A thermodynamic model for predicting the stress–strain relation of stochastic heterogeneous materials with experimental verification

Abstract

Materials are intrinsic stochastic heterogeneity regardless of their natural or artificial origin. Traditional models for predicting mechanical properties of materials typically involve homogenization, which exhibits certain limitations in practical applications, such as investigating the size effect in stress–strain relationships. In this study, a random field thermodynamic theory for predicting the mechanical properties of stochastic heterogeneous materials was proposed, and its applicability and reliability were verified by testing hard-drawn 304 stainless-steel wires with gauge lengths of 10–500 mm. In these wires composed of the lamellar martensite with a thickness of ∼47.1 nm, it is found that failure strains decreased significantly with increasing gauge length, whereas fracture stresses show little dependence on the gauge length leading to a great increase of the effective modulus. Digital image correlation investigations revealed a significant strain heterogeneity during the tensile process, even at the elastic deformation stage. Nanoindentation tests show the non-uniformly distributed reduced modulus and hardness, which can be attributed to the intrinsic stochastic heterogeneity of materials. Taking Young's modulus as a one-dimensional stationary random field along the longitudinal direction, our random field model can well demonstrate the variation of failure strain and effective modulus with changing gauge lengths. The size effect on the macroscopic mechanical properties mainly originated from the microscopic mechanical property correlation of different points within the materials. These findings could provide new insights into the size effect on the mechanical properties of materials.