A numerical study of stress-strain state evolution in structurally inhomogeneous materials subjected to uniaxial loading

Describing structurally inhomogeneous materials as complex hierarchical systems allows deriving a consistent pattern of stress-strain state related to history dependence of damage evolution. In this work we use a random microstructure subvolume to describe a methodology of a numerical study of stress-strain response evolution of a structurally inhomogeneous material subjected to uniaxial tension and compression. The study involves micro- and macrolevel and takes both internal structure and rheological properties of material constituents into account. We use a particle reinforced metal matrix composite with a 99.8% pure aluminum matrix and silicon carbide reinforcing particles. Particles are considered to have an irregular prism shape. The geometric structure of a composite subvolume on the microlevel is modeled by the piecewise-homogenous medium. The medium consists of particle model volumes surrounded by a matrix model volume. To take a surrounding material into account, we introduce an additional buffer layer with averaged macromechanical properties of the composite. A microlevel computational model based on the above assumptions complies to the macrolevel representative volume of the composite with the microstructure fragment in the geometric center. Simulating the model loading behavior allows studying a stress-strain evolution of the random microstructure subvolume and describing it. Boundary conditions in the microlevel model are imposed in the way to represent the macrolevel strain in a point of material. The strain is obtained from macrolevel simulations. A buffer layer is used to improve accuracy of transferring the stress strain state from the macrolevel to the microlevel. The rheological properties of a matrix and buffer layer are taken into account by assigning experimentally obtained strain-hardening curves of the pure aluminum and composite. The matrix material is modeled by an elastoplastic medium with isotropic hardening. The buffer layer is assigned to have isotropic elastoviscoplastic properties. The silicon carbide particle material is considered to be isotropic linear elastic. A finite element discretization is generated with the aid of an in-house software. The software implements special techniques to generate three-dimensional model volumes of inhomogeneous materials with a complex internal structure. The numerical simulation allowed obtaining data on the evolution of the stress tensor components and strain increment tensor components in finite element mesh nodes. Contrary to homogenous macrolevel stress and strain fields emerging in loading simulations with the quasi-homogenous model of the composite material, computations yield peculiar heterogeneous stress-strain state of the microstructure subvolume. We describe features of the stress concentration area emergence and the local plastic strain regions development. We depict strain dependence of stress stiffness coefficient fields and Lode-Nadai coefficient fields. The statistical sampling of such microstructure subvolumes followed by a numerical study adhering to the computational model allows generalizing modeling results and deriving general laws of the stress-strain state evolution of the material on the microlevel.