An Eulerian projection method for quasi-static elastoplasticity

A well-established numerical approach to solve the Navier--Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. We highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.Comment: 49 pages, 20 figure

Parallel three-dimensional simulations of quasi-static elastoplastic solids

Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. In this work, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier-Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.Comment: Final version. Accepted for publication in Computer Physics Communication

CRYSTAL PLASTICITY FINITE ELEMENT MODELING OF MAGNESIUM ALLOYS AND EXPERIMENTAL CHARACTERIZATION OF A TRIP HIGH ENTROPY ALLOY

This work presents two crystal plasticity finite element studies on magnesium alloys and an experimental characterization of a high entropy alloy. The first of two crystal plasticity studies presents a high strain rate deformation characterization via a split Hopkinson bar Taylor impact of a WE43 magnesium alloy. This study showed that crystal plasticity finite element modeling (CPFE) was able to model WE43 texture evolution, twin volume fraction along the length of the cylinder, and anisotropy with four different material orientations at high strain rates when compared to experimental data. The second study investigated the Taylor-type model homogenization response of the virtual polycrystal and how to best spread the crystal orientations over the finite element (FE) mesh for accurate modeling of Mg alloys specifically AZ31. It was found that 6 embedded crystals per integration point proved most optimal when compared to a full-field explicit grain mesh model. The third study investigated phase transformation hardness values and strain hardening characteristics for a four-phase high entropy alloy by nanoindentation. The material exhibited great strength based on phase transformation during plastic deformation upon compression

Particle displacements in the elastic deformation of amorphous materials: local fluctuations vs. non-affine field

We study the local disorder in the deformation of amorphous materials by decomposing the particle displacements into a continuous, inhomogeneous field and the corresponding fluctuations. We compare these fields to the commonly used non-affine displacements in an elastically deformed 2D Lennard-Jones glass. Unlike the non-affine field, the fluctuations are very localized, and exhibit a much smaller (and system size independent) correlation length, on the order of a particle diameter, supporting the applicability of the notion of local "defects" to such materials. We propose a scalar "noise" field to characterize the fluctuations, as an additional field for extended continuum models, e.g., to describe the localized irreversible events observed during plastic deformation.Comment: Minor corrections to match the published versio

Study on Ductile Fracture with Anisotropic and Strain Rate Effects in Manufacturing Processes

Ductile fracture is a topic of great importance in automotive and aerospace industries. Prediction of ductile fracture in engineering structures relies on developing robust material models under complex loading conditions. This dissertation addresses the anisotropic and strain rate effects in constitutive and ductile fracture models of lightweight metals. In the present modeling framework, the anisotropic plasticity behavior is modeled by combination of an initial anisotropic yield function and an isotropic hardening correction by Lode dependence. A new all-strain based anisotropic fracture model is proposed based on the approach of linear transformation on plastic strain rate tensor. The strain rate effects in ductile fracture is considered as an extension of the modified Mohr-Coulomb (MMC) fracture model by coupling strain rate with stress state in terms of Lode angle parameter. The rate-dependent MMC model provides a well-bound solution up to the intermediate strain rate range ( \u3c 1000/s) for metal forming and crashworthiness applications. The present modeling framework is calibrated from coupon tests of aluminum alloy and advanced high strength steel (AHSS) sheets using digital image correlation (DIC) technique and validated through correlations by finite element (FE) simulations. This study also demonstrates the applications of ductile fracture modeling in manufacturing processes. The thermo-mechanical FE simulations of orthogonal cutting processes using the Johnson-Cook constitutive and damage models show that the highly damaged regions in zones of material separation form a thin boundary layer at the tool tip. The numerical simulation results explain the success of analytical model with uncoupled component works of plasticity, friction and separation. The FE modeling results of formability and component-level testing suggest that part behavior and material failure is well predicted using calibrated ductile fracture models under different loading conditions

Deformation Behavior of Tungsten Single Crystals During Wedge Nanoindentation - a Numerical Study

The present work aims at the numerical investigations on the plastic deformation behavior of tungsten single crystals on the microscale, based on finite-element (FE) wedge nanoindentation simulations. These numerical studies on plasticity of body-centered cubic materials in the range of nanometers to few micrometers require not only an incorporation of a crystal plasticity model to describe slip dominated plastic deformation in the FE-simulations but moreover, the consideration of geometrically necessary dislocations (GND) and non-Schmid effects. Thus, an existing crystal plasticity model was extended to determine gradients of plastic shear and non-Schmid effects for the implementation of enhanced FE-simulations of wedge nanoindentation. A comprehensive evaluation of the influence of GNDs and non-Schmid effects on the plastic deformation response of the single crystal was performed under plane strain conditions. Dependent on the applied model, a significant difference in the stress state, the plastic shear on active slip systems and material pile-up around the indenter was observed. In contrast, solely slight deviations in the density of GNDs and crystal lattice rotation under the residual imprint were found. With the gradient-based crystal plasticity model, a size dependency of the plastic deformation could be described in addition. Further, a comparison between numerical and experimental results regarding GNDs, crystal lattice rotation and the residual geometry of the indent was performed. A very good agreement between the experimental and simulated deformed geometry of the specimen was found in the crystal plasticity simulation. The comparison of the GND density and lattice rotation in the region under the indenter flanks showed a good agreement as well. However, all numerical simulations overestimate both, the crystal lattice rotation and density of GNDs that occur in the region under the indenter tip

Micromechanics of ultra-high molecular weight polyethylene fibre composites

Ultra-high molecular weight polyethylene (UHMWPE) fibre composites are considered to be state-of-the-art materials for penetration and ballistic impact protection applications. The composites are made of strong UHMWPE fibres with a soft compliant matrix. The extreme anisotropy caused by the mismatch between the stiffness and strength of the fibres and the matrix resulted in unique deformation and failure mechanisms which cannot be found in conventional engineering materials. Therefore, the thesis contributes towards understanding the governing mechanisms of UHMWPE composites that resulted in their high penetration and impact resistance, as well as characterizing their mechanical response under dynamic loading. In the first part of the thesis, we focus on the quasi-static penetration response of UHMWPE composites by sharp-tipped punches. It is shown that the punch penetrates the composites without fibre fracture but by the formation of mode-I cracks along the fibre directions. The results indicate that the high penetration resistance of the composites by sharp-tipped punches is attributed to the high toughnesses of the composites. In the second part of the thesis, failure mechanism maps are developed to illustrate the mechanisms by which failure can initiate in UHMWPE composite beams impacted by blunt projectiles. We reveal that beams with low shear strengths fail by the indirect tension mode at high impact velocities while beams with high shear strengths fail by the bending mode at significantly lower impact velocities. The study thus provides a mechanistic understanding of the experimental observations that high ballistic performance composites require low matrix shear strength. Finally, in the third part of the thesis we investigate the dynamic in-plane compressive response of the composites. It is revealed that compressive deformation of the composites occurs by ply level kink band formation. Additionally, the study shows that the composites become strongly strain rate dependent at strain rates above 100 s^{-1} and the observed strain rate dependency is mainly attributed to that of the matrix. The findings presented throughout this thesis reveal the key mechanisms and material parameters of the UHMWPE composites which governs their impact and penetration resistance, hence open new avenues and additional routes towards the design of composite materials with ultimate performance

Dynamic necking in materials with strain induced martensitic transformation

This work investigates the interplay between inertia and strain induced martensitic transformation (SIMT) on necking inception and energy absorption in dynamically stretched cylindrical rods. For that task a linear stability technique, derived within a quasi-1D framework and specifically accounting for SIMT, has been developed. Likewise, finite element simulations have been performed, using a specific constitutive equation to consider SIMT. Stability analysis and numerical simulations demonstrate that, at high strain rates, inertia may take the dominant role in stabilizing the material, on top of the transformation hardening effects. Furthermore, under certain loading conditions the martensitic transformation may penalize either ductility or energy absorption capacity.Ministerio de Ciencia e Innovación de España (Projects DPI/2011-24068 and DPI/2011-23191)Publicad