Uncertainty quantification (UQ) plays a major role in verification and validation of computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allow numerical predictions, providing the bridge from microstructure to properties and performances. Several constitutive models have been proposed to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method to quantify the uncertainty of the three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curves, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.
This work presents a three-dimensional constitutive model for shape memory alloys considering the TRansformation-Induced Plasticity (TRIP) as well as the Two-Way Shape Memory Effect (TWSME) through a large deformation framework. The presented logarithmic strain based model is able to capture the large strains and rotations exhibited by SMAs under general thermomechanical cycling. By using the martensitic volume fraction, transformation strain, internal stress, and TRIP strain tensors as internal state variables, the model is capable to capture the stress-dependent TRIP generation when SMAs are…
We deform representative volume elements of amorphous carbon obtained from melt-quenches in molecular dynamics calculations using bond-order and machine learning interatomic potentials. A Drucker-Prager law with a zero-pressure flow stress of $41.2$~GPa and an internal friction coefficient of $0.39$ describes the deviatoric stress during flow as a function of pressure. We identify the mean coordination number as the order parameter describing this flow surface. However, a description of the dynamical relaxation of the quenched samples towards steady-state flow requires an additional order para…
Many engineering applications of Shape Memory Alloys (SMAs) involve passing back and forth through phase transformation many times. Repeated phase transformation develops permanent deformations originating from the significant distortion that phase transformation induces at the austenite-martensite interfaces and grain boundaries. This distortion drives dislocation activity resulting in an observable macroscopic Transformation-Induced Plastic (TRIP) deformation, which occurs at effective stress levels much lower than the plastic yield limit of the material. TRIP strains may accumulate up to 20…
Shape memory alloys (SMAs) have been intensively investigated as actuators for the past several decades. Due to their high actuation energy density compared to other active materials, their current and potential applications in engineering fields are expanding rapidly. Prior to being used as actuators, SMAs are usually subjected to a training process to stabilize their behavior. During the training process, permanent changes are introduced in the microstructure of the material which results in the generation of internal stresses and a large amount of irrecoverable Transformation Induced Plasti…
Gradient structured (GS) metals processed by severe plastic deformation techniques can be designed to achieve simultaneously high strength and high ductility. Significant kinematic hardening is key to their excellent strain hardening capacity which results in a favorable strength-ductility combination. Unfortunately, no constitutive model has been established to simulate and analyze the characteristic kinematic hardening behavior of GS metal to understand the relationship between their microstructure and macroscopic response. In this work, we developed a deformation-mechanismbased strain gradi…
In this paper we present a thermodynamically consistent material model which is capable of modelling ductile-to brittle failure mode transition in ductile material undergoing deformations at high strain rates, and demonstrate the performance of the model in a numerical study using a fully coupled thermal-structural finite element analysis of a notched aluminium alloy specimen loaded in cyclic tension. The model is based on an objective representation of the deformation and stress measures and on a rate type constitutive equations. It does not only complies with the principles of material model…
Gradient plasticity theory proposed initially by Aifantis and co-workers has proven very useful in problems dealing with material heterogeneity and material instabilities. Although it has been used successfully in many applications by many authors, still some open questions remain unanswered. The modest goal of the present short note is to provide some thoughts on these open questions, providing a new interpretation of the gradient terms leading to a successful interpretation of both extrinsic and intrinsic size effect phenomena.
Shape Memory Alloys (SMAs) are materials with the ability to recover apparently permanent deformation under specific thermomechanical loading. The majority of constitutive models for SMAs are developed based on the infinitesimal strain theory. However, such assumption may not be proper in the presence of geometric discontinuities, such as cracks, and repeated cycling loading that has been reported to induce irrecoverable strains up to 20% due to transformation induced plasticity. In addition to finite strains, SMA-based devices may also undergo large rotations. Thus, it is indispensable to dev…
We propose an Eulerian thermodynamically compatible model for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space. The model is based on the additive splitting of the velocity gradient into the crystal lattice part and the plastic part. The approach extends a Gibbs-potential-based formulation developed by Rajagopal and Srinivasa for obtaining the response functions for elasto-visco-plastic crystals. The framework makes constitutive assumptions for two scalar functions: the Gibbs potential and the rate of dissipation. The constitutive eq…
Plastic deformations in body-centered-cubic (BCC) crystals have been of critical importance in diverse engineering and manufacturing contexts across length scales. Numerous experiments and atomistic simulations on BCC crystals reveal that classical crystal plasticity models with the Schmid law are not adequate to account for abnormal plastic deformations often found in these crystals. In this paper, we address a continuum mechanical treatment of anomalous plasticity in BCC crystals exhibiting non-Schmid effects, inspired from atomistic simulations recently reported. Specifically, anomalous fea…
A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the constitutive inclusion of the plastic spin, as proposed by Gurtin (2004) through the prescription of a free energy dependent on Nye's dislocation density tensor. The proposed numerical scheme is developed by following and extending the mathematical principles established by Fleck and Willis (2009). The modeling of thin metallic foils under bending reveals a s…
In this paper is presented a new single crystal plasticity model with yielding accounting for the tetragonal symmetry of molecular energetic crystals. This new tetragonal yield criterion has been developed using representation theorems for anisotropic tensor functions. It is defined for any type of loadings and depends on the characteristics of the tetragonal lattice (c/a ratio). It involves three independent plastic anisotropy parameters that can be expressed analytically in terms of the uniaxial yield stresses along four crystallographic directions. Illustration of the capabilities of this m…
Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters beyond the requirements of standard classical crystal plasticity theory. The dislocation microstructures shown are decoupled from deformation microstructures, and emerge without any consideration of latent hardening or constitutive assumptions related to cross-slip. Crystal orientation effects on the pattern formation and mechanical response are also demonstr…
Decoupling Strain-Rate Sensitivity and Deformation Length Scale Effects in Neutron-Irradiated Tungsten: A Coupled Nano-Indentation, HR-EBSD and Crystal Plasticity Study
Indian Institute of Science（印度科学学院）；University of Oxford（牛津大学）；UK Atomic Energy Authority（英国原子能管理局）
Temperature-Aware Recurrent Neural Operator for Temperature-Dependent Anisotropic Plasticity in HCP Materials
organization= Mechanics \& Materials Laboratory, Department of Mechanical；Process Engineering, ETH Zürich , city= Zürich , postcode= 8092 , country= Switzerland；organization= Department of Engineering, University of Cambridge , addressline= Trumpington Street , city= Cambridge , postcode= CB2 1PZ , country= UK
The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The finite strain kinematics of the viscoplastic material is modelled by the multiplicative decomposition of the deformation gradient tensor. Numerical algorithms originally developed for unstressed materials are extended to materials with pre-stresses. Owing to the weak invariance of constitutive equations, the incorporation of pre-stresses happens without addition…
Shape Memory Alloys (SMAs) has been widely aware of working as actuators for active/smart morphing structures in the engineering industry. Because of the high actuation energy density of SMAs, compared to other active materials, structures integrated with SMA-based actuators has high advantage in terms of trade-offs between overall structure weight, integrity and functionality. The majority of available constitutive models for SMAs are developed within the infinitesimal strain regime. However, it was reported that particular SMAs can generate transformation strains nearly up to 8%-10%, for whi…
Unraveling the temperature dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal plasticity calculations
University of California Los Angeles（加州大学洛杉矶分校）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Universidad Politécnica de Madrid（马德里理工大学）；Max-Planck-Institut für Eisenforschung（马克斯·普朗克铁研究所）
Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps, and constitutive models simultaneously is currently …
Uncertainty quantification (UQ) plays a critical role in verifying and validating forward integrated computational materials engineering (ICME) models. Among numerous ICME models, the crystal plasticity finite element method (CPFEM) is a powerful tool that enables one to assess microstructure-sensitive behaviors and thus, bridge material structure to performance. Nevertheless, given its nature of constitutive model form and the randomness of microstructures, CPFEM is exposed to both aleatory uncertainty (microstructural variability), as well as epistemic uncertainty (parametric and model-form …
A novel, concurrent multiscale approach to meso/macroscale plasticity is demonstrated. It utilizes a carefully designed coupling of a partial differential equation (pde) based theory of dislocation mediated crystal plasticity with time-averaged inputs from microscopic Dislocation Dynamics (DD), adapting a state-of-the-art mathematical coarse-graining scheme. The stress-strain response of mesoscopic samples at realistic, slow, loading rates up to appreciable values of strain is obtained, with significant speed-up in compute time compared to conventional DD. Effects of crystal orientation, loadi…
The present report describes a big data numerical study of crystal plasticity finite element (CPFE) modelling using static and grain-based meshing to investigate the dependence of the results on the discretization approach. Static mesh refers to the integration point-based representation of the microstructure in which the integration points (IPs) within a finite element may belong to different grains, while in the grain-based meshing the minimum discretization unit is an element that may only belong to one grain. The crystal plasticity constitutive law was coded using UMAT subroutine within co…
Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline, polycrystalline and other materials --- feature a predominantly elastic response at small stresses, plasticity onset at a rather well-defined yield stress and rate-dependence. Necking instabilities involve a unique coupling between the system's geometry and its constitutive behavior. We consider generic elasto-viscoplastic constitutive relations involving an i…
Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for micr…
Accurate predictions of thermo-mechanically coupled process in metals can lead to a reduction of cost and an increase of productivity in manufacturing processes such as forming. For modeling these coupled processes with the finite element method, accurate descriptions of both the mechanical and the thermal responses of the material, as well as their interaction, are needed. Conventional material modeling employs empirical macroscopic constitutive relations but does not account for the actual thermo-mechanical mechanisms occurring at the microscopic level. However, the consideration of the latt…
A non-local model for the description of twinning in polycrystalline materials in the context of infinitesimal strains: application to a magnesium alloy
Calibrating and verifying crystal plasticity material models is a significant challenge, particularly for materials with a number of potential slip and twin systems. Here we use digital image correlation on coarse-grained $α$-uranium during tensile testing in conjunction with crystal plasticity finite element simulations. This approach allows us to determine the critical resolved shear stress, and hardening rate of the different slip and twin systems. The constitutive model is based on dislocation densities as state variables and the simulated geometry is constructed from electron backscatter …
The origin of cube recrystallization texture in medium to high stacking-fault energy fcc metals has been debated for almost 70 years. Despite numerous experimental and simulation studies, many issues regarding the nucleation and growth of cube grains remain unresolved. Here we apply a full field crystal plasticity model utilizing a dislocation density based constitutive theory to study the deformation and texture evolution in copper (Cu) under plane strain compression. Additionally, we use the phase field method, along with a stochastic nucleation model, for static recrystallization simulation…
In this study, we use the mechanism-based strain gradient plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on non-linear amplitude factors. The two planar classical stress-strain states are examined, namely, plane strain and plane stress, both under pure mode I and pure mode II loading conditions. The constitutive relations are based on Taylor's dislocation model, which enables gaining insights into the role of the increased dislocation density associated with large gradients i…
Previous studies demonstrate that grain-boundary sliding could accelerate creep rate and give rise to large internal stresses that can lead to damage development, e.g. formation of wedge cracks. The present study provides more insight into the effects of grain-boundary sliding (GBS) on the deformation behaviour of realistic polycrystalline aggregates during creep, through the development of a computational framework which combines: i) the use of interface elements for sliding at grain boundaries, and ii) special triple point (in 2D) or triple line (in 3D) elements to prevent artificial dilatio…
The University of Sydney（悉尼大学）；Nantes Université（南特大学）；Ecole Centrale Nantes（南特中央理工学院）；CNRS（法国国家科学研究中心）；Institut de Recherche en Génie Civil et Mécanique（土木工程与力学研究所）
Data-driven and deep learning approaches have demonstrated to have the potential of replacing classical constitutive models for complex materials. Yet, the necessity of structuring constitutive models with an incremental formulation has given rise to data-driven approaches where physical quantities, e.g. deformation, blend with artificial, non-physical ones, such as the increments in deformation and time. Neural networks and the consequent constitutive models depend, thus, on the particular incremental formulation, fail in identifying material representations locally in time, and suffer from p…
