Forbidden directions for the fracture of thin anisotropic sheets: an analogy with the Wulff plot

Asymmetric bending boundary layer: The λ-test

We investigate the mechanics of two asymmetric ribbons bound at one end and pulled apart at the other ends. We characterize the elastic junction near the bonding and conceptualize it as a bending boundary layer. While the size of this junction decreases with the pulling force, we observe the surprising existence of the binding angle as a macroscopic signature of the bending stiffnesses. Our results thus challenge the standard assumption of neglecting bending stiffness of thin shells at large tensile loading. In addition, we show how the rotational response of the structure exhibits a nonlinear and universal behavior regardless of the ratio of asymmetry. Leveraging the independence of the binding angle to the pulling force, we finally introduce the λ-test-a visual measurement technique to characterize membranes through simple mechanical coupling.

Crosslinking degree variations enable programming and controlling soft fracture via sideways cracking

Large deformations of soft materials are customarily associated with strong constitutive and geometrical nonlinearities that originate new modes of fracture. Some isotropic materials can develop strong fracture anisotropy, which manifests as modifications of the crack path. Sideways cracking occurs when the crack deviates to propagate in the loading direction, rather than perpendicular to it. This fracture mode results from higher resistance to propagation perpendicular to the principal stretch direction. It has been argued that such fracture anisotropy is related to deformation-induced anisotropy resulting from the microstructural stretching of polymer chains and, in strain-crystallizing elastomers, strain-induced crystallization mechanisms. However, the precise variation of the fracture behavior with the degree of crosslinking remains to be understood. Leveraging experiments and computational simulations, here we show that the tendency of a crack to propagate sideways in the two component Elastosil P7670 increases with the degree of crosslinking. We explore the mixing ratio for the synthesis of the elastomer that establishes the transition from forward to sideways fracturing. To assist the investigations, we construct a novel phase-field model for fracture where the critical energy release rate is directly related to the crosslinking degree. Our results demonstrate that fracture anisotropy can be modulated during the synthesis of the polymer. Then, we propose a roadmap with composite soft structures with low and highly crosslinked phases that allow for control over fracture, arresting and/or directing the fracture. The smart combination of the phases enables soft structures with enhanced fracture tolerance and reduced stiffness. By extending our computational framework as a virtual testbed, we capture the fracture performance of the composite samples and enable predictions based on more intricate composite unit cells. Overall, our work offers promising avenues for enhancing the fracture toughness of soft polymers.

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.

Programming fracture patterns of thin films

Controlled fracture presents opportunities for the advanced fabrication of thin films. However, programmability analogous to that of Chinese paper cutting is still challenging, where fracture patterns can be created as required without preformed cracks for guidance. Here, we establish a design framework for tearing adhesive thin films from foldable substrates with such programmability. Our analytical model captures the observed crack behavior, demonstrating that the deflection of crack paths can exceed 90^{∘}. Besides, for thick foldable substrates with multiple ridges, we additionally propose a robust method of directional fracture where the cracks are forced to extend along the ridges.

Crack path selection in orientationally ordered composites

While cracks in isotropic homogeneous materials propagate straight, perpendicularly to the tensile axis, cracks in natural and synthetic composites deflect from a straight path, often increasing the toughness of the material. Here we combine experiments and simulations to identify materials properties that predict whether cracks propagate straight or kink on a macroscale larger than the composite microstructure. Those properties include the anisotropy of the fracture energy, which we vary several fold by increasing the volume fraction of orientationally ordered alumina (Al_{2}O_{3}) platelets inside a polymer matrix, and a microstructure-dependent process zone size that is found to modulate the additional stabilizing or destabilizing effect of the nonsingular stress acting parallel to the crack. Those properties predict the existence of an anisotropy threshold for crack kinking and explain the surprisingly strong dependence of this threshold on sample geometry and load distribution.

Collaborative Oscillatory Fracture

We report a new oscillatory propagation of cracks in thin films where three cracks interact mediated by two delamination fronts. Experimental observations indicate that delamination fronts joining the middle crack to the lateral crack tips swap contact periodically with the crack tip of the middle crack. A model based on a variational approach analytically predicts the condition of propagation and geometrical features of three parallel cracks. The stability conditions and oscillating propagation are found numerically and the predictions are in favorable agreement with experiments. We found that the physical mechanism selecting the wavelength structure is a relaxation process in which the middle crack produces a regular oscillatory path.

Predicting tearing paths in thin sheets

This study investigates the tearing of a thin notched sheet when two points on the sheet are pulled apart. The concepts that determine the crack trajectory are reviewed in the general anisotropic case, in which the energy of the fracture depends on the fracture direction. When observed as a flat sheet a purely geometric "tearing vector" is defined through the location of the crack tip and the pulling points. Both Griffiths's criterion and the maximum energy release rate criterion (MERR) predict a fracture path that is parallel to the tearing vector in the isotropic case. However, for the anisotropic case, the application of the MERR leads to a crack path that deviates from the tearing vector, following a propagation direction that tends to minimize the fracture energy. In the case of strong anisotropy, it is more difficult to obtain an analytical prediction of the tearing trajectory. Thus, simple geometrical arguments are provided to give a derivation of a differential equation accounting for crack trajectory, according to the natural coordinates of the pulling, and in the case that the anisotropy is sufficiently weak. The solution derived from this analysis is in good agreement with previous experimental observations.

Computational modeling of progressive damage and rupture in fibrous biological tissues: application to aortic dissection

This study analyzes the lethal clinical condition of aortic dissections from a numerical point of view. On the basis of previous contributions by Gültekin et al. (Comput Methods Appl Mech Eng 312:542-566, 2016 and 331:23-52, 2018), we apply a holistic geometrical approach to fracture, namely the crack phase-field, which inherits the intrinsic features of gradient damage and variational fracture mechanics. The continuum framework captures anisotropy, is thermodynamically consistent and is based on finite strains. The balance of linear momentum and the crack evolution equation govern the coupled mechanical and phase-field problem. The solution scheme features the robust one-pass operator-splitting algorithm upon temporal and spatial discretizations. Based on experimental data of diseased human thoracic aortic samples, the elastic material parameters are identified followed by a sensitivity analysis of the anisotropic phase-field model. Finally, we simulate an incipient propagation of an aortic dissection within a multi-layered segment of a thoracic aorta that involves a prescribed initial tear. The finite element results demonstrate a severe damage zone around the initial tear and exhibit a rather helical crack pattern, which aligns with the fiber orientation. It is hoped that the current contribution can provide some directions for further investigations of this disease.

Crystallographic orientation errors in mechanical exfoliation

We evaluate the effect of mechanical exfoliation of van der Waals materials on crystallographic orientations of the resulting flakes. Flakes originating from a single crystal of graphite, whose orientation is confirmed using STM, are studied using facet orientations and electron back-scatter diffraction (EBSD). While facets exhibit a wide distribution of angles after a single round of exfoliation ([Formula: see text]), EBSD shows that the true crystallographic orientations are more narrowly distributed ([Formula: see text]), and facets have an approximately [Formula: see text] error from the true orientation. Furthermore, we find that the majority of graphite fractures are along armchair lines, and that the cleavage process results in an increase of the zigzag lines portion. Our results place values on the rotation caused by a single round of the exfoliation process, and suggest that when a 1-2 degree precision is necessary, the orientation of a flake can be gauged by the orientation of the macroscopic single crystal from which it was exfoliated.

The tearing path in a thin anisotropic sheet from two pulling points: Wulff's view

We study the crack propagation in a thin notched sheet of a polymeric material when two points in the sheet are pulled away. For materials of isotropic fracture energy, we show that an effective tearing vector predicting the direction of fracture propagation can be defined. In the flat sheet state, this vector is the perpendicular bisector of the vectors joining the pulling points and the fracture tip. The tearing vector is then differently oriented than the pulling direction. The "maximum energy released rate" criterion predicts a crack path that is tangential to the instantaneous tearing vector, or equivalently trajectories that are hyperbolas whose focal points are the pulling points. However, experiments indicate that fracture paths rarely follow this prediction because any small anisotropy existing in real thin sheets deviates the crack path from being parallel to the tearing vector. Although these deviations are locally small, as crack progresses a cumulative effect which results in large errors for long crack paths are observed. We therefore introduce the anisotropy effect through the generalization of the "maximum energy released rate" criterion and demonstrate that the crack trajectory and the minimum force to sustain tearing can be found through a Wulff's type geometrical construction. Systematic experiments show that the tearing force and fracture path are in good agreement with this prediction.

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.