Anisotropic strain hardening behavior in simple shear for cube textured aluminum alloy sheets

Finite element (FE) simulations of the simple shear test were conducted for 1050-O and 6022-T4 aluminum alloy sheet samples. Simulations were conducted with two different constitutive equations to account for plastic anisotropy: Either a recently proposed anisotropic yield function combined with an isotropic strain hardening law or a crystal plasticity model. The FE computed shear stress–shear strain curves were compared to the experimental curves measured for the two materials in previous works. Both phenomenological and polycrystal approaches led to results consistent with the experiments. These comparisons lead to a discussion concerning the assessment of anisotropic hardening in the simple shear test.     

Effect of texture and microstructure on strain hardening anisotropy for aluminum deformed in uniaxial tension and simple shear

Uniaxial and simple shear stress–strain curves were obtained for a 1050-O aluminum alloy sheet sample in different specimen orientations with respect to the material symmetry axes. For uniaxial tension, a strong anisotropy of strain hardening was observed leading to about 30% difference in uniform tensile elongation between the extreme conditions. For simple shear, the hardening was also significantly different. These results were rationalized with an analysis that accounts for dislocation substructure observations, crystallographic texture measurements and polycrystal modeling of texture-induced strength evolution.     

Influence of deformation path on the strain hardening behavior and microstructure evolution in low SFE FCC metals

Following our recent studies of the influence of mechanical twinning on the strain hardening of low SFE FCC metals deformed by simple compression, the investigation was extended to two different deformation modes. These were plane strain compression and simple shear carried out on 70/30 brass, which exhibits only strain hardening, and on MP35N, a Co–Ni based alloy that also shows secondary hardening by deformation promoted precipitation. It was found that the magnitude of the primary strain hardening in both alloys, and the secondary hardening in MP35N, was dramatically reduced under simple shear compared to the other deformation paths. This reduced hardening in simple shear appears to be a consequence of the bulk of the deformation twins, and also the secondary hardening precipitates, forming on planes that were parallel to the primary {111} slip planes in this deformation path. These hypotheses are supported by deformation path change tests in which the shear samples that show low flow stress under continued shear, when subjected to simple compression showed a significant increase (jump) in the flow stress, reaching values that are similar to those of the alloy continuously compressed to the same equivalent strain. That is, the reduced strain hardening in shear deformation is due not to reduced twinning, but to the twins produced by shear providing only limited barriers to continued strain by simple shear. Shear banding was found to be more marked in plane strain compression than in simple compression after cold working, and particularly after the additional secondary hardening in MP35N.     

A simple model for dislocation behavior,strain and strain rate hardening evolution in deforming aluminum alloys

In this work, modeling of the stress–strain behavior is carried out using a simple dislocation model. This model uses three variables to characterize the dislocation population: The average forest and mobile dislocation densities, ρ_f and ρ_m, and the average dislocation mean free path L. However, it is shown that within reasonable assumptions, only two of these variables are independent. The mathematical form derived from this dislocation-based model was applied to experimental stress–strain data determined at room temperature for pure aluminum, 3003-O, 2008-T4, 6022-T4, 5182-O and 5032-T4 aluminum alloy sheets. The evolution of the state variables was calculated for these materials from a single stress–strain curve. The average dislocation mean free paths at a strain of 0.5 were compared with TEM observations of dislocation cell sizes or inter-dislocation spacing for specimens deformed equal biaxially with the hydraulic bulge test. A very good agreement was obtained between predictions and experiments.     

Adiabatic shear localization in the dynamic punch test,part I: experimental investigation

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during a dynamic punch test is investigated. Specifically, the possibility and affects of adiabatic shear localization are examined. The three materials are chosen to encompass a wide range of physical properties. Punch tests are conducted at average shear strain rates from 10⁻³ to 10⁴ s⁻¹ on a servo-hydraulic compression machine, a mechanical press, and a Hopkinson bar apparatus. Experimental load displacement curves are obtained and fractographic and metallographic analysis is performed. Finite element simulations of punching operations are performed in the second part of this two part investigation to examine internal deformation not visible during experimental tests. More specifically, the role of adiabatic shear localization in burr formation is determined. Adiabatic shear localization occurs in the titanium alloy for the mechanical press and Hopkinson bar tests, while localization is not present for the 6061-T6 aluminum in any test. The 1018 steel begins to exhibit some transitional behavior toward shear localization in the Hopkinson bar experiments. It is seen that in the materials tested here, a combination of high strength and low strain hardening make a material more susceptible to adiabatic shear localization in punching operations.     

Adiabatic shear localization in the dynamic punch test,part II: numerical simulations

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during the dynamic punch test is investigated using the finite element method. Specifically, the possibility and effects of adiabatic shear localization and its role in burr formation are examined, and comparisons to experimental tests in the first part of this two part study are made. A maximum stress criterion involving strain and strain rate hardening and thermal softening is used to determine the occurrence of shear localization in the simulations. It is observed that adiabatic shear localization occurs in the simulations of the titanium alloy. This material exhibits narrow regions of concentrated shear strain during the deformation, and the shear localization criterion is satisfied in these regions. The strain is more widely distributed in the other two metals, and the same criterion is not satisfied. In the calculations of the shear localization criterion it is seen that strain rate hardening has a significant effect when compared to strain hardening and thermal softening. Also, contact between specimen and punch is lost around the center of the punch during operation. This loss of contact is important as it leads to higher stress concentrations at the punch corner and dishing of the blank.     

A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming

In this paper an anisotropic material model based on non-associated flow rule and mixed isotropic–kinematic hardening was developed and implemented into a user-defined material (UMAT) subroutine for the commercial finite element code ABAQUS. Both yield function and plastic potential were defined in the form of Hill’s [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. Lond. A 193, 281–297] quadratic anisotropic function, where the coefficients for the yield function were determined from the yield stresses in different material orientations, and those of the plastic potential were determined from the r-values in different directions. Isotropic hardening follows a nonlinear behavior, generally in the power law form for most grades of steel and the exponential law form for aluminum alloys. Also, a kinematic hardening law was implemented to account for cyclic loading effects. The evolution of the backstress tensor was modeled based on the nonlinear kinematic hardening theory (Armstrong–Frederick formulation). Computational plasticity equations were then formulated by using a return-mapping algorithm to integrate the stress over each time increment. Either explicit or implicit time integration schemes can be used for this model. Finally, the implemented material model was utilized to simulate two sheet metal forming processes: the cup drawing of AA2090-T3, and the springback of the channel drawing of two sheet materials (DP600 and AA6022-T43). Experimental cyclic shear tests were carried out in order to determine the cyclic stress–strain behavior and the Bauschinger ratio. The in-plane anisotropy (r-value and yield stress directionalities) of these sheet materials was also compared with the results of numerical simulations using the non-associated model. These results showed that this non-associated, mixed hardening model significantly improves the prediction of earing in the cup drawing process and the prediction of springback in the sidewall of drawn channel sections, even when a simple quadratic constitutive model is used.     

不同加载状态下TA2钛合金绝热剪切破坏响应特性

一般认为绝热剪切现象在宏观上表现为材料动态本构失稳,即热软化大于应变硬化.本文采用帽型受迫剪切试样研究TA2钛合金的动态力学特性和本构失稳过程.首先对剪切区加载应力状态进行理论和数值分析,通过合理设计帽型试样,剪切区变形可近似按剪切状态处理;结合二维数字图像相关法(two-dimensional digital image correlation,DIC-2D)直接测试试样剪切区应变演化,给出帽型受迫剪切实验的等效应力-应变响应曲线.进一步,利用Hopkinson压杆对TA2钛合金开展动态压缩及帽型剪切对比试验研究,比较压缩、剪切试验得到的等效应力-应变曲线,采用"冻结"试样方法分析试样中绝热剪切局域化演化过程,探讨不同加载状态下TA2钛合金的绝热剪切破坏现象及其动态力学响应特性.实验结果表明,在塑性变形初始阶段,动态压缩及剪切加载下的等效应力-应变曲线符合较好,但随塑性损伤发展及绝热剪切带形成,两者出现分离,表明损伤及绝热剪切演化过程与应力状态相关.剪切试样实验得到的本构"软化"特性能够反映绝热剪切带起始、破坏演化过程的力学响应特性,而在动态压缩实验中,即使试样中已出现双锥形的绝热剪切带及局部裂纹分布,其表观等效应力-应变曲线并不出现软化特征,动态压缩实验无法得到关于绝热剪切起始、发展以及破坏的本构软化响应特性.     

宽应变率范围下2A16-T4铝合金动态力学性能

为了研究2A16-T4铝合金的动态力学性能,利用电子万能试验机、高速液压伺服试验机及霍普金森压杆(SHPB)装置进行常温下准静态、中应变率和高应变率的动态力学性能实验,得到不同应变率下的应力应变曲线,基于修正的Johnson-Cook本构模型对它进行拟合,并分析材料中应变率力学特性对模型应变率敏感参量的影响。结果表明:2A16-T4铝合金在应变率10-4~102 s-1范围内应变率敏感性较弱,而在102~103 s-1范围内应变率敏感性较强,且应变率强化效应随塑性应变的增大而减小;同时,在10-4~103 s-1范围内具有较强的应变硬化效应,且应变硬化效应随应变率的增大而减小;此外,修正Johnson-Cook本构模型的拟合结果与实验结果吻合很好,能够很好表征材料的动态力学行为,且考虑材料中应变率力学特性可提高本构模型参量的准确性。     

高速列车用6008铝合金动态变形本构与损伤模型参数研究

高速列车在实际服役过程中会经受复杂的应力状态和环境条件,铝合金型材以其优良的力学和加工性能被广泛应用于新型高速列车的吸能结构,其防撞性能对高速列车的安全运行至关重要。本文针对一种新型轨道车辆用材料6008-T4铝合金型材进行了多种力学性能测试,包括动静态拉压实验、准静态高低温实验、不同应力路径的断裂实验等,提出了一种计算局部断裂应变的新方法,进而标定和获取了Johnson-Cook本构和损伤模型参数。最后利用平板侵彻实验来对所获取的参数进行检验,发现模拟和实验结果吻合良好,说明本文所获取的参数和参数标定方法都是有效的。     

Incorporation of yield surface distortion in finite deformation constitutive modeling of rigid-plastic hardening materials based on the Hencky logarithmic strain

In this paper a constitutive model for rigid-plastic hardening materials based on the Hencky logarithmic strain tensor and its corotational rates is introduced. The distortional hardening is incorporated in the model using a distortional yield function. The flow rule of this model relates the corotational rate of the logarithmic strain to the difference of the Cauchy stress and the back stress tensors employing deformation-induced anisotropy tensor. Based on the Armstrong–Fredrick evolution equation the kinematic hardening constitutive equation of the proposed model expresses the corotational rate of the back stress tensor in terms of the same corotational rate of the logarithmic strain. Using logarithmic, Green–Naghdi and Jaumann corotational rates in the proposed constitutive model, the Cauchy and back stress tensors as well as subsequent yield surfaces are determined for rigid-plastic kinematic, isotropic and distortional hardening materials in the simple shear deformation. The ability of the model to properly represent the sign and magnitude of the normal stress in the simple shear deformation as well as the flattening of yield surface at the loading point and its orientation towards the loading direction are investigated. It is shown that among the different cases of using corotational rates and plastic deformation parameters in the constitutive equations, the results of the model based on the logarithmic rate and accumulated logarithmic strain are in good agreement with anticipated response of the simple shear deformation.     

Modeling the evolution of anisotropy in Al–Li alloys: application to Al–Li 2090-T8E41

It is widely reported in current literature that the precipitation hardened Al–Li sheet alloys exhibit extremely high anisotropy in yield (and ultimate tensile) strength, which is well beyond what can be explained as purely a consequence of the strong crystallographic texture in the material (e.g. J. Mater. Sci. Eng. A265, 1999, 100). This paper presents a crystal plasticity based modeling framework that will (i) facilitate the segregation of the contributions to the overall anisotropy from crystallographic texture and precipitation hardening, and (ii) correlate the contribution from precipitate hardening to either co-planar slip activity or the non-coplanar slip activity in the cold-working step prior to the aging heat treatment. More specifically, a Taylor-type (fully-constrained) crystal plasticity model was formulated to predict the yield strength of the fully processed sheet and its anisotropy, while accounting for the initial texture in the hot-worked sheet, its evolution during the cold-working step prior to aging, and the inhomogeneous nucleation of the T₁ phase platelets (these are known to form on {111} planes, but not usually in equal amounts on the different {111} planes in a given crystal). In an effort to illustrate the methodology developed in the study, a limited set of experiments was conducted on Al–Li 2090-T8E41 alloy sheet. Off-axis stretches were applied on the sheet at room temperature prior to the aging treatment, and the mechanical anisotropy in the fully processed sheets was characterized by performing tension tests on coupons cut from the sheet at 0, 30, 45, 60 and 90° to the original rolling direction (RD). Both the initial texture in the sheet and its evolution during the different off-axis stretches were characterized. The alloys processed in this study showed pronounced anisotropy. The application of the methodology developed in this study revealed that much of the observed anisotropy in this particular data set could be explained by accounting for the texture in the sample in the processed condition. Although the data set available was inadequate to establish clear correlations of the anisotropy with preferential hardening mechanisms arising from either co-planar or non-co-planar slip activity during the off-axis stretch, there were indications favoring the latter. This case study, however, illustrates the application of the methodology developed in this study to obtain better insight into the nature of the anisotropy in these sheets and its physical origin.     

Creep and anelasticity in the springback of aluminum

Draw-bend tests, devised to measure springback in previous work, revealed that the specimen shapes for aluminum alloys can continue to change for long periods following forming and unloading. Steels tested under identical conditions showed no such time-dependent springback. In order to quantify the effect and infer its basis, four aluminum alloys, 2008-T4, 5182-O, 6022-T4 and 6111-T4, were draw-bend tested under conditions promoting the time-dependent response (small tool radius and low sheet tension). Detailed measurements were made over 15 months following forming, after which the shape changes were difficult to separate from experimental scatter. Earlier tests were re-measured up to 7 years following forming. The shape changes are generally proportional to log(time) up to a few months, after which the kinetics become slower. In order to understand the basis of the phenomenon, two models were considered: residual stress-driven creep, and anelastic deformation. In the first case, creep properties of 6022-T4 were measured and used to simulate creep-based time-dependent springback. Qualitative agreement was obtained using a crude finite element model. For the second possibility, novel anelasticity tests following reverse-path loading were performed for 6022-T4 and drawing-quality silicon-killed (DQSK) steel. Based on the experiments and simulations, it appears that anelasticity is unlikely to play a large role in long-term time-dependent springback of aluminum alloys.     

6061-T6铝合金动态拉伸本构关系及失效行为

采用HMH-206高速材料试验机开展了6061-T6铝合金在0.001～100 s-1应变率范围内的静、动态拉伸力学性能实验,分析了其应力-应变响应特征和应变率敏感性,讨论了应变率对6061-T6铝合金流动应力和应变率敏感性指数的影响,并基于实验结果对Johnson-Cook本构模型进行了修正。结合缺口试件的实验结果和模拟数据,得到了材料的Johnson-Cook失效模型参数,并对模型的准确性和适用性进行了验证。结果表明,在拉伸载荷作用下,6061-T6铝合金表现出明显的应变硬化特征和应变率敏感性,其流动应力随应变率的升高而提高,修正的Johnson-Cook本构模型可以描述材料的动态塑性流动行为,建立的Johnson-Cook失效模型能够表征材料的断裂失效行为。     

On dimensionless numbers for dynamic plastic response of structural members

Summary A dimensional analysis is reported for the dynamic plastic response and failure of structural members, which includes material strain hardening, strain rate and temperature effects. Critical shear failure conditions are also discussed based on the dimensional analysis results. It is shown that the response number R _n proposed in [3], is an important independent dimensionless number for the dynamic plastic bending and membrane response of structural members. However, additional dimensionless numbers are necessary when transverse shear, strain hardening, strain rate, and temperature effects are important. Received 22 February 1999; accepted for publication 15 June 1999     

Mechanical properties of 6061 Al-Mg-Si alloy after very rapid heating

The effects of time, temperature and strain rate on the yield strength determined at elevated temperature have been investigated for 6061-T6 Al-Mg-Si alloy. To achieve very short times-at-temperature, nanosecond pulse heating produced by electron beam energy deposition was used along with one-dimensional stress-wave loading. When a relatively thick sample is heated in this way it cannot expand on the same time scale as the temperature increase. As a result, stress relief waves propagate in the material after energy deposition, and this deformation occurring at high strain-rates and elevated temperatures produces microstructural changes that reduce the strength of the alloy on the time scale of a few μs. This strength reduction occurs in addition to that due to the lowered shear modulus at-temperature, and is an essentially permanent change reflected in the greatly reduced room temperature strength of the material following nanosecond pulse heating.If the material is heated slowly enough so that the sample can expand as the temperature increases, and if the soaking time at temperature is less than required for microstructural changes in the alloy (e.g. approximately 3 s at 260°C), the yield strength measured at-temperature under wave propagation conditions drops in proportion to the shear modulus. In addition, the yield strength measurement is sensitive to the rate of deformation at elevated temperatures even for short times-at-temperature. The nature of this sensitivity is discussed in terms of thermally-activated dislocation motion.     

Deformation and microstructure-independent Cottrell-Stokes ratio in commercial Al alloys

Cottrell-Stokes-type experiments are performed with AA6022, a heat treatable commercial Al alloy, at different stages of precipitation. It is shown that the ratio of the flow stress at given temperature and that extrapolated to 0 K, measured at given material state, is independent of the strain and of the precipitation state. The ratio depends only on temperature and strain rate. However, when probed using strain rate jump experiments, the Cottrell-Stokes law appears not to be fulfilled in any of these materials, and the strain rate sensitivity parameter depends on the precipitation state. A model based on the interaction of dislocations with populations of obstacles of various types is used to provide an interpretation of the Cottrell-Stokes law. The model indicates that as the dislocation velocity increases, the effective Cottrell-Stokes ratio in systems with various obstacle compositions takes values in a narrow range close to the critical value of 1 (i.e. “microstructure” insensitivity). Conversely, the model suggests that the Cottrell-Stokes ratio should become more sensitive to the microstructure under creep conditions.     

The viscoplastic behavior of hastelloy-X single crystal

A viscoplastic constitutive model for Hastelloy-X single crystal material is developed based on crystallographic slip theory. The constitutive model was constructed for use in a viscoplastic self-consistent model for isotropic Hastelloy-X polycrystalline material, which has been described in a recent publication. It is found that, by using the slip geometry known from the metallurgical literature, the anisotropic response can be accurately predicted. The model was verified by using tension and torsion data taken at 982°C (1800°F). The constitutive model used on each slip system is a simple unified visoplastic power law model in which weak latent interaction effects are taken into account. The drag stress evolution equations for the octahedral system are written in a hardening/recovery format in which both hardening and recovery depend on separate latent interaction effects between the octahedral crystallographic slip systems. The strain rate behavior of the single crystal material is well correlated by the constitutive model in uniaxial and torsion tests, but it is necessary to include latent information effects between the octahedral slip systems in order to obtain the best possible representation of biaxial cyclic strain rate behavior. Finally, it was observed that the single crystal exhibited dynamic strain aging at 871°C (1600°F). Similar dynamic strain aging occurs at 649°C (1200°F) in the polycrystalline version of the alloy.     

Kinematic hardening in large strain plasticity

A finite strain hyper elasto-plastic constitutive model capable to describe non-linear kinematic hardening as well as non-linear isotropic hardening is presented. In addition to the intermediate configuration and in order to model kinematic hardening, an additional configuration is introduced – the center configuration; both configurations are chosen to be isoclinic. The yield condition is formulated in terms of the Mandel stress and a back-stress with a structure similar to the Mandel stress.It is shown that the non-dissipative part of the plastic velocity gradient not governed by the thermodynamical framework and the corresponding quantity associated with the kinematic hardening influence the material behaviour to a large extent when kinematic hardening is present. However, for isotropic elasticity and isotropic hardening plasticity it is shown that the non-dissipative quantities have no influence upon the stress–strain relation.As an example, kinematic hardening von Mises plasticity is considered, which fulfils the plastic incompressibility condition and is independent of the hydrostatic pressure. To evaluate the response and to examine the influence of the non-dissipative quantities, simple shear is considered; no stress oscillations occur.