Figure 13: Evolution with strain for (a ) correlation length \(\xi\), (b ) microcrack volume exponent \(\beta\), and (c ) fractal dimension\(D\), for the untreated (blue) and heat-treated (orange) samples. Error bars show (b ) the standard error (\(\beta/\sqrt{N}\)) of the maximum likelihood estimate of \(\beta\), where \(N\) is the number of cracks, and (c ) the 95% confidence intervals of the linear regression fit for \(D\). Dash-dot lines show the strain at which each sample failed, while dashed lines show the onset of localization as seen in the μCT volumes.