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Generalized grain boundary constitutive description implemented in a strain-gradient large-strain FFT-based formulation: Application to nano-metallic laminates

Herein this paper presents a general treatment of grain boundary constitutive behavior in the context of strain-gradient (SG) plasticity, and its numerical implementation in a large-strain (LS) elasto-viscoplastic (EVP) fast Fourier transform (FFT)-based micromechanical model. Two novel grain boundary constitutive equations are proposed, allowing for more accurate description of the Burgers vector flow at the grain boundary. The capabilities of the generalized SG-LS-EVPFFT formulation are illustrated for the case of kink-band formation during layer-parallel compression of nano-metallic laminates (NMLs), requiring consideration of the interaction between dislocations and interfaces.

36 MATERIALS SCIENCE↗

New large-strain FFT-based formulation and its application to model strain localization in nano-metallic laminates and other strongly anisotropic crystalline materials

This paper presents a new robust large-strain (LS) elasto-viscoplastic (EVP) formulation based on Fast Fourier Transforms (FFTs) for the prediction of the micro-mechanical response and microstructure evolution of polycrystalline and multiphase materials, with emphasis on the effect of strong crystallographic and/or morphologic anisotropy on localization of plastic deformation. In this work, the novel LS-EVPFFT formulation allows treatment of complex initial geometries and large deformations considering three grids of material points: a regular grid in the reference configuration, where FFTs can be performed; an irregular grid in the initial configuration, created by applying a stress-free displacement field to the reference regular grid; and an irregular grid in the current configuration, undergoing large strains and rotations as the material is loaded. Further numerical stability of the new formulation also required the use of a novel expression for the discrete modified Green’s operator, which reduces spurious field oscillations. After presenting and validating the new formulation by comparison with preexisting implementations and analytical solutions, LS-EVPFFT is applied to the prediction of slip and kink bands formation in polycrystalline columnar ice, and kink bands in single crystal zinc wires, showing good agreement with classic experiments. Finally, the model is used to study kink band formation during compression of Cu–Nb nano-metallic laminates (NMLs), in which accurate treatment of the complex geometry associated with the tortuosity of interfaces and large deformations become critical, showing consistency with corresponding micropillar experiments.

36 MATERIALS SCIENCE↗

Non-local large-strain FFT-based formulation and its application to interface-dominated plasticity of nano-metallic laminates

Here, this paper presents a novel formulation and its robust numerical implementation of strain-gradient (SG) crystal plasticity within a large-strain (LS) elasto-viscoplastic (EVP) fast Fourier transform (FFT)-based micromechanical model. The resulting non-local SG-LS-EVPFFT formulation is used to model and understand the process of kink band formation during layer-parallel compression of nano-metallic laminates (NMLs). NMLs are layered composites with nanoscale thicknesses, thus requiring consideration of the interaction between dislocations and interfaces within the micromechanical model. The length-scale parameter of the SG model is calibrated by simulating a double pile-up and comparing predictions to analytical solution. This required new expressions for the defect energy, resulting in more accurate double pile-up predictions. The calibrated SG-LS-EVPFFT model is then used to simulate layer-parallel compression of copper-niobium NML. Formation of kink bands is predicted, and the model is used to rationalize the microscopic mechanisms enabling the formation process. It is found that accumulation of dislocations at interfaces leads to activation of layer-parallel slip, which in turn leads to kink band formation.

36 MATERIALS SCIENCE↗