Self-emitted surface corrugations in dynamic fracture of silicon single crystal.

When a dynamic crack front travels through material heterogeneities, elastic waves are emitted, which perturb the crack and change the morphology of the fracture surface. For asperity-free crystalline materials, crack propagation along preferential cleavage planes is expected to present a smooth crack front and form a mirror-like fracture surface. Surprisingly, we show here that in single crystalline silicon without material asperities, the crack front presents a local kink during high-speed crack propagation. Meanwhile, local oscillations of the crack front, which can move along the crack front, emerge at the front kink position and generate periodic fracture surface corrugations. They grow from angstrom amplitude to a few hundred nanometers and propagate with a long lifetime at a frequency-dependent speed, while keeping a scale-independent shape. In particular, the local front oscillations collide in a particle-like manner rather than proceeding with a linear superposition upon interaction, which presents the characteristic of solitary waves. We propose that such a propagating mode of the crack front, which results from the fracture energy fluctuation at a critical crack speed in the silicon crystal, can be considered as nonlinear elastic waves that we call "corrugation waves."

Elastic coupling between layers in two-dimensional materials.

Two-dimensional materials, such as graphene and MoS2, are films of a few atomic layers in thickness with strong in-plane bonds and weak interactions between the layers. The in-plane elasticity has been widely studied in bending experiments where a suspended film is deformed substantially; however, little is known about the films' elastic modulus perpendicular to the planes, as the measurement of the out-of-plane elasticity of supported 2D films requires indentation depths smaller than the films' interlayer distance. Here, we report on sub-ångström-resolution indentation measurements of the perpendicular-to-the-plane elasticity of 2D materials. Our indentation data, combined with semi-analytical models and density functional theory, are then used to study the perpendicular elasticity of few-layer-thick graphene and graphene oxide films. We find that the perpendicular Young's modulus of graphene oxide films reaches a maximum when one complete water layer is intercalated between the graphitic planes. This non-destructive methodology can map interlayer coupling and intercalation in 2D films.

Approach of Pavement Surface Layer Degradation Caused by Tire Contact Using Semi-Analytical Model.

New methods of degradations on the pavement's surface, such as top-down cracking and delamination, caused by the repeated passage of heavy vehicles led to questions about the impact of the contact between the tire and the pavement. In fact, to increase the service life of the structures, future road design methods must have a precise knowledge of the consequences of the contact parameters on the state of stress and deformation in the pavement. In this paper, tractive rolling contact under the effect of friction is modeled by Kalker's theory using a semi-analytical method (SAM). A tire profile is performed thanks to a digitization by fringes or a photogrammetry technique. The effect of rolling on the main surface extension deformations is then highlighted to study top cracking. At the end of the SAM calculation, contact areas are closed to 200 µdef, exceeding the allowable micro-deformation limit for the initiation of cracking. In addition, results on the main strain directions also give information on the direction of cracking (initiation of longitudinal or transverse cracks). The cracking then becomes evident, leading to a reduced service life.

Velocity correlated crack front and surface marks in single crystalline silicon.

Single crystalline silicon fractures on low-energy cleavage planes such as (111) and (110). The crack propagation cannot accurately be predicted by linear elastic fracture mechanics since it does not account for small scale and inelastic phenomena such as atomic lattice trapping. Here we show that, under pure bending load, (110) cleavage in silicon single crystal rapidly accelerates to 3700 m/s without crack path deviation or crack branching, contrasting previous observations. We highlight that the crack front shape involves strong velocity dependence and presents a curvature jump during very high-speed crack growth. In addition, we observe special marks-a kind of periodic surface undulation-that exclusively arise on the rapid fracture surfaces, and we suggest that they are front wave traces resulting from an intrinsic local velocity fluctuation. This finding gives insight to the wavy nature of the crack front in the absence of material asperity.