热弹性马氏体相变材料单晶体的细观力学统一本构模型

基于马氏体相变的晶体学理论和Hill Rice内变量本构理论 ,建立了热弹性马氏体相变材料单晶体的细观力学统一本构模型并对它进行了详细的讨论 .该本构模型能描述在复杂热力学加载条件下 ,热弹性马氏体相变材料微结构正向相变、反向相变以及重取向过程在单晶体中所表现出来的宏观本构特性 .理论预测与实验结果符合很好 .     

形状记忆合金相变过程三维大变形有限元模拟

形状记忆合金（SMA）一直被作为智能材料开发,并被用于阻尼器、促动器和智能传感器元件．形状记忆合金（SMA）的一项重要特性,是它具有恢复在机械加卸载周期下产生的大变形而不表现出永久变形的能力．该文旨在介绍一种由应力产生的相变且可以描述马氏体和奥氏体之间的超弹性滞回环现象本构方程．形状记忆合金的马氏体系数假设为应力偏张量的函数,因此形状记忆合金在相变过程中锁定体积．本构模型是在大变形有限元的基础上执行的,采用了现时构型Lagrange大变形算法．为了方便地使用Cauchy应力和线性应变本构关系,使用了与旋转无关的Jaumann应力增率计算应力．数值分析结果表明,相变引起的超弹性滞回环可以有效地通过该文提出的本构方程和大变形有限元模拟．     

计及相变与塑性的NiTi形状记忆合金循环伪弹性特性描述

结合NiTi形状记忆合金单轴循环变形试验研究结果,采用基于混合物理论的计及相变、重取向与塑性变形的形状记忆合金本构模型发展了相应的算法和程序.对NiTi形状记忆合金单轴循环变形行为进行了描述.通过试验结果与模拟结果的比较,验证了本构模型与算法的有效性.     

ZrO2相变多晶体塑性变形局部化行为的宏观—细观实验研究

本文首次综合运用高密度光栅、形貌仪以及激光Raman微探针技术对ZrO₂相变多晶体陶瓷材料的应力协助相变塑性行为进行了宏观—细观实验研究,发现了室温下材料受单轴拉伸和单轴压缩均匀应力以及受三点弯曲载荷时的塑性变形局部化行为,实验结果表明:相变塑性变形局部化以体膨胀剪切带的形式发生,宏观的变形局部化对应着微观上马氏体相变的局部化,这为进一步深入研究相变塑性局部化和相变塑性本构关系提供了重要的实验依据。     

保持时间对镍钛形状记忆合金单轴循环相变的影响

对镍钛形状记忆合金在不同保持时间下的循环变形行为进行了实验研究。结果表明:循环加载下,峰值和谷值载荷保持会促进材料持续发生相变和逆相变,峰值保持时间越长,峰值应变越大,耗散能越大;峰值保持时间对残余应变的演化影响不大;进而有谷值保持时间比没有谷值保持时间的峰值应变、残余应变和耗散能都大。发生在保持时间内的相变应变随循环周次的增加逐渐减小,随保持时间的增加而增加。当加载的峰值应力接近相变结束应力时,保持时间的增加对马氏体相变的促进作用相对微弱。     

CuNiAl形状记忆合金相变和裂纹形核及扩展的原位研究

采用扫描电子显微镜(SEM)和透射电镜(TEM)原位拉伸技术研究了形状记忆合金CuNiAl应力诱发马氏体相变以及它与裂纹形核、扩展的交互作用.结果表明,裂尖应力集中能诱发层错及不同形态的马氏体.在TEM中加载时,裂纹前方的马氏体能从一种形态转变为另一种形态,甚至逆变成母相.微裂纹可以在马氏体/母相界面以及两个马氏体的交汇处形核.当裂纹扩展一段距离,裂尖应力集中足够大时,可产生滑移带,这时微裂纹更容易沿滑移带形核.     

基于有限变形弹塑性模型模拟伪弹性合金全程变形行为

提出一个J2流的有限弹塑性本构方程来显式、全面地模拟了形状记忆合金(SMAs)在3个不同阶段加载并卸载所表现出来的应力-对数应变关系.这3个阶段包括变形完全恢复的伪弹性阶段、变形部分恢复的塑性阶段以及软化破坏阶段.该文的主要思想在于从实验数据的形函数出发,得到用形函数表达的多轴硬化函数,进而代入到本构方程,建立一个能模拟任意形状应力-对数应变关系,多轴有效的本构方程.该文方法的优势在于避免考虑微观到宏观的平均方法、相变条件等一系列复杂处理,大大减少了计算量.所得到的数值结果可以精确匹配实验数据.     

各向同性弹性损伤本构方程的一般形式

直接从不可逆热力学基本定律出发,推导出弹性各向同性损伤材料本构方程的一般形式,克服了由应变等效假设建立的经典损伤本构方程的缺陷,并阐明了两种各向同性弹性损伤模型(单标量模型与双标量模型)之间的联系.研究表明,采用单标量描述的损伤模型,在材料损伤本构方程中含有两个“损伤效应函数”,反映损伤对于两个弹性常数的不同影响.应变等效假设给出的损伤本构方程,是该文方程的一个近似形式,常常不能满意地描述实际材料的损伤行为.     

一种显式子步应力点积分算法及其在SMA数值模拟中的应用

形状记忆合金（shape memory alloys,简称SMA）具有复杂的热力本构关系,为了模拟SMA及其组合结构复杂的受力和变形行为,在数值模拟中需要采用可靠且高效的应力点积分算法．隐式应力点回映算法已经成功应用于形状记忆合金的数值模拟,但在复杂加载条件下,荷载增量较大时有可能导致整体非线性迭代求解不收敛．推广了局部误差控制的显式子步积分算法,首次将其应用于形状记忆合金及其组合结构这类热力相变问题的应力点积分,并通过数值算例对所提算法和隐式应力点回映算法进行了比较．数值结果表明:对于大规模数值模拟和计算,整体子步步数决定着总体计算时间;所提出的修正Euler自动子步方案可以有效减少整体子步步数,在保证相同计算精度的前提下能够大幅提高有限元计算效率,因而更适合大规模形状记忆合金智能结构的数值模拟.     

关于损伤张量的阶次

本文首先讨论了较为广泛的连续介质材料的应力变形本构关系,得到了通常以泛函表示的应力变形本构关系的张量表达式.以此为基础,研究了各向异性材料各向异性损伤时,无论从连续介质力学模型出发还是从缺陷模型出发,描述损伤的张量都存在最高阶次的限制;指出了在什么条件下,损伤变量可用低于最高阶次的张量来描述.     

Simulation of pseudo-plasticity in shape-memory-alloys

The name shape memory originates from the material's capability to recover its original shape after an apparent plastic deformation. The secret of this property lies in the specific microstructure. During mechanical loading, alloys of this particular kind change their crystallographic structure from randomly orientated martensite to ordered martensite. With austenite as high-temperature inter-state induced by heat supply, a recovery from the ordered to the unordered martensite is possible. This is accompanied by a macroscopic "healing" process. We apply our material model for shape-memory alloys to this special property and present numerical results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress and deformation states in the annulus made from shape memory material

The contribution deals with the stress and deformation states in an annulus made of shape memory material (SMM). The loading‐unloading process is going on at constant temperature, which is below temperature M_f (martensite finish temperature). The research is focused on the determination of the stress and deformation states in the annulus after loading and unloading process. These results are necessary for treating process of constrained recovery in shape memory annulus. The real loading‐unloading function in the stress‐strain coordinate system of shape memory material (Ni–Ti–Cu) is included in the mathematical model.     

A second-order conservational difference scheme for the one-dimensional model of martensitic transformations with nonlinear boundary conditions

In this work, the one-dimensional equilibrium model of martensitic transformations with nonlinear boundary conditions is considered. Some a prior energy identities are obtained by a rigor mathematical analysis. A second-order conservational difference scheme is proposed and solved by the iterative method. Its efficient implement is carried out and the fixed and the random initial input are discussed. Moreover, a convergence criterion based on the total free energy and the Landau energies are proposed, which can be also used to other iterative method. The solution with nonlinear boundary conditions is obtained. The simulation of the surface martensite, the thermoelastic (shape memory) and the nonthermoelastic martensite formations and the autocatalysis are performed.     

Micro‐Mechanical Modelling of the Constitutive Behaviour of NiTi Shape Memory Alloys

The superelasticity and shape memory effect in NiTi alloys are examined on the basis of micromechanics within the energy minimization framework. We describe the behaviour of polycrystalline shape‐memory alloys via orientation‐distribution of the various martensite‐variants (domains) present in the material. Stress‐strain curves are presented and special attention is payed to the volume fraction of martensite for specific NiTi alloys (Nitinol) specimen under uniaxial tension. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical model for vibration damping resulting from the first-order phase transformations

A numerical model is constructed for modelling macroscale damping effects induced by the first-order martensite phase transformations in a shape memory alloy rod. The model is constructed on the basis of the modified Landau–Ginzburg theory that couples nonlinear mechanical and thermal fields. The free energy function for the model is constructed as a double well function at low temperature, such that the external energy can be absorbed during the phase transformation and converted into thermal form. The Chebyshev spectral methods are employed together with backward differentiation for the numerical analysis of the problem. Computational experiments performed for different vibration energies demonstrate the importance of taking into account damping effects induced by phase transformations.     

Modeling of deformation-induced phase transformation during very high cycle fatigue (VHCF) using the boundary element method

A microstructural simulation model is proposed which accounts for damage accumulation in shear bands and deformation-induced martensite formation in a metastable austenitic stainless steel (AISI304). The model is numerically solved using the two-dimensional (2-D) boundary element method. By using this method, sliding displacements can be directly evaluated in shear bands and austenite grains as well as generated martensite domains with their individual mechanical properties and shape deformation can be considered. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Functional Fatigue in polycrystalline Shape Memory Alloys

Shape memory alloys show the well known effect of pseudo-elasticity associated with the formation of two stress plateaus in the stress/strain diagram for tension tests. Due to cyclic loading, the stress plateaus decrease with every load cycle, particularly the upper one. This important effect of functional fatigue results from plastic deformations that are produced during solid-solid phase transformations between the austenitic and martensitic state. Outgoing from a polycrystalline approach for shape memory alloys we develop a micromechanical material model that is based on the Principle of the Minimum of the Dissipation Potential and predicts the evolution of plastic strains. Therefore, only a small number of material parameters is necessary and additionally, only a few assumptions are sufficient to model the effect of functional fatigue. We present yield functions as well as evolution equations for the volume fractions of austenite and martensite, and the plastic strains. Furthermore, we show an exemplary calculation for Nickel Titanium and compare it with experimental measurements to demonstrate the ability of our model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques

In this work, an incremental energy minimization technique is proposed to simulate the magnetomechanically-coupled, nonlinear, anisotropic and hysteretic response of single crystalline magnetic shape memory alloys (MSMA). The model captures the three key physical mechanisms that cause this characteristic behavior, namely the field- or stress-induced martensite variant reorientation (twin boundary motion), magnetic domain wall motion, and local magnetization rotation, through an (incremental) energy minimizing evolution of internal state variables. Representative numerical response predictions are presented, compared to experimental observations, and discussed with respect to the associated microstructure evolution. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The structure-analytic theory of memory of shape

For media undergoing martensite transformations of first kind we give the data of analytic computations of several functional-mechanic properties interpretable as memory of shape. For definiteness and comparison of results these properties are computed in the case of a uniaxial load.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 34–42.