
In Fig. 7, it appears there is a demarcation between the \emph{FCGR} of
\emph{NR} and \emph{TMCP} in the Paris Region. The arbitrary line drawn
as shown appears to be the separation line. The \emph{FCGR} in G8 and
G10 steels are essentially the same and significantly lower than that of
the J2N steels under the same experimental conditions. Generally, the
\emph{FCGR} increased with increase in load level from 10kN to 12kN in
J2N and also from 9kN to 10kN in \emph{TMCP} . This is the expected
trend in air, where increase in the fatigue load level increases the
\emph{FCGR} . We can also observe that the \emph{FCGR} in J2N for 10kN
under 2Hz and 5Hz are essentially the same. This tends to confirm that
frequency has no effect on the\emph{FCGR} of steel in air under the same
loading conditions. To validate this finding, a comparative study of
\emph{FCGR} in \emph{NR}and \emph{TMCP} was carried out. The steel
grade, chemical composition in wt\% (approximated to two decimal places)
and mechanical properties of the steels studied and compared with the
data in this study are included in Table 4. The composition range for
the steels in Table 4 is shown in Table 5. It is pertinent to note that
BS4360 Grade 50D, Q345, RD480 and EH36 are equivalent to S355J2+N
hot-rolled normalized steel. Q345 is common structural steel in China
and used in the nuclear industry and petrochemical plants. Laurito
studied \emph{FCGR} in intercritical-isothermally-quenched
grain-modified steel designated as RD480. Though the chemical
composition is comparable to other steels, the properties of the
microstructure generated may differ significantly due to this heat
treatment. Two microstructures of the same ABS grade EH36 steel produced
by \emph{NR} and \emph{TMCP} are presented. This steel is often used in
shipbuilding. Comparing these two microstructures of the same alloy will
clearly support this study. Table 6 lists all the studies and test
conditions considered. All the steels are designed to be used in both
onshore and offshore structures. They are fundamentally the same. The
only difference perhaps is that the steels were produced under different
proprietary methods by different steel plants. All the tests were done
under constant-amplitude sinewave, except Cheng {[}40{]} who performed
his test under random waveform. The general range for temperature of the
studies is about 27 \textsuperscript{o}C to 0\textsuperscript{o}C.

From the conclusions in the literatures
{[}41{]}{[}42{]}{[}43{]}{[}44{]}{[}45{]}{[}46{]}{[}47{]}, stress ratio
(R) in the range 0.1- 0.85, frequency in the range 0.005Hz -- 50Hz and
waveforms appear to have little or no effect on the \emph{FCGR} in
the\selectlanguage{greek}\emph{α-P}\selectlanguage{english} steels in air. Thus, the inferences here are within these
limits.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

\par\null

Fig. 7: Plot of FCGR in air for NR (J2N) and TMCP steel subgrades (G8 \&
G10)

Table 4: Chemical compositions of the ferritic steels for comparative
study\selectlanguage{english}
\begin{longtable}[]{@{}llllllllllll@{}}
\toprule
\begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
Study\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
Steel Grade\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
C\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
Mn\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
Ni\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
Si\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
Cu\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
Cr\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
Mo\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
E\%\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
YS (Mpa)\strut
\end{minipage} & \begin{minipage}[b]{0.08\columnwidth}\raggedright\strut
UTS (Mpa)\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Scott {[}48{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
BS4360-50D (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.18\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.38\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.37\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
370\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
538\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Appleton {[}49{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
BS4360-50D (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.13\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.22\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.32\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
368\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
508\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Thorpe {[}50{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
BS4360-50D \emph{(NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.17\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.35\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.07\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.35\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.17\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.09\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
370\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
538\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Musuva, {[}41{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
BS4360-50D (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.18\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.40\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.10\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.36\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.16\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.11\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
30\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
386\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
560\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Thompson {[}51{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
BS4360-50D (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.15\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.38\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.10\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.41\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.11\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
30\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
386\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
536\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Correia {[}52{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
P355NL1 (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.13\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.38\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.12\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.35\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.14\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
418\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
568\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Jesus {[}42{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
EN 10025 S355 (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.10\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.64\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.10\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.15\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.38\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.08\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
419\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
766\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Adedipe {[}53{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
S355J2+N (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.22\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.60\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.50\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.55\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.55\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.10\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
345\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Xiong {[}54{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Q345 (NR)\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.15\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.54\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.34\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
26\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
370\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
585\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Laurito {[}55{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
RD480 (\emph{IGM})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.09\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.17\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.05\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
459\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
541\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Cheng {[}40{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
EH36 (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.12\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.39\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.38\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.05\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.05\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
350\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Callister {[}56{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
K-50 (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.05\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.13\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.29\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.23\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.24\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.20\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
470\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Tsay {[}57{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
EH36 (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.13\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.32\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.31\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
420\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
Chapetti {[}58{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
UFG -- steel (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.15\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.80\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.20\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
14\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
696\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1183\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
PS (T)\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
S355G10+M (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.06\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.57\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.33\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.27\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.24\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
38\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
435\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
545\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
PS \& Ali {[}59{]}{[}60{]}\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
S355G8+M (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.05\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
1.52\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.32\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.27\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.24\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
35\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
447\strut
\end{minipage} & \begin{minipage}[t]{0.06\columnwidth}\raggedright\strut
549\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 6: Experimental conditions for the studied steels in Table 4\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
\begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{Study by}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{Steel grade}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{Wave} \textbf{form}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{Freq. (Hz)}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{R}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{\%EL}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{YS (MPa)}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Scott {[}48{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
BS4360-50D\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
1 - 10\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0 - 0.85\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
370\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Appleton {[}49{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
BS4360-50D\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
368\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Thorpe {[}50{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
BS4360-50D\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
1 - 10\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
370\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Musuva {[}41{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
BS4360-50D\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
30\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.08, 0.5, 0.7\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
30\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
386\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Thompson {[}51{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
BS4360-50D\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
30\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
386\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Correia {[}52{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
P355NL1 (\emph{NR})\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.0\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
418\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Jesus {[}42{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
S355\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
[?] 20\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.25, 0.5 \& 0.75\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
22\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
419\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Adedipe {[}53{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
S355J2+N\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
20\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
345\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Xiong {[}54{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Q345\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1 - 0.5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
26\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
370\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Laurito {[}55{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
RD480\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
32\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
459\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Cheng {[}40{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
ABS grade EH36\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
r\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
10\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1 \& 0.5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
350\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Callister {[}56{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Kontroll-50 (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.6\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
470\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
Tsay {[}57{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
EH36 (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
21\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
420\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
PS (T)\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
S355G10+M (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
4\&5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
38\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
435\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
PS \& Ali {[}59{]}{[}60{]}\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
S355G8+M (\emph{TMCP})\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2\&5\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.1\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
35\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
447\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s = sine, r = random, PS = present study\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s = sine, r = random, PS = present study\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s = sine, r = random, PS = present study\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s = sine, r = random, PS = present study\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s = sine, r = random, PS = present study\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s = sine, r = random, PS = present study\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
s = sine, r = random, PS = present study\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

The marine steels have microstructures consisting essentially of small
volume fraction of \emph{P} in a \selectlanguage{greek}\emph{α} \selectlanguage{english}matrix. The morphology of the
phases varied from banded to unbanded depending on the production
process and sample thickness. The general microstructures of the steels
in Table 4 are shown in Fig. 8. The grade of steel and the reference
sources are also given. Fig. 8(a, b, c, d) are microstructures
of\emph{NR} steels. The black etching is a banded \emph{P} forming in
the rolling direction and the light etching is the \selectlanguage{greek}\emph{α} . \selectlanguage{english}Fig. 8(e
\& f) are microstructures of the same \emph{NR} steels, but taken from
directions that are un-banded {[}37{]}. Fig. 8(g) is
\emph{TMCP}microstructure of the EH36 steel studied by Tsay {[}57{]}.
The microstructure of \emph{TMCP} steels is greatly refined as compares
to those of conventional or \emph{NR} steels, resulting in a significant
improvement in strength and toughness. Hardness was measured to be
around 168HV\textsubscript{0.1} with equiaxed grains of average size of
15\selectlanguage{greek}µ\selectlanguage{english}m, measured in the through-thickness direction.

Fig. 9 presents the plots of the \emph{FCGR} studies on the \emph{NR}and
\emph{TMCP} steels listed in Table 6, including the results of the
present study (\emph{PS} ) in Fig. 7. For the test IDs in the \emph{PS}
, each sample is denoted with material type (e.g. J2N, G8 and G10),
followed by the environmental air (A), the maximum load applied,
P\textsubscript{max}, on the sample (e.g. 10 kN), and the
applied\emph{f} (e.g. F of 0.2, 0.3 and 0.5 Hz). The \emph{NR} data
points are denoted with circles in Fig. 9. The J2N data points in the PS
are coloured yellow, the NR data points extracted from the literatures
are green or black. The \emph{TMCP} data points are denoted with
squares. The same trend observed in Fig. 7 is also seen in Fig. 9. It
can be observed that in the Paris Region taken in the interval 20[?]
\selectlanguage{greek}Δ\selectlanguage{english}K[?]35, the\emph{FCGR} for the two microstructures separated into two
domains, but with diffused inter-boundaries. The dash line is drawn
arbitrarily to show possible demarcating line. Occupying upper half is
the fatigue data points of \emph{NR} steels and the lower half the
\emph{FCGR} data points for the \emph{TMCP} . In other words, the
\emph{FCGR} in \emph{NR}are generally higher than that of \emph{TMCP} in
air.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

Fig. 8\textbf{:} Typical microstructures of low alloy \selectlanguage{greek}\emph{α- P}\selectlanguage{english} steels

One interesting note here is that even though the steels have similar
micro-constituents, the \emph{FCGR} s are significantly apart,
especially at low \emph{SIFR} . Often, many researchers associate this
variation in the Paris Region with material variability or crack closure
(R-factor), but we could see that the margin of separation is very much
significant -- up to a factor of about 4 from the two extremes. An
important observation also is that the\emph{FCGR} of the two
microstructural variants (\emph{NR} \&\emph{TMCP} ) of the EH36 steel
studied by Cheng {[}40{]} (\emph{NR} ) and Tsay {[}57{]} (\emph{TMCP} )
under similar experimental conditions are different. The \emph{FCGR}
data of the EH36 (\emph{NR} ) denoted with black circle in Fig. 9
partitioned into the \emph{NR} domain while that of EH36 (\emph{TMCP} )
separated into the \emph{TMCP} domain as shown by the black square. Note
that within this region the effect of crack closure is insignificant or
negligible. In general, Fig. 9 tends to suggest that microstructure
affected the \emph{FCGR} in air.

\subsection*{Microstructure and FCG path in
air}

{\label{microstructure-and-fcg-path-in-air}}

Post-failure examination of the fatigued surfaces in air revealed
features shown in Fig. 10. The fractographs Fig. 10(a \& b) were
obtained from the \emph{NR} steel (J2N), while that of Fig. 10(c \& d)
were obtained by Adedipe {[}63{]} for the same steel grade. Fig. 10(e)
is the fractograph obtained in air for the \emph{TMCP} steel. The part
in a red box in Fig. 10(e) was magnified as shown in Fig. 10(f) and the
area in the red box in Fig. 10(g) was magnified to that shown in Fig.
10(h). From all the fractographs, it is very obvious that the failure in
air had occurred by ductile striation mechanism (\emph{DSM} ) with
secondary crackings (\emph{SC} ) as shown by the arrows. Few \emph{SC}
in the normalised steel, J2N and more \emph{SC} in the \emph{TMCP} were
observed. The occurrence of the \emph{SC} increased with increase
in\emph{SIFR} . Striations were seen even inside the secondary cracks as
can be seen in Fig. 10(f \& h). This shows that the groove was made by a
moving crack front and not due to brittle cracking or cleavage.
The\emph{DSM} as seen in the fractograph is typical of the failure
mechanism in the Paris Region for low carbon steel. These fractographs
do not give significant clue to the observed difference in
the\emph{FCGR} in Fig. 7 and Fig. 9. An altervative approach is to
examine the crack path and the features influencing crack growth in the
materials.

To understand the disparity in the \emph{FCGR} between \emph{NR} and
the\emph{TMCP} steels as presented in Fig. 7 and Fig. 9, a crack path
metallography was carried out and the result is presented in Fig. 11 for
the \emph{TMCP} steel, G8. Fig. 11(a) shows the general crack paths seen
in the \emph{TMCP} steels in air for 10kN, 5Hz, stress ratio of 0.1,
under sinewave. The yellow double line arrow in the figures shows the
direction of the applied fatigue load. The long crack path was obtained
for [?]\emph{K} of about 18.52 to 34.25 MPa[?]m, i.e. fully in the Paris
Region. It is very clear that the crack path is non-planar and complex.
The traces of the crack path are given in Fig. 11(b). The crack path has
extensive high degree of large angle crack diversions, multiple
bifurcations and crumb formations as noted clearly in Fig. 11(b).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

Fig. 9\textbf{:} The FCGR in NR and TMCP in air in the Paris Region with
demarcation line\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}

Fig. 10: Fractographs of fatigued surfaces (a-d) for J2N, (e-h) for the
G10 in air

(Ductile striation mechanism (\emph{DSM} ) with secondary crack
(\emph{SC} ))

\par\null

The metal crumbs were formed in between branched and re-joined crack
fronts. It can also be observed that several small metal crumbs were
formed as the crack propagated in air and the occurrence increased with
increase in [?]\emph{K} . In other words, the tendency for crack branching
and re-joining tends to increase with increase in the driving force for
crack propagation. The length of the branched crack is considerably
long, and the extent of bifurcation angle is substantially large. Fig.
11(c) is the magnification of the locations 1 to 8 marked with the
yellow boxes. It was observed that the branched crack fronts generally
followed the thin ribbon \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} phase as shown in
the magnified locations. This tends to suggest
that\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} is the path of least resistance. An
important feature of the crack growth is that generally the tip of the
propagating crack was always sharp as can be seen from the tip of the
branched crack front as shown in the magnified micrographs in Fig.
11(c).

\textbf{Hosted file}

\verb`image15.emf`  available at \url{https://authorea.com/users/311001/articles/441756-the-influence-of-microstructure-on-the-fatigue-crack-growth-rate-in-ferrite-pearlite-steels-in-the-paris-region}

Fig. 11\textbf{:} Crack path (a) in \emph{TMCP} steels in air: G8, 10kN,
5Hz, sinewave at a scale of 20 \selectlanguage{greek}µ\selectlanguage{english}m, crack length between about 20.33 mm
(18.52 MPa[?]m) to 30.09 mm (34.25 MPa[?]m), (b) schematic of the crack
path, (c) magnification of the crack front

(direction: from right to left)

The crack tip maintained its sharpness throughout the Paris Region in
the range 18.52 to 34.25 MPa[?]m. For the fact
that\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} could influence crack front diversion in
the Paris Region is very important in the design of fatigue resistant
steel. The fractographs of fatigued surfaces as shown in Fig. 10 can
only show mechanism of the growth but cannot show these phenomena found
in Fig. 11 specially the formation of the metal crumbs, which has not
been reported in any literature. Due to many branched and arrested
cracks, it is expected that the fractography of the fractured surface
for this sample will likely show many occurrences of \emph{SC} s. This
is evident in Fig. 10(e \& g) where many secondary cracks are present.

Fig. 12(a) shows the crack path observed in \emph{NR} steel in this
study. Relative to the crack morphology in the \emph{TMCP} (see Fig.
11(a)), a low-angle crack diversion and low-angle, short-length
branching were seen. The red arrows show the low-angle crack diversion,
the black arrows the low angle crack branching and the white arrows show
some metal bits or crumbs. Fig. 12(b) is the schematic of the crack path
showing clearly the enumerated features. This \emph{NR} crack path is
clearly different from that of the \emph{TMCP} (Fig. 11(b)) and it is a
function of the microstructural features. In comparison with the crack
growth path in J2N, the crack path in the \emph{TMCP} is more complex
with extensive high angle crack diversion and crack branching. The
lengths of the branched cracks are considerably longer than that of J2N.
There was also severe formation of relatively large metal crumbs in air
in \emph{TMCP} than in J2N. Several small metal crumbs were also seen as
the [?]\emph{K} increased. The crack-tip diversion, branching and creation
of metal crumbs can reduce the effective stress at the local crack tips
resulting in retardation of the \emph{FCGR} . Fundamentally, the degree
of crack tip stress shielding will vary with the angle of crack-tip
diversion and the nature of metal crumbs created. The metal bit will be
effective in retarding the crack growth if it re-orients and causes
mismatch or wedging action. The tendency to re-orient may increase if
the crumbs are smaller in rough-round shape rather than in
plate-elongated form. These two natures of metal crumbs will be a
function of the steel microstructure

\textbf{Hosted file}

\verb`image16.emf`  available at \url{https://authorea.com/users/311001/articles/441756-the-influence-of-microstructure-on-the-fatigue-crack-growth-rate-in-ferrite-pearlite-steels-in-the-paris-region}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image17/image17}

\end{center}
\end{figure}

Fig. 12: Fatigue crack path (a) in J2N steel in air (10kN, 5Hz at a
scale of 20 \selectlanguage{greek}µ\selectlanguage{english}m) (b) schematic of the crack path

(direction: from right to left)

Fig. 13 shows the \emph{FCGR} s in two samples of the \emph{NR} (the
circle data) and three samples of the \emph{TMCP} (the square data)
steels. As noted, the tests were performed in air under similar test
conditions at 10kN and 2Hz, 5Hz for the three materials - J2N, G8 and
G10. Note that the microstructures of G8 and G10 are generally the same
(see Fig. 4). The \emph{FCGR} s at 10kN, 2Hz (J2N-A10F2) and that of
10kN, 5Hz (J2N-A10F5) are generally the same, though that of J2N-A10F2
is slightly higher. This may be because the maximum fatigue loading,
P\textsubscript{max} can be fully delivered during test at reduced
frequency. Generally, these tests show that the effect of frequency
on\emph{FCGR} in air is negligible within the same steel subgrade. An
important feature of the crack growth is that generally the tips of the
propagating cracks in the \emph{TMCP} steel are always sharp throughout
the Paris Region (see Fig. 11(c)). High angle crack bifurcation and
diversion are generally absent, and the formation of metal crumbs are
few in the \emph{NR} steel. This explains the reason for the
higher\emph{FCGR} in the \emph{NR} as compared with the \emph{TMCP}
steel. This implies that, the longer the branched arms; the more the
diversions and branching angles; the more the crack growth is retarded
due to re-distribution and reduction of the driving force at the main
crack tip. Where the three phenomena are few, one would expect a
high\emph{FCGR} .\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image18/image18}

\end{center}
\end{figure}

Fig. 13: \emph{FCG} curves in NR and TMCP steels

\subsection*{Assessment of FCGR path and mechanism in
air}

{\label{assessment-of-fcgr-path-and-mechanism-in-air}}

From the previous discussions, it is obvious that the material
microstructure influenced the \emph{FCGR}by crack path diversion,
branching and formation of metal crumbs in-between branched and
re-joined crack fronts. High \emph{FCG} retardation was obtained when
large angle diversion, large angle branching and change in the
orientation of metal crumbs occurred. Some of the distinct micrographs
showing phases and morphologies influencing the \emph{FCGR} are
presented in Fig. 14 for the NR steel and Fig. 15 for the
\emph{TMCP}steel. The phases where obtained by scanning along the entire
length of the fatigue crack from the initiation point to point of test
stoppage.

\textbf{Hosted file}

\verb`image19.emf`  available at \url{https://authorea.com/users/311001/articles/441756-the-influence-of-microstructure-on-the-fatigue-crack-growth-rate-in-ferrite-pearlite-steels-in-the-paris-region}

\par\null

Fig. 14: Effect of microstructure on FCGR in NR steel in air, for 10kN,
5Hz

Fig. 14(a, b \& c) shows instances of the propagation of the crack that
initiated from the C(T) specimen notch of length 20.50 mm. In existing
theory, a long crack is regarded as a fully developed crack with
attendant plastic-induced crack closure effect and of length usually
greater than 0.5 mm {[}18{]}, the plastic zone is larger than
one-fiftieth of the crack length (\emph{r} \textgreater{} 1/50\emph{a} )
and the rate of crack propagation is described by the Paris law. At a
length of 20.50 mm, the crack shown in Fig. 14 is a very long one. The
dotted yellow line shows the boundaries of the grains. The encircled
spaces by the yellow dotted lines are the ferrite grains while the red
dotted lines, where used, encircled the pearlite nodules. The white
solid line shows the movement of the fatigue crack through the
microstructural phases. The dots in Fig. 14(a) showed crack fronts that
stopped growing while the arrow indicates the mean active crack front.
In Fig. 14(a, b \& c), the crack appears to have initiated from and then
propagated along what appears as the grain boundaries or
`intergranularly'. A closer observation shows that the crack propagated
through the thin ribbon of the high alloy ferrite
phase,\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} , that surrounds
the\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} grain surfaces. This mode therefore is
properly referred here as \emph{quasi-intergranular} cracking mode. At
the point marked X in Fig. 14(a), the thin ferrite phase ribbons, shown
by the blue triangular arrows is not favourably aligned to the crack
front -- i.e., they are aligned at a very high angle, towards the
vertical, to the crack front. In this case, the crack will have to
advance transgranularly through the grain \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} in
front of it. In Fig. 14(b), the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} is aligned
favourably or lies at low angle to the crack front, hence, the crack
advanced following this ferrite ribbon. Similar situation is seen in
Fig. 14(c), however, it appears that the grain
of\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} in front of the advancing crack front
resisted transgranular propagation of the crack in the direction 1 and
this caused the nucleation of another crack front that attempted to
follow the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} (shown by the blue arrow) in
direction 2. This resulted to crack bifurcation and tends to suggest
that the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} or
the\selectlanguage{greek}\emph{α\textsubscript{LR}/α\textsubscript{HR}}\selectlanguage{english} boundary is the
preferred path for the crack growth, especially when the boundary is
lying at low angle to the crack growth plane. Note that in Fig. 14(a, b
\& c), the\selectlanguage{greek}\emph{α} \selectlanguage{english}phase dominated the local area with no \emph{P}
phase.

As the [?]\emph{K} increased and the crack moved into local areas of
mixed\selectlanguage{greek}\emph{α} \selectlanguage{english}and \emph{P} phases as in Fig. 14(d to k). This region is
dominated by the \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} phase and some few
\emph{P}colonies. The \selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} is almost absent in
this region. It appears that the \emph{P} is equally likely to cause
crack-tip diversion and crack branching, but a closer examination showed
that these phenomena had been influenced to some extent by
the\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} which appears to serve as the origin or
starting phsase for the \emph{P} formation. Fig. 14(d) shows
intragranular crack growth and bifurcations, however, one could see that
some of the crack tip followed \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} phase. Fig.
14(e) shows the formation of metal crumb and this microstructural region
is also dominated by the \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} . Fig. 14(f to j)
show crack branching in the \emph{P} phase. The tendency for crack
branching in the \emph{P} may be attributed to the orientation of
the\emph{P} -colonies and \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} boundaries. In the
first case, this tendency may be because the pearlite has two
alternating phases -- ferrite, \selectlanguage{greek}\emph{α} \selectlanguage{english}(iron, \emph{Fe} ) and
cementite,\selectlanguage{greek}\emph{θ} \selectlanguage{english}(\emph{Fe\textsubscript{3}C} ) {[}64{]}{[}65{]} with
different physical and chemical properties. Daeubler {[}66{]} studied
the influence of microstructure on the surface \emph{FCG} behaviour of
pearlitic steels and presented a classical case where the\emph{P}
-colony orientation influenced the crack growth, especially when the
lamellae are favourably oriented to the load axis. In the present study
(\emph{PS} ), it was observed
that\selectlanguage{greek}\emph{α\textsubscript{LR}/α\textsubscript{HA}}\selectlanguage{english} or
and\selectlanguage{greek}\emph{α\textsubscript{HA}/P}\selectlanguage{english} boundaries are preferred paths
of\emph{FCG} . The blue arrow in Fig. 14(i) shows a branched crack that
followed the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} and the black arrow in Fig.
14(j) shows what appears to be a branched crack front
following\selectlanguage{greek}\emph{α\textsubscript{LR}/P}\selectlanguage{english} boundary. Fig. 14(k) shows another
metal crumb that formed in the vicinity of mainly
\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english}and \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} phases. It
appears that the formation of the metal crumb occurs in the
\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} and\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} phase fields as
shown in Fig. 14(e \& k).

Fig. 15 shows crack path for G8 test in air, under 10kN, 5Hz stress
ratio of 0.1 and sinewave. The crack length measured about 10 mm
obtained under [?]\emph{K} of about 18.50 to 34.25 MPa[?]m. The number of
high angle diversion and crack branching is by far more in
the\emph{TMCP} steel as compared with low angle crack-tip diversion and
crack branching that was consistently found in \emph{NR} (see Fig. 14).
Measurements of the angle of crack branching in \emph{NR} steel show
that they are generally below 45\textsuperscript{o}. The only time high
angle diversion was found to be a little above 45\textsuperscript{o}
in\emph{NR} steel is when the crack is
avoiding\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} phase or following the
\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} or \selectlanguage{greek}\emph{α/P}\selectlanguage{english} boundaries that is favourably
oriented in its path. The \selectlanguage{greek}\emph{α} \selectlanguage{english}is shown in Fig. 15 by the blue
triangular arrow. The space enclosed by the red dotted line is the
\emph{P} while the yellow dotted line is the \selectlanguage{greek}\emph{α} . \selectlanguage{english}Multiple
formations of metal crumbs are also shown. These micrographs show that
the \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} dominated the microstructure with
extensive formation of the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} . Many of
the\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} appear as sub-grain phases inside the
\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} grains. The presence of
\selectlanguage{greek}\emph{α\textsubscript{HR}}\selectlanguage{english} is very small and the\emph{P} -nodules are
very small also - even some nodules are purely single colonies. The
crack path in the \emph{TMCP} steel is completely non-planar and more
complex than that of the \emph{NR} steel.

\par\null

\textbf{Hosted file}

\verb`image20.emf`  available at \url{https://authorea.com/users/311001/articles/441756-the-influence-of-microstructure-on-the-fatigue-crack-growth-rate-in-ferrite-pearlite-steels-in-the-paris-region}

Fig. 15: Fatigue crack growth in TMCP, G8, 10kN, 5Hz in air

It was observed that the crack-tip diversion and branching in Fig. 15
were caused by the crack tip following path of least resistance created
mainly by the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} or
the\selectlanguage{greek}\emph{α\textsubscript{LR}/α\textsubscript{HR}}\selectlanguage{english} boundaries - but
mostly by the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} ribbons. The crack bifurcation
is quite extensive with long arms as can be seen in Fig. 15(a to e) and
the diversion of the main active crack front as shown in Fig. 15(f) was
measured to be about 43\textsuperscript{?} \selectlanguage{english}to the horizontal plane. The
branched arms are measured to be in the range 38\textsuperscript{?} -
\selectlanguage{english}46\textsuperscript{?}. \selectlanguage{english}It is interesting to see that the path of least
resistant caused many of the branched arms to deviate almost at an angle
within this range. This simply implies that both tensile and shear
stresses continuously acted on the crack as it propagated in
the\emph{TMCP} , even in the Paris Region! The metal crumbs as noted in
Fig. 15 are by far more in the \emph{TMCP} than the \emph{NR} steel. It
was observed also that the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} does not only have
the potency to divert and branch out crack front, it can as well
facilitate re-joining of branched crack fronts into one main crack front
resulting to the crumb formation. This crumb is found to be a tore-off
of the steel grain or block of grains. In other words, the fatigue crack
front in \selectlanguage{greek}\emph{α-P}\selectlanguage{english} steel appears not to have a horizontal crack-tip
edge, but rather series of fluctuating wavelike crack front, whose
nature depends on the steel grains and the phases surrounding the grain
surfaces. It is important to note that this metal crumb along the crack
path has not been reported elsewhere in the literatures or considered in
any theoretical formation or treatment. The \emph{P-} colonies in
the\emph{NR} steel are large, blocky and dense. In the \emph{TMCP}
steels, the \emph{P} appears to grow in two forms -- small-blocky colony
and a thin, elongated or needle-like morphology colony along what may be
described as the \selectlanguage{greek}\emph{α} \selectlanguage{english}grain boundaries as shown, in some cases, by
the space enclosed with the red dotted line in Fig. 15. The effect of
thermomechanical control rolling process appears to be the disruption of
the \emph{P} banding and blocky morphology into randomly distributed
thin \emph{P} needles. From the observation, it appears that the
interface between the \selectlanguage{greek}\emph{α} \selectlanguage{english}and \emph{P} is an additional effective
preferable path for the crack growth if the \emph{P} -nodule is
elongated and aligns favourably to the crack front. In Fig. 15, the
branched cracks did not just move about linearly but tends to trace
the\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} phase. This suggests that the energy
needed to propagate through the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} is much less
than that for traversing the \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} grain. The
influence of the phase morphology persisted to a length of 9 mm and at
32 MPa[?]m.

The existing theory says that the crack path in the Stage II of
the\emph{da/dN} vs. [?]\emph{K} sigmoidal curve is generally across the
grains - transgranular {[}17{]} and the material microstructure has
little or negligible effect in this region
{[}3{]}{[}5{]}{[}6{]}{[}18{]}. It can be seen that the crack path in
the\emph{NR} in Fig. 14 and that of \emph{TMCP} in Fig. 15 are not the
same. The extensive crack diversion, bifurcation and metal crumbs
formation retarded the \emph{FCGR} and explains why the \emph{FCGR} in
the \emph{TMCP} is lower than that of the \emph{NR} in Fig. 13. This
finding appears to show that microstructure has a strong influence on
the rate at which fatigue crack grows in \selectlanguage{greek}\emph{α-P}\selectlanguage{english} steel in air. This
assertion is contrary to the existing theory that microstructure of a
steel has little or negligible effect on the \emph{FCGR} in air. Again,
both transgranular and intergranular modes of propagation were observed
in air. What appears as the intergranular cracking mode predominated in
the \emph{TMCP} steel. However, what appears as an intergranular mode is
actually the growth of the crack through the thin layer
of\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} in between the grains
of\selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} or the \emph{P} . Hence this mode is
identified here as the \emph{quasi-intergranular} mode. The morphology
and chemistry of the microstructural phases and load level appear to
determine which mode the crack growth will adopt.

Another factor is that the angle the crack front makes with the phases
ahead of it tends to determine if it would propagate in transgranular or
\emph{quasi-intergranular} mode. However, in Fig. 10(f) ductile
striations were found inside the secondary crack -- which actually
appears as a branched crack when viewd from the crack line. This clearly
shows that the mode is not strictly intergranular, but the crack moved
in the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} phase ribbon immediately adjacent to
the \selectlanguage{greek}\emph{α\textsubscript{LR}}\selectlanguage{english} or the \emph{P} interface, justifying the
use of word - \emph{quasi-intergranular} . In general, \emph{TMCP} steel
is more resistant to crack propagation than \emph{NR} steel of the same
steel grade. This is made possible by its refined microstructure that
branched (with long arms) and diverted the crack front at large angles
as compared to the small angle path diversion found in the
\emph{NR}steel. It must be noted that the ability of the
\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} to deviate crack front appears to lie in its
alloying composition relative to the surrounding phases.
The\selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english} clearly has more of carbon, silicon and
oxygen contents than other phases (see Table 3). The increase in the
amount of these elements might have embrittled the phase, making it the
least resistant path.

\section*{FCGRs in NR and TMCP S355 steels in
seawater}

{\label{fcgrs-in-nr-and-tmcp-s355-steels-in-seawater}}

A similar study described in Section 3 was carried out in \emph{SW} .
The authors assessed the \emph{FCG} resistance of J2N, G8 and G10 given
in Table 2 in \emph{SW} . The details of the experimental procedures
have been discussed in Refs {[}22{]}{[}36{]}{[}67{]}. The experimental
results are shown in Fig. 16. Three corrosion fatigue crack growth rate
(\emph{CFCGR} ) curves, obtained at 12kN, 9kN and under 0.3Hz, for the
J2N studied by Adedipe {[}53{]} (abbrev. `Ade') were plotted from the
data extracted from \(a\) vs. \(N\) curves
given in Ref {[}53{]}. In the present study, one test on the J2N was
performed at 9kN, 0.3Hz, R = 0.1 to validate the results obtained in the
Adedipe's study. Mehmanparast {[}59{]} studied \emph{CFCG} in G8 under
similar loading conditions and at three different test locations noted
as (A3, A4), (B3, B4) and C3. In identifying the experimental samples,
the prefix gives the steel subgrade -- J2N, G8, G10, followed by S (S =
sinewave), P\textsubscript{max} (maximum load), F (frequency, followed
by the frequency value) and the last is the test centre for the
Mehmanparast {[}59{]} study. All the tests were performed in \emph{SW}
and under sinewave.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image21/image21}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image22/image22}

\end{center}
\end{figure}

Fig. 16: Plot of FCGR in \emph{SW} (a) NR and TMCP steels in the present
study (b) CFCGR curves of \selectlanguage{greek}\emph{α-P}\selectlanguage{english} steels reported in the literatures

Fig. 16(a) appears to show the partitioning of the \emph{FCGR} s
of\emph{NR} and \emph{TMCP} steels in \emph{SW} into two domains as
demarcated by the arbitrary dash line. The \emph{CFCGR} s for
the\emph{NR} steel occupy the upper region of the dash line and that of
the\emph{TMCP} the lower region. The result of the \emph{NR} steel tends
to show that decreasing the fatigue load level has more accelerating
effect than increasing the load as shown by the 9kN and 12kN under
0.3Hz. Selected results for the G8 steel study by Mehmanparast {[}59{]}
show that increasing the fatigue load level to 10kN at 0.3Hz did not
necessarily increased the \emph{CFCGR} above that of 9kN. In fact, below
about 18.50 MPa[?]m, the \emph{CFCGR} of the 10kN decreased below that of
9kN. For the G10 steels, two load levels -- 9kN, 10kN and two
frequencies 0.3Hz, 0.5Hz were used. At about 20 MPa[?]m and above, there
is no obvious difference in the \emph{CFCGR} for the test conditions. In
general, the \emph{CFCGR} s of G10 for all the test conditions were
slightly lower than that of G8 and the \emph{CFCGR} s of all
the\emph{TMCP} subgrades were lower than that of the J2N steel. In fact,
the dash line shows possibly the line of demarcation, though diffused,
between the \emph{CFCGR} s of the \emph{NR} and \emph{TMCP} S355 steel
subgrades.

In a similar way to air study, the trend found in Fig. 16(a) is
validated by carrying out a comparative study of \emph{CFCGR} s between
\emph{NR} and \emph{TMCP} \selectlanguage{greek}\emph{α-P}\selectlanguage{english}steels reported in the literature.
The steel grades and mechanical properties of the steels compared with
the \emph{CFCGR} data in the present study are shown in Table 7. It must
be mentioned that there are limited studies on the corrosion fatigue of
marine steels under the conditions listed in Table 7. Fig. 16(b)
presents the \emph{CFCGR}studies on the steels listed in Table 7. A
large separation in the\emph{CFGCR} s between the \emph{NR} and
\emph{TMCP} steel is once again observed. It can be observed from Table
7 and Fig. 16(b) that\emph{CFCGR} s of even some studies carried out at
low stress ratios, such as 0.08 by Musuva {[}41{]} where higher than
those of the\emph{TMCP} in Fig. 16(b). It is often reported in the
literatures that plasticity-induced, roughness-induced and oxide-induced
crack closure can cause crack growth retardation. It is pertinent to
note that during fatigue, the surface asperities or roughness is caused
by the ductile stretching or tearing of the fractured surface. These
features are areas of high energy and would corrode very fast if in
contact with corrosive environment, leaving a smooth surface or deep
contour in the case of plastically deformed regions. Hence, they would
not contribute significantly to crack retardation. The only factor that
may likely cause retardation is oxide-induced crack closure and the
extent may depend on the flow rate of the corroding medium and the
stress ratio.

Table 7: Experimental conditions for the CFCGR data used in this study\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
\textbf{Study by} & \textbf{Steel grade} & \textbf{Wave form} &
\textbf{Env.} & \textbf{Freq. (Hz)} & \textbf{R} & \textbf{\%EL} &
\textbf{YS (MPa)} & \textbf{UTS (Mpa)}\tabularnewline
\midrule
\endhead
Bhuyan & CSA G40.21M 350 WT & s & SW & 0.05 & 0.1 & 29 & 405 &
513\tabularnewline
& & p-s & SW & 0.1 & 0.1 & 29 & 405 & 513\tabularnewline
Scott & BS4360-50D & p-s & SW & 0.2 & 0.5 & 32 & 370 &
538\tabularnewline
& & t & SW & 0.1 & 0.5 & 32 & 370 & 538\tabularnewline
& & n-s & SW & 0.2 & 0.5 & 32 & 370 & 538\tabularnewline
Appleton & BS4360-50D & s & SW & 0.17 & 0.5 & 32 & 368 &
508\tabularnewline
& & t & SW & 0.17 & 0.5 & 32 & 368 & 508\tabularnewline
Cheng & ABS grade EH36 & s & SW & 0.1 & 0.1 & 21 & 350 &
-\tabularnewline
Dhinakaran & C-Mn steel & s & NaCl & 1.0 & 0.5 & 32 & 459 &
530\tabularnewline
Thorpe & BS4360-50D & s & SW & 0.1 & 0.0, 0.1 & 32 & 370 &
538\tabularnewline
Adedipe & S355J+2N & s & SW & 0.3, 0.35, 0.4 & 0.1 & 20 & 385 &
531\tabularnewline
Musuva & BS4360-50D & s & 3.5\%NaCl & 0.25 & 0.08 & 30 & 386 &
560\tabularnewline
& & s & 3.5\%NaCl & 0.06 & 0.08 & 30 & 386 & 560\tabularnewline
Gill & HSLA (MF-80) & s & 3.5\%NaCl & 0.5 & 0.67 & - & 653 &
742\tabularnewline
& & s & 3.5\%NaCl & 0.5 & 0.1 & - & 653 & 742\tabularnewline
PS & S355G8+M & s & SW & 0.3 & 0.1 & 35 & 447 & 549\tabularnewline
PS & S355G10+M & s & SW & 0.3 \& 0.5 & 0.1 & 36 & 447 &
545\tabularnewline
& S355J+2N & s & SW & 0.3, 0.35, 0.4 & 0.1 & 20 & 345 & -\tabularnewline
s = sine, t = triangular, p-s = positive sawtooth, n-s = negative
sawtooth, SW = seawater & s = sine, t = triangular, p-s = positive
sawtooth, n-s = negative sawtooth, SW = seawater & s = sine, t =
triangular, p-s = positive sawtooth, n-s = negative sawtooth, SW =
seawater & s = sine, t = triangular, p-s = positive sawtooth, n-s =
negative sawtooth, SW = seawater & s = sine, t = triangular, p-s =
positive sawtooth, n-s = negative sawtooth, SW = seawater & s = sine, t
= triangular, p-s = positive sawtooth, n-s = negative sawtooth, SW =
seawater & s = sine, t = triangular, p-s = positive sawtooth, n-s =
negative sawtooth, SW = seawater & s = sine, t = triangular, p-s =
positive sawtooth, n-s = negative sawtooth, SW = seawater & s = sine, t
= triangular, p-s = positive sawtooth, n-s = negative sawtooth, SW =
seawater\tabularnewline
\bottomrule
\end{longtable}

\par\null

\subsection*{Microstructure and FCG path in seawater under
sinewave}

{\label{microstructure-and-fcg-path-in-seawater-under-sinewave}}

A metallographic study was carried out to assess the cause of the
disparity in the \emph{FCGR} s between \emph{NR} and \emph{TMCP} as
observed in Fig. 16. The fractographs for the \emph{NR} and
\emph{TMCP}steels in \emph{SW} are shown in Fig. 17. Fig. 17(a) is the
fractograph obtained in the present study for J2N and Fig. 17(b) is for
the same steel obtained by Adedipe {[}63{]}. Fig. 17(c) is the
corrosion-fatigued surface of the G10 obtained at about 20MPa[?]m and Fig.
17(d) is the common feature of the corrosion-fatigued surface of the
same material above about 23 MPa[?]m. Generally, cleavage cracking was not
observed and the failure mode remains by ductile striation which is
typical of the failure mechanism in the Paris Region for low carbon
steel.The striations in \emph{SW} simply appeared to be washed out by
the corrosion process and the surfaces were covered by the corrosion
products. This washing out progressed with time as can be seen from (c)
to (d) in Fig. 17. The secondary cracks in the \emph{TMCP} steel were
larger than that of \emph{NR} and the corrosion products appear to
collect into these secondary cracks over time as seen in Fig. 17(d).

The collection of the corrosion products into the cracks has the
potential of reducing the crack driving force, hence, the rate at which
the crack is moving. However, the flow of test environment and pumping
of the\emph{SW} in and out of the crack tip as a result of the cyclic
action -- especially under sinewave, has the capacity of removing
corrosion products at the crack tip. Hence, oxide-induced retardation
effect may be minimal. Moreover, crack closure phenomenon is little or
negligible in the Paris Region. Since there was no cleavage cracking in
the J2N, retardation due to the corrosion product or the oxide-induced
crack closure is not sufficient to account for the large difference
in\emph{CFCGR} s in Fig. 16. An altervative approach again is to examine
the crack path and the microstructural features influencing crack growth
in the medium. Fig. 18(a) shows crack path in the G10 material
in\emph{SW} . Fig. 18(b) is a schematic of Fig. 18(a). The direction of
all the crack growth is from left to right and the direction of applied
fatigue force is as given by the yellow double-edge arrow. The crack
path was observed for the G10 under sinewave, 9kN and 0.2Hz between the
[?]\emph{K} of 19.34 and 30.19 MPa[?]m. The same phenomena of high angle
crack path diversion, multiple crack branching and metal crumbs
phenomena characteristic of this \emph{TMCP} steel in air were also
observed in \emph{SW} (as shown in Fig. 18(b)). But, the number of the
branched crack fronts is somewhat less and the extension or length of
the branched arm is short compared to that of air. It then appears that
the corrosion process had limited the length of the arm of the branched
crack through a blunting process. Metal crumbs were also observed, but
the extent is small compared to the air test.

Another feature that can be seen is the corrosion attack of the
separated surfaces which resulted to widening of the fatigued surfaces
as compared with the test in air (see Fig. 11). This widening process
may be due to elimination of the small metal crumbs, plastically
deformed wake and the `\emph{microplastic} -zone by the corrosion
process. The\emph{microplastic zone} as used, refers to the closest
area(s) to the crack tip that experienced the greatest lattice
distortion, stress intensity or plastic deformation as a result of the
amplified cyclic force at the crack tip as it opens and closes. These
are areas of high lattice energy and are expected to be the points of
greatest corrosion rate. Another observation of high importance is that
the crack tips of both the main and branched crack fronts from number 1
to 5 are largely sharp as shown by the magnified micrographs of Fig.
18(c). However, the areas immediately behind the crack tips are widened
by the corrosion process as compared with that of the air. It was
observed also that the sharpness of the crack tip decreased gradually
with increase in the [?]\emph{K} . It may be that at high [?]\emph{K} , the
crack-tip was sufficiently open to allow some degree of blunting by the
corrosion process. This generally suggests that the crack tip under 9kN,
0.2Hz, sinewave was always sharp up to a particular [?]\emph{K} , before
it started experiencing some significant blunting effect of the
corrosion process. Note that the sharpness of crack tip ensured that the
crack growth was not retarded. The blunting phenomenon may not have much
retarding effect at very high [?]\emph{K} because the crack driving force
is enough to continually nucleate sharp crack fronts. In other words,
the mechanical fatigue component leads the corrosion process in this
domain. This suggests then that at the Paris Region, two domains appear
to exist -- corrosion dominated and mechanical-fatigue dominated
domains. The corrosion-controlled domain appears to be strongly
influenced by the \emph{K} \textsubscript{max} and time of crack tip
exposure to the corrosive environment {[}67{]}.

Fig. 19(a) is a typical nature of the crack path in the J2N steel
in\emph{SW} . Fig. 19(b) is a schematic of Fig. 19(a). The crack
propagated with predominance of low angle crack-tip diversion, very
limited low angle crack branching with the shorter arm in comparison
with the\emph{TMCP} steels. The crack moved on a horizontal plane with
minimal zig-zag motion. The crack growth pattern is generally the same
with that of air (see Fig. 12(a)) except that the branched arms are
shorter and there is widening of the crack gap as a result of the
corrosion process. The branched crack tips are relatively blunted, but
the main crack tip appeared to maintain its sharpness. No crumb
formation was seen, and crack diversion and bifurcation are less than
that in air. Hence, one would expect a very high \emph{CFCGR} for this
crack growth pattern if blunting of the main active crack tip did not
occur.

In Fig. 19, it appears that there is no predominant features of the
phases influencing the crack growth, except that the crack diverted in a
zig-zag manner which is a consequence of the crack propagation
mechanism. A closer observation shows some influencing microstructural
features. Some of the distinct micrographs showing phases and
morphologies influencing the \emph{CFCGR} for the J2N are presented in
Fig. 20. However, we could see that the branched crack tips appeared to
be following the \selectlanguage{greek}α/α \selectlanguage{english}and\selectlanguage{greek}\emph{α/P}\selectlanguage{english} interfaces as shown by the arrows. In
other words, the preferred crack paths appeared to be the \selectlanguage{greek}α/α \selectlanguage{english}and \selectlanguage{greek}α/\selectlanguage{english}P
boundaries. The black arrow is the \selectlanguage{greek}α/α \selectlanguage{english}while the blue arrow is the \selectlanguage{greek}α/\selectlanguage{english}P.
In fact, these boundaries are decorated by the ferrite phase ribbon of
high alloy content and the crack followed the \selectlanguage{greek}\emph{α\textsubscript{HA}}\selectlanguage{english}
phase. We can also note the widening activity near and immediately
behind the crack tip as it propagated. This is likely to be as a result
of intense corrosion activity around the \emph{microplastic} zone.

Fig. 21 shows the comparison of the \emph{FCGR} curves for the air
and\emph{SW} tests under sinewave and the experimental conditions are
shown in Table 8. Fig. 21(a) shows that \emph{CFCGR} of the 0.2Hz is
higher than that of air by an average factor of 2.5 for the J2N steel.
Above about 24 MPa[?]m, the rate increased up to an average factor of 4.0.
These values are typical of normalised\selectlanguage{greek}\emph{α-P}\selectlanguage{english} steels of the same
microstructure. The sudden jump in the \emph{CFCGR} to a factor of about
4 can be explained by examining the crack path in air and \emph{SW} .

Table 8: Specimen dimensions and loading conditions in air and SW\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
\begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\#\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Test ID.\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
W\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
B\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
a\textsubscript{o}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
a\textsubscript{f}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
f (Hz)\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
P\textsubscript{max} (kN)\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
J2N-A10F5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
50.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
16.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
20.50\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
29.53\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
J2N-S10F0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
50.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
16.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
18.32\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
28.02\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
G8-A10F5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
50.15\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
15.90\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
20.33\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
32.12\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
G10-A10F5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
50.01\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
16.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
20.30\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
29.53\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
G10-S9F0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
50.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
16.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
22.68\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
30.16\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
9\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
6\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
G10-S10F0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
50.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
16.00\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
21.26\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
29.11\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
G10-S10F0.5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
50.03\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
16.04\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
21.20\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
29.61\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
10\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
(in mm), R = 0.1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
(in mm), R = 0.1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
(in mm), R = 0.1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
(in mm), R = 0.1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
(in mm), R = 0.1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
(in mm), R = 0.1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
(in mm), R = 0.1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
(in mm), R = 0.1\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

In air (Fig. 12), bifurcation, crumb formation and some zig-zag crack
propagation were sustained to high [?]\emph{K} . In the \emph{SW} , at
[?]\emph{K} above the 24 MPa[?]m, the crumb formation and crack branching
were almost absent (Fig. 19) and this resulted to a sudden increase in
the \emph{FCGR} to the factor of 4. In Fig. 21(b), the crack growth
rates of the G8 and G10 denoted by the triangular data points, at 10kN,
5Hz are basically the same, confirming that the microstructures are
similar. In the Paris Region taken from 19.50 MPa[?]m, the \emph{CFCGR} is
just higher than that of the air by a factor of about 1.5 measured from
their respective mean lines (not shown). There is no obvious trend in
the \emph{CFCGR} s of the three tests in \emph{SW} under sinewave in
Fig. 21(b). We can reasonably say that the \emph{CFCGR} s are the same
above about 20.50 MPa[?]m, but below this value the 9kN, 0.2Hz test is
somewhat higher. Fig. 21(c) shows the crack growth rates for the two
microstructures -- J2N and TMCP in air and \emph{SW} . It is very clear
that the crack path with the least crack diversion, branching and crumb
formation gave the highest \emph{FCGR} . The extent of these three
phenomena is a function of the nature of the material microstructure and
crack tip condition. If the microstructure, environment and loading
condition are such that the three phenomena are extensive then crack
growth retardation occurs - otherwise the rate may increase. High
loading condition in \emph{SW} tends to limit the extent of crack
diversion and branching. This happens as a result of generation of
relatively large plastically deformed areas around and ahead of the
crack tip by the high loading condition and subsequent rapid dissolution
of these areas by the electrochemical process resulting to various
degrees of crack tip blunting. An incessant blunting of the crack front
will limit the length of the diversion and branched arm, forcing the
crack to propagate in a zig zag amplitude along the horizontal plane.
Small zig zag amplitudes will increase the crack growth rate. This
perhaps explains why the crack path found in J2N-A10F5 (Fig. 12) and
J2N-S10F0.2 (Fig. 19) produced the highest crack propagation rate in air
and \emph{SW} respectively as shown in Fig. 21(c). In general, we
observed that the crack path having considerable diversion, bifurcation
and crumbs will lower the rate of the crack propagation. In Fig. 21(c),
the \emph{CFCGR} of the J2N is higher than that of \emph{TMCP} steel by
a factor of about 2.0 and this implies that the microstructure of the
\emph{TMCP} steel is superior to that of J2N in resisting crack growth
in \selectlanguage{greek}\emph{α-P}\selectlanguage{english} steel. Technologically, this implies that the
microstructure of steel can be engineered to retard \emph{FCG} in the
Paris Region!

We mentioned earlier that a general stress ratio, R = 0.1 has been used
in this comparative study. This is an attempt to exclude the effect of
the so-called crack closure, as if such effect exited it would affect
the steels equally. In fact, the elimination of the asperities or rough
edges makes roughness induced crack closure in corrosive environment
unlikely. In the case of interlocking of deviated cracks, in
\emph{SW}the corrosion process will be rapid in these areas too because
the mechanical rubbing action will exposure fresh surfaces for fast
attack. Thus, the superiority of \emph{TMCP} steels over the \emph{NR}
in\emph{SW} , even in air cannot be attributed to crack closure and is
unlikely for interlocking. A plausible reason in this study remains that
under stress ratio range of 0.1 -- 0.67, temperature range of
0\textsuperscript{o}C to room temperature and frequency range of 0.05 --
0.7Hz, the microstructure of\selectlanguage{greek}\emph{α-P}\selectlanguage{english} steel strongly affected the rate
at which the crack propagated in air and \emph{SW} in the Paris Region.
This study therefore asserts that, the existing theory that the
microstructure does not significantly affect the Paris Region appears to
be incorrect. This tends to be so, when the same grade of steel, but
with different phase morphologies are put into considerations. The major
factor responsible for this difference appears to be the ferrite and
pearlite phase morphologies and properties, which are function of the
processing method and chemical composition of the steel.

\textbf{Conclusions}

This study investigated the influence of microstructure on the
\emph{FCGR} in advanced \selectlanguage{greek}\emph{α-P}\selectlanguage{english}steels in the Paris Region, both in
air and \emph{SW} under sinewave fatigue loading. Three phenomena -
crack diversion, crack bifurcation and metal crumb formation were
identified as primary factors that retarded crack growth in the steels.
The angle of crack-tip diversion and bifurcation affected the
\emph{FCGR} . The metal crumb affected\emph{FCGR} by wedging action. The
extent of formation of the three phenomena appears to be a function of
the material microstructure, environment and crack-tip condition. If the
microstructure, environment and loading condition are such that the
three phenomena are extensive then crack growth retardation occurs -
otherwise the rate may increase. That is, decrease in the crack
diversion angle, branched-crack length and number of metal crumbs formed
is found to increase \emph{FCGR} . High angle crack-tip diversion,
bifurcation and re-orientation of the metal crumb resulting to a
mismatch or wedging action, retarded \emph{FCG} . The three factors
appear to retard the crack growth by reducing or re-distributing the
effective stress or driving force at the main active crack tip. In
\emph{SW} , high angle crack diversion and bifurcation are considerably
reduced and this is a consequence of the repeated crack tip blunting by
the electrochemical dissolution process. If the branched crack tips are
blunted such that the length is short and the main active crack tip is
sharp, \emph{CFCGR} can increase to about a factor of 4. If the main
active crack tip is blunted as well, the crack propagation speed is
considerably reduced. \emph{Microplastic} zone appears to control
\emph{CFCGR} in \selectlanguage{greek}\emph{α-P}\selectlanguage{english} steels. The \emph{microplastic zone}size and
the extent of the electrochemical dissolution of the zone (or crack tip
blunting) appear to be additional primary factors influencing crack
growth in \selectlanguage{greek}α-\selectlanguage{english}\emph{P} steel. The microstructural phases and morphology
local to the main crack front and \emph{microplastic} zone size appear
to determine which mode the crack growth will adopt. The angle the crack
front makes with the phases ahead of it tends to determine if it would
propagate in transgranular or by\emph{quasi-intergranular} mode under
low \emph{SIFR} . This study, therefore, asserts that the nature of the
microstructures of the \selectlanguage{greek}α-\selectlanguage{english}\emph{P} steels has a strong influence on the
\emph{FCGR} in the Paris Region of the \emph{da/dN} vs. [?]\emph{K}
sigmoidal curve in air and\emph{SW} . However, considering the
relatively small number of tests involved, more experiments are needed
to confirm and increase the confidence in the results obtained in this
work.

\textbf{Acknowledgements}

This work was supported by grant EP/L016303/1 for Cranfield, Oxford and
Strathclyde Universities' Centre for Doctoral Training in Renewable
Energy Marine Structures - REMS (http://www.rems-cdt.ac.uk/) from the UK
Engineering and Physical Sciences Research Council (EPSRC).

Data availability: the raw data required to reproduce these findings
cannot be shared at this time as the data also forms part of an ongoing
study.

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