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>A three-dimensional cohesive-frictional grain-boundaryudmicromechanical model for intergranular degradation and failureudin polycrystalline materials
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A three-dimensional cohesive-frictional grain-boundaryudmicromechanical model for intergranular degradation and failureudin polycrystalline materials
In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranularuddegradation and failure in polycrystalline materials is presented. The polycrystalline microstructuresudare generated as Voronoi tessellations, that are able to retain the main statistical features ofudpolycrystalline aggregates. The formulation is based on a grain-boundary integral representation of theudelastic problem for the aggregate crystals, that are modeled as three-dimensional anisotropic elasticuddomains with random orientation in the three-dimensional space. The boundary integral representationudinvolves only intergranular variables, namely interface displacement discontinuities and interface tractions,udthat play an important role in the micromechanics of polycrystals. The integrity of the aggregateudis restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onsetudand evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversibleudcohesive linear law, able to address mixed-mode failure conditions. The derivation of the tractionseparationudlaw and its relation with potential-based laws is discussed. Upon interface failure, a non-linearudfrictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces.udTo avoid a sudden transition between cohesive and contact laws, when interface failure happens underudcompressive loading conditions, the concept of cohesive-frictional law is introduced, to model theudsmooth onset of friction during the mode II decohesion process. The incremental-iterative algorithmudfor tracking the degradation and micro-cracking evolution is presented and discussed. Several numericaludtests on pseudo- and fully three-dimensional polycrystalline microstructures have been performed. Theudinfluence of several intergranular parameters, such as cohesive strength, fracture toughness and friction,udon the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. Theudtests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescenceudof multiple damage and cracks, under either tensile or compressive loads.
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