Modelling and simulation of dynamic recrystallisation based on multi-phase-field and dislocation-based crystal plasticity models

ABSTRACT

The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.     

On the modified grain-size-distribution method to evaluate the dynamic recrystallisation fraction in AISI 304 stainless steel

The purpose of the present work was to verify the grain size distribution (GSD) method, which was recently proposed by one of the present authors as a method for evaluating the fraction of dynamic recrystallisation (DRX) in a microalloyed medium carbon steel. To verify the GSD-method, we have selected a 304 stainless steel as a model system and have measured the evolution of the overall grain size distribution (including both the recrystallised and unrecrystallised grains) during hot compression at 1,000 °C in a Gleeble machine; the DRX fraction estimated using the GSD method is compared with the experimentally measured value via EBSD. The results show that the previous GSD method tends to overestimate the DRX fraction due to the utilisation of a plain lognormal distribution function (LDF). To overcome this shortcoming, we propose a modified GSD-method wherein an area-weighted LDF, in place of a plain LDF, is employed to model the evolution of GSD during hot deformation. Direct measurement of the DRX fraction using EBSD confirms that the modified GSD-method provides a reliable method for evaluating the DRX fraction from the experimentally measured GSDs. Reasonable agreement between the DRX fraction and softening fraction suggests that the Kocks-Mecking method utilising the Voce equation can be satisfactorily used to model the work hardening and dynamic recovery behaviour of steels during hot deformation.     

关于PCG迭代矩阵特征值近似计算

对于预处理共轭梯度法,本文给出其迭代矩阵AM^-1与三对角阵B_s之间的关系,并对B_s的特征值分布作了分析,进而得到关于AM^-1特征值的一些性质。通过算例对两者的特征值及条件数进行了探讨。     

一类PCG迭代的强初值效应

预处理共轭梯度法的大量计算结果都表明,当迭代终止标准要求将余量的模减小某个倍数时,初值的选取对迭代次数仅有微弱影响。然而,本文给出的一类算例却表明,采用零初值或不同的随机初值,迭代次数之间会出现数倍的差别。同一种随机初值对不同参数模型问题的迭代次数也有很大差别。这种强初值效应对于方法的研究和比较是不利的。本文讨论和分析了这种现象。     

TEM and HRTEM study of influence of thermal cycles with stress on dynamic recrystallization in Ti46Al8Nb1B during creep

Short-term tension creep and thermal cycles under compressive stress were performed on Ti46Al8Nb1B in order to explore the dynamic recrystallization (DRX) grains formed during the creep and the impact of thermal cycles under stress to the DRX. After 1600 times' thermal cycles from 300 degrees C to 800 degrees C under 300 MPa compressive stress, high density of ledges and thick ledges are found in the interfaces. Two kinds of moiré fringes, instead of 9R structure, can be found in the thick ledges. Ti46Al8Nb1B sample and another sample which was treated by thermal cycles with stress were crept under 300 MPa compressive stress at 800 degrees C. DRX grains are found in the interfaces in those samples. Those grains, formed at the ledges, have an orientation relationship of [101](gamma)//[011](gammaR), (1 1 1)(gamma)//(1 11 )(gammaR) with the matrix of gamma phases. Thermal cycles with stress could lead to more DRX grains during creep.     

三维预处理技术初探

本文应用高阶近似LU分解法对三维椭圆型方程的正规七点差分矩阵给出了预处理阵,并对典型问题给出了预处理共轭梯度法的计算结果。文中所采用的分阶方论以及阶矩阵等概念,适用于一般的非奇异对角优势稀疏矩阵。对不同网格点数的计算结果表明,三维预处理共轭梯度法仍具有超线性的收敛速率,在高阶情形下超线性的特征尤为突出,由于非零对角线数增长过快,高阶的三维预处理方法不宜采用,零阶方法和一阶方法是值得推荐的。     

Two-wave mixing bistability based on mixed grating formation in photorefractive crystals

1 L) and the relative strength (x) of PCG compared with PRG in two cases: (i) when g₁L>0 and x>1 so that there exists either pure PRG or PRG dominates over PCG, and (ii) when g₁L<0 and x<-1 so that there exists either pure PCG or PCG dominates over PRG. The threshold condition g₁L>(g₁L)_Th=2x(1+1/R) with R>1 and the effective coupling strength, g₂L=g₁L/x>0 with 1<x<-1, need to be satisfied for the bistability. Possible regions of bistability affect the position of the region for the intensity ratio (m) of the incident beams where two branched multiple solutions exist and hysteresis in the gain is expected. Gain solutions are found to be single valued without bistability when g₂L<0. A comparison between the mixed grating gain and pure PRG/PCG gains with the occurance of bistability is presented and interpreted physically. Received: 9 January 1996/Revised version: 17 September 1996     

Dynamic recrystallization as a potential cause for adiabatic shear failure

Dynamic recrystallization (DRX) is almost universally observed in the microstructure of adiabatic shear bands. It is usually admitted that DRX results from the large temperatures that develop in the band along with very high local strains. This paper reports the observation of dynamically recrystallized nanograins in Ti6Al4V alloy specimens that were impact loaded to only half the failure strain at which the adiabatic shear band develops. This observation shows that DRX not only precedes adiabatic shear failure but it is also likely to be a dominant micromechanical factor in the very generation of the band. This result means that adiabatic shear failure is not only a mechanical instability but also the outcome of strong microstructural evolutions leading to localized material softening prior to any thermal softening.     

Evolution and characterization of dynamically recrystallized microstructure in a titanium-modified austenitic stainless steel using ultrasonic and EBSD techniques

A C-scan ultrasonic imaging system was used to investigate the microstructural evolution during dynamic recrystallization (DRX) of a 15Cr–15Ni–2.2Mo–Ti modified austenitic stainless steel (alloy D9). Four specimens were forged at 1273 K to different strains in the range 0.1–0.5. Specimens with true strains of 0.2 or lower did not show any variation in the amplitude of the first back-wall echo. However, a visible variation in the C-scan image was observed at and above the 0.3 strain level. This variation was attributed to the evolution of fine grains. The formation of fine grains was related to DRX, as indicated by electron backscattered diffraction. This study also revealed the characteristics of the DRX or ‘necklace grains’, as opposed to the so-called parent grains or rest of the microstructure.     

Design and properties analysis of multi-layer dielectric used in pulse compressor gratings

Used in chirped-pulse amplification system and based on multi-layer thin film stack, pulse compressor gratings (PCG) are etched by ion-beam and holographic techniques. Diffraction efficiency and laser-induced damage threshold rely on the structural parameters of gratings. On the other hand, they depend greatly on the design of multi-layer. A theoretic design is given for dielectric multi-layer, which is exposed at 413.1 nm and used at 1053 nm. The influences of coating design on optical characters are described in detail. The analysis shows that a coating stack of H3L (H2L)9H0.5L2.01H meets the specifications of PCG well. And there is good agreement of transmission between experimental and the theoretic design.     

Millimeter Wave Scattering of 2-D Frequency Selective Surface by Efficient Method of Lines with Preconditioned CG Technique

In this paper, both banded and symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) techniques are combined with method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. The electromagnetic wave scattering of 2-D frequency-selective surface is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, helmholtz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. Both banded and effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method are chosen to solve this matrix equation. Our numerical results show that PCG methods can converge to accurate solution in much fewer iteration steps for analysis of the electromagnetic wave scattering from 2-D frequency-selective surface.     

Fe-C合金中形变诱导动态相变的蒙特卡罗模拟

采用蒙特卡罗（MC）方法模拟了Fe-C合金在奥氏体-铁素体相变的平衡温度之上的形变诱导动态相变过程.通过建立合适的MC规则,在一个MC模型中同时实现了奥氏体-铁素体相变、铁素体-奥氏体逆相变以及奥氏体动态再结晶过程的模拟.同时,一个基于矢量变换的拓扑模型被嵌入此MC相变模型,用来跟踪由于塑性变形导致的晶粒形貌变化.在此基础上模拟分析了动态相变过程中铁素体的形成特点,讨论了由于相变、逆相变和动态再结晶交互作用所带来的影响. 关键词： 形变诱导动态相变 蒙特卡罗模型 动态再结晶 介观模拟     

脉宽压缩光栅用的多层膜设计和性能分析

应用于啁啾脉冲放大技术中的脉宽压缩光栅是基于多层膜作为基底,利用全息干涉技术和离子束技术刻蚀而成。脉宽压缩光栅的衍射效率和抗激光损伤阈值一方面依赖于光栅结构的设计,另一方面很大程度上取决于作为基底的多层膜的设计。给出了以413.1nm作为写入波长,1053nm作为使用波长的多层介质光栅膜的设计,样品在ZZS-800F型真空镀膜机上采用电子束蒸发方式沉积而成,并给出了膜系结构对光学性能影响因素的详细分析,结果表明膜系H3L(H2L)9H0.5L2.03H满足光栅膜的指标。给出了样品光学特性测试,其使用波长处的透射率<0.5%,写入波长处的透射率>90%,测试表明样品满足设计要求且实验结果和理论设计符合得很好。     

Out-of-focus color camera calibration with one normal-sized color-coded pattern

Conventional camera calibration methods always require well-focused target images for accurate feature detection. This requirement brings many challenges for long-range vision systems, due to the difficulty of fabricating an equivalent size target to the sensing field-of-view (FOV). This paper presents an out-of-focus color camera calibration method with one normal-sized color-coded pattern as the calibration target. The red, green and blue (RGB) channels of the color pattern are encoded with three phase-shift circular grating (PCG) arrays. The PCG centers used as feature points are extracted by ellipse fitting of the 2π-phase points. Experiments demonstrate that the proposed method can achieve accurate calibration results even under severe defocus.     

On the discrete dynamic nature of the conjugate gradient method

The primary objective of this technical note is to establish an equivalence between the (preconditioned) conjugate gradient (PCG) algorithm and a special central difference based DR procedure, thereby revealing a discrete dynamic nature of the CG iterative procedure. This may therefore provide an alterative viewpoint to gain a further understanding of the CG method and its variants.     

The effect of pH value on the formation of gold nanoshells

The effect of the pH value of gold ion plating (PCG) solution on the growth of gold nanoshells with about 100-nm silica cores and 15-nm gold shells was systematically investigated by dynamic light scattering, UV–Vis spectroscopy, scanning electron microscopy, and transmission electron microscopy. The results showed that in PCG solutions, the rapid formation of monomers which intensively influenced by the reducibility of formaldehyde contributed to the growth of gold nanoshells. The reducibility of formaldehyde increased following the increasing pH value from 4.70 to 11.71. Thus at high pH value, it was easy to fabricate the complete gold nanoshells (except of the Cannizzaro reaction of formaldehyde at high pH value). Furthermore, we found that chloride ions also influenced the surface morphology of gold nanoshells by Ostwald ripening process through the Au–Cl complex.     

EBE技术在结构分析中的应用(Ⅲ)-EBE-PCG法

在建立单元向量、伪单元向量等概念的基础上,提出了当不形成总刚度矩阵时,预处理共轭梯度法(PCG)的一种高度并行的EBE计算方法,其基本思想是把PCG法各步的计算都单元化。文[3]中的数值试验结果表明了它的有效性。     

Nucleation of dynamic recrystallization and variant selection in copper bicrystals

Orientation-controlled copper bicrystals containing [001] symmetrical tilt boundaries aligned parallel to the loading axis were deformed in tension at 923?K and a strain rate of 4.2?×?10^?4?s^?1. The nucleation of dynamic recrystallization (DRX) was investigated along the grain boundary. For this purpose, both optical and orientation imaging microscopy methods were used. After grain-boundary migration (GBM) and bulging, nuclei appeared behind the most deeply indented grain boundary regions. The critical strain for nucleation was about one-quarter to one-half of the peak strain and depended on the misorientation angle. All the nuclei were twin-related (Σ3) to the matrices. Furthermore, all the primary twin traces were parallel to those of the inactive slip planes of the parent single crystals. Crystallographic analysis revealed the important role of the direction of GBM on twinning-plane variant selection. The characteristics of grain boundary nucleation depended sensitively on grain boundary character and on grain boundary mobility. The observed DRX nucleation mechanism is discussed in relation to the occurrence of GBM and twinning.     

High temperature deformation and extended plasticity in Mg single crystals

The high temperature deformation behavior of Mg single crystals was precisely investigated using orientation imaging microscopy. For this purpose, Mg single crystals of various orientations were tensile tested in vacuum at temperatures between 473 and 673?K. A strain rate of 4.2?×?10^?4?s^?1 was employed. The elongations to fracture depended strongly on crystal orientation, the lowest fracture strains being associated with multiple slip. Single crystals in which single slip was activated exhibited extended ductilities corresponding to more than 1.5 in true strain. The strong orientation dependence of the ductility can also be correlated with the ease of occurrence of dynamic recrystallization (DRX), which took place in the multiple-slip specimens. The role of twinning in the initiation of DRX is also discussed.     

复代数方程组几种迭代法的比较

本文从二维非线性Schrödinger方程出发,推导出五对角的复代数方程组,并应用高斯-赛德尔迭代法、SOR迭代法、复双共轭梯度法以及预处理复双共轭梯度法等对求解的计算量进行了比较。同时,又将复代数方程组化成七对角的实代数方程组,用高斯-赛德尔迭代法、SOR迭代法以及PCG法(预处理共轭梯度法)等进行了比较。结果表明,PCG法在上述几种方法中是最有效的。本文还对SOR松弛因子的选择进行了讨论。