The method of indentation of an indenter into a material or substrate is widely utilized to characterize one of the mechanical properties of a material, namely hardness. This method is performed on different scales of indenting force, indenter size/dimensions, and size/dimensions of the indented material/substrate. The different scales do not always yield the same hardness output or reading due to material length scales. One of the length scales in a material is related to its heterogeneity, such as in reinforcing particles or second phases. This work performs 3D non-linear finite element analysis using a purely elastic indenter on a composite material. In addition to the scales above that could affect the results, the parameters of particle size, shape, spacing, and volume fraction are all shown to affect the hardness readout in the current work. One of our new findings is that the length scale effect is more phenomenal, especially at scales when the size of the indenter is comparable to any characteristic length in the material beneath the indented surface.

Discrete Dislocation Dynamics (DDD) simulations are a powerful simulation methodology that can predict a crystalline material’s constitutive behavior based on its loading conditions and micro-constituent population/distribution. In this paper, a 3D DDD model with spiral dislocation sources is developed to study size-dependent plasticity in a pure metal material (taken here as Aluminum). It also shows, for the first time, multipole simulations of spirals and how they interact with one another. In addition, this paper also discusses how the free surface of a crystalline material affects the plasticity generation of the spiral dislocation. The surface effect is implemented using the Distributed Dislocation Method. One of the main results from this work, shown here for the first time, is that spiral dislocations can result in traditional Frank–Read sources (edge or screw character) in a crystal. Another important result from this paper is that with more dislocation sources, the plastic flow inside the material is more continuous, which results in a lowering of the flow stress. Lastly, the multipole interaction of the spiral dislocations resulted in a steady-state fan-shaped action for these dislocation sources.

Material defects resulting from manufacturing and processing can significantly affect material properties. Voids and dislocations are material defects considered in this study, in which a numerical solution of the 3D stress field of a dislocation line (infinite or finite) outside a cylindrical void (either parallel to the cylinder axis or not) is developed using the collocation point method. The collocation point method is utilized to solve ordinary differential equations, partial differential equations, differential-algebraic equations, and integral equations by enforcing the solution at a set of spatial collocation points. Analytical solutions for such three-dimensional (3D) problems, e.g., a dislocation line or segment near an internal void of any shape, were not found. Therefore, a numerical solution for this problem has been constructed in this paper. The numerical solution developed is verified using an existing two-dimensional analytical solution. The numerical results and the 2D analytical solution are in perfect agreement as long as the cylindrical void is sufficiently long and the Saint-Venant’s principle is followed.