Papers by Keyword: Crystal Plasticity

Abstract: Crystal plasticity finite element (CPFE) simulations of three-dimensional representative volume elements (RVEs) enable the prediction of polycrystalline material behavior under complex loading conditions. Plastic deformation is modeled through crystallographic slip on lattice slip systems, subject to the Schmid yield criterion based on the maximum resolved shear stress (CRSS). In this work, an efficient rate-independent crystal plasticity (CP) and gradient enhanced crystal plasticity (GECP) formulation is used to investigate the influence of microstructural characteristics on the mechanical performance of FCC materials. Three-dimensional periodic RVEs with irregular grain morphologies are simulated within Abaqus/Standard to study the effects of grain size, grain size distribution, and grain shape under uniaxial loading. Comparative analyses between the CP and GECP frameworks are performed to assess the predictive capabilities and applicability for increasingly heterogeneous microstructures. The results demonstrate that GECP accurately captures grain size dependent work hardening and grain size distribution effects through the intrinsic length scale introduced by strain gradient calculations. In contrast, grain shape variations result in only minor changes in the macroscopic response for both frameworks.

Abstract: The plastic deformation behavior of polycrystalline copper is strongly governed by microstructural attributes such as grain boundaries and crystallographic orientation. In this study, the individual and coupled effects of grain size and orientation distribution on the mechanical response of copper are systematically investigated using the crystal plasticity finite element method (CPFEM). Uniaxial compression simulations are performed employing an Abaqus UMAT subroutine, and the resulting stress–strain response, slip system activity, and strain localization are examined. Polycrystalline representative volume elements (RVEs) with varying grain sizes and textures are generated to quantify their influence on flow behavior and dislocation density. The results indicate that grain refinement diminishes orientation sensitivity and the influence of individual grains, while enhancing material strength. Moreover, grain boundaries promote heterogeneous slip, localized deformation near grain edges, and increased stress–strain heterogeneity.

Abstract: Macroscopic damage models can describe the toughness behavior and formability of metals in terms of limit strains. However, it requires time-, cost-, and material-intensive calibration. In this work, a simulation framework is proposed to derive macroscopic damage model parameters and related properties directly from the microstructure. For this purpose, statistically Representative Volume Elements of the investigated DP1000 steel were generated utilizing the Python framework DRAGen. This was based on quantitative characterization of EBSD measurements of the present microstructure. Mechanical properties were assigned to the geometrical microstructure model by calibrating a phenomenological Crystal Plasticity model for distinct phases. Martensite cracking was identified as the predominant damage mechanism. This behavior on the microscale was represented by an isotropic brittle damage model in DAMASK, using a fracture mechanical literature value as the critical energy release rate parameter. The presented modeling approach enables stress state-dependent prediction of macroscopic damage properties out of the present microstructure.

Abstract: Understanding the relationships between microstructure and (mechanical) properties is inevitable for the design of modern structural metallic materials. A crucial property for most high-strength steels is ductile damage tolerance, since ductile damage can accumulate during cold forming, which either leads to failure in the forming process or subsequently affects the performance. Structure-property relations are often investigated using numerical methods, e.g. crystal plasticity (CP) modeling with representative volume elements (RVE). In a previous study, CP-simulations on 3D-RVE were coupled with surrogate modeling techniques performing a variance-based sensitivity analysis. This analysis enables quantitative descriptions of the relationships between microstructure features with the damage tolerance, quantified by individual indicators for individual damage mechanisms. To investigate the effect of the material model and the corresponding phase properties, 500 sRVE simulations were carried out with different CPparameter sets and the damage tolerance is investigated. All sets stem from the same DP800 but were calibrated with different approaches. Surrogate models were trained on the simulative database to calculate Sobol Indices (SI), which are a measure of how strong damage tolerance is affected by a particular microstructure feature. The SI are compared for the individual material models and damage indicators. The structure-property quantification is heavily influenced by the different material models, resulting in different values for the SI and a different order for the individual microstructure features. The main factor for the pronounced differences is the differently evolving mechanical phase contrast between ferrite and martensite.

Abstract: In metal forming, the flattening of asperities on the workpiece surface is important to understand both for the impact it has on the properties of finished parts and the influence that real contact area has on tribological conditions during forming. The current study presents a method for the numerical modeling of asperity flattening of a deep drawing steel under high normal loads and no subsurface strain. At the microscale, a crystal plasticity model is employed to capture the propensity of grains to deform differently depending on their orientation. The continuum scale model is used to provide the boundary conditions to the microscale. The mechanical and microstructural properties of a DC04 deep drawing steel are used to provide the necessary parameters for the continuum and microscale models. The initial surface topography of the experimental material is measured by confocal microscopy and is mimicked in the input to the simulations. Surface topography measurements after flattening the experimental surface are used as validation for the simulated results, with real contact area, mean surface roughness, and autocorrelation length used as the primary figures of merit.

Abstract: The mechanical behaviour of materials is influenced by processing and thermomechanical exposure. In safety-sensitive industries there is a need to make predictions on the envelope of safe use beyond proven constitutive equations. Microstructural simulations, such as crystal plasticity modelling, can model features like grain size, morphology and texture. However, they are computationally demanding and it can be hard to translate measured microstructures into meaningful or representative statistical distributions. Surrogate models incorporate machine learning regression and statistical methods to emulate the response of a complex model. As they are much faster, they can model the response over a wide range of material parameters, permitting sensitivity analysis and uncertainty quantification. Preferred orientation (texture) can be challenging to incorporate into surrogate models as accurate representations can require a lot of parameters. In this study, reduced-order representations of crystallographic texture are presented to represent the bulk response of a polycrystal volume element. These representations are used as inputs to a gaussian process regression (GPR) model that is used to predict the macroscopic stress-strain response of a polycrystal for different crystallographic textures. The GPR acts as a surrogate model of the underlying crystal plasticity model and allows an inherent quantification of the model epistemic uncertainty and the uncertainty related to unobserved effects not captured by the texture parameterization. Incorporation of the surrogate model into finite element coding will be used as an application of the method.

Abstract: The crystal plasticity finite element method (CPFEM) has emerged as an important method for studying materials on a mesoscopic scale. However, a significant obstacle to the application of CPFEM is the numerous material parameters associated with it. This study selected a physics-based CPFEM incorporating the non-crystalline shear band formation mechanism as it can stimulate both work-hardening and strain-softening mechanisms. A three-dimensional smooth specimen model was established to simulate the tensile test. The effects of six fitting crystal plasticity material parameters on the yielding stress, work-hardening behavior, and strain localization behavior are. In addition, the influencing mechanisms are discussed.

Abstract: In this paper, macroscopic behavior obtained from crystal plasticity finite element simulations of irregularly shaped 3D and 2D volume elements (VEs) are compared. These morphologically periodic VEs are generated using the open-source software library Voro++. Periodic boundaryconditions are utilized to homogenize the material response employing a prescribed macroscopic deformation gradient tensor. To accelerate the assignment of periodic boundary conditions, a conformalmesh is employed by which periodic couples of faces on the hull of the volume element have identicalmesh patterns. In the simulations, plane strain conditions are assumed, which means that the averagethickness strain in 3D VEs is set to zero. However, grains are allowed to strain in the thickness direction. In the case of 2D VEs, plane strain elements are used. The principal goal of this comparison isto evaluate the accuracy of 2D VEs simulations. In the current study, two kinds of 2D VEs are generated: 1) Slicing 3D VEs normal to the thickness direction, 2) Separately generating 2D VEs. The firstmethod corresponds to sectioning 3D microstructures using EBSD. This approach is generally usedas an assumed more accurate alternative to 2D VEs. Based on the results, there is a large gap betweenthe flow curves of 2D and 3D VEs. Additionally, 2D sectioning of 3D VEs does not necessarily endup in higher precision in material behavior predictions.

Abstract: The properties of individual grains affect the mechanical behaviors and response of materials in micro-scaled deformation, viz., microforming, and there are unknown phenomena and deformation behaviors existing and limiting the wide application of microforming due to size effect. In this paper, a composite model combining crystal plasticity and grain boundary strengthening theories was developed for numerical investigation into the effect of grain boundaries on the plastic deformation of copper micro-upsetting. By comparing the results with and without grain-boundary structure, it is revealed that grain boundaries, which act as the barriers of crystal slip, result in the enhanced flow stress and the discontinuous distribution of stress and strain. The grain size effect is also considered in this research, and the results show the coarse-grained material reduces the flow stress and enhances the inhomogeneous deformation.

Abstract: In this paper, a micromechanical finite element (FE) model has been proposed to investigate the effect of the nanoscale precipitates on the development of microplasticity for Inconel 718 (IN718) superalloy. A strain gradient crystal plasticity formulation has been developed with the considerations of the evolution of statistically stored dislocation density and geometrically necessary dislocation density. The mesh convergence has been examined, showing that sufficiently fine mesh is required in the FE model. The results show that the model with strain gradient effect incorporated shows less peak plastic strain and higher value of dislocation density than the model with no strain gradient effect. The present study indicates that the strain hardening process at the scale of strengthening precipitate is mainly governed by the evolution of geometrically necessary dislocation densities.