Interpretation of Microstructural Effects on Porosity Evolution Using a Combined Dilatational/Crystal Plasticity Computational Approach RICARDO A. LEBENSOHN 1,2 and REEJU POKHAREL 1 1.—Los Alamos National Laboratory, Los Alamos, NM 87545, USA. 2.—e-mail: lebenso@lanl.gov A novel formulation based on fast Fourier transforms for the prediction of ductile damage of polycrystalline materials that combines crystal plasticity and dilatational plasticity is reviewed and applied to understand the micro- structural origin of available experimental evidence of porosity evolution in incipiently spalled Cu polycrystals. The influence of the Taylor factor of the crystalline ligaments linking interacting voids and the microstructural origin of a nonmonotonic grain-size dependence on porosity evolution is investigated and rationalized by means of numerical simulations using the new model. INTRODUCTION The failure of structural materials has a signifi- cant economic impact. Consequently, great effort is devoted to gain a fundamental understanding of failure mechanisms of these materials to enable the development of more reliable components. Most metallic structural materials are aggregates of sin- gle crystals with anisotropic mechanical properties. Failure models of these materials remain empiri- cally calibrated due to a lack of knowledge of the controlling processes at the scale of the aggregate’s heterogeneity. As a contribution to overcome this limitation, this article reviews a recent formulation for microstructure-sensitive, three-dimensional prediction of ductile damage of polycrystals. Spe- cifically, two widely used micromechanical models, i.e., polycrystal plasticity and dilatational plasticity, have been combined within the framework of an efficient spectral formulation to predict microstruc- tural effects on porosity evolution with crystals and voids represented explicitly. The classic crystal plasticity theory, a constitutive description based on considering the stress-con- trolled contribution to single crystal deformation of different slip systems, has been extensively used to solve the micromechanical behavior of crystalline materials in the context of mean-field (e.g., homoge- nization-based 1,2 ) and full-field (e.g., FEM-based 3,4 ) approaches. In this work, crystal plasticity constitu- tive laws are used in conjunction with the full-field fast Fourier transform (FFT)-based formulation pioneered by Moulinec and Suquet for composite materials 5,6 and adapted by us to polycrystals. 7,8 The viscoplastic formulation (VP-FFT) that resulted from the latter has been successfully applied to study microstructural effects on the plastic behavior of fully dense polycrystalline aggregates (e.g., Refs. 8 and 9). Dilatational plasticity models based on limit analysis of an isotropic hollow sphere 10,11 and extensions of the latter to anisotropic behavior (e.g., Refs. 12–14) are successful in describing void growth in a homogeneous matrix. However, unlike such homogeneous matrix assumption, most poly- crystalline structural materials have complex het- erogeneous microstructures that affect damage evolution. With the goal of establishing correlations between the dilatational plastic behavior and the heterogeneous character of the matrix, we have re- cently extended the VP-FFT model to the case of voided polycrystals with intergranular cavities. 15,16 Such dilatational viscoplastic formulation (D-VP- FFT) was first used to study the influence of dif- ferent microstructural features (overall porosity, texture of the matrix material, single crystal anisotropy, etc.) and type of loading on the instan- taneous dilatational behavior of polycrystalline aggregates with intergranular voids, 15 and later it was extended to follow the evolution of local poros- ity, i.e., growth of individual voids as determined by their local environment. 16 To isolate the influence of microstructure on void growth, the D-VP-FFT formulation was used to compare the dilatational plastic behavior of two unit JOM, Vol. 66, No. 3, 2014 DOI: 10.1007/s11837-013-0849-z Ó 2013 The Minerals, Metals & Materials Society (Published online January 1, 2014) 437