Anisotropy effects on crack path and effective toughness in heterogeneous materials
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Understanding the impact of anisotropy on crack propagation and effective toughness in heterogeneous materials is of paramount importance for optimizing material design and engineering applications. Anisotropic behavior, influenced by factors such as interfaces, crystallographic structure, and material contrast, introduces directional variations in a material's mechanical properties. This understanding, particularly in fracture mechanics, enables precise predictions of crack propagation and failure. Informed material selection, guided by anisotropic properties, facilitates the customization of fracture characteristics, including effective toughness. This thesis delves into unraveling the intricate relationship between anisotropy, crack path, and effective toughness across multiple length scales to advance material science, structural design, and engineering practices.
At the atomic scale, the investigation focuses on crack deflection and penetration at slanted interfaces. The study demonstrates the persistent nature of toughness ratio criteria that govern crack deflection and penetration, extending from the continuum scale to the atomic scale. The introduction of a slant interface establishes a linear relationship between the interfacial orientation angle and critical cohesive energy, delineating a transition point from crack deflection to penetration. A critical orientation angle, denoted as $\theta_c = 9.5^\circ$, significantly influences the overall effective toughness. For angles $\theta \leqslant \theta_c$, smaller angles correlate with heightened toughness enhancement ($\Delta\Pi_{c}$) due to deflection, while for $\theta > \theta_c$, the $\Delta\Pi_{c}$ converges towards zero.
Subsequently, a novel approach is introduced involving the construction of Crystal-Symmetry-Based Representative Atomic Volumes (CRAVs) to capture crystallographic anisotropy at the continuum scale. The CRAV scheme is applied to investigate crack paths in porous media and ellipsoidal fiber-matrix composites. Results indicate that the CRAV scheme proficiently reproduces key aspects of crack path formation induced by crystallographic anisotropy, such as deflection, penetration, and bifurcation, providing a computationally efficient alternative to atomic simulations. This scheme holds promise for modeling fracture behavior in composites at the microscale, eliminating the need for computationally expensive atomic simulations at lower length scales.
In the continuum, a variable stiffness boundary condition is proposed as a novel computational framework for measuring effective fracture toughness. The variable stiffness boundary condition induces nonuniform deformation within the domain while maintaining uniform displacement at the remote boundary, enabling macroscopic steady crack propagation in brittle materials. This innovative method demonstrates versatility across various finite element software platforms. The analysis reveals that greater toughness heterogeneity correlates with an augmentation in overall effective toughness. Experimentally validated through 3D printing technology, the variable stiffness design allows for stable crack propagation and the potential for easy calculation of effective toughness through a simple uniaxial deformation test, eliminating the need for a complex experimental setup.