基于微结构动态演化机制的单晶镍基高温合金晶体塑性本构及其有限元模拟

因其优异的高温力学性能,镍基单晶高温合金在航空航天和能源等领域得到了广泛的应用.镍基单晶高温合金优异的高温性能来源于其特有的两相微结构.基于代表体胞模型及分块均匀化方法,以位错密度为主要内变量,发展了一个包含两相微结构和位错演化信息的单晶镍基高温合金塑性行为的本构模型.该本构模型充分考虑了镍基单晶合金中位错在基体相和沉淀增强相中的多种演化机制,例如,基体位错八面体滑移、立方滑移、位错攀移、交滑移、位错弓出、位错切过沉淀增强相以及位错Kear-Wilsdolf(K-W)锁形成与解锁等.在商用有限元软件ABAQUS的框架下,编制了UMAT用户材料子程序.利用该用户子程序,对单晶和多晶镍基高温合金在不同温度、不同加载方向下的单调塑性、循环塑性、蠕变等典型行为进行了计算模拟.结果表明:该晶体塑性本构模型能"统一地"刻画镍基高温合金在不同温度、不同方向下的多种变形行为,并与实验结果具有良好的一致性.     

含冷却孔镍基合金次级取向效应的应变梯度晶体塑性有限元研究

单晶镍基合金具有优异的耐高温、高强、高韧等性能, 这些力学性能受制造过程引入的次级取向和冷却孔的影响. 已有研究大多关注单孔薄板的变形机理和力学性能, 而工程中应用的往往是多孔薄板, 当前亟需阐明多孔的塑性滑移带变形机理、次级取向效应以及冷却孔引起的应变梯度效应. 文章采用基于位错机制的非局部晶体塑性本构模型对含冷却孔镍基单晶薄板的单拉变形进行了数值模拟. 此模型基于塑性滑移梯度与几何必需位错的关系引入了位错流动项, 因此可有效刻画非均匀变形过程中的应变梯度效应. 为了全面揭示含孔镍基薄板的次级取向效应, 系统研究了[100]和[110]取向(两种次级取向)下镍基薄板的单拉变形行为, 并重点探究了在两种次级取向下冷却孔数量对薄板塑性行为的影响. 此外, 还分析了镍基合金板变形过程中各个滑移系上分切应力变化、主导滑移系开动以及几何必需位错密度的演化过程, 并讨论了塑性滑移量及其分布特征对不同次级取向镍基合金板强度的影响. 研究表明, 单孔和多孔的[110]薄板抗拉强度均低于[100]薄板, 多孔薄板的塑性变形过程比单孔薄板更为复杂且受次级取向影响更大, 并且发生滑移梯度位置主要位于冷却孔附近以及塑性滑移带区域. 研究结果可为工程中镍基合金的设计和服役提供理论指导.      

延性单晶非均匀变形的三维有限元模拟

对延性单晶在拉伸载荷作用下的应变局域化和颈缩等非均匀变形过程进行了三维有限元数值模拟。将相关晶体塑性本构模型及一种新的数值积分方法补充到ABAQUS6.1商用有限元软件中。该方法的特点是，利用晶体塑性的动力学方程，获得一个关于晶体弹性变形梯度的演化方程，采用半隐式积分方案进行求解。本文推导出一种新的应力变本构矩阵。按此方式更新本构矩阵，计算速度和计算稳定性大大提高。加载方式，边界条件和变形程度等因素影响着滑移系的启动状况，这是平面模型所不能预测的。本文利用三维有限元方法模拟了不同取向下滑移系的启动状况，全面地考虑了FCC单晶材料12个可能滑移系在变形过程中的启动状况，合理地模拟了FCC面心立方单晶沿不同取向加载时晶轴旋转导致的应变局域化和颈缩等非均匀变形过程。     

有限变形下单晶变温本构模型

本文构造了单晶热弹粘塑性的本构模型,模拟材料在不同温度下的力学行为。该模型以晶体热运动学作为分析变形的基础,即考虑温度变化情况下总体变形梯度的乘式分解,建立温度影响下的以弹性变形梯度为基本变量的控制方程来描述单晶材料的变形,算法采用隐式积分方法来求解控制方程以保证计算的稳定性。模型能反映单晶材料变形过程中温度对应力-应变响应的影响。     

SS304不锈钢高温非比例多轴循环变形行为的粘塑性本构描述

在350℃和700℃下SS304不锈钢的非比例多轴循环变形行为进行了系统的实验研究。在此基础上,在统一粘塑性本构理论的框架下改进和发展了一个新的循环本构模型。该模型给出了新的背应力演化方程,引入了非比例度参量,考虑了温度效应和最大塑性应变幅值记忆效应,能够对材料的高温非比例多轴应变循环变形行为和棘轮行为进行统一描述。模型的模拟结果与实验结果比较表明:该模型对SS304不锈钢高温非比例多轴循环变形行为的描述比较合理。     

单晶体和双晶体微观层次变形行为的有限元分析

从微观层次上研究金属材料的变形行为,将位错引入到本构关系中,用硬化函数描述材料的硬化规律,考虑了变形的率相关性,采用三维模型用大变形有限单元法对单晶体在单向拉伸载荷和循环载荷作用下的变形行为、双晶体在单向拉伸作用下滑移系的开动进行了模拟计算,得到了与实验一致的计算结果。     

非稳态纯滚动接触弹塑性分析

建立了二维弹塑性非稳态循环纯滚动接触有限元模型.材料本构采用一种较好的循环塑性模型,并通过材料用户子程序在通用有限元软件ABAQUS中自定义该本构模型.通过在弹塑性无限半空间表面上重复移动随时间按简谐规律变化的赫兹法向载荷来模拟非稳态循环纯滚动接触过程.通过数值模拟,得到接触表面附近的残余累积变形、应变和残余应力.不同的最大赫兹接触压力对残余应力和残余应变影响较大.在简谐变化的法向接触载荷作用下接触表面的变形呈波浪形,随着滚动次数的增加,该波状表面沿载荷移动相反方向逐渐移动,但移动速率要衰减.波状表面波谷处的残余应力、应变和变形大于波峰处.随滚动次数的增加,残余应力增大但很快趋于稳定,残余应变也增大但增大速率衰减.     

有限元实现含应变非强化区的双面循环塑性模型

在有限单元方法的框架下,由广义径向返回法来实现含有应变非强化区的循双面环塑性本构模型.在小变形的假设下,本文详细描述了有限元方法实现率无关的双面循环塑性本构模型的完整算法.采用向后Euler隐式算法进行离散积分,其最终可化简为一个非线性方程,并且由Peg-asus方法来求解.对径向返回法进行线性化,可以得到切向刚度算子.最后,文中通过两个算例表征了离散积分的精确性和材料模型的正确性.     

沉淀相的尺寸与形态对镍基合金蠕变行为的影响

镍基合金具有优良的高温力学性能,广泛应用于涡轮叶片等热端部件。沉淀相的尺寸和形态是影响镍基合金力学性能的重要因素。本文在考虑应变梯度的镍基合金晶体塑性本构模型的基础上,引入了各向异性损伤张量,研究了包含两种不同尺寸和三种不同长细比的沉淀相形态的镍基合金蠕变行为。结果表明,该模型能够很好地反映沉淀相的尺寸对镍基合金蠕变行为的影响,与实验结果符合较好。同时,沉淀相的形态也对镍基合金的力学性能产生重要影响,随着沉淀相长细比的增加,镍基合金的蠕变寿命延长,这体现了粗化和形态对镍基合金蠕变行为影响的一种竞争的机制。     

超弹性镍钛形状记忆合金单轴相变棘轮行为的宏观唯象本构模型

超弹性镍钛形状记忆合金因其良好的力学性能以及独特的超弹性和形状记忆效应已广泛应用于土木工程、航空航天和生物医疗等多个领域,在实际服役环境中超弹性镍钛合金元件不可避免地会承受不同应力水平的循环载荷作用,亟待建立描述相变棘轮行为(即峰值应变和谷值应变随着正相变和逆相变循环的进行不断累积)的循环本构模型.为此,基于已有的超弹性镍钛形状记忆合金在不同峰值应力下的单轴相变棘轮行为实验研究结果,在广义黏塑性框架下,对Graesser等提出的通过背应力非线性演化方程反映超弹性镍钛形状记忆合金超弹性行为的一维宏观唯像本构模型进行了拓展,考虑了正相变和逆相变过程中特征变量的差异及其随循环的演化,以非弹性应变的累积量为内变量引入了正相变开始应力、逆相变开始应力、相变应变和残余应变的演化方程,同时通过峰值应力与正相变完成应力的比值来确定演化方程中的相关系数,建立了描述超弹性镍钛合金单轴相变棘轮行为的本构模型.将模拟结果与对应的实验结果进行对比发现,建立的宏观唯像本构模型能够合理地描述超弹性镍钛形状记忆合金的单轴相变棘轮行为及其峰值应力依赖性,模型的预测结果和实验结果吻合得很好.     

Study on the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy based on a new crystal plasticity constitutive model

In this paper, a crystal plasticity based constitutive model (Yu et al., 2013) is extended to describe the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy by considering the internal heat production. Two sources of internal heat productions are included in the proposed model, i.e., the mechanical dissipations of inelastic deformation and the transformation latent heat in the NiTi shape memory alloy. With an assumption of uniform temperature field in the alloy specimen, a simplified evolution law of temperature field is obtained by the first law of thermodynamics and the heat boundary conditions. An explicit scale-transition rule is adopted to extend the proposed single crystal model to the polycrystalline version. The capability of the extended polycrystalline model to describe the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy is verified by comparing the predictions with the corresponding experimental ones. The comparison demonstrates that the proposed constitutive model considering the internal heat production predicts the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy fairly well.     

A new constitutive analysis of hexagonal close-packed metal in equal channel angular pressing by crystal plasticity finite element method

Most of hexagonal close-packed (HCP) metals are lightweight metals. With the increasing application of light metal products, the production of light metal is increasingly attracting the attentions of researchers worldwide. To obtain a better understanding of the deformation mechanism of HCP metals (especially for Mg and its alloys), a new constitutive analysis was carried out based on previous research. In this study, combining the theories of strain gradient and continuum mechanics, the equal channel angular pressing process is analyzed and a HCP crystal plasticity constitutive model is developed especially for Mg and its alloys. The influence of elevated temperature on the deformation mechanism of the Mg alloy (slip and twin) is novelly introduced into a crystal plasticity constitutive model. The solution for the new developed constitutive model is established on the basis of the Lagrangian iterations and Newton Raphson simplification.     

A three-invariant cap model with isotropic–kinematic hardening rule and associated plasticity for granular materials

In this paper, a three-invariant cap model is developed for the isotropic–kinematic hardening and associated plasticity of granular materials. The model is based on the concepts of elasticity and plasticity theories together with an associated flow rule and a work hardening law for plastic deformations of granulars. The hardening rule is defined by its decomposition into the isotropic and kinematic material functions. The constitutive elasto-plastic matrix and its components are derived by using the definition of yield surface, material functions and non-linear elastic behavior, as function of hardening parameters. The model assessment and procedure for determination of material parameters are described. Finally, the applicability of proposed plasticity model is demonstrated in numerical simulation of several triaxial and confining pressure tests on different granular materials, including: wheat, rape, synthetic granulate and sand.     

A physically based model of temperature and strain rate dependent yield in BCC metals: Implementation into crystal plasticity

In this work, we develop a crystal plasticity finite element model (CP-FEM) that constitutively captures the temperature and strain rate dependent flow stresses in pure BCC refractory metals. This model is based on the kink-pair theory developed by Seeger (1981) and is calibrated to available data from single crystal experiments to produce accurate and convenient constitutive laws that are implemented into a BCC crystal plasticity model. The model is then used to predict temperature and strain rate dependent yield stresses of single and polycrystal BCC refractory metals (molybdenum, tantalum, tungsten and niobium) and compared with existing experimental data. To connect to larger length scales, classical continuum-scale constitutive models are fit to the CP-FEM predictions of polycrystal yield stresses. The results produced by this model, based on kink-pair theory and with origins in dislocation mechanics, show excellent agreement with the Mechanical Threshold Stress (MTS) model for temperature and strain-rate dependent flow. This framework provides a method to bridge multiple length scales in modeling the deformation of BCC metals.     

一类新的超弹性-循环塑性本构模型

目前,很多经典的超弹性-有限塑性本构模型已被提出,但由于超弹性理论中中间构型的引入使得随动硬化法则相对复杂,故多数文献均采用的是经典的Armstrong-Frederick(A-F)随动硬化法则.本文基于已有的本构理论,利用多机制过程的概念拓展了Lion塑性变形分解理论,明确提出了多重中间构型的概念,并在此基础上,对经典理论中客观性的定义进行了概念上的推广,使其更好地适用于超弹性本构理论分析,同时提出了一类新的超弹性-有限塑性本构模型.这类本构模型满足热动力学法则,且可融合多种小变形循环塑性理论中常用的随动硬化法则(如经典的A-F模型,Chaboche模型,Ohno-Wang(O-W)模型以及Karim-Ohno(K-O)模型等),使得小变形理论中背应力的加法分解性质及其演化的临界面阶跃特性在大变形领域中均有所体现,故本文提出的本构理论可看作是小变形循环塑性模型在大变形理论中的扩展.本文最后以K-O模型为例,对推荐模型进行了详细探讨,并与相应的次弹性模型进行了对比.      

织构可调塑性本构模型标定及其应用

提出了利用率相关晶体塑性模型标定织相可调本构模型的求解步骤,得出了一组依赖于晶粒间相互作用假设而独立于具体板材织构的本构相关系数.以此为基础再结合板材织构系数所得出的本构模型系数可避免出现屈服面非外凸的情形.利用所提求解步骤对在不同热处理条件下产生不同织构的AL5052铝合金板的深拉成形过程进行了有限元模拟.结果再现了典型织构在板材成形过程中所出现的塑性各向异性,从而表明求解步骤的可行性.     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

Creep,plasticity, and fatigue of single crystal superalloy

Single crystal components in gas turbine engines are subject to such extreme temperatures and stresses that life prediction becomes highly inaccurate resulting in components that can only be shown to meet their requirements through experience. Reliable life prediction methodologies are required both for design and life management. In order to address this issue we have developed a thermo-viscoplastic constitutive model for single crystal materials. Our incremental large strain formulation additively decomposes the inelastic strain rate into components along the octahedral and cubic slip planes. We have developed a crystallographic-based creep constitutive model able to predict sigmoidal creep behavior of Ni base superalloys. Inelastic shear rate along each slip system is expressed as a sum of a time dependent creep component and a rate independent plastic component. We develop a new robust, computationally efficient rate-independent crystal plasticity approach and combined it with creep flow rule calibrated for Ni-based superalloys. The transient variation of each of the inelastic components includes a back stress for kinematic hardening and latent hardening parameters to account for the stress evolution with inelastic strain as well as the evolution for dislocation densities. The complete formulation accurately predicts both monotonic and cyclic tests at different crystallographic orientations for constant and variable temperature conditions (low cycle fatigue (LCF) and thermo-mechanical fatigue (TMF) tests). Based on the test and modeling results we formulate a new life prediction criterion suitable for both LCF and TMF conditions.     

Thermomechanical behavior of shape memory alloy under complex loading conditions

The thermo-mechanical behavior of polycrystalline shape memory alloy (SMA) under multi-axial loading with varying temperature conditions has been studied by experiments. Recently the research has been extended theoretically and a mechanical model of polycrystalline SMA and the corresponding mesoscopic constitutive equations have been developed. The model presented in this paper is constructed on the basis of the crystal plasticity and the deformation mechanism of SMA. The variants in the crystal grains and the orientations of crystal grains in the polycrystal are considered in the proposed model; the constitutive equations are derived on the basis of the proposed model. The volume fraction of the martensite variants in the transformation process and the influence of the stress state on the transformation process are also considered. Some calculated results obtained by the constitutive equations are presented and compared with the experimental results. It is found that the deformation behavior of SMA under complex loading conditions can be well reproduced by the calculation of the constitutive equations.     

Mechanism-based strain gradient crystal plasticity—I. Theory

We have been developing the theory of mechanism-based strain gradient plasticity (MSG) to model size-dependent plastic deformation at micron and submicron length scales. The core idea has been to incorporate the concept of geometrically necessary dislocations into the continuum plastic constitutive laws via the Taylor hardening relation. Here we extend this effort to develop a mechanism-based strain gradient theory of crystal plasticity. In this theory, an effective density of geometrically necessary dislocations for a specific slip plane is introduced via a continuum analog of the Peach-Koehler force in dislocation theory and is incorporated into the plastic constitutive laws via the Taylor relation.