A Semi-analytical Model of Stress Interaction with Inclusions and Cracks in an Infinite Plane
The mechanical properties of materials are affected by inevitable defects such as inclusions and cracks.Accurate knowledge of their elastic fields is required to prevent stress concentration,which can lead to fracture and plastic damage.To study mutual interactions in an isotropic plane with cracks and inclusions,heterogeneous inclusions are approximated as homogeneous inclusions with the same elastic modulus as the matrix plus unknown eigenstrain based on the equivalent inclusion method,while mixed-mode Ⅰ/Ⅱ cracks are approximated as climb/glide dislocations with unknown densities according to the distributed dislocation technology.Interactions in the plane are fully considered in the governing equation system,and a solvable matrix is established with all unknowns in a unified framework.The conjugate gra-dient method is used to iteratively solve the unknowns,and the fast Fourier transform is introduced to im-prove computational efficiency.The stress field of cracks in any direction is settled by the stress transfor-mation law,and the stress intensity factors at crack tips are determined by the converged dislocation densi-ties with the assumption of crack-induced displacements in parabolic shapes.The influence of the heteroge-neous properties of inclusions on stress intensity factors at crack tips is then properly captured.The situa-tions of cracks/inclusions are discussed in detail,providing a description of the elastic fields and stress in-tensity factors.The complexity does not necessarily increase with the number of inclusions and cracks,and the calculation cost depends only on the mesh density.The effectiveness of the model developed in this study is verified using the finite element method.This model has potential application prospects in the fracture failure of heterogeneous materials and the plastic zone problems near crack tips.The conclusions may offer insight into the modeling scheme of various defective structures and the fracture behavior of ma-terials.
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