Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Lightweight magnesium alloys, such as AZ31, constitute alternative materials of interest for many industrial sectors such as the transport industry. For instance, reducing vehicle weight and thus fuel consumption can actively benefit the global efforts of the current environmental industry policies. To this end, several research groups are focusing their experimental efforts on the development of advanced Mg alloys. However, comparatively little computational work has been oriented towards the simulation of the micromechanisms underlying the deformation of these metals. Among them, the model developed by Staroselsky and Anand [Staroselsky, A., Anand, L., 2003. A constitutive model for HCP materials deforming by slip and twinning: application to magnesium alloy AZ31B. International Journal of Plasticity 19 (10), 1843–1864] successfully captured some of the intrinsic features of deformation in Magnesium alloys. Nevertheless, some deformation micromechanisms, such as cross-hardening between slip and twin systems, have been either simplified or disregarded. In this work, we propose the development of a crystal plasticity continuum model aimed at fully describing the intrinsic deformation mechanisms between slip and twin systems. In order to calibrate and validate the proposed model, an experimental campaign consisting of a set of quasi-static compression tests at room temperature along the rolling and normal directions of a polycrystalline AZ31 rolled sheet, as well as an analysis of the crystallographic texture at different stages of deformation, has been carried out. The model is then exploited by investigating stress and strain fields, texture evolution, and slip and twin activities during deformation. The flexibility of the overall model is ultimately demonstrated by casting light on an experimental controversy on the role of the pyramidal slip 〈c + a〉 versus compression twinning in the late stage of polycrystalline deformation, and a failure criterion related to basal slip activity is proposed.     

镁合金晶体塑性本构模型与非均匀孪生变形分析

微结构演化对镁合金材料力学性能有着显著的影响，为了揭示镁合金宏观塑性各向异性特性与非均匀孪生变形的关系，开展了不同路径下的单轴加载试验以及采用含滑移、孪生机制的晶体塑性本构模型对试验条件下的镁合金变形行为进行数值模拟研究。文中本构模型描述了滑移与孪生变形机制以及晶格转动的机制，同时研究采用三维微结构代表性有限元模型，其包含晶粒尺寸、晶向和晶界倾角等微结构参数。研究结果表明，轧制镁合金具有强烈的宏观塑性各向异性行为，并对这种镁合金塑性各向异性行为的模拟结果以及多晶织构的模拟演化结果与试验测量进行对比，结果都基本吻合。对孪生非均匀变形模拟分析表明，镁合金宏观塑性各向异性行为与滑移、孪生变形机制的不同启动组合紧密相关，同时多晶体内应力的非均匀分布受到孪生变形的严重影响。而不同晶粒尺寸的晶粒所发生的孪生变形有比较大的差异，造成孪晶变体在晶粒内的分布极不均匀。本研究可为通过微结构的合理配置来设计和控制材料的力学性能提供理论依据.     

In situ neutron diffraction investigation of deformation twinning and pseudoelastic-like behaviour of extruded AZ31 magnesium alloy

In situ neutron diffraction has been used to investigate the deformation twinning and untwinning during cyclic uniaxial straining of hydrostatically extruded AZ31 magnesium alloy. The development of the internal stresses and microstructure in the polycrystalline alloy when twinning takes place is explained on the basis of the two pairs of parent {10.0}_||, {11.0}_|| and twin {00.2}_||, {10.3}_|| grain families. The experimentally observed pseudoelastic-like behaviour in stress–strain cycles is interpreted as being due to the activation of reversal twinning processes during loading–unloading cycles. It is proposed that the driving force for the observed untwinning is the existence of high tensile stresses in favourably oriented grains which result from significant twinning activity prior to unloading from the peak stress.     

Microstructural parameters affecting creep induced load shedding in Ti-6242 by a size dependent crystal plasticity FE model

This paper is aimed at identifying critical microstructural parameters that cause local stress concentration due to load shedding between microstructural regions of varying strengths. This stress is viewed as one of the fundamental reasons for crack initiation in Ti-6242. A rate dependent, anisotropic, elasto-crystal plasticity based finite element model (CPFEM) for poly-phase Ti-6242 is used in this study to identify the critical variables responsible for localized stress concentration due to load shedding. The model can account for various microstructural features like grain size, orientation and misorientation distributions. Various microstructural variables, such as crystal orientation, misorientation, grain size, Schmid factor and composition of phases, are considered in a detailed parametric study. Critical combinations of these parameters that result in high stress due to load shedding are identified. Finally, load shedding in a microstructure model of polycrystalline Ti-6242 is discussed from the results of CPFEM simulations. The model is statistically equivalent with respect to features observed in OIM scans.     

SIMULATIONS OF MECHANICAL BEHAVIOR OF POLYCRYSTALLINE COPPER WITH NANO-TWINS

Mechanical behavior and microstructure evolution of polycrystalline copper with nano-twins were investigated in the present work by finite element simulations. The fracture of grain boundaries are described by a cohesive interface constitutive model based on the strain gradient plasticity theory. A systematic study of the strength and ductility for different grain sizes and twin lamellae distributions is performed. The results show that the material strength and ductility strongly depend on the grain size and the distribution of twin lamellae microstructures in the polycrystalline copper.     

Hardening evolution of AZ31B Mg sheet

The monotonic and cyclic mechanical behavior of O-temper AZ31B Mg sheet was measured in large-strain tension/compression and simple shear. Metallography, acoustic emission (AE), and texture measurements revealed twinning during in-plane compression and untwinning upon subsequent tension, producing asymmetric yield and hardening evolution. A working model of deformation mechanisms consistent with the results and with the literature was constructed on the basis of predominantly basal slip for initial tension, twinning for initial compression, and untwinning for tension following compression. The activation stress for twinning is larger than that for untwinning, presumably because of the need for nucleation. Increased accumulated hardening increases the twin nucleation stress, but has little effect on the untwinning stress. Multiple-cycle deformation tends to saturate, with larger strain cycles saturating more slowly. A novel analysis based on saturated cycling was used to estimate the relative magnitude of hardening effects related to twinning. For a 4% strain range, the obstacle strength of twins to slip is 3 MPa, approximately 1/3 the magnitude of textural hardening caused by twin formation (10 MPa). The difference in activation stress of twinning versus untwinning (11 MPa) is of the same magnitude as textural hardening.     

Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study

A multi-scale, theoretical study of twin nucleation from grain boundaries in polycrystalline hexagonal close packed (hcp) metals is presented. A key element in the model is a probability theory for the nucleation of deformation twins based on the idea that twins originate from a statistical distribution of defects in the grain boundaries and are activated by local stresses at the grain boundaries. In this work, this theory is integrated into a crystal plasticity constitutive model in order to study the influence of these statistical effects on the microstructural evolution of the polycrystal, such as texture and twin volume fraction. Recently, a statistical analysis of exceptionally large data sets of {101?2} deformation twins was conducted for high-purity Mg (Beyerlein et al., 2010a). To demonstrate the significantly enhanced accuracy of the present model over those employing more conventional, deterministic approaches to twin activation, the model is applied to the case of {101?2} twinning in Mg to quantitatively interpret the many statistical features reported for these twins (e.g., variant selection, thickness, numbers per grain) and their relationship to crystallographic grain orientation, grain size, and grain boundary misorientation angle. Notably the model explains the weak relationship observed between crystal orientation and twin variant selection and the strong correlation found between grain size and the number of twins formed per grain. The predictions suggest that stress fluctuations generated at grain boundaries are responsible for experimentally observed dispersions in twin variant selection.     

Detection of plastic deformation patterns in a binary aluminum alloy

A whole-field, in-plane strain-mapping technique is evaluated for in situ monitoring of plastic deformation patterns in aluminum sheet metals. This technique is built on the recent developments in digital image correlation and improved data reduction procedures. The sensitivity and accuracy of the measured local strain variations are critically examined in terms of random and systematic experimental errors, free-surface roughening due to large plastic deformation and microscopic surface grain deformation. Tensile specimens made from an annealed Al−Mg alloy sheet metal are subjected to a large plastic and macroscopically uniform deformation, and no visible deformation patterns can be identified by direct surface observation. Using an incremental strain-mapping approach, the existence of nonstationary deformation bands in the annealed Al−Mg alloy is uncovered. The developed technique can be used to study the formation and evolution of plastic deformation patterns and their effect on tensile ductility, formability and surface finish of sheet metals.     

磁控溅射Ag膜磨斑微结构与耐磨机理研究

在铜基底上制备了磁控溅射银膜,采用激光共聚焦显微镜(LSCM)、透射电镜(TEM)、扫描电子显微镜(SEM)及电子背散射衍射(EBSD)等分析技术对载流摩擦试验后的磨斑微结构进行了分析. 结果表明:磨斑表面较平滑,可见犁沟、微坑及塑性流动等形貌,磨斑边缘存在堆积和剥落. 磨斑表面颗粒形态为短棒状和球状,颗粒尺寸为20~150 nm. 磨斑微结构中存在(012)和有利的(111)择优取向,晶粒平均粒度为582 nm,多数晶粒极细小,起到细晶强化作用. 在磨斑微结构中发现大量孪晶,(111)取向孪晶占比达到93.5%,这种高密度孪晶夹杂非孪晶的微结构,有利于材料内部的滑移和提高耐磨性. 在孪晶界发现存在大量{111}晶面族层错结构,有利于材料晶粒间滑移并提升宏观摩擦性能.      

结合数码显微镜的数字散斑相关方法精度分析及应用

结合数字散斑相关方法和一种新型的显微镜数码显微镜,提出了一种测量多晶材料晶粒尺度面内变形的新方法,并通过零变形校准实验、重聚焦实验和平移实验等一系列验证实验分析了该方法的精度和实用性.作为应用实例,对一种镍基合金试件进行了单向拉伸和疲劳实验,得到了晶粒尺度下具有较大应变梯度的应变分布图像.结果表明,该方法能够得到精确的位移测量数据,是一种理想的测量晶粒尺度变形的光测方法.     

Quantitative Study of Residual Strain and Geometrically Necessary Dislocation Density Using HR-EBSD Method

Background

Optical metrology is widely used to measure materials’ deformation and mechanical properties but current fundamental research requires more precise measurement of microstructure and deformation in internal materials. Electron backscattered diffraction (EBSD) technique measures crystal orientation in individual grain and high resolution EBSD (HR-EBSD) method provides information about residual strain and GND density.

Objective

Deformation of two stainless steels Nitronic 60 and Tristelle 5183 with different proportions of ferrite and carbides are characterised.

Methods

Push-release bend testing was used to provide progressive increasing bending stress in two iron-based material samples. HR-EBSD and high resolution digital image correlation (HR-DIC) methods characterised residual strain, GND density and plastic strain distributions in each sample.

Results

Nitronic 60 and Tristelle 5183 were deformed and obtained 3.8% and 0.9% plastic strain ?xx. High GND densities distributed neighbouring grain boundaries in Nitronic 60 while high GND densities distributed around carbides, especially intragranular carbides in Tristelle 5183.

Conclusions

HR-EBSD and HR-DIC quantitative characterised deformation in two iron-based alloys, grain/twin boundaries and carbides resulted in GND density increase, promoted work hardening and accumulated high residual elastic strain. Heterogeneous grain/carbide size distribution leaded to stress concentration and cause carbide decohesion and brittle fracture of sample.

     

EBSD Study of Delamination Fracture in Al–Li Alloy 2090

Aluminum–lithium (Al–Li) alloys offer attractive combinations of high strength and low density for aerospace structural applications. However, a tendency for delamination fracture has limited their use. Identification of the metallurgical mechanisms controlling delamination may suggest processing modifications to minimize the occurrence of this mode of fracture. In the current study of Al–Li alloy 2090 plate, high quality electron backscattered diffraction (EBSD) information has been used to evaluate grain boundary types exhibiting delamination fracture and characterize microtexture variations between surrounding grains. Delamination was frequently observed to occur between variants of the brass texture component, along near-Σ3, incoherent twin boundaries. EBSD analyses indicated a tendency for intense deformation along one side of the fractured boundary. A through-thickness plot of grain-specific Taylor factors showed that delaminations occurred along boundaries with the greatest difference in Taylor factors. Together, these suggest a lack of slip accommodation across the boundary, which promotes significantly higher deformation in one grain, and stress concentrations that result in delamination fracture.     

Mechanical Testing of Thin Sheet Magnesium Alloys in Biaxial Tension and Uniaxial Compression

Tension and compression experiments on magnesium rolled sheets and extruded products of AZ31 (Mg?+?3%Al?+?1%Zn) and ZE10 (Mg?+?1%Zn?+?0.3%Ce based misc metal) were performed at room temperature. The tests were conducted along the longitudinal and the transverse direction to quantify the in-plane anisotropy. Samples built from adhesively-bonded layers of sheets were used for in-plane as well as through-thickness compression testing. It was verified that this simple testing method leads to identical results as using comb-like dies and equi-biaxial bulge testing, respectively. In the case of uniaxial loading, the longitudinal and transverse strain components were measured using independent extensometers. R-values were calculated from these signals. The mechanical responses were correlated to the microstructure and the texture. The recorded differences between tensile and compressive response reveal the strength differential effect of the materials. The distortional character of the plastic behaviour is evidenced through their responses to equi-biaxial tensile loading. Significant differences in the compressive responses of the two alloys were identified by comparing the respective hardening rates.     

Intra-granular plastic slip heterogeneities: Discrete vs. Mean Field approaches

In this paper, we derive the mechanical fields (internal stresses, elastic energy) arising from the presence of an inelastic distortion field representing a typical intra-granular “microstructure” as the one observed during the plastification of metallic polycrystals. This “microstructure” is due to the formation of discrete intra-granular plastic slip heterogeneities characterized by at least two internal lengths: the first one is the individual grain size which represents a stochastic parameter inherent to the processing route (prior working, annealing), and, the second one is the spatial distance between active slip lines or slip bands associated with inhomogeneous plastic slip in the interior of grains. These internal lengths can be observed and measured using conventional experimental techniques (EBSD, TEM, AFM). The micro-mechanical modeling of the mechanical fields associated with plastic slip events inside grains is performed with two different assumptions. The first one is based on the well-known Eshelby’s problem of plastic inclusion where only the grain diameter is considered as internal length scale. This classical method considers homogeneous plastic distortion in the grain and leads to a uniform and grain size independent total strain field in the grain. The second method accounts for a non-uniform plastic distortion in the grain characterized by its discrete nature and the two aforementioned internal lengths. Both methods consider grains as spherical inclusions with a given diameter embedded in a homogeneous medium. For the second method, plastic slip is constrained by grain boundaries seen as impenetrable obstacles to dislocations. Thus, plastic strain is embodied by distributions of discrete circular glide loops. After writing the field equations and the free energy of the medium, a micro-mechanical formulation based on the Fourier transform method is developed. It is then found that in contrast with the mean-field approach, the internal stress fields as well as the elastic energy corresponding to different dislocation configurations depend on internal lengths associated to the deformed medium. Different possible configurations associated with intra-granular plastic flow due to circular glide dislocation loops are analyzed. Finally, the results are discussed with respect to the grain size dependence of the flow strength and the Bauschinger effect for plastically deforming polycrystals and perspectives to develop new micro–macro transition schemes accounting for internal length scales are sketched out.     

两种压铸镁合金的微动磨损行为研究

采用液压高精度材料试验机考察了压铸镁合金AZ91D和AM60B在平面-球面接触条件下的微动磨损行为,研究了循环次数、位移幅值、法向载荷和频率等参数对镁合金摩擦磨损性能的影响,分析了其磨斑表面和磨屑的微观形貌,并探讨了其微动磨损机理.结果表明:镁合金AZ91D和AM60B的摩擦系数随着法向载荷的增加而减小,磨损体积损失随频率增加而减小;AZ91D镁合金的抗微动损伤能力优于AM60B镁合金,二者的微动磨损机理相似,其主要磨损形式包括粘着磨损、表面疲劳(脱层)磨损、磨粒磨损以及明显的氧化磨损.     

Grain Boundary Sliding and Slip Transmission in High Purity Aluminum

Despite its significance in polycrystalline materials, there have been few experimental investigations of the activity of grain boundary sliding (GBS) and the relationship between GBS and slip transmission at grain boundaries. The present work addresses this knowledge gap by the characterization of full-field strain and microstructural information in an experimental system of high-purity (99.99%) columnar aluminum subjected to uniaxial tension at 190 °C. High-resolution, full-gage strain fields were characterized on an unloaded specimen by distortion-corrected and stitched scanning electron microscope-enabled digital image correlation (SEM-DIC). Alignment between the lower-resolution electron backscatter diffraction (EBSD) and higher-resolution strain fields was significantly improved by clustering of strain data within an EBSD-defined boundary mantle. Grain boundary sliding was investigated at select boundaries, and it was determined that GBS magnitude profiles can have large gradients along a single boundary and vary significantly between boundaries. Using a geometric compatibility factor (m′) to quantify favorability of slip transmission, the two grain boundaries that exhibited the largest average GBS magnitude experienced contiguous slip on moderately well aligned slip systems, although the exact nature of this slip activity, whether transmission or nucleation, remains under investigation.

     

Detwinning of High-Purity Zirconium: <Emphasis Type="Italic">In-Situ</Emphasis> Neutron Diffraction Experiments

Twinning is an important deformation mode in hexagonal metals to accommodate deformation along the c-axis. It differs from slip in that it accommodates shear by means of crystallographic reorientation of domains within the grain. Such reorientation has been shown to be reversible (detwinning) in magnesium alloy aggregates. In this paper we perform in-situ neutron diffraction reversal experiments on high-purity Zr at room temperature and liquid nitrogen temperature, and follow the evolution of twin fraction. The experiments were motivated by previous studies done on clock-rolled Zr, subjected to deformation history changes (direction and temperature), in the quasi-static regime, for temperatures ranging from 76 K to 450 K. We demonstrate here for the first time that detwinning of { 10[`1] 2 } á 10[`1][`1] ñ\left\{ {10\overline 1 2} \right\}\left\langle {10\overline 1 \overline 1 } \right\rangle tensile twins is favored over the activation of a different twin variant in grains of high-purity polycrystalline Zr. A visco-plastic self-consistent (VPSC) model developed previously, which includes combined slip and twin deformation, was used here to simulate the reversal behavior of the material and to interpret the experimental results in terms of slip and twinning activities.