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Characterization and modelling

Characterization and modelling

Theory and simulations reveal why propagating cracks sometimes repel each other

04 Jul 2018
Fish hook cracks
Cracking study: two cracks that have repelled each other to form hook patterns. (Courtesy: M-É Schwaab et al/Phys. Rev. Lett.)

New insights into why propagating cracks sometimes repel each other have been made by a team of physicists led by Loïc Vanel at France’s University Claude Bernard. The curious effect has been modelled for the first time by the physicists, who have combined theoretical and numerical methods to provide an explanation of why the repulsion occurs. Their work could explain how cracking occurs on geological scales and could also find a wide range of industrial applications.

When solid materials such as wood, metal and concrete are placed under stress, cracks may start to form on their surfaces. Over time, these cracks can grow in order to minimize the stress in the material. Where a single crack will propagate can be predicted by the physics of linear elastic fracture mechanics. However, when multiple cracks are present it becomes difficult to predict their trajectories.

Fracture mechanics explains how when two relatively long, collinear cracks approach each other nearly head-on, they will initially move towards each other through mutual attraction. However, when they have almost met, the cracks will repel each other for a short distance. Then, the will attract each other – forming a hook-like pattern (see figure). This repulsive behaviour appears to contradict the predictions of fracture mechanics, and so far, no previous studies have offered a satisfying explanation why it occurs.

Quantitative prediction

Vanel’s team tackled the problem using finite element analysis, which calculated the forces acting on infinitesimal elements of a material due to stress. Then an integration technique was used to simulate the behaviour of the material at the macroscopic scale. After combining this numerical technique with the theoretical predictions underlying fracture mechanics, the researchers could quantitively predict repulsive behaviour for the first time.

The study reveals that the angles at which two collinear cracks will repel away from each other has a strong dependence on both the distance between the cracks and the lengths of the cracks. Repulsion occurs when the separation is less than 10% of each crack’s length, highlighting a need to consider different length scales when predicting crack repulsion.

The new technique could soon be used to analyse phenomena on geological scales, where cracks hundreds of kilometres long in tectonic plates and ice floes repel each other when separated by a few hundred metres, before overlapping. On much smaller scales, the research could prove invaluable for industrial applications that require control over cracking behaviour in devices such as mechanical sensors and stretchable electronics.

The research is described in Physical Review Letters.

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