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。     

一种考虑应变幅值和应变速率影响的超弹性SMA宏观唯象本构模型

为充分发挥超弹性SMA的减振特性,奠定应用理论基础,对SMA丝进行了力学性能试验研究,探讨了循环训练次数、应变幅值和应变速率对SMA滞回性能的影响。基于SMA丝力学性能测试结果,在广义粘塑性框架下,对Graesser宏观唯象本构模型进行了拓展。新模型考虑了马氏体正/逆相变过程中特征参量的差异以及大应变幅值下的马氏体硬化特性,并通过引入的内变量演化方程,描述了应变幅值和应变速率对超弹性SMA滞回性能的影响;通过Matlab/Simulink模块对超弹性SMA滞回曲线进行了模拟,并将预测结果和试验结果进行了对比。结果表明:所建立的应变幅值-应变速率相关型SMA宏观唯象本构模型可较为精确地描述SMA在应力诱发相变过程中的超弹性力学行为,同时可反映应变速率和应变幅值对SMA滞回性能的影响。     

形状记忆合金的本构模型

借助Tanaka用一维形核动力学方程导出的指数形式的相变分数,建立了一个新的形状记忆合金本构模型,提出承不同相变条件下可恢复形状记忆应变的表达式,考虑了材料在变形过程中马氏体的对优取向作用,克服了Tanaka系列模型不能描述材料处于完全马氏体状态时的力学行为的缺点,本模型比现有的形状记忆合金本构模型简单,其正确怀已得到实验的检验。     

基于不可逆热力学的Ni-Ti合金动态本构模型及其有限元实现

为了准确描述Ni-Ti形状记忆合金在高应变率下的动态压缩力学行为,基于不可逆热力学理论框架假定了两个内变量表征Ni-Ti合金应力诱发马氏体相变与塑性屈服的不可逆变形过程,分别推导了马氏体相变与塑性屈服演化规律的主控方程,构建了Ni-Ti合金的三维动态本构模型。根据材料单轴动态压缩实验的应力-应变曲线并采用最小二乘法对本构参数进行了优化识别,然后采用应力补偿更新算法,通过隐式用户子程序接口UMAT将动态本构模型嵌入ABAQUS有限元软件,实现了Ni-Ti合金在高应变率下动态压缩力学行为的数值模拟。通过比对发现,模拟结果与实验数据吻合良好,验证了动态本构模型与UMAT子程序的准确性。本工作为Ni-Ti合金在高速冲击、切削等极端条件下的工程应用奠定了基础。     

考虑磁场影响的磁性形状记忆合金分段线性化超弹性本构模型研究

磁性形状记忆合金(Magnetic Shape Memory Alloy,MSMA)作为一种新型智能材料,同传统温控形状记忆合金一样具有形状记忆效应和超弹性效应。现有的MSMA本构模型大多存在理论性强、形式繁杂、参数较多等问题,不利于实际工程应用。为此,该文借助线性化方法,建立了超弹性MSMA分段线性化应力-应变关系;引入应力择优取向马氏体变体体积分数作为内变量,基于塑性理论框架,构建了MSMA分段线性化超弹性本构模型;提出了描述临界应力与环境磁场关系的Logistic关系函数,并基于试验数据拟合了关键参数;利用所建立的本构模型对考虑磁场影响下的MSMA超弹性进行了数值模拟,并从滞回曲线形状和滞回耗能两个方面与试验结果对比。结果表明:所提出的临界应力与环境磁场关系函数拟合优度可达0.993;材料本构模型预测曲线与试验结果较为接近,理论耗能能力与试验结果误差平均为11.9%。因此,模型能够较为准确地模拟MSMA的超弹性变形过程和耗能能力,为预测考虑磁场影响的MSMA超弹性特性提供了一种简便方法。     

外加载荷对热弹性马氏体正-逆相变影响机制的相场模拟研究

本工作建立了一种新的马氏体逆相变的相场模型,以Cu-Al-Ni合金为例,研究了热弹性马氏体正相变和逆相变的演化规律,揭示了热弹性马氏体的形状记忆效应。同时模拟了拉伸释放弹性应变能这种机制对热弹性马氏体相变和热弹性马氏体逆相变的作用,研究了外加载荷对马氏体逆相变温度As的影响。模拟结果表明：应变能是形状记忆合金马氏体相变的阻力,是其逆相变的驱动力。在马氏体正相变过程中,拉伸载荷释放了应变能,降低了相变阻力,从而对马氏体相变起促进作用;在马氏体的逆相变过程中,由于拉伸载荷降低了马氏体所储存的应变能,因而降低了逆相变过程的驱动力,使合金逆相变As温度升高,进而提高了热弹性马氏体的低温稳定性。模拟结果与实验结果相一致。     

SMA增强复合材料力学特性的细观力学模型

基于细观力学的理论 , 将 SMA增强复合材料视为三相等效系统进行分析 , 即基体相、 奥氏体相和马氏体相 ; 求解了 SMA增强复合材料的有效热膨胀系数和有效相变应变系数的一般表达式 , 该表达式适用于各种形状的纤维增强复合材料。在整个相变和逆相变过程中 , 奥氏体相和马氏体相都表现为弹性特性 , 避免了传统方法的强非线性问题。该模型计算过程简单 , 同时还考虑了奥氏体、 马氏体和基体间的相互作用 , 理论分析更接近实际。并分析了纤维的含量、 形状和尺寸等因素对宏观模量的影响 , 通过比较可知 , 所得结果可靠 , 为 SMA增强复合材料的设计和使用提供理论依据。      

基于SMP破坏准则的土体弹塑性动力本构模型

利用土体的塑性流动理论,提出了用于描述饱和砂土动力反应性质的弹塑性本构模型。土体总的变形由三部分组成:即弹性应变、与体积屈服机制相关的塑性应变和与剪切屈服机制相关的塑性应变。土体在初始加载与卸载和重新加载阶段性质的差别通过采用不同的模型参数加以反映。该模型能够较为准确地描述饱和砂土在单调加载和循环加载条件下的反应性质。     

马氏体相变诱发塑性量化表征及合金元素的影响

利用亚稳奥氏体不锈钢低温拉伸曲线的特点,提出了表征相变诱发塑性增量的量化指标：单位体积分数的马氏体诱发的平均塑性增量D及本征塑性量D1,且D近似等于D1,对三种材料的相变诱发塑性的研究表明：钢中碳含量的增加使D值降低,降低层错能的合金元素有利于D的增加,而应变速率对D不产生明显的影响。     

混凝土坝地震动力损伤分析

基于塑性损伤本构理论,将损伤变量作为内变量,在Drucker-Prager本构模型中引入损伤变量,考虑材料损伤引起的材料劲度的退化,基于非关联流动法则计算材料的塑性应变,根据材料的有效塑性应变计算损伤量,考虑到张开裂缝闭合时材料弹性劲度的恢复,推导了考虑塑性损伤的混凝土动态本构关系,并给出了内变量的计算步骤和动力方程的迭代格式。最后利用建立的动态本构模型对Koyna重力坝进行了非线性地震响应时程分析,并给出了关键时刻坝体最大受拉损伤分布,结果表明在坝颈和坝基处出现了较大的损伤,坝颈处的损伤最终形成由下游向上游的开裂破坏,这与该坝的实际震害较为一致。     

Micro-thermomechanical constitutive model of transformation induced plasticity and its application on armour steel

Based on the crystallographic theory of martensitic transformation and internal variable constitutive theory, a micromechanical constitutive model of martensitic transformation induced plasticity was developed. Plastic strains of product and parent phases as well as the volume fraction of each martensitic variant were considered as internal variables describing the microstructure evolution. The plasticity flow both in austenite and martensitic variants domain is described by J₂ flow theory. The thermodynamic driving force acting on these internal variables was obtained through the determination of the intrinsic dissipation due to plastic flow and the growth of martensitic domains. The evolution laws of the internal variables are derived, furthermore macroscopic response due to the change of internal variables is obtained. Thermomechanical behavior of armour steel under uniaxial loading was tested which showed a good agreement with experimental results.     

Thermodynamic conditions for stability in materials with rate-independent dissipation

A distinctive feature of the examined class of solids is that a part of the entropy production is due to rate-independent dissipation, as in models of plasticity, damage or martensitic transformations. The standard condition for thermodynamic stability is shown to be too restrictive for such solids and, therefore, an extended condition for stability of equilibrium is developed. The classical thermodynamic theory of irreversible processes is used along with the internal variable approach, with the emphasis on the macroscopic effects of micro-scale instabilities in the presence of two different scales of time. Specific conditions for material stability against internal structural rearrangements under deformation-sensitive loading are derived within the incremental constitutive framework of multi-mode inelasticity. Application to spontaneous formation of deformation bands in a continuum is presented. Conditions for stability or instability of a quasi-static process induced by varying loading are given under additional constitutive postulates of normality and symmetry. As illustration of the theory, the stability of equilibrium or a deformation path under uniaxial tension is analysed for a class of inelastic constitutive laws for a metal crystal deformed plastically by multi-slip or undergoing stress-induced martensitic transformation.     

Perspective in Development of Shape Memory Materials Associated with Martensitic Transformation

By consideration of the characteristics of martensitic transformation and the derivation from the application of the group theory to martensitic transformation, it may be concluded that the shape memory effect (SME) can be attained in materials through a martensitic transformation and its reverse transformation. only when there forms single or nearly single variant of martensite, with an absence of the factors causing the generation of the resistance against SME. on this principle, various shape memory materials including nonferrous alloys. iron-based alloys and ceramics containjng zirconia are expected to be further developed. A criterion for thermoelastic martensitic transformation is presented, Factors which may act as the resistance against SME in various materials are briefly described     

Stress induced martensite transformation texture in AISI 304 austenitic stainless steel

Abstract

The phenomenological theory of martensitic transformation was applied to a tension induced martensitic transformation in an AISI 304 austenitic stainless steel in order to estimate the transformation texture. Input data were obtained from the published literature. Calculated pole figures were constructed assuming a variant selection process based on Patel and Cohen’s theory, which emphasises that a mechanical component of free energy is the driving force for martensitic transformation at temperatures above martensite start M_s. The results showed a remarkably good match between the calculated and published measured data.     

磁场对Ni51.5Mn24Ga24.5单晶马氏体相变的影响

分析了Ni51.5Mn24Ga24.5单晶样品在不同磁场下的马氏体相变温度和热滞后温度,并基于相界摩擦理论计算了样品在不同磁场下马氏体相变过程中相界摩擦所产生的能耗(FHr).结果表明,对于不同磁场下相界推移所产生的能耗与实验观察到的热滞后温度变化规律基本一致,说明了相界摩擦理论较好地解释了Ni-Mn-Ga合金在外加磁场情况下相变过程中的热力学问题.     

A multi-dimensional constitutive model for shape memory alloys

This paper presents a multi-dimensional thermomechanical constitutive model for shape memory alloys (SMAs). This constitutive relation is based upon a combination of both micromechanics and macromechanics. The martensite fraction is introduced as a variable in this model to reflect the martensitic transformation that determines the unique characteristics of shape memory alloys. This constitutive relation can be used to study the complex behavior associated with 2-D and 3-D SMA structures. A simple example using this constitutive model is also presented, which reveals a new and interesting phenomenon of 3-D SMA structures.     

SMA纤维混杂层合梁的振动分析

提出一类形状记忆合金(SMA)纤维混杂层合梁的数学模型。采用多胞模型、形状记忆合金一维本构关系分析方法,同时考虑铁木辛柯剪切和马氏体相变的影响。目的是为了更进一步了解层合梁的振动控制。SMA纤维用来作为驱动器,它能够改变弹性模量和回复力,以此改变梁的频率。分析了SMA纤维含量、铺设角度和横向剪切变形的影响。结果表明,通过激活形状记忆合金纤维及改变初始变形,对层合梁的自振频率有很强的控制和调节能力。     

Thermodynamic Analysis on Relation Between T0 and σM in a Ti44Ni47Nb9 Shape Memory Alloy

The effect of heat treatment on martensitic transformation behavior has been investigated in Ti44Ni47Nb9 alloy.The relation between transformation temperatures and critical stress of stress induced martensitic transformation is interpreted in terms of thermodynamic theory.It is shown that the decrease in transformation temperature in specimens of slow cooling rate or low temperature aging after solution heat treatment results from the changes of Ni/Ti ratio in the matrix.The increase of critical stress of stress induced martensitic transformation is a consequence of the decrease of transformation temperatures.     

铁基合金中马氏体形核动力学探讨

根据马氏体相变的经典形核理论,重新估算了铁基合工中马氏体均匀形核激活能,研究了激活能与界面能和相变驱动力的关系。结果表明,热激活形核具有很低的形核激活能,热激活能形核动力学与马氏体形核动力学实验研究结果一致,在动力学研究的基础上,提出了马氏体相变的形核机制,在形核机制中,除了热激活菜核,还考虑了应力对马氏体形核的作用,特别是在低温时由于急应内应力对形核的贡献。     

Numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm

The numerical simulation of structures made of shape memory materials is of increasing interest in different fields. Among others, the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge. In such practical applications the pseudoelastic effect as well as the one‐way and two‐way shape memory effects are utilized. These material properties are caused by martensitic phase transitions between austenite and martensite. In the present contribution, a recently proposed constitutive theory is numerically treated in the context of the finite element method. This constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys. For the numerical integration of the evolution equations, the backward Euler method is applied. In spite of the complexity of the constitutive theory, it is shown that an improved integration procedure can be formulated, which merely involves the solution of three non‐linear equations for three scalar‐valued unknown variables. Numerical examples show the capability of the proposed model and the improved integration algorithm. Copyright © 2006 John Wiley & Sons, Ltd.