Utilization of the finite element and Monte Carlo model for simulating the recrystallization of inhomogeneous deformation of copper

In this paper the finite element method and Monte Carlo model are coupled to simulate the grain size distribution of inhomogeneously deformed copper wire after annealing. The wire flat rolling process is chosen as an inhomogeneous deformation. The finite element method is utilized to calculate the stored energy distribution due to deformation and is then used in Monte Carlo model to obtain the distribution of grain size. A new relationship is developed to simulate the nucleation in recrystallization phenomenon. The modeling results are compared with the experimental results and an acceptable agreement is achieved.     

Coupling kinetic dislocation model and Monte Carlo algorithm for recrystallized microstructure modeling of severely deformed copper

By coupling a kinetic dislocation model and Monte Carlo algorithm, the recrystallized microstructure of severely deformed Oxygen Free High Conductivity Copper (OFHC) is predicted at different strains imposed by Equal-Channel-Angular-Pressing (ECAP) and annealing temperatures. From a flow field model, the strain rate distribution during the ECAP of the material in a curved die is calculated. Then using the kinetic dislocation model, the total dislocation density and correspondingly the stored energy after each ECAP pass is estimated. Utilizing the Monte Carlo algorithm and the stored energy, the recrystallized microstructure is predicted. The results show that the recrystallized grain size is decreased rapidly from the strain of first to fourth pass and then it is decreased slowly. Also, it is achieved that with increasing the annealing temperature, the grain size is increased. Moreover, a good agreement is observed between the predicted results and experimental data.     

薄规格取向硅钢二次再结晶过程中Goss织构演变的Monte Carlo模拟

通过EBSD实验获取了薄规格取向硅钢(0.18 mm厚)初次再结晶样品表面晶粒组织的取向数据,并以此构建模拟的初始组织.采用Potts模型Monte Carlo方法对薄规格取向硅钢初次再结晶样品的二次再结晶过程进行了模拟仿真,研究了表面能对Goss织构演变的影响.模拟结果表明:Goss取向晶粒与相邻晶粒的表面能差是Goss取向晶粒异常长大的重要驱动力;表面能差存在一个临界值(约12％),只有当表面能差大于此临界值时才会发生表面能驱动Goss取向晶粒的异常长大.     

铸锻联合成形工艺晶粒分布预测协同仿真技术

开发了一种铸锻联合成形工艺的协同仿真技术.采用ProCAST软件的CAFE模块进行铸造模拟,获得初始不均匀的铸态晶粒尺寸.编译了一组Fortran程序作为Deform-3D软件的功能模块,用以建立初始不均匀铸态晶粒尺寸的分布与Deform-3D锻造模型之间的耦合.通过对Deform-3D的二次开发,实现了锻造过程中微观组织演变的数值模拟.最终实现了对动态再结晶晶粒尺寸和动态再结晶体积分数的预测.采用开发的协同仿真技术对截齿齿体的铸锻联合成形工艺进行了数值模拟分析.模型分别采用了初始均匀的晶粒尺寸和由铸造模拟获得的初始不均匀的晶粒尺寸,获得了两种模型的动态再结晶晶粒尺寸和动态再结晶体积分数的分布.通过对比分析,证明了铸锻联合成形工艺晶粒分布预测协同仿真技术的可行性.     

Yield surface simulation for partially recrystallized aluminum polycrystals on the basis of spatially discrete data

The paper presents simulations of the yield surface evolution of plastically deformed aluminum polycrystals during recrystallization. The yield surfaces are calculated using a viscoplastic Taylor–Bishop–Hill strain rate polycrystal homogenization method. The input data for the yield surface calculations are the crystal orientations, their volume fractions, and their shear stresses. While the crystal orientations determine the kinematic portion of the yield surface the threshold shear stress of each individual orientation determines the kinetic portion of the yield surface. The input data for the homogenization calculations are generated through a spatially discrete simulation, where crystal deformation and primary static partial recrystallization are simulated by coupling a viscoplastic crystal plasticity finite element model with a cellular automaton. The crystal plasticity finite element model accounts for crystallographic slip and for crystal rotation during plastic deformation using space and time as independent variables and the crystal orientation and the accumulated slip as dependent variables. The cellular automaton uses a switching rule which is formulated as a probabilistic analogue of Turnbull's rate equation for the motion of grain boundaries. The actual decision about a switching event is made using a simple-sampling Monte Carlo step. The automaton uses space and time as independent variables and the crystal orientation and a stored energy measure as dependent variables. The kinetics produced by the switching algorithm are scaled through grain boundary mobility and driving force data. The crystallographic texture and the orientation-dependent resistance to shear are for each interpolation point extracted after each time step during recrystallization. The data serve as input for the calculation of discrete yield surfaces.     

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.     

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.     

Microstructure evolution during dynamic recrystallization of hot deformed superalloy 718

Microstructure evolution during dynamic recrystallization (DRX) of superalloy 718 was studied by optical microscope and electron backscatter diffraction (EBSD) technique. Compression tests were performed at different strains at temperatures from 950 °C to 1120 °C with a strain rate of 10⁻¹ s⁻¹. Microstructure observations show that the recrystallized grain size as well as the fraction of new grains increases with the increasing temperature. A power exponent relationship is obtained between the dynamically recrystallized grain size and the peak stress. It is found that different nucleation mechanisms for DRX are operated in hot deformed superalloy 718, which is closely related to deformation temperatures. DRX nucleation and development are discussed in consideration of subgrain rotation or twinning taking place near the original grain boundaries. Particular attention is also paid to the role of continuous dynamic recrystallization (CDRX) at both higher and lower temperatures.     

无取向硅钢形变储能取向依赖性及其对再结晶织构的影响

采用晶体塑性有限元模拟与实验相结合的方式,研究无取向硅钢冷轧过程中不同初始织构组分的取向流动与形变储能累积。结果表明:冷轧后形成了较强的α,γ形变织构和较弱的λ形变织构。再结晶织构由γ,α,η和λ织构组成,其取向密度依赖于冷轧压下率。随冷轧压下率增大,λ再结晶织构逐渐增强,η织构先增强后减弱,γ织构先减弱后增强,α织构稍有弱化。冷轧过程中形变储能累积具有明显的初始取向依赖性,初始γ取向储能累积速率在低于50%压下率时与初始α取向接近,高于50%压下率时则明显大于后者,初始λ取向储能累积速率始终显著低于γ和α取向,转至同一形变取向的不同初始取向间的储能累积也会产生差异。冷轧过程中不同初始织构组分的取向流动与形变储能累积规律,决定了无取向硅钢再结晶织构组分的发展。     

Study of microstructural evolution during static recrystallization in a low alloy steel

Hot compression tests of 42CrMo steel were carried out on Gleeble-1500 thermo-mechanical simulator. The effects of forming temperature, strain rate, deformation degree, and initial austenite grain size on the microstructural evolution during static recrystallization in hot deformed 42CrMo steel were discussed. Based on the experimental results, the grain size model for static recrystallization was established. It is found that the effects of the processing parameters on the microstructural evolution during static recrystallization are significant, while those of the initial austenitic grain size are not obvious. Additionally, a good agreement between the experimental and predicted grain sizes was also obtained.     

Characterization of Austenite Dynamic Recrystallization under Different Z Parameters in a Microalloyed Steel

A low carbon Nb-Ti microalloyed steel was subjected to hot torsion testing over the temperature range 850-1100℃ and strain rates 0.01-1s-1 to study the influence of deformation conditions on the dynamic recrystallization characteristics of austenite.The results show that dynamic recrystallization occurs more easily with the decrease of strain rate and the increase of deformation temperature.The complete dynamically recrystallized grain size as a function of Zener-Hollomon parameter was established.It was found that dynamically recrystallized grain sizes decrease with increasing strain rate and decreasing deformation temperature.The effect of microalloying elements on peak strain was investigated and the solute drag corrected peak strain was determined.Also,the dynamic recrystallization map of austenite was obtained by using recrystallization critical parameters.     

Dynamic recrystallization of Ni-base alloys—Experimental results and comparisons with simulations

The dynamic recrystallization of the Ni-base alloy Böhler L306 VMR (Alloy 80A) in a transient state was investigated both by light microscopy and electron backscatter diffraction (EBSD), and the experimental results were compared with those from simulations. Subgrain structures of the size of the recrystallized grains were observed close to the grain boundaries of the original grains. With increasing strain a texture developed in the deformed fraction. Strong twinning was found in the recrystallized fraction, with area fractions of the twinned grains of around 80% for higher strains. Thus the measured grain sizes strongly depend on the handling of the twins. A pronounced increase in the average grain size of the recrystallized fraction with increasing strain (time) was only observed after twin removal. There was generally good agreement between the measured and the simulated results.     

The role of grain size in static and cyclic deformation behaviour of a laser reversion annealed metastable austenitic steel

Different grain sizes were created in a metastable 17Cr‐7Mn‐7Ni steel by martensite‐to‐austenite reversion at different temperatures using a laser beam. Two fully reverted material states obtained at 990°C and 780°C exhibited average grain sizes of 7.7 and 2.7 μm, respectively. The third microstructure (610°C) consisted of grains at different stages of recrystallization and deformed austenite. A hot‐pressed, coarse‐grained counterpart was studied for reference. The yield and tensile strengths increased with refined grain size, maintaining reasonable elongation except for the heterogeneous microstructure. Total strain‐controlled fatigue tests revealed increasing initial stress amplitudes but decreasing cyclic hardening and fatigue‐induced α′‐martensite formation with decreasing grain size. Fatigue life was slightly improved for the 2.7‐μm grain size. Contrary, the heterogeneous microstructure yielded an inferior lifetime, especially at high strain amplitudes. Examinations of the cyclically deformed microstructure showed that the characteristic deformation band structure was less pronounced in refined grains.     

Mechanism of cube grain nucleation during recrystallization of deformed commercial purity aluminium

Cube texture is a sharp recrystallization texture component infcc metals like aluminium, copper, etc. It is described by an ideal orientation i.e. (100) (100). The subject of cube texture nucleation i.e. cube grain nucleation, from the deformed state of aluminium and copper is of scientific curiosity with concurrent technological implications. There are essentially two models currently in dispute over the mechanism of cube grain nucleation i.e. the differential stored energy model founded on the hypothesis proposed by Ridha and Hutchinson and the micro-growth selection model of Dugganet al. In this paper, calculations are made on the proposal of Ridha and Hutchinson model and the results are obtained in favour of the differential stored energy model. It is also shown that there is no need for the micro-growth model.     

Influence of the second-phase particle size on grain growth based on computer simulation

A three-dimensional Monte Carlo simulation method for grain growth in two-phased materials is set up, basing on a micro-physical analysis of the interaction between the second-phase particle and the grain boundary. Two-phased systems containing second-phase particles with the same quantity but different sizes are designed, and the complete processes of grain growth are simulated. The influences of the particle size on grain growth are observed and studied quantitatively.     

Grain boundary sliding and migration in copper: the effect of vacancies

The atomic structure and mechanism of the interface sliding of the Σ = 5(2 1 0)[0 0 1] symmetric tilt grain boundary (GB) in copper and its interaction with vacancies at an elevated temperature has been studied using a computationally efficient potential based on the Embedding Atom Method in connection with the finite temperature Monte Carlo technique. Grain boundary sliding is performed for pure copper as well as copper containing a vacancy at a selected position. The discontinuous changes of the GB energy at certain sliding distances are associated with GB migrations. Elevated temperature reduces the grain boundary sliding/migration energy by a factor of about 2 but does not increase the rate of migration. Migration of the GB is mediated by the flow of atoms along the interface in coordination with the atoms in bulk. The sliding and migration properties partially depend on the position of the vacancy in the GB core. We found that the grain boundary sliding energy profile in the presence of a vacancy placed at the interface increased the GB energy, but reduces the sliding energy. The sliding process invokes the interface migration in such a way that the vacancy effectively migrates to a more convenient position and reduces the GB energy.     

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.     

On the quasi-stationary grain size distribution from two Gamma size distributions in three-dimensional grain growth

Two different grain structures of which the grain size distribution could be well described by the Gamma distribution were generated by the combination of the Laguerre tessellation and Monte Carlo technique. Monte Carlo simulation shows that the three-dimensional grain growth process can evolve to the quasi-stationary state. The quasi-stationary grain size distribution could be well fit by the Gamma distribution with different parameters. The results in literature from various simulation methods support this point.     

Predicting recrystallized grain size in friction stir processed 304L stainless steel

A major dilemma faced in the nuclear industry is repair of stainless steel reactor components that have been exposed to neutron irradiation. When conventional fusion welding is used for repair, intergranular cracks develop in the heat-affected zone(HAZ). Friction stir processing(FSP), which operates at much lower peak temperatures than fusion welding, was studied as a crack repair method for irradiated 304 L stainless steel. A numerical simulation of the FSP process in 304 L was developed to predict temperatures and recrystallized grain size in the stir zone. The model employed an Eulerian finite element approach,where flow stresses for a large range of strain rates and temperatures inherent in FSP were used as input. Temperature predictions in three locations near the stir zone were accurate to within 4%, while prediction of welding power was accurate to within 5% of experimental measurements. The predicted recrystallized grain sizes ranged from 7.6 to 10.6 μm, while the experimentally measured grains sizes in the same locations ranged from 6.0 to 7.6 μm. The maximum error in predicted recrystallized grain size was about 39%, but the associated stir zone hardness from the predicted grain sizes was only different from the experiment by about 10%.     

INFLUENCE OF TWO-PHASE REGION ROLLING ON TRANSFORMATION AND RECRYSTALLIZATION BEHAVIOUR OF FERRITE IN COPPER-CONTAINING HSLA STEEL

Hot deformation of copper-containing microalloyed steels in the two-phase region was carried out to study the effect of copper on transformation and recrystallization behaviour of ferrite in HSLA steels. it was found that presence of copper could decrease the austenite to ferrite transformation temperature. The precipitation of epsilon-copper in ferrite could retard recovery and recrystallization by dislocation and grain boundary pinning in deformed ferrite. Retardation of transformation and ferrite recrystallization resulted in a less mixed structure consisting of fine transformed and recrystallized ferrite in the copper-containing steels.