Modelling of the microstructure: From classical cellular automata approach to the frontal one

A frontal cellular automata (FCA) approach for modelling of the microstructure is described. The approach allows for computation time reduction. The developed model contains the following two parts, namely the deformation and the microstructure part. The cellular automata (CA) cells are deformed according to the deformation. The model of recrystallization includes both the nucleation and the new grain growth stage. These stages depend on the deformation parameters such as: temperature, strain, strain rate, dislocation density and crystallographic orientation. The results related to the simulation of the dynamic recrystallization are also presented in the paper.     

基于多尺度模型的镁合金薄板温轧再结晶和织构

建立多尺度模型阐明了镁合金薄板再结晶和织构演变机制.先用有限元法数值计算异步温轧工艺过程,得到了等效塑性应变、应变速率等结果,并以此作为初始边界条件引入基于位错密度演化的硬化方程,得到了 VPSC(Visco-Plastic Self-Consistent)粘塑性自洽模型、实现了 CA(Cellular Automat...     

Static recrystallization simulations by coupling cellular automata and crystal plasticity finite element method using a physically based model for nucleation

This study presents a 2D cellular automata simulation of static recrystallization (SRX) arising from the subgrain growth in single-phase material following cold deformation by coupling with a crystal plasticity finite element (CPFE) method. The spatial distribution of the stored deformation energy was obtained by CPFE simulation, based on which the initial deformed microstructure consisting of nonuniformly distributed subgrains was predicted. To simulate grain/subgrain growth during annealing, a curvature-driven mechanism was used, in which the grain/subgrain boundary energy and mobility were misorientation-dependent. On the SRX nucleation, a physically based model using critical subgrain size as criterion was adopted, which could provide better insight into the recrystallization nucleation mechanism involving grain boundary bulging. Simulations under different pre-deformation conditions were performed, and the influence of strain rate and strain on the SRX microstructure evolution and the transformation kinetics were investigated. Results show that deformation at higher strain rate can accelerate the SRX kinetics, and the SRX behavior depends more on the deformation state of individual grain than the nominal strain due to the relatively small computational domain.     

Prediction of fatigue crack nucleation life in polycrystalline AA7075‐T651 using energy approach

A crystal plasticity (CP) simulation and an energy‐based model is presented to predict the fatigue nucleation onset for polycrystalline AA 7075‐T651. Different microstructure morphology and grain sizes are employed in the simulations. Using a simple method, statistically stored dislocation (SSD) and geometrically necessary dislocation (GND) as decoupled with crystal plasticity model are estimated using a double round‐notch specimen test data, and CP simulation. The dislocation density parameter approximated from plastic energy density, stored energy density, elastic energy and accumulated slip validated with double hole experimental data. Sensitivity analysis is performed with respect to different microstructures and dislocation density parameters. Roughly, maximum 30% difference between experimental nucleation life and the simulated one is observed. The simulated predictions are in fair agreement with test data. The proposed strategy is suitable to study the scatter of fatigue nucleation life.     

A comparative discrete-dislocation/crystal-plasticity analysis of bending of a single-crystalline microbeam

Bending of a micron-size single-crystalline beam is analyzed using both discrete-dislocation plasticity and crystal-plasticity formulations. Within the discrete-dislocation plasticity formulation, dislocations are treated as infinitely long straight-line defects residing within a linear elastic continuum. Evolution of the dislocation structure during bending is simulated by allowing the dislocations to glide in response to long-range interactions between different dislocations, and between dislocations and the applied stresses, and by incorporating various short-range reactions which can result in dislocation nucleation, annihilation or pinning. At each stage of bending, the stress and deformation fields are obtained by superposing the dislocation fields and the complementary fields obtained as a solution of the corresponding linear-elastic boundary value problem. The results obtained show that there is a continuing accumulation of geometrically necessary dislocations during bending which is expected due to the gradient in the strain throughout the beam height. In addition, it is found that localization of plastic flow into slip bands is a salient feature of materials deformation at the micron-length scale. Within the crystal-plasticity analysis, of beam bending, a small displacement gradient formulation is used and the material parameters selected in such a way that plastic flow localizes into deformation bands at low strains. It is found that, while the global response of the beam predicted by the two approaches can be quite comparable, fine details of the dislocation-based stress and deformation fields cannot be reproduced by the continuum crystal-plasticity model.     

A two-site mean field model of discontinuous dynamic recrystallization

The paper describes a new model of discontinuous dynamic recrystallization (DDRX) which can operate in constant or variable thermomechanical conditions. The model considers the elementary physical phenomena at the grain scale such as strain hardening, recovery, grain boundary migration, and nucleation. The microstructure is represented through a set of representative grains defined by their size and dislocation density. It is linked to a constitutive law giving access to the polycrystal flow stress. Interaction between representative grains and the surrounding material is idealized using a two-site approach whereby two homogeneous equivalent media with different dislocation densities are considered. Topological information is incorporated into the model by prescribing the relative weight of these two equivalent media as a function of their volume fractions. This procedure allows accounting for the well-known necklace structures. The model is applied to the prediction of DDRX in 304 L stainless steel, with parameters identified using an inverse methodology based on a genetic algorithm. Results show good agreement with experimental data at different temperatures and strain rates, predicting recrystallization kinetics, recrystallized grain size and stress-strain curve. Parameters identified with one initial grain size lead to accurate results for another initial grain size without introducing any additional parameter.     

金属热变形微观组织精密控制的研究进展

大多数承力关键金属构件在其生产过程中均需经历热变形工步。探讨了典型金属结构材料热变形中3种主要动态再结晶机制的流变行为、微观组织演变特征,并对热变形间隔及热变形后的亚动态再结晶行为进行分析,提出了相应的微观组织控制策略。讨论了第二相颗粒对热变形微观组织演变的影响以及通过第二相颗粒实现微观组织控制的方法。对在热变形中及热变形后冷却过程中会发生相变材料的热变形微观组织演变规律进行了分析。分析热变形过程中的微观组织演变规律,并建立相应的数值模型是实现微观组织精密控制的有效途径,因此简要讨论了不同微观组织演变数值模型的特点及适用性。综合考虑动态再结晶、亚动态再结晶的演变过程以及第二相颗粒和相变的影响规律,并结合基于物理冶金基础理论微观组织演变数值模型是实现热变形微观组织精密控制的必由之路。     

Analysis of work hardening and recrystallization during the hot working of steel using a statistically based internal variable model

A mathematical model has been developed which describes the hot deformation and recrystallization behavior of austenite using a single internal variable: dislocation density. The dislocation density is incorporated into equations describing the rate of recovery and recrystallization. In each case no distinction is made between static and dynamic events, and the model is able to simulate multideformation processes. The model is statistically based and tracks individual populations of the dislocation density during the work-hardening and softening phases. After tuning using available data the model gave an accurate prediction of the stress–strain behavior and the static recrystallization kinetics for C–Mn steels. The model correctly predicted the sensitivity of the post deformation recrystallization behavior to process variables such as strain, strain rate and temperature, even though data for this were not explicitly incorporated in the tuning data set. In particular, the post dynamic recrystallization (generally termed metadynamic recrystallization) was shown to be largely independent of strain and temperature, but a strong function of strain rate, as observed in published experimental work.     

5083铝合金的热变形组织演变及晶粒度模型

通过等温压缩实验、光学显微镜与透射电镜研究了变形温度300~450℃、应变速率0.01~1s-1、真应变0.36~1.2范围内变形条件对5083铝合金热变形组织演变的影响。结果表明:升高热变形温度或降低应变速率均可促进5083铝合金的动态再结晶发生,使变形后5083铝合金位错密度降低,再结晶晶粒尺寸增大;随着应变量的增加,变形后合金的位错密度降低,动态再结晶程度增大。根据唯象理论的指数模型,利用线性回归方法建立了5083铝合金动态再结晶晶粒度模型,模型计算值与实测值吻合良好,平均相对误差仅为4.6%。     

金属材料动态再结晶模型研究现状

动态再结晶是热塑性变形过程中重要的材料软化、晶粒细化、组织控制和塑性成形能力改善方法,而材料发生动态再结晶过程形成的组织结构直接决定其综合性能,因此,长期以来动态再结晶一直是热成形过程中的研究热点。概述了动态再结晶的物理机理,介绍了位错密度模型、动力学模型和微观组织演化数值模拟,并对目前研究现状进行分析,展望其未来发展前景。     

18.5%Cr高Mn型节镍双相不锈钢大变形热压缩的组织和再结晶行为

使用热模拟试验机在1123~1423 K/0.01~10 s^-1变形条件下对18.5%对Cr高Mn节镍型双相不锈钢进行了变形量为70%的大变形热压缩,研究其在热变形过程中两相的亚结构特征和软化机理。结果表明,在0.01~0.1 s^-1/1123~1223 K范围的热压缩软化以铁素体相的再结晶为主,而在0.1 s^-1/1323~1423 K和10 s^-1/1223 K范围的热压缩软化以奥氏体相的再结晶为主。在变形温度为1223 K、应变速率由0.01 s^-1增大到10 s^-1的条件下铁素体相内的位错缠结向胞状结构演化并出现位错线,奥氏体相内的亚结构则转变为细小的再结晶晶粒。应变速率为0.1 s^-1、变形温度由1123 K提高到1323 K时铁素体相内的位错增加,变形晶粒向胞状组织演化而奥氏体相内的位错减少,由回复组织转变为再结晶组织。根据热变形方程计算出表观应力指数n=7.13,热变形激活能Q=514.29 kJ/mol,并建立了Z参数关系本构方程。根据加工硬化率得到再结晶临界条件,并确定了Z参数与再结晶临界条件的关系。对热加工图的分析结果表明,随着变形量的增大失稳区逐渐减小,最佳加工区域为1348~1423 K/1~10 s^-1,功率耗散系数大于0.4。     

Recrystallization of the hot isostatic pressed nickel-base superalloy FGH4096: I. Microstructure and mechanism

Hot isostatic pressed (HIPed) nickel-based superalloy FGH4096 behaves a unique flow behavior in hot compression process due to the formation of necklace microstructure and leads to its characteristic dynamic recrystallization (DRX). In this process, dislocations activate the occurrence of DRX at prior particle boundaries (PPB) and the PPB is entirely covered with DRX grains, which forms the first layer in necklace structure. In this paper, two nucleation mechanisms, viz., bulge corrugation (BC) nucleation and dislocation induce phase (DIP) nucleation, are proposed. Based on the proposed mechanisms, the recrystallization firstly occurs in PPB via BC mechanism. The DIP nucleation occurs when the hot plastic deformation is carried out at the temperature below the γ′ phase solution temperature. To verify the proposed mechanisms, hot compression experiments were conducted. The models are then verified based on the experiments. Furthermore, the recrystallization activation energy of 922 kJ/mol is determined, which includes the growth energy and the two nucleation energies, viz., BC and DIP nucleation energies.     

新型Al-Zn-Mg-Cu合金热变形组织演化

采用Gleeble-1500D热力模拟试验机研究新型Al-Zn-Mg-Cu高强铝合金在变形温度为300~450℃,应变速率为0.001~10s~(-1)条件下的热变形组织演化。利用光学显微镜(OM)和透射电子显微镜(TEM)观察合金不同热变形条件下的组织形貌特征。结果表明:随着变形温度的升高和应变速率的减小,位错密度减小,亚晶粒尺寸增大;合金热压缩变形过程中主要的软化机制为动态回复和动态再结晶。变形温度为300~400℃时,主要发生动态回复;变形温度为450℃,应变速率为0.001~10s~(-1)时,软化机制以动态再结晶为主,存在晶界弓出、亚晶长大、亚晶合并3种再结晶形核机制。     

Modelling of microstructure evolution during hot rolling of AA5083 using an internal state variable approach integrated into an FE model

Hot rolling, a critical process in the manufacturing of aluminum sheet products, can significantly impact the final properties of the cold rolled sheet. In this research, a mathematical model was developed to predict the through-thickness thermal and deformation history of a sheet undergoing single stand hot rolling using the commercial finite element (FE) package, ABAQUS^™. A physically based internal state variable microstructure model has been incorporated into the FE simulation for an AA5083 aluminum alloy to predict the evolution of the material stored energy and the subsequent recrystallization after deformation is complete. The microstructure predictions were validated against experimental measurements conducted using the Corus pilot scale rolling facility in IJmuiden, the Netherlands for an AA5083 aluminum alloy. The model was able to predict the fraction recrystallized as well as the recrystallized grain size reasonably well under a range of industrially relevant hot deformation conditions. A sensitivity analysis was carried out to determine the influence of changing the material constants in the microstructure model and deformation conditions on the predicted recrystallization behaviour. The analysis showed that the entry temperature was the most sensitive process parameter causing significant changes in the predicted driving force for recrystallization, nucleation density, fraction recrystallized, and recrystallized grain size.     

Extension of the Tanaka-Mura model for fatigue crack initiation in thermally cut martensitic steels

A multi scale numerical approach for evaluation of crack initiation and propagation in thermally cut structural elements made of martensitic steel is presented. A numerical simulation of micro-crack initiation is based on the Tanaka-Mura micro-crack nucleation model, where individual grains of synthetic microstructure are simulated using the Voronoi tessellation. Three improvements are added to this model (multiple slip bands, micro-crack coalescence and segmented micro-crack generation). Crack propagation is then solved on a macro scale model using linear elastic fracture mechanics approach. Some experimental tests have also been performed to check the accuracy of the numerical model. The results of the proposed computational model show a reasonable correlation with the experimental results.     

Dynamic softening mechanism of 30 % SiCp/2024Al composite during hot deformation process

Using Gleeb‐1500D simulator, the isothermal compression tests of 30 % SiCp/2024Al (volume fraction) are conducted at a temperature range of 623 K ‐ 773 K and a strain rate range of 0.01 s^‐1 ‐ 10 s^‐1. The softening mechanism of composites during hot deformation has been proposed based on the Zener‐Hollomon parameter Z, deformation temperature T and microstructure analysis. Cross slip of dislocation plays a dominant role under the conditions of lnZ≥59.634 and T≤673 K. While, deformation mechanisms such as cross slip, climb of dislocation and unzipping of the three dimensional dislocation network play a joint role when lnZ≤61.933 and T≥623 K. Particularly, dynamic recrystallization occurred when lnZ≤55.669 and T≥723 K. The cross slip, climb and unzipping of dislocation and dynamic recrystallization are the main softening mechanisms. The role of the dynamic recrystallization mechanisms become more significant and the critical strain of dynamic recrystallization decrease with the decrease of lnZ. Dynamic recrystallization nucleation mechanisms are mainly constituted of the subgrain combination and the bulging of the grain boundary.     

Crystal plasticity analysis of earing in deep-drawn OFHC copper cups

The theory of thermally-activated slip is used to derive a crystal-plasticity materials constitutive model for deformation of OFHC copper single crystals. The mechanical response of the polycrystalline material is next determined from the single-crystalline materials constitutive relations using the classical Taylor approximation for apportionment of the deformation gradient between grains. Simulations of the deep drawing of cylindrical cups from as-rolled OFHC-copper blanks are next carried out using an explicit finite element formulation. The results obtained show that the crystallographic texture in as-rolled sheets, which can be accounted for through the use of crystal-plasticity, gives rise to rim-earing in fully-drawn cups. It is further shown that the extent of rim-earing can be greatly reduced by properly modifying the shape of the blank. A procedure is next proposed for optimization of the blank shape.     

Multiscale Modeling of Deformation in Polycrystalline Thin Metal Films on Substrates

The time‐dependent irreversible deformation of a thin metal film constrained by a substrate is investigated by a mesoscopic discrete dislocation simulation scheme incorporating information from atomistic studies of dislocation nucleation mechanisms. The simulations take into account dislocation climb along the grain boundaries in the film as well as dislocation glide along slip planes inclined and parallel to the film/substrate interface. The calculated flow stress and other features are compared with relevant experimental observations. The work is focused on deformation of a polycrystalline film without a cap layer, for which diffusive processes play an important role. The dislocation‐based simulations reveal information on the prevailing deformation mechanisms under different conditions and for different film thicknesses. Despite of the limitations of the two‐dimensional dislocation model, the simulations exhibit a film thickness dependent transition between creep dominated and dislocation glide dominated deformation, which is in good agreement with experimental observations.     

相场模型凝固组织模拟进展

本文对相场模型的物理本质、数值计算方法以及在凝固微观组织模拟中的应用和进展进行了综述，并指出相场模型凝固微观组织模拟的发展方向。     

Mesoscale Simulation of Recrystallization Textures and Microstructures

The paper presents mesoscale simulations of textures and microstructures formed during recrystallization. It gives an overview of the method and demonstrates how microstructure and texture simulations can be performed by incorporating realistic input data for the boundary character and for the initial deformation microstructure. Particular attention is placed on the simulation of primary static recrystallization in a deformed aluminum polycrystal on the basis of crystal plasticity finite element data. Various nucleation scenarios are discussed also with respect to macroscopic effects such as friction and shear localization.