Micromechanics of Wedge and Cone Indentation of Metallic Specimens with Subsurface Voids

Abstract

Near-surface voids and pores occur in metal parts manufactured by processes as diverse as casting, powder metallurgy, and additive manufacturing. These pores range in size from a few microns to a few mm, depending on the processing route. The presence of near-surface voids in the specimen can significantly influence its mechanical response. The behavior of voids in tension has, of course, been studied extensively due to its critical role in ductile damage and failure and in constitutive modeling of porous metal plasticity. In the compressive regime, especially in cast metals, there has been considerable interest in the modeling and simulation of void closure during post-casting hot-working including rolling, forging, and hot-isostatic pressing. However, the fundamental micromechanics problem of indentation of a void-containing metal specimen by a hard pyramidal or wedge indenter has not been studied. This is of course key to micro and nano-indentation testing, but in the literature the modeling and simulation of indentation of metal specimens with voids has largely focused on the homogenized, low-porosity regime using Gurson-type plasticity models. The present thesis uses finite element analysis (FEA) to simulate the indentation of metallic specimens with near-surface holes or voids under both plane strain and axisymmetric conditions. The corresponding indenter shapes are a wide-angle wedge and cone, respectively. Commercially-pure (CP) aluminum Al 1100, a representative ductile metal, is used throughout this thesis. A critical enabling tool in the present thesis is the development and use of a remeshing and mesh-to-mesh transfer scheme, which helps accommodate the complex patterns of void-wall self-contact and void closure during indentation. Notably, the conventional updated Lagrangian FE scheme, widely used in the literature to simulate indentation of void-free (homogeneous) specimens, is inadequate for this purpose. The FE simulations for both plane strain and axisymmetric indentation reveal the subsurface kinematic fields (plastic strain, plastic strain-rate, and velocity) and stress fields (von Mises stress and hydrostatic stress) with very high-fidelity. Importantly, these fields are radically different from the well-known radial indentation field in a void-free specimen. A wide, representative range of void locations, depths, and radii are studied in this work to better understand the effect of voids on the deformation field. Importantly, the high-fidelity simulations allow a quantitative, parametric study of the global indentation response, particularly the effect of void presence on the dynamic indentation hardness as a function of depth; this is the first of its kind in the indentation literature. For on-axis voids, the maximum reduction in apparent hardness ΔH in wedge indentation varies from 9.5% to 55%. For off-axis voids, ΔH varies from 8% to 20%, which is notably smaller than the ΔH for otherwise identical on-axis voids. Notably, the effect of a spherical (axisymmetric) void on ΔH is less than that of cylindrical (plane strain) voids of the same diameter and depth, with ΔH ranging from 2% to 30%. Interestingly, the extent of apparent reduction in the elastic modulus due to the presence of a void is much smaller; for instance it is only about 6.5% in a case where the apparent reduction in hardness ΔH is as high as 55%. The global response study also examines the indentation force-displacement curves and normalized void-area evolution curves for a range of simulations. Unlike voids under uniform compression, the void-area evolution in indentation shows a characteristic sigmoidal pattern of area reduction with indentation depth for all but the smallest voids. Examination of the indented surface profiles is also valuable; for instance, some voids can exhibit a one-sided surface pile-up feature, which is diagnostic of the presence of an eccentrically located sub-surface void. The remeshing scheme is very versatile and allows for the study of the deformation associated with two or more voids under the indenter. Several such examples are considered in this work. This thesis also systematically examines the role of prior work hardening of the specimen to various extents, from fully annealed specimens to specimens with an initial plastic strain of 1.0. Notably, the patterns of void closure and the indentation hardness response are quite different in the annealed and pre-strained specimens. Interestingly, this difference is considerable even with an initial strain as low as 0.1. The findings in this thesis are of interest in indentation testing and grid-indentation testing as they reveal and quantify the potential softening effect of subsurface voids on the measured indentation response e.g. in additively manufactured products. Moreover, in the absence of remeshing or other measures to ensure control of element quality, void-closure simulations in forming operations in the literature are likely erroneous, and their predictions of quantities like the void-closure evolution must be treated with skepticism.