Universal shapes formed by two interacting cracks

Recent progress on crack pattern formation in thin films

Fascinating pattern formation by quasi-static crack growth in thin films has received increasing interest in both interdisciplinary science and engineering applications. The paper mainly reviews recent experimental and theoretical progress on the morphogenesis and propagation of various quasi-static crack patterns in thin films. Several key factors due to changes in loading types and substrate confinement for choosing crack paths toward different patterns are summarized. Moreover, the effect of crack propagation coupled to other competing or coexisting stress-relaxation processes in thin films, such as interface debonding/delamination and buckling instability, on the formation and transition of crack patterns is discussed. Discussions on the sources and changes in the driving force that determine crack pattern evolution may provide guidelines for the reliability and failure mechanism of thin film structures by cracking and for controllable fabrication of various crack patterns in thin films.

Interacting Cracks Obey a Multiscale Attractive to Repulsive Transition

The observed repulsive behavior of two initially collinear cracks growing towards each other and leading to a hook-shaped path questioned recently the validity of the principle of local symmetry within linear elastic fracture mechanics theory. Our theoretical and numerical work solves this dilemma, providing the precise geometric conditions for the existence of this repulsive phase. We moreover reveal a multiscale behavior of the repulsive-attractive transition, explaining its ubiquitous occurrence, but also the difficulty to predict the final cracks' paths.

An in situ simultaneous measurement system combining photoelasticity and caustics methods for blast-induced dynamic fracture

Photoelasticity and caustics methods are extensively used in the history of dynamic fracture mechanics. However, there is little work for the combination of them in the same experiment associated with high loading rate in extreme conditions. In the present work, it is the first time to build a simultaneous measurement system which can use photoelasticity and caustics methods at the same instant for in situ optical investigations of blast-induced dynamic fracture. To illustrate the capability of this system, an explosion experiment using a 2D epoxy plate is conducted, yielding consistent results between two methods. This novel system provides rich experimental data including local-field information for the crack tip and full-field information for blasting waves.

Path (un)predictability of two interacting cracks in polycarbonate sheets using Digital Image Correlation

Crack propagation is tracked here with Digital Image Correlation analysis in the test case of two cracks propagating in opposite directions in polycarbonate, a material with high ductility and a large Fracture Process Zone (FPZ). Depending on the initial distances between the two crack tips, one may observe different complex crack paths with in particular a regime where the two cracks repel each other prior to being attracted. We show by strain field analysis how this can be understood according to the principle of local symmetry: the propagation is to the direction where the local shear - mode K_II in fracture mechanics language - is zero. Thus the interactions exhibited by the cracks arise from symmetry, from the initial geometry, and from the material properties which induce the FPZ. This complexity makes any long-range prediction of the path(s) impossible.

Intertwined Multiple Spiral Fracture in Perforated Sheets

We study multiple tearing of a thin, elastic, brittle sheet indented with a rigid cone. The n cracks initially prepared symmetrically propagate radially for n≥4. However, if n<4 the radial symmetry is broken and fractures spontaneously intertwine along logarithmic spiral paths, respecting order n rotational symmetry. In the limit of very thin sheets, we find that fracture mechanics is reduced to a geometrical model that correctly predicts the maximum number of spirals to be strictly 4, together with their growth rate and the perforation force. Similar spirals are also observed in a different tearing experiment (this time up to n=4, in agreement with the model), in which bending energy of the sheet is dominant.

The dynamics of interacting folds under biaxial compressive stresses

The gradual in-plane compression of a solid film bonded to a soft substrate can lead to surface wrinkling and even to the formation of a network of folds for sufficiently high strain. An understanding of how these folds initiate, propagate, and interact with each other is still lacking. In a previous study, we developed an experimental system to observe the wrinkle-to-fold transition of layered elastic materials under biaxial compressive stresses. Here we focus on the dynamic interaction of a pair of propagating folds under biaxial compression. We find experimentally that their behavior is mediated through their tips and depends on the separation of the tips and their angle of interception. When the angle is lower than 45°, the two folds either form a unique fold by the coalescence of their tips when close enough, or bend their trajectories to intersect each other and form a lenticular region in analogy with cracks. When the angle is higher then 45°, the folds simply intersect and form a T-like junction. We rationalize this behavior by conducting numerical simulations to visualize the stress field around the two tips and find that the initial geometric position of the tips primarily determines the final state of the folds.

Crack patterns over uneven substrates

Cracks in thin layers are influenced by what lies beneath them. From buried craters to crocodile skin, crack patterns are found over an enormous range of length scales. Regardless of absolute size, their substrates can dramatically influence how cracks form, guiding them in some cases, or shielding regions from them in others. Here we investigate how a substrate's shape affects the appearance of cracks above it, by preparing mud cracks over sinusoidally varying surfaces. We find that as the thickness of the cracking layer increases, the observed crack patterns change from wavy to ladder-like to isotropic. Two order parameters are introduced to measure the relative alignment of these crack networks, and, along with Fourier methods, are used to characterise the transitions between crack pattern types. Finally, we explain these results with a model, based on the Griffith criteria of fracture, that identifies the conditions for which straight or wavy cracks will be seen, and predicts how well-ordered the cracks will be. Our metrics and results can be applied to any situation where connected networks of cracks are expected, or found.

Unstable crack propagation in LAPONITE® gels: selection of a sinusoidal mode in an electric field

We report observation of wavy cracks and naturally patterned fracture surfaces in drying LAPONITE® paste.

Crack Front Segmentation and Facet Coarsening in Mixed-Mode Fracture

A planar crack generically segments into an array of "daughter cracks" shaped as tilted facets when loaded with both a tensile stress normal to the crack plane (mode I) and a shear stress parallel to the crack front (mode III). We investigate facet propagation and coarsening using in situ microscopy observations of fracture surfaces at different stages of quasistatic mixed-mode crack propagation and phase-field simulations. The results demonstrate that the bifurcation from propagating a planar to segmented crack front is strongly subcritical, reconciling previous theoretical predictions of linear stability analysis with experimental observations. They further show that facet coarsening is a self-similar process driven by a spatial period-doubling instability of facet arrays.

Modeling growth paths of interacting crack pairs in elastic media

The problem of predicting the growth of a system of cracks, each crack influencing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which we apply to the 'En-Passant' family of crack growth problems, in which a pair of initially parallel, offset cracks propagate nontrivially toward each other under far-field opening stress. We utilize boundary integral and perturbation methods of linear elasticity, linear elastic fracture mechanics, and common crack opening criteria to calculate the first analytical model for curved En-Passant crack paths. The integral system is reduced under a hierarchy of approximations, producing three methods of increasing simplicity for computing crack paths. The last such method is a major highlight of this work, using an asymptotic matching argument to predict crack paths based on superposition of simple, single-crack fields. Within the corresponding limits of the three methods, all three are shown to agree with each other. We provide comparisons to exact results and existing experimental data to verify certain approximation steps.

Repulsion and Attraction between a Pair of Cracks in a Plastic Sheet

We study the interaction of two collinear cracks in polymer sheets slowly growing towards each other, when submitted to uniaxial stress at a constant loading velocity. Depending on the sample's geometry-specifically, the initial distances d between the two cracks' axes and L between the cracks' tips-we observe different crack paths with, in particular, a regime where the cracks repel each other prior to being attracted. We show that the angle θ characterizing the amplitude of the repulsion-and specifically its evolution with d-depends strongly on the microscopic behavior of the material. Our results highlight the crucial role of the fracture process zone. At interaction distances larger than the process zone size, crack repulsion is controlled by the microscopic shape of the process zone tip, while at shorter distances, the overall plastic process zone screens the repulsion interaction.

Wrinkle motifs in thin films

On length scales from nanometres to metres, partial adhesion of thin films with substrates generates a fascinating variety of patterns, such as ‘telephone cord’ buckles, wrinkles, and labyrinth domains. Although these patterns are part of everyday experience and are important in industry, they are not completely understood. Here, we report simulation studies of a previously-overlooked phenomenon in which pairs of wrinkles form avoiding pairs, focusing on the case of graphene over patterned substrates. By nucleating and growing wrinkles in a controlled way, we characterize how their morphology is determined by stress fields in the sheet and friction with the substrate. Our simulations uncover the generic behaviour of avoiding wrinkle pairs that should be valid at all scales.

Tearing of thin sheets: cracks interacting through an elastic ridge

We study the interaction between two cracks propagating quasistatically during the tearing of a thin brittle sheet. We show that the cracks attract each other following a path described by a power law resulting from the competition between elastic and fracture energies. The power law exponent (8/11) is in close agreement with experiments. We also show that a second (asymptotic) regime, with an exponent of 9/8, emerges for small distances between the two crack tips due to the finite transverse curvature of the elastic ridge joining them.

Evolving fracture patterns: columnar joints, mud cracks and polygonal terrain

When cracks form in a thin contracting layer, they sequentially break the layer into smaller and smaller pieces. A rectilinear crack pattern encodes information about the order of crack formation, as later cracks tend to intersect with earlier cracks at right angles. In a hexagonal pattern, in contrast, the angles between all cracks at a vertex are near 120°. Hexagonal crack patterns are typically seen when a crack network opens and heals repeatedly, in a thin layer, or advances by many intermittent steps into a thick layer. Here, it is shown how both types of pattern can arise from identical forces, and how a rectilinear crack pattern can evolve towards a hexagonal one. Such an evolution is expected when cracks undergo many opening cycles, where the cracks in any cycle are guided by the positions of cracks in the previous cycle but when they can slightly vary their position and order of opening. The general features of this evolution are outlined and compared with a review of the specific patterns of contraction cracks in dried mud, polygonal terrain, columnar joints and eroding gypsum-sand cements.

How geometry controls the tearing of adhesive thin films on curved surfaces

Flaps can be detached from a thin film glued on a solid substrate by tearing and peeling. For flat substrates, it has been shown that these flaps spontaneously narrow and collapse in pointy triangular shapes. Here we show that various shapes, triangular, elliptic, acuminate, or spatulate, can be observed for the tears by adjusting the curvature of the substrate. From combined experiments and theoretical models, we show that the flap morphology is governed by simple geometric rules.