A wavelet-enriched adaptive hierarchical, coupled crystal plasticity – phase-field finite element model is developed in this work to simulate crack propagation in complex polycrystalline microstructures. The model accommodates initial material anisotropy and crack tension-compression asymmetry through orthogonal decomposition of stored elastic strain energy into tensile and compressive counterparts. The crack evolution is driven by stored elastic and defect energies, resulting from slip and hardening of crystallographic slips systems. A FE model is used to simulate the fracture process in a statistically equivalent representative volume element reconstructed from electron backscattered diffraction scans of experimental microstructures. Multiple numerical simulations with the model exhibits microstructurally sensitive crack propagation characteristics.
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The numerical treatment of the whole process of ductile fracture remains a challenging task, particularly when FEM is employed. The main issue regards pathologically mesh dependence of the numerical results, not only in the softening regime but also in the stages of strain localization and further crack propagation. In the literature, non-local approaches are adopted to mitigate these effects but they require a calibrated length scale and mesh refinement, thus being time consuming. This work focuses on the numerical treatment of ductile fracture in metal materials via a three-dimensional unified methodology that combines (i) the GTN model to describe diffuse damage using the standard FEM, the (ii) XFEM to represent the crack and (iii) the coupling of the XFEM with a cohesive zone model to account for the intermediate localization phase. We rely upon the Updated Lagrangian formulation to include large strains and rotations. The methodology, implemented in Abaqus commercial code as a user finite element (UEL), is capable of reproducing numerically the overall response of structures until rupture.
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The present work demonstrates how gradient strengthening at the micron scale affects the macroscopic strain at coalescence under intense shearing conditions. The coalescence mechanism relies on severe flattening, rotation, and elongation of the voids causing severe heterogeneous plastic strain to develop near the voids and in the ligament between voids. These gradients are associated with geometrically necessary dislocations, causing a delay in the coalescence process.
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We present a theory with a structure that enables analyses of ductile fracture under any type of loading. The theory builds on the standard concept of homogeneous yielding and further proceeds from the concept of unhomogeneous yielding on a (yield) system that depends on the spatial distribution of voids. Depending on the desired level of refinement in analysis, a given simulation employs one or more yield systems with the isotropic limit being reached for an infinite number. We illustrate the predictive capabilities of the theory by considering simulations of three-dimensional crack initiation and growth in a round notched bar, a shear specimen and a compression pin.
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