Figure 1

(a) Picture of the experimental setup. The neutron beam is schematized in red, incoming from the last slit of the collimator, reflecting on the sample and going within the slit in front of the detector. (b) Picture of the broken sample, showing the two black sheets of ${\mathrm{B}}_4\mathrm{C}$ used to select one area of interest (see text). (c) Sketch of the broken sample, with the two parts described in the text.Reuse & Permissions

Figure 2

Experimental neutron reflectivities plotted as a function of $q$ for: the control sample ($△$), the specimen broken at a stress intensity factor $K_I=0.61\mathrm{MPa}·{\mathrm{m}}^{1/2}$ (zone 1, ●) and for the specimen broken at a stress intensity factor $K_I=0.77\mathrm{MPa}·{\mathrm{m}}^{1/2}$ (zone 2, blue squares). We have superimposed to the experimental curve corresponding to the control sample the theoretical Fresnel reflectivity curve (red plain line) as well as the result of the second order Born approximation (red dashed dotted line). The experimental results corresponding to zone 1 and zone 2 are fitted using Eqs. (3, 5, 6), and are fitted by a dashed green line and a black dashed dotted line, respectively. The best fits correspond to ${\varphi }_0^I=0.348\pm 0.003$, ${\ell }^I\approx 43\AA$ and ${\Lambda }^I\approx 35\AA$ in zone 1, and ${\varphi }_0^{II}=0.567\pm 0.003$, ${\ell }^{II}\approx 46\AA$ and ${\Lambda }^{II}\approx 23\AA$ in zone 2. Inset: Contour lines of the fit root-mean square error in the plane ($\ell$, $\Lambda$) in zone 2, showing that while the combination ${\ell }_{\mathrm{eff}}=\Lambda +\ell$ is rather well pinned down by the fit, $\Lambda -\ell$ is a “soft” direction. The relative experimental rms error per point is 0.075, whereas the minimum relative error achieved by the fit is 0.06.Reuse & Permissions

Figure 3

Finite element simulations of the dilation field $D(x,y)={ϵ}_{xx}(x,y)+{ϵ}_{yy}(x,y)$ in the vicinity of the crack tip in the midplane of the specimen for an external loading $K=0.61\mathrm{MPa}·{\mathrm{m}}^{1/2}$. The crack propagates from right to left, and the color code indicates the amplitude of $D(x,y)$.Reuse & Permissions