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We present an efficient approach to evaluate the size dependency of elastic and plastic properties of metallic polycrystalline materials. Specifically, we consider different volume fractions of ferrite and martensite phases for the construction of three macroscopic domains. Statistical Volume Elements (SVEs) of different sizes are extracted from these domains using the moving window method. Linear and Crystal Plasticity (CP) simulations provide elastic and plastic properties of the SVEs such as the bulk and shear moduli, yield strength, and hardening modulus. We use a variation-based criterion to determine the Representative Volume Element (RVE) size of these properties. This RVE size corresponds to a size beyond which the given property can be idealized as homogeneous. We also use anisotropy indices and an additional RVE size criterion to determine the size limits beyond which these properties can be idealized as isotropic. Numerical results show that the plastic properties often reach their homogeneity and isotropy limits at larger sizes compared to elastic properties. This effect is more pronounced for the hardening modulus compared to the yield strength. [ABSTRACT FROM AUTHOR]

Selective laser melting (SLM) is an additive manufacturing technique commonly used in the rapid prototyping of components. The complexity of the SLM microstructure poses a unique challenge to deriving effective mechanical properties at different length scales. Representative volume elements (RVEs) are often used to homogenize the material properties of composites. Instead of RVEs, we use statistical volume elements (SVEs) to homogenize the elastic and fracture properties of the material. This relates the inherent variation of a material's microstructure to the variation in its mechanical properties at different observation scales. The convergence to the RVE limit is examined from two perspectives: the stability of the mean value as the SVE size increases for the mean-based approach, and the tendency of the normalized variation in homogenized properties to zero as the SVE size increases for the variation-based approach. Fracture properties tend to make the RVE limit slower than do elastic properties from both perspectives. There are also differences between vertical (normal to printing plane) and horizontal (in-plane) properties. While the elastic properties tend to make the RVE limit faster for the horizontal direction, i.e., having a smaller variation and more stable mean value, the fracture properties exhibit the opposite effect. We attributed these differences to the geometry of the melt pools. [ABSTRACT FROM AUTHOR]

We present a stochastic bulk damage model for rock fracture. The decomposition of strain or stress tensor to its negative and positive parts is often used to drive damage and evaluate the effective stress tensor. However, they typically fail to correctly model rock fracture in compression. We propose a damage force model based on the Mohr-Coulomb failure criterion and an effective stress relation that remedy this problem. An evolution equation specifies the rate at which damage tends to its quasi-static limit. The relaxation time of the model introduces an intrinsic length scale for dynamic fracture and addresses the mesh sensitivity problem of earlier damage models. The ordinary differential form of the damage equation makes this remedy quite simple and enables capturing the loading rate sensitivity of strain-stress response. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used for macroscopic simulations. To study the effect of rock inhomogeneity, the Karhunen-Loeve method is used to realize random fields for rock cohesion. It is shown that inhomogeneity greatly differentiates fracture patterns from those of a homogeneous rock, including the location of zones with maximum damage. Moreover, as the correlation length of the random field decreases, fracture patterns resemble angled-cracks observed in compressive rock fracture. [ABSTRACT FROM AUTHOR]