Development of numerical scheme for phase field crystal deformation simulation

The phase field crystal (PFC) method is anticipated as a new multiscale method, because this method can reproduce physical phenomena depending on atomic structures in metallic materials on the diffusion time scale. Although the PFC method has been applied to some phenomena, there are few studies related to evaluations of mechanical behaviors of materials by appropriate PFC simulation. In a previous work using the PFC method, tensile deformation simulations have been performed under conditions where the volume increases during plastic deformation. In this study, we developed a new numerical technique for PFC deformation simulation that can maintain a constant volume during plastic deformation. To confirm that the PFC model with the proposed technique can reproduce appropriate elastic and plastic deformations, we performed a series of deformation simulations in one and two-dimensions. In one- and two-dimensional single-crystal simulations, linear elastic responses were confirmed in a wide strain rate range. In bicrystal simulations, we could observe typical plastic deformations due to the generation, annihilation and movement of dislocations, and the interaction between the grain boundary and dislocations. Moreover, the deformation behaviors of a nanopolycrystalline structure at high temperature were simulated and the intergranular deformations caused by grain rotation and grain boundary migration were reproduced.     

Computer experiments on nano-indentation: A molecular dynamics approach to the elasto-plastic contact of metal copper

Molecular dynamics simulations are used to investigate the micro-mechanisms of nano-indentation for tip to substrate contact. The method combines a many-body interatomic potential derived from the nearest-neighbor EAM and brownian dynamics (BD) approach to simulate a rigid tip indenting Cu (001) surface. Elastic contact and plastic instability of the crystal are investigated through the loading-unloading cycle, the variations of the system potential energy versus the tip approach, the atomic stress distributions and the portraits of atomic trajectories and configurations. For elastic indentation, we find that atomistic stress distributions resembling roughly to those of the continuum Hertzian fields, except for a jump-to-contact phenomenon in the initial contact stage. When the tip approach is beyond some critical value, plastic instability of the substrate occurs, and both the contact load and potential energy decrease dramatically. Detailed calculations reveal that material yield at the atomic level is still governed by the von Mises shear strain-energy criterion, while atomistic trajectories show that the displacements in (010) plane of atoms near the contact region is similar to that in Johnson's cavity model, accompanied by atomic cross-layer movements in [010] direction to release the strain energy. The crystal defects after plastic indentation include subsurface cavities, surface atomic steps and plastic indent.     

Influence of particle elasticity in shear testers

Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft particle molecular dynamics simulations (Particle Flow Code, PFC) for elastic particles and contact dynamics simulations (CD) for the limit of perfectly rigid particles. As soon as the system dilates to form shear bands, it relaxes the elastic strains so that one finds the same stresses for rigid respectively elastic particles in steady state flow. The principal stresses in steady state flow are determined. They are proportional to each other, giving rise to an effective macroscopic friction coefficient which is about 10% smaller than the microscopic friction coefficient between the grains.     

Atomistic simulation and modeling of localized shear deformation in metallic glasses

Since the end of 1980s, bulk metallic glasses became available for various multi-component alloys. Because bulk metallic glasses are applicable to structural materials, their mechanical properties have become a matter of great interest in these decades. A characteristic feature of plastic deformation of metallic glasses at the ambient temperature is the localized shear deformation. Since we have no appropriate experimental technique, unlike crystalline matter, to approach microscopic deformation process in amorphous materials, we have to rely on computer simulation studies by use of atomistic models to reveal the microscopic deformation processes. In this article, we review atomistic simulation studies of deformation processes in metallic glasses, i.e., local shear transformation (LST), structural characterization of the local shear transformation zones (STZs), deformation-induced softening, shear band formation and its development, by use of elemental and metal-metal alloy models. We also review representative microscopic models so far proposed for the deformation mechanism: early dislocation model, Spaepen’s free-volume model, Argons’s STZ model and recent two-state STZ models by Langer et al.     

The birth of dislocations in shock waves and high-speed friction

Large-scale atomistic simulations by non-equilibrium molecular dynamics have revealed that shock-wave loading and high-speed friction between dry metal interfaces have surprising similarities, in that plastic deformation occurs by the violent birth of dislocations. Shock-wave deformation is initiated at the shock front, while in sliding friction, the interface produces dislocations that move first within the plane and then out of it, so as to generate a microstructure that accommodates the slippage. For both shocks and friction in perfect, or nearly perfect, crystals, there is a threshold driving force that needs to be overcome in order to induce plastic flow. Below that threshold, pre-existing extended defects are able to trigger plastic microstructure that resembles the kind seen above the threshold. This revised version was published online in July 2006 with corrections to the Cover Date.     

Study on plastic deformation behavior of hot splitting spinning of TA15 titanium alloy

The plastic deformation behavior of hot splitting spinning of TA15 titanium alloy is a complex metal forming problem with multi-factor coupling interactive effects. In this paper, on condition of considering various thermal effects, a three-dimensional (3D) elastic–plastic coupled thermo-mechanical finite element (FE) model of hot splitting spinning of TA15 titanium alloy is established using the dynamic, temp-disp, explicit module of FE software ABAQUS. Based on the analysis of flow behaviors of TA15 titanium alloy, the mechanism and influence of materials plastic deformation behavior during the forming process are studied. The results show that, the flow stress of TA15 titanium alloy generally decreases with the increase of deformation temperature; at the same strain rate, the higher temperature is, the lower flow stress is. The temperature distributions along the circumferential direction of disk blank are even and the temperature of plastic deformation area is about 984 °C. The heat from plastic deformation and friction at local plastic deformation area is less than the dissipated heat, so the temperature just falls into approximately 945 °C. Radial spinning force as the driving force of plastic deformation increases gradually and reaches about 35 kN at the end. The maximum value of equivalent stress is presented in fillet part between disk blank and two mandrels. The distributions of equivalent plastic strain appear the large strain gradients and the obvious characteristics of inhomogeneous deformation. When friction factor on interfaces between disk blank and dies ranges from 0.4 to 0.6, the forming quality and precision are highest.     

超声振动辅助塑性成形及形性预测研究进展

随着微机电系统等领域的快速发展,对零件成形精度与性能的要求日益增加。超声振动辅助塑性成形是一种典型的能场辅助塑性成形工艺,相比于传统塑性成形工艺,具有流动应力低、材料成形能力高、界面摩擦少、成形质量较好等优势,被广泛应用于难成形材料加工、微成形、复杂构件成形等塑性成形过程。然而,由于不同塑性成形工艺中金属的变形行为特性存在较大差异,对塑性成形质量与成形性能进行预测有利于实现成形过程的形性协同控制。介绍了超声振动辅助塑性成形在体积成形工艺（镦粗、挤压、拉拔等）与板料成形工艺（拉伸、拉深、渐进成形、冲压等）中的应用及发展概况,讨论了超声振动对材料塑性变形过程中宏观表现与微观演化的影响。在已有研究基础上,重点分析了超声振动辅助塑性成形过程中成形能力预测（流动应力、成形极限等方面）和成形性能预测（表面性能、力学性能、微观组织等方面）的研究进展,为金属零部件成形高质量形性调控提供理论参考,并展望了超声辅助塑性成形工艺的发展趋势。     

Modeling effects of crystalline microstructure, energy storage mechanisms, and residual volume changes on penetration resistance of precipitate-hardened aluminum alloys

An anisotropic nonlinear crystal mechanics model is developed for a class of ductile aluminum alloys, with the intent of relating microscopic features and properties to performance of the alloys deformed at high strain rates that may arise during impact and blast events. A direct numerical simulation of dynamic tensile deformation of an aluminum polycrystal demonstrates a tendency for shear localization to occur in regions of the microstructure where the ratio of the rate of residual (i.e., stored) elastic energy to plastic dissipation is minimal. By coarse-graining predictions of the crystal plasticity framework using a Taylor averaging scheme, a macroscopic constitutive model is developed to investigate effects of microstructure on ballistic perforation resistance of plates of an Al–Cu–Mg–Ag alloy. Specific aspects of microstructure investigated include random and rolled cubic textures as well as stored elastic energy and residual volume changes associated with lattice defects, impurities, and inclusions such as second phases in the metal–matrix composite. Results suggest performance could be improved by tailoring microstructures to increase the shear yield strength and the ratio of residual elastic energy to dissipated heat.     

晶体弹塑性接触的微观机制

用分子动力学和金属固体的镶嵌原子模型研究了ｆｃｃ晶体Ｃｕ探针－基体微观接触的加载卸载规律、系统能量特性、基体微观应力场分布以及塑性失稳的缺陷形成机制。计算结果显示，在表面开始接触时，存在不稳定的突然粘着接触（ｊｕｍｐ－ｔｏ－ｃｏｎｔａｃｔ）。在压入状态（ｉｎｄｅｎｔａｔｉｏｎ）晶体的原子应力分布与宏观Ｈｅｒｔｚ理论的应力场相似。对弹性卸载，探针－基体分离的粘着拉应力接近Ｇｒｉｆｆｉｔｈ理论断裂强度     

Multiscale constitutive modeling for plastic deformation of nanocrystalline materials

Macroscopic and microscopic constitutive modeling that can display large plastic deformation with shear band were presented for nanocrystalline materials subjected to uniaxial load over a wide strain rate range. The macroscopic model implemented with parameters microscopic meaning was established based on the theory of plastic dissipation energy. The microscopic model based on deformation mechanisms was composed of two parts: hardening and softening stages. In the hardening stage, the phase mixture model was used and a shear band deformation mechanism was proposed in the softening stage. Numerical simulations shown that the predications were in good agreement with experimental data. Finally, a parameter of normalized softening rate was proposed and its characteristics were evaluated quantitatively. It can be concluded that the failure strain could be prolonged when the normalized softening rate decrease through changing the softening path.     

Modeling of radiation hardening in ferritic/martensitic steel using multi-scale approach

Fe-Cr based ferritic/martensitic (FM) steels are the candidate structural materials for future fusion reactors. In this work, a multi-scale approach comprising atomistic and dislocation dynamic simulations are used to understand the hardening of these materials due to irradiation. At the atomic scale, molecular dynamics (MD) simulations are used to study the mobility of an edge dislocation and its interaction with irradiation induced voids and bubbles. The dislocation dynamics (DD) simulations are used to estimate the change in flow stress of the material as a result of irradiation hardening. The key input to the DD simulations are the friction stress and maximum shear stress for the edge dislocation to overcome the defects as determined from atomistic simulations. The results obtained from the MD and DD simulations are in qualitative agreement with experimental results of hardening behavior of irradiated FM steels.     

Two-scale analysis for deformation-induced anisotropy of polycrystalline metals

The anisotropic macroscopic mechanical behavior of polycrystalline metals is characterized by incorporating the microscopic constitutive model of single crystal plasticity into the two-scale modeling based on the mathematical homogenization theory, which enables us to derive both micro- and macro-scale governing equations. The two-scale simulations are conducted to evaluate the macroscopic anisotropy induced by microscopic plastic deformation histories of the polycrystalline aggregate. In the simulations, the representative volume element (RVE) composed of several crystal grains is uniformly loaded in one direction, unloaded to macroscopically zero stress in a certain stage of deformation and then re-loaded in the different directions. The last re-loading calculations provide different macroscopic responses of the RVE, which can be the appearance of material anisotropy. We then try to examine the effects of the intergranular and intragranular behaviors on the anisotropy by means of various illustrations of microscopic plastic deformation process without referring to the change of crystallographic orientations.     

Macroscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strains

The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the macroscopic rate-independent and rate-dependent analysis of micromechanics of metal single crystals undergoing finite elastic-plastic deformations which is based on the assumption that inelastic deformation is solely due to crystallographic slip. The formulation relies on a multiplicative decomposition of the material deformation gradient into incompressible elastic and plastic as well as a scalar valued volumetric part. Furthermore, the crystal deformation is described as arising from two distinct physical mechanisms, elastic deformation due to distortion of the lattice and crystallographic slip due to shearing along certain preferred lattice planes in certain preferred lattice directions. Macro- and microscopic stress measures are related to Green’s macroscopic strains via a hyperelastic constitutive law based on a free energy potential function, whereas plastic potentials expressed in terms of the generalized Schmid stress lead to a normality rule for the macroscopic plastic strain rate. Estimates of the microscopic stress and strain histories are obtained via a highly stable and very accurate semi-implicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step, and, furthermore, the development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical simulation of finite strain elastic-plastic tension tests is presented to demonstrate the efficiency of the algorithm.     

Coupled thermomechanical analysis of transformation-induced plasticity in multiphase steels

The thermomechanical response of low-alloyed multiphase steels assisted by transformation-induced plasticity (TRIP steels) is analyzed taking into account the coupling between the thermal and mechanical fields. The thermomechanical coupling is particularly relevant since in TRIP steels the phase transformation that occurs during mechanical loading is accompanied by the release of a considerable amount of energy (latent heat) that, in turn, affects the mechanical response of the material. The internal generation of heat associated with the martensitic phase transformation and the plastic deformation are modeled explicitly in the balance of energy. The momentum and energy equations are solved simultaneously by using a fully-implicit numerical scheme. The simulations are conducted using a micromechanical formulation for single crystals of austenite and ferrite. The characteristics of the model are illustrated by means of simulations for a single crystal of austenite and an aggregate of austenitic and ferritic grains. For a single crystal of austenite, it is found that the increase in local temperature due to transformation actually hinders further transformation and, instead, promotes plastic deformation. However, for an aggregate of austenitic and ferritic grains in a multiphase steel, the increase in temperature due to transformation is limited since the heat generated in the austenite is conducted to the ferritic matrix, effectively lowering the temperature in the austenitic phase.     

Insights on slip transmission at grain boundaries from atomistic simulations

To fully understand the plastic deformation of metallic polycrystalline materials, the physical mechanisms by which a dislocation interacts with a grain boundary must be identified. Recent atomistic simulations have focused on the discrete atomic scale motions that lead to either dislocation obstruction, dislocation absorption into the grain boundary with subsequent emission at a different site along the grain boundary, or direct dislocation transmission through the grain boundary into the opposing lattice. These atomistic simulations, coupled with foundational experiments performed to study dislocation pile-ups and slip transfer through a grain boundary, have facilitated the development and refinement of a set of criteria for predicting if dislocation transmission will occur and which slip systems will be activated in the adjacent grain by the stress concentration resulting from the dislocation pile-up. This article provides a concise review of both experimental and atomistic simulation efforts focused on the details of slip transmission at grain boundaries in metallic materials and provides a discussion of outstanding challenges for atomistic simulations to advance this field.     

Computer simulations of martensitic transformations in NiAl alloys

Ni_{1 − x}Al_x alloys in the concentration range 34% < x < 40% exhibit a martensitic transformation from an austenitic phase with bcc structure to a close-packed structured martensitic phase. Above the transformation temperature electron microscopy shows the occurrence of tweed like structures which are accompanied by a considerable softening of the phonon energies at . We have done molecular dynamics simulations employing a semi-empirical model which allows us to study the transformation on an atomistic length scale. Our results show that local distortions of the crystal lattice, which come from the atomic disorder of the alloys, are responsible for the occurrence of tweed phenomena.     

Deformation response of grain boundary networks at high temperature

The deformation response of random grain boundary networks as a function of temperature and strain rate is explored using molecular dynamics atomistic simulations and an embedded atom method interatomic potential. We find that deformation at higher temperatures promotes both dislocation emission and grain boundary accommodation processes. The results allow estimating the activation energies and volumes for the deformation process. We find activation energy values for the deformation process similar to those for grain boundary diffusion and activation volumes consistent with an atomic shuffling mechanism. Our results suggest a picture of the deformation process as governed by the combination of the applied stress and thermally activated processes.     

Numerical simulation of the plastic flow properties of iron single crystals

Summary The present paper deals with the numerical simulation of the plastic flow properties of iron single crystals as well as their influence on the macroscopic elastic-plastic deformation and localization behavior affected by superimposed hydrostatic pressure. Based on experimental observations the onset of plastic yielding on the microscale is described by an extended microscopic yield condition taking into account various microscopic stress components acting on the respective slip systems. In addition, to be able to compute inelastic deformations from a plastic potential, the latter is expressed in terms of workconjugate microscopic stress and strain measures which leads to a non-associated flow rule for the macroscopic plastic strain rate. On the numerical side, generalized functions for constitutive parameters will be used to be able to simulate the single crystal's microscopic deformation behavior observed in experiments. Estimates of the current microscopic stresses and strains are obtained via an efficient and remarkably stable plastic predictor-elastic corrector technique which is incorporated into a nonlinear finite element program. Numerical simulations of uniaxial tests show quantitatively the influence of hydrostatic pressure on current material data. Further numerical studies on the additional constitutive non-Schmid terms elucidate their effect on iron single crystal's macroscopic deformation and localization behavior.