A crystal plasticity theory was developed for use in simulations of dynamic loading at high pressures and strain rates. At pressures of the order of the bulk modulus, compressions o(100%) may be induced. At strain rates o(10^9)/s or higher, elastic strains may reach o(10%), which may change the orientation of the slip systems significantly with respect to the stress field. Elastic strain rather than stress was used in defining the local state, providing a more direct connection with electronic structure predictions and consistency with the treatment of compression in initial value problems in continuum dynamics. Plastic flow was treated through explicit slip systems, with flow on each system taken to occur by thermally-activated random jumps biased by the resolved stress. Compared with simple Arrhenius rates, the biased random jumps caused significant differences in plastic strain rate as a function of temperature and pressure, and provided a seamless transition to the ultimate theoretical strength of the material. The behavior of the theory was investigated for matter with approximate properties for Ta, demonstrating the importance of the high pressure, high strain rate contributions.
High-energy synchrotron x-rays are used to track grain rotations and the micromechanical evolution of a hexagonal Ti-7Al microstructure as it is cyclically loaded below its macroscopic yield stress. The evolution of the grains through 200 cycles reveals a continual change in von Mises stress and orientation across the entire specimen indicating a slow accumulation of plasticity even though the sample was cycled below its macroscopic yield. Grain reorientation is consistent with the development of a tension texture despite the negligible magnitude of (macroscopic) plastic strain. It is observed…
Transformation-mediated twinning governs plasticity in body-centered cubic nanocrystals under extreme loading
University of West Bohemia in Pilsen（西波希米亚大学）；University of Helsinki（赫尔辛基大学）；National Centre for Nuclear Research（国家核研究中心）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
The influence on macroscopic work hardening of small, spherical, elastic particles dispersed within a matrix is studied using an isotropic strain gradient plasticity framework. An analytical solution, based on a recently developed yield strength model is proposed. The model accounts for random variations in particle size and elastic properties, and is numerically validated against FE solutions in 2D/3D material cell models. Excellent agreement is found as long as the typical particle radius is much smaller than the material length scale, given that the particle volume fraction is not too large…
A 3D unit cell model containing eight different spherical particles embedded in a homogeneous strain gradient plasticity (SGP) matrix material is presented. The interaction between particles and matrix is controlled by an interface model formulated within the higher order SGP theory used. Strengthening of the particle reinforced material is investigated in terms of the increase in macroscopic yield stress. The results are used to validate a closed form strengthening relation proposed by the authors, which suggests that the increase in macroscopic yield stress is governed by the interface stren…
Three-dimensional discrete dislocation dynamics simulations are used to study strain-controlled plastic deformation of face-centered cubic aluminium single crystals. After describing the rate and size dependence of the average stress-strain curves, we study the power-law distributed strain bursts and the average avalanche shapes, and find a universal power-law exponent $τ\approx 1.0$ for all imposed strain rates and system sizes, characterizing both the event sizes and their durations. We discuss the dependence of our results on loading rate and compare these with previous studies of strain-co…
This work proposes a dislocation density-based strain gradient $J_2$ plasticity framework that models the strength contribution due to Geometrically Necessary Dislocations (GNDs) using a lower order, Taylor hardening backstress model. An anisotropy factor is introduced to phenomenologically represent the differential hardening between grains in this $J_2$ plasticity framework. An implicit numerical algorithm is implemented for the time integration of the finite deformation plasticity model. The framework is first used to predict directional hardening due to the GND-induced backstress during cy…
Crystal-level strain rate sensitivity and temperature sensitivity are investigated in Zircaloy-4 using combined of bending creep test, digital image correlation, electron backscatter detection and thermo-mechanical tensile tests with crystal plasticity modelling. Crystal rate-sensitive properties are extracted from room temperature microscale creep, and temperature sensitivity from thermal polycrystalline responses. Crystal plasticity results show that large microscale creep strain is observed near notch tip increased up to 50% due to cross-slip activation. Grain-level microscale SRS is highly…
The purpose of continuum plasticity models is to efficiently predict the behavior of structures beyond their elastic limits. The purpose of multiscale materials science models, among them crystal plasticity models, is to understand the material behavior and design the material for a given target. The current successful continuum hyperelastoplastic models are based in the multiplicative decomposition from crystal plasticity, but significant differences in the computational frameworks of both approaches remain, making comparisons not straightforward. In previous works we have presented a theory …
Fifth-degree elastic potential for predictive stress-strain relations and elastic instabilities under large strain and complex loading in Si
在复杂载荷下的材料产生大的应变，并且通常通过弹性不稳定性转变，如在简单和复杂系统中所观察到的。在这里，我们提出了硅我在大应变的拉格朗日应变方面的$5^{th}$阶弹性势通过最小化误差相对于密度泛函理论（DFT）的结果。任意复杂载荷下的Cauchy应力-Lagrangian应变曲线与密度泛函理论（DFT）结果吻合良好，包括驱动Si I $\rightarrow$ II相变（PT）的弹性不稳定性和剪切不稳定性。PT条件下的Si I $\rightarrow$ II的作用下的立方轴向应力是线性的柯西应力与DFT预测。这样的弹性势允许研究弹性不稳定性和取向依赖性，导致不同的PT，滑移，孪生，或断裂，提供了一个基本的基础，连续模拟极端负载下的晶体行为。
Coarse-grained, metallic materials undergo microstructure refinement during tribological loading. This in turn results in changing tribological properties, so understanding deformation under tribological load is mandatory when designing tribological systems. Single-trace experiments were conducted to understand the initiation of deformation mechanisms acting in various tribological systems. The main scope of this work was to investigate the influence of normal and friction forces as well as crystal orientations on the dominating deformation mechanism in a face-centred cubic concentrated solid …
To reduce reliance on experimental fitting data within the crystal plasticity finite element method (CPFEM), an approached is proposed that integrates first-principles calculations based on density functional theory (DFT) to predict the strain hardening behavior of pure Ni single crystals. Flow resistance was evaluated through the Peierls-Nabarro equation using the ideal shear strength and elastic properties calculated by DFT-based methods, with hardening behavior modeled by imposing strains on supercells in first-principles calculations. Considered alone, elastic interactions of pure edge dis…
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）
As an extension to strain-gradient models of size-dependent plastic behaviour, this work proposes a model for a stress-gradient theory. The model is distinguished from earlier works on the topic by its being embedded in a thermodynamically consistent framework. The development is carried out in the context of single-crystal plasticity, and draws on thermodynamically consistent models for single-crystal conventional and strain-gradient plasticity. The model is explored numerically using the example of torsion of a thin wire comprising a face centred cubic crystal, and its behaviour compared wit…
The evolution of deformation from plasticity to localization to damage is investigated in ferritic-pearlitic steel through nanometer-resolution microstructure-correlated SEM-DIC (u-DIC) strain mapping, enabled through highly accurate microstructure-to-strain alignment. We reveal the key plasticity mechanisms in ferrite and pearlite as well as their evolution into localization and damage and their relation to the microstructural arrangement. Notably, two contrasting mechanisms were identified that control whether damage initiation in pearlite occurs and, through connection of localization hotsp…
There is a long standing technological problem in which a stress dwell during cyclic loading at room temperature in Ti causes a significant fatigue life reduction. It is thought that localised time dependent plasticity in soft grains oriented for easy plastic slip leads to load shedding and an increase in stress within a neighbouring hard grain poorly oriented for easy slip. Quantifying this time dependent plasticity process is key to successfully predicting the complex cold dwell fatigue problem. This work uses a novel approach of in situ synchrotron X-ray diffraction during stress relaxation…
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）
Precipitation of fine particles into the base material of a metal is a potent strengthening mechanism. This is numerically analyzed within a continuum framework based on a higher order strain gradient plasticity theory and by use of an axi-symmetric unit cell model. The unit cell contains a spherical particle which is resilient to inelastic deformation and embedded in a homogeneous matrix material. An interface with special characteristics, that separates the particle from the matrix, plays a key role for the overall strengthening. Based on a systematic parametric study a closed form relation …
A phase field model for ductile fracture considering Hencky strain and finite J2 plasticity is presented using the nonlocal operator method. A variational derivation of J2 plasticity at finite strain with a phase field model is performed. The method includes a logarithmic strain tensor and an exponential mapping in the plasticity evolution. A spectral decomposition based algorithm for computing the first and second order derivatives of the composite matrix function is implemented. A consistent tangential stiffness matrix is derived and used in Newton-Raphson iterations. Several numerical examp…
Sensitivity of grain-averaged elastic strain and orientation predictions on the mesh density and boundary conditions in crystal plasticity finite element simulations
The University of Alabama（阿拉巴马大学）；Mines Saint-Etienne（圣艾蒂安国立高等矿业学校）；The Pennsylvania State University（宾夕法尼亚州立大学）
We present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial tension. The proposed constitutive model has two components: a generalized Taylor relation connecting resolved shear stresses to dislocation densities on individual slip systems, and a generalized Kocks-Mecking model for dislocation multiplication. The DDD data strongly suggests a logarithmic dependence of flow stress on the plastic shear strain rate on each sl…
The measurement of real contact area between rough surfaces is one of most challenge problems in contact mechanics and is of importance to understand some physical mechanisms in tribology. Based on the frustrated total internal reflection, a new apparatus is designed to measure the real contact area. For brass samples with various surface topographies, the relation between normal load and real contact area is measured. Our experiments verify the linear relationship between load and real contact area during loading process. More importantly, the unloading process is firstly considered to distin…
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…
