金属和合金高温变形过程本构模型的研究进展

本构模型是预测金属和合金高温变形行为的重要途径,在不同金属和合金选择合适的变形工艺参数、预防缺陷等方面起着至关重要的作用。在近年对金属和合金高温变形过程的研究中,常通过不同工艺参数下的各类高温变形试验来获取建立本构模型的原始数据,并将所获本构模型导入Deform、Ansys等模拟软件相应模块,以预测材料在锻造等过程中应力、应变速率、温度的分布规律,进而优化实际加工参数、避免缺陷的产生,同时减少耗材及资源浪费。鉴于本构模型在优化加工参数、预防缺陷等方面的重要作用,对金属和合金本构模型的建立、选择等方面的研究较多,选择何种试验方法来获取建立材料本构模型的试验数据、运用何种数学或物理方法来建立材料的本构模型、选择何种本构模型进行预测、各类本构模型的优缺点及修正方法等都是金属和合金高温变形过程本构模型的研究重点。在近些年的研究中,常运用热压缩、热拉伸、热扭转、分离式霍布金森压杆等高温变形试验方法来获取材料不同高温变形工艺参数下的原始数据,进而建立其本构模型。常用的本构模型大致可分为唯象型、物理基型及基于人工神经网络型。各类模型分别具有不同的适用性及优缺点,而缺点最终主要体现在部分工艺参数下的拟合偏差较大,针对该现象,各国学者不断对模型进行完善、修正,其中,除了模型本身的原因外,引起偏差的原因还包括没有考虑摩擦及变形热等宏观问题的影响。目前,常用的典型唯象型本构模型包括Arrhenius型本构模型、Johnson-Cook模型等,物理基模型如Zerilli-Armstrong型等,而基于人工神经网络模型则主要是利用输入层、隐含层及输出层进行预测,各类模型在数据处理的复杂性、物理意义等方面各有优缺点。文章从金属和合金高温变形过程获取本构模型原始数据的试验方法、本构模型的种类及修正、模型的应用等方面综述了本构模型的研究及发展,分析并总结了不同本构模型的优缺点,指出了模型预测过程中个别参数下预测值与试验值偏差较大的现象及其修正方法,并展望了金属和合金高温变形过程本构模型未来的研究方向。     

超弹性NiTi合金循环相变诱发塑性本构模型

为定量描述镍钛形状记忆合金循环相变诱发塑性导致的超弹性退化行为,在广义粘塑性框架下对Graesser模型进行了拓展,考虑了奥氏体和马氏体弹性模量的差异以及马氏体非线性硬化行为,引入循环相变过程中相变应力和残余应变的演化方程,建立了超弹性Ni Ti合金循环相变诱发塑性本构模型,总结了模型参数确定方法.通过镍钛形状记忆合金微管的循环相变试验结果和模拟结果的对比表明,提出的模型能够很好地预测镍钛形状记忆合金的循环相变诱发塑性行为。     

微薄板塑性成形本构关系研究

尺寸效应的影响使得传统的成形理论和变形机制不再适用于微塑性成形.在考虑尺寸效应对微薄板成形性能影响的基础上,对已有的CuZn36黄铜薄板微拉伸实验结果进行处理,提出了一种研究微塑性成形本构关系的方法.根据弹性和塑性变形过程,分阶段分析了t/d(板厚/晶粒大小)对屈服强度和切线模量的影响,修正了双线性弹塑性本构关系,获得了考虑尺寸效应的微塑性成形本构关系.借鉴宏观增量本构关系,结合微拉伸实验,采用Mises屈服准则和随动强化模型,得出适合微塑性成形的弹塑性增量本构方程,为微塑性成形的理论研究和实际应用奠定了基础.     

基于黏塑性理论的碾压混凝土动态剪切本构模型

由于碾压混凝土大坝是逐层碾压而成,坝体层面处的静动抗剪强度均低于其本体强度,在地震、振动或冲击作用下,坝体层面(包括坝基界面)有可能发生沿层面的动态滑移失稳破坏。基于Perzyna黏塑性连续理论,提出了一个用于描述碾压混凝土层面动态剪切断裂行为的本构模型。该模型的特点有：混凝土材料的软化塑性和扩容特性直接与界面处断裂失效过程相联系;使用Carol率相关界面方程作为屈服判据来描述碾压混凝土材料的率相关性;使用经典塑性断裂理论来描述剪切面上的断裂失效和摩擦滑动过程,并且只需要较少的模型参数。利用该模型与含层面碾压混凝土的动态强度试验结果进行了对比分析,包括在不同的应力路径如单轴拉、压和压剪状态下和不同加载速率下的试验结果。结果表明模型与试验得出的结论吻合较好,这种弹-黏塑性动态剪切本构模型对预测包含薄弱层面的碾压混凝土动力破坏性能是有效的,这为相关工程问题的研究提供有益的思路和有效的工具。     

考虑体积塑性应变的岩石损伤本构模型研究

采用Eshelby等效夹杂方法建立岩石弹塑性损伤本构模型是一种有效方法,但相关文献目前还极少。在连续介质损伤力学框架内利用细观力学的Eshelby等效夹杂方法建立了考虑损伤相塑性体积变形的岩石的Helmholtz自由比能函数。利用连续介质损伤力学方法推导出了考虑损伤相塑性变形的岩石损伤本构关系,给出了损伤演化方程和塑性应变发展方程。并通过数值模拟证实该模型能够反映岩石体积塑性应变、损伤的变化规律和损伤部分不能承受拉应力等力学特性。     

大块非晶合金复杂应力状态塑性本构方程

为得到复杂应力状态下大块非晶合金的塑性本构方程,对Zr41.2Ti13.8Ni10Cu12.5Be22.5大块非晶合金进行简单拉伸、压缩和扭转实验,得到相应的一维本构关系,并应用弹塑性力学的相关理论,将一维本构方程延拓到多维应力空间.研究结果表明:该材料符合Mises屈服条件并具有强化特性;利用简单压缩和扭转实验结果可推导出材料在复杂应力状态下的塑性本构方程,且这两个塑性本构方程是一致的.     

箍筋约束混凝土单轴受压塑性损伤本构模型

基于所建立的素混凝土单轴塑性损伤模型,研究箍筋约束作用对混凝土单轴受压作用下损伤行为的影响,引入损伤约束因子来综合体现在约束作用下不同物理量对材料损伤演化规律的影响,将单轴受压混凝土的塑性段分成塑性第一阶段和塑性第二阶段,确定了方形箍筋和圆形箍筋约束下混凝土的损伤演化方程,并给出相应的塑性变形关系的经验公式,建立了箍筋约束混凝土的单轴受压塑性损伤本构模型。通过与单轴荷载作用下约束混凝土的试验结果对比分析,验证了所建模型的有效性,结果表明所建模型能较好反映混凝土材料在约束作用下的本构关系。     

GH742合金高温塑性的研究

通过对ＧＨ７４２合金双真空冶炼φ２５０ｍｍ自耗锭铸态材料的高温拉伸试验和合金的加工再结晶图，固溶再结晶图绘制，找出合金热加工塑性的规律，成功地生产出了ＧＨ７４２合金φ１８０ｍｍ×１０５ｍｍ的圆饼。     

用本构关系及有限元法研究高温管道剩余寿命

以辐射加热炉ＰＧ２０３２高温合金离心铸管为例，用试验得到的高温蠕变与损伤演变的本构关系，通过有限元分析计算模型给出了在工况条件下高温管道临界损伤随服役时间的变化规律，这一结论可以与在设高温管的无损检测结果相比较，在此基础上能够为准确地推断出在役高温管道的剩余寿命。     

Al-Zn合金热成形本构模型

目的 表征Al-Zn合金在预时效强化温热成形工艺下的流动行为。方法 利用MMS200热模拟机对Al-Zn合金进行热拉伸试验,变形参数分别为变形温度180～220℃、应变速率0.01～1 s^-1。通过对试验值进行修正,可得到不同变形条件下的真应力-应变曲线,并建立应变补偿的含Z参数本构模型和PSO-BP人工神经网络本构模型。结果 Al-Zn合金热变形过程中呈现正的应变速率敏感性和热软化效应;应变补偿的含Z参数本构模型的R值和E_AARE值分别为0.961和8.761%;而PSO-BP人工神经网络本构模型的R值和E_AARE值分别为0.993 5和2.51%。结论 PSO-BP人工神经网络本构模型的预测值和试验值高度吻合,拥有更准确、更快速的数据采集和分析能力,对铝合金及其他合金材料的热变形行为预测有着重要意义。     

A crystal plasticity study of cyclic constitutive behaviour, crack-tip deformation and crack-growth path for a polycrystalline nickel-based superalloy

Crystal plasticity has been applied to model the cyclic constitutive behaviour of a polycrystalline nickel-based superalloy at elevated temperature using finite element analyses. A representative volume element, consisting of randomly oriented grains, was considered for the finite element analyses under periodic boundary constraints. Strain-controlled cyclic test data at 650 °C were used to determine the model parameters from a fitting process, where three loading rates were considered. Model simulations are in good agreement with the experimental results for stress–strain loops, cyclic hardening behaviour and stress relaxation behaviour. Stress and strain distributions within the representative volume element are of heterogeneous nature due to the orientation mismatch between neighbouring grains. Stress concentrations tend to occur within “hard” grains while strain concentrations tend to locate within “soft” grains, depending on the orientation of grains with respect to the loading direction. The model was further applied to study the near-tip deformation of a transgranular crack in a compact tension specimen using a submodelling technique. Grain microstructure is shown to have an influence on the von Mises stress distribution near the crack tip, and the gain texture heterogeneity disturbs the well-known butterfly shape obtained from the viscoplasticity analysis at continuum level. The stress–strain response near the crack tip, as well as the accumulated shear deformation along slip system, is influenced by the orientation of the grain at the crack tip, which might dictate the subsequent crack growth through grains. Individual slip systems near the crack tip tend to have different amounts of accumulated shear deformation, which was utilised as a criterion to predict the crack growth path.     

Anisotropic viscoplasticity constitutive model for directionally solidified superalloy

Abstract

The macroscopic deformation behaviour of a Ni-based directionally solidified (DS) superalloy was experimentally investigated, and an anisotropic constitutive model of the material was developed. Monotonic and creep tests were performed on uniaxial test specimens machined from DS plates so that the angle between the loading direction and the solidified grain direction varied between 0 and 90°. Tension-torsion creep tests were also conducted to examine the anisotropic behaviour under multiaxial stress conditions. The material exhibited marked anisotropy under elastic and viscous deformation conditions, whereas it showed isotropy under plastic deformation conditions of high strain rates. Then crystal plasticity analyses were carried out to identify slip systems under creep loading conditions, assuming the anisotropic creep behaviour of the DS material. A viscoplastic constitutive model for expressing both the anisotropic elasticity-viscosity and the isotropic plasticity was proposed. The elastic constants were determined using a self-consistent approach, and viscous parameters were modelled by crystal plasticity analyses. The calculation results obtained using the constitutive model were compared with the experimental data to evaluate the validity of the model. It was demonstrated that the constitutive model could satisfactorily describe the anisotropic behaviour under uniaxial and multiaxial stress conditions with a given set of material parameters.     

A variational constitutive model for porous metal plasticity

This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.     

A thermomechanical crystal plasticity constitutive model for ultrasonic consolidation

We present a micromechanics-based thermomechanical constitutive model to simulate the ultrasonic consolidation process. Model parameters are calibrated using an inverse modeling approach. A comparison of the simulated response and experimental results for uniaxial tests validate and verify the appropriateness of the proposed model. Moreover, simulation results of polycrystalline aluminum using the identified crystal plasticity based material parameters are compared qualitatively with the electron back scattering diffraction (EBSD) results reported in the literature. The validated constitutive model is then used to simulate the ultrasonic consolidation process at sub-micron scale where an effort is exerted to quantify the underlying micromechanisms involved during the ultrasonic consolidation process.     

Eulerian constitutive model for finite deformation plasticity with anisotropic hardening

A constitutive model is presented for finite strain plasticity. The model incorporates both isotropic and kinematic hardening of the Ziegler type. The corotational rate used here is in line with the theory suggested by Paulun and Pecherski (1985) but not necessarily confined to the von Mises type yield criterion and the Prager hardening rule. The aspect of integration of the corotational rates is also discussed here. The use of the integration of the material rate of tensors with time as a substitute for the proper integration with time of corotational rates leads to mathematical inconsistencies of the theory of Lie derivatives. The problem of simple shear is investigated and compared with other works.     

Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

Summary An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space — a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure — encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, noad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed model are studied in case of associative plasticity with the aid of the maximum intrinsic dissipation theorem. It is shown that the material behaves like a standard one as long as its hardening state either is not saturated, or undergoes a desaturation from a saturated hardening state, whereas, for saturated hardening states not followed by desaturation, it conforms to a combined yielding law in which the static internal variable rates obey a nonlinear hardening rule similar to that of analogous models of the literature. Additionally, the material is shown to behave as a perfectly plastic material for a class of (critical) saturated hardening states for which the stress state is on the limit surface. For nonassociative material models, it is shown that, under a special choice of the plastic and saturation potentials and through a suitable parameter identification, the well-known Chaboche model is reproduced. A few numerical examples are presented to illustrate the associative material response under monotonic and cyclic loadings.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

A plasticity model for multiaxial cyclic loading and ratchetting

Summary The nonlinear behavior of metals when subjected to monotonic and cyclic non-proportional loading is modeled using the proposed hardening rule. The model is based on the Chaboche [1], [2] and Voyiadjis and Sivakumar [3], [4] models incorporating the bounding surface concept. The evolution of the backstress is governed by the deviatoric stress rate direction, the plastic strain rate, the backstress, and the proximity of the yield surface from the bounding surface. In order to ensure uniqueness of the solution, nesting of the yield surface with the bounding surface is ensured. The prediction of the model in uniaxial cyclic loading is compared with the experimental results obtained by Chaboche [1], [2]. The behavior of the model in multiaxial stress space is tested by comparing it with the experimental results in axial and torsional loadings performed by Shiratori et al. [5] for different stress trajectories. The amount of hardening of the material is tested for different complex stress paths. The model gives a very satisfactory result under uniaxial, cyclic and biaxial non-proportional loadings. Ratchetting is also illustrated using a non-proportional loading history.     

A constitutive model for cyclic actuation of high-temperature shape memory alloys

In this work, a three dimensional constitutive model for High Temperature Shape Memory Alloys (HTSMAs) is presented. To describe the evolution of the cyclic actuation behavior of such alloys, viscoplastic mechanisms and transformation induced plasticity are introduced in addition to the classical transformation behavior of shape memory alloys. Based on continuum thermodynamics, the evolution of phase transformation, plasticity induced transformation, retained martensite and viscoplasticity are described. Deformation mechanisms that occur over the operational range of such HTSMAs have been identified from the thermomechanical behavior of a NiTiPd alloy. The proposed model has therefore been calibrated and validated based on the thermomechanical response of the studied NiTiPd HTSMA alloy during thermal cycles under compression. Careful attention is devoted to the calibration procedure to identify the contribution of the different mechanisms independently. Finite Element Analysis (FEA) is performed to demonstrate the capabilities of the model to describe the cyclic behavior of HTSMA devices.     

Hot deformation characteristics and strain-dependent constitutive analysis of Inconel 600 superalloy

The hot deformation characteristics and constitutive analysis of Inconel (IN) 600 superalloy were investigated at elevated temperatures. Hot compressive tests were carried out in the temperature and strain rate ranging from 900 to 1150 °C and 1 × 10⁻³–10 s⁻¹, respectively. The flow behavior analyses and microstructural observations indicate that the softening mechanisms were related to dynamic recrystallization (DRX) and grain growth. DRX played a dominant role in the microstructural evolution at low temperatures (or high strain rates). DRX was the dominant softening effect at low strains on testing at high temperatures with low strain rates, whereas growth of the dynamically recrystallized grains was responsible for softening at high strains. The flow stress of IN 600 was fitted well by the constitutive equation of the hyperbolic sine function under the deformation conditions performed in this study. A constitutive equation as a function of strain was established through a simple extension of the hyperbolic sine constitutive relation.     

A generalized Eulerian two-surface cyclic plasticity model for finite strains

Summary A cyclic theory of plasticity is formulated for finite deformation in the Eulerian reference system. A new kinematic hardening rule is proposed based on the experimental observations made by Phillips et al. [11]–[15]. The Tseng-Lee model [9] is also obtained as a special case of the proposed model.Qualitative examples are presented to demonstrate the behavior of materials under different loading paths using the proposed model. These include both proportional and nonproportional loading paths.