基于孔洞体胞模型铸造镁合金ML308的本构方程

铸造镁合金不可避免地包含许多微孔洞,这些微孔洞在材料的后续加工及服役过程中将发生演化,并对材料的力学行为产生重要影响.基于球形孔洞体胞模型,提出微孔洞长大及形核方程,它们构成微孔洞的演化方程.根据孔洞演化将造成材料性质弱化的物理机制,将微孔洞演化以弱化函数的形式引入到非经典弹塑性本构方程,得到考虑孔洞演化的铸造镁合金弹塑性本构方程.发展与本构方程相应的有限元数值分析程序,用其模拟了铸造镁合金ML308的微孔洞演化及力学行为,计算结果与实验结果符合较好. 关键词： 铸造镁合金 孔洞体胞模型 孔洞演化方程 本构方程     

泡沫铝柱壳对药柱水下爆炸压力场影响的数值研究

基于流体弹塑性模型,建立了描述泡沫铝在爆炸载荷下的冲击响应方程;采用Lagrange差分格式,在均匀网格上对方程进行了离散;编写数值计算程序,进行了药柱水下爆炸的一维数值计算,重点考虑了泡沫铝对水中爆炸冲击波分布的影响。结果表明,数值计算结果与实验数据、LS-DYNA模拟结果基本吻合,证明所建立的泡沫铝流体弹塑性本构方程可以用来描述泡沫铝的冲击响应行为,且泡沫铝对水中爆炸冲击波压力场的影响显著。     

冲击载荷下线性硬化材料中球面应力波场的理论计算方法研究

基于线性硬化塑性本构模型,建立了冲击载荷作用下弹塑性球面应力波场的理论求解方法.首先,分析了冲击载荷卸载速率对球面应力波传播的影响,得到了3种不同类型的应力波传播图像.在此基础上,建立了弹性阶段、塑性加载阶段以及卸载阶段球面波动方程的理论求解方法,给出了质点位移、质点速度、应力和应变等物理量的计算方案.与已有理论方法相比,该方法考虑了不同载荷卸载速率条件下应力波的不同传播情况,并且给出了卸载阶段应力波参量计算方法,具有更广的适用范围.利用上述方法计算了恒定冲击载荷和不同指数衰减冲击载荷作用下弹塑性球面应力波场参量,在弹性阶段和塑性加载阶段,理论计算得到的物理量与已有理论方法和数值模拟结果基本吻合,在卸载阶段,已有理论方法不再适用,而本文理论计算得到的物理量与数值模拟结果基本吻合,验证了该理论方法的正确性.     

高压、高应变率与低压、高应变率实验的本构关联性

 指出Johnson-Cook（J-C）、Zerilli-Armstrong（Z-A）、Bodner-Parton（B-P）本构方程在一定条件下的适用性,表明对于低压、高应变率实验,单一曲线假定似乎可以采用。通过等效应力、等效应变,可以将不同应力状态下的流动应力函数采用统一的方程描述。然而,这些本构方程的确立,并不包括平面冲击波实验。对适合于平面冲击波实验的Steinberg-Cochran-Guinan（SCG）本构方程,讨论了其方程中所包含的高压与高应变率耦合效应。指出,以剪切模量度量的流动应力具有应变率相关性。基于温度效应的新发现以及直接测量平面冲击波流动应力的新进展,分别用J-C本构及SCG本构方程估算了钨材料在高压、高应变率加载下的流动应力。结果表明,采用J-C本构估算的流动应力仅在压力为10 GPa以下才能与实验数据相近,当压力高于10 GPa时,流动应力只能采用SCG本构估算。也指出了高压、高应变率本构方程与低压、高应变率本构方程所对应的不同物理背景。     

Ni53.2Mn22.6Ga24.2单晶的两步热弹性马氏体相变及其应力应变特性

对具有两步完全热弹性的Ni_53.2Mn_22.6Ga_24.2单晶的物性采用多种测量手段进行了表征,特别研究了不同温度下的应力-应变特性.研究表明,热诱发的中间马氏体相变应变远大于马氏体相变应变.在较低的形变温度下,沿单晶母相［001］方向的压应力诱发的是两步马氏体相变,材料表现出赝弹性;在较高的形变温度下,只能观察到一步马氏体相变,材料展现出完全超弹性特性.此外,利用热力学理论分别计算了诱发马氏体相变和中间马氏体相变的临界应力与形变温度的关系,与实验测量得到的结果相符. 关键词： 马氏体相变 形状记忆效应 应变 超弹性     

基于温度与应变率相互耦合的泡沫铝本构关系

根据分离式Hopkinson压杆实验以及准静态实验得到的泡沫铝材料在不同温度以及不同应变率下的应力-应变曲线,分析了泡沫铝本构方程中温度效应与应变率效应之间的耦合关系,即温度越高,泡沫铝的应变率效应越显著。基于Sherwood和Frost提出的泡沫材料本构关系框架,对常温下的应变率敏感系数进行了温度项修正,修正后的本构方程在高温高应变率下与实验结果具有较好的一致性。最终得到泡沫铝在一定密度范围内包含温度项、应变率项较为完备的本构方程。     

准等熵压缩下金属钽的屈服强度分析

 为分析固体材料的准等熵压缩实验数据,引入了率相关本构方程和流体弹塑性模型,建立了考虑材料强度效应的反积分数据处理方法。利用CQ-1.5磁压驱动装置中多晶钽的准等熵压缩实验数据,对钽的屈服强度和流应力进行了反积分数值模拟和分析,计算了钽的拉格朗日声速和应变率分布情况。得到了钽在准等熵压缩过程中样品内部及加载面上压力和速度的分布及演变规律,获得了30 GPa压力下钽的准等熵屈服强度约为1.85 GPa,准等熵弹性屈服极限约为2.9 GPa。此外,计算得到了与Sandia实验室数据高度吻合的应力-应变曲线和准等熵p-V参考线。     

HMX晶体热致相变对损伤的影响

HMX基PBX炸药混合体系中炸药晶体在发生高温熔化和分解反应之前，会率先发生非均匀热膨胀和固相晶型转变，使材料的力学性能和安全性能发生突变。为探究HMX晶体的热致相变对材料内部损伤演化的影响机制，发展了考虑HMX晶体热膨胀和相变等变形机制的热力耦合晶体本构模型，从力学角度揭示了黏结剂包覆HMX晶体相变对体积变形、应力状态以及裂纹成核演化过程的影响机理，量化分析了升温速率对材料相变和裂纹损伤状态的影响规律。结果表明：随着加载温度升高，HMX晶体的热膨胀和β→δ相变导致体积增大，晶体内部形成拉伸应力状态，同时晶体与黏结剂相互挤压形成的局部压剪作用使晶体内部出现裂纹成核和扩展现象。相变温度附近HMX晶体内部裂纹成核和扩展数量显著增加，晶体内部发生不可逆损伤。外界升温速率对晶体内部裂纹形核扩展与损伤造成显著影响，较高的升温速率会加大晶体损伤程度，增加炸药内潜在热点源及意外点火风险。     

纯铁相变和层裂损伤的数值模拟

基于Hayes多相状态方程、非平衡相变速率模型、非平衡损伤演化模型和含损伤的本构关系,建立了同时考虑相变和损伤的数值模拟方法。利用该方法对纯铁的对称碰撞实验进行了数值模拟,分析了纯铁的相变和层裂损伤的相互作用。结果表明,纯铁材料中发生相变时,等厚样品中才会发生层裂,并且数值计算的样品自由面速度、层裂位置与实验结果吻合。     

固定温度界面对相变波传播规律的影响

冲击载荷作用下,相变波的传播及相互作用是一热力耦合过程。采用理论和实验相结合的方法研究了固定温度界面对相变波传播特性的影响。首先基于形状记忆本构模型和一维特征线理论分析了各类间断面和温度界面的基本相互作用规律,发现温度界面对相变波的作用与相变波强度及界面两侧温度的相对高低有关;然后进行了相变波在具有固定温度界面的形状记忆TiNi杆中的传播实验,并实时测量了相变波传播过程中的温度变化。实验结果与理论分析基本一致,冲击载荷作用下相变波不仅是物质间断面,还是移动的温度界面。     

A macro-mechanical constitutive model of shape memory alloys

It is of practical interest to establish a precise constitutive model which includes the equations describing the phase transformation behaviors and thermo-mechanical processes of shape memory alloy (SMA). The microscopic mechanism of super elasticity and shape memory effect of SMA is explained based on the concept of shape memory factor defined by the author of this paper. The conventional super elasticity and shape memory effect of SMA are further unified as shape memory effect. Shape memory factor is redefined in order to make clear its physical meaning. A new shape memory evolution equation is developed to predict the phase transformation behaviors of SMA based on the differential relationship between martensitic volume fraction and phase transformation free energy and the results of DSC test. It overcomes the limitations that the previous shape memory evolution equations or phase transformation equations fail to express the influences of the phase transformation peak temperatures on the phase transformation behaviors and the transformation from twinned martensite to detwinned martensite occurring in SMA. A new macro-mechanical constitutive equation is established to predict the thermo-mechanical processes realizing the shape memory effect of SMA from the expression of Gibbs free energy. It is expanded from one-dimension to three-dimension with assuming SMA as isotropic material. All material constants in the new constitutive equation can be determined from macroscopic experiments, which makes it more easily used in practical applications. Supported by the National Natural Science Foundation of China (Grant No. 95505010), the National High Technology Research and Development Program of China (Grant No. 2006AA03Z109), the China Postdoctoral Science Foundation (Grant No. 20080430933), the Open Foundation of Institute of Engineering Mechanics of National Seism Bureau of China (Grant No. 2007B02), and the Harbin Talent Foundation of Scientific and Technical Innovation (Grant No. RC2009QN-017046)     

Residual Symmetry of the Alice-Bob Modified Korteweg-de Vries Equation

Starting from the truncated Painlev′e expansion, the residual symmetry of the Alice-Bob modified Kortewegde Vries(AB-mKdV) equation is derived. The residual symmetry is localized and the AB-mKdV equation is transformed into an enlarged system by introducing one new variable. Based on Lie's first theorem, the finite transformation is obtained from the localized residual symmetry. Further, considering the linear superposition of multiple residual symmetries gives rises to N-th B?cklund transformation in the form of the determinant. Moreover, the P_sT_d(the shifted parity and delayed time reversal) symmetric exact solutions(including invariant solution, breaking solution and breaking interaction solution) of AB-mKdV equation are presented and two classes of interaction solutions are depicted by using the particular functions with numerical simulation.     

Diffusion-controlled transformation plasticity of steel under externally applied stress

The transformation plasticity of steel during phase transformation under external stress was modelled on a migrating interface diffusion mechanism. Atomic diffusion along the migrating phase interface is assumed to cause transformation plasticity by an accelerated Coble creep. A creep equation on transformation plasticity is derived as a function of transformation rate, temperature and externally applied stress. Predictions are compared with dilatometric measurements during the austenite-to-ferrite and ferrite-to-austenite transformation of steel under various levels of uniaxial compressive stress. Good agreement was found between the calculated and experimental transformation strain. The model proposed also successfully describes the thermally activated behaviour of the transformation strain. The evaluated effective diffusion coefficients on the migrating interface are three to four orders of magnitude larger than those reported for stationary boundaries.     

关于相变本构关系的一个一维模型

 以一含缺陷的一维杆模型模拟实际材料的相变得到了率相关相变本构关系。该本构预测的硫化镉（CdS）晶体的冲击相变波形,除了前驱波后的松弛沟外,在主要特征方面能很好地描述实验波形。预测的波形在形态上与Fe和锑化铟（InSb）的相变波形比较接近,说明这种本构可适合于更广泛的情况。     

Phase transitions in shape memory alloys: A non-isothermal Ginzburg–Landau model

We propose a model to describe non-isothermal transitions from the austenite to the martensite phase occurring in shape memory materials. The phenomenon is set in the context of the Ginzburg–Landau theory of phase transitions, postulating a free energy depending on the temperature, the stress and the order parameter. In the one-dimensional case, when only two martensitic variants are involved and stress and deformation have a fixed direction, our choice of free energy allows us to deduce a phase diagram describing the main features of a typical SMA. The Ginzburg–Landau equation ruling the evolution of the order parameter is coupled with the equations of thermoelasticity by assuming a constitutive equation relating stress, strain and order parameter. The consistency of the model with the second law of Thermodynamics in the form of the Clausius–Duhem inequality is proved. Finally a possible generalization to a three-dimensional model is proposed, by introducing a tensor-valued order parameter.     

Transient deformation of thin metal sheets during pulsed laser forming

The transient deformation of thin grade 304 stainless steel metal sheets heated by a single pulse of a CO₂ laser beam is simulated in this paper. The laser beam is assumed to be line-shaped and the problem is treated as three-dimensional thermo-elastoplastic. The temperature field, deformation pattern, stress–strain states and the residual stress distribution of the specimens have been calculated numerically and the transient response of the bending angle has been validated by experiments. Good agreement has been obtained between the numerical simulation and the experiments under various operating conditions. The numerical study reveals that a high temperature gradient exists for a positive bending angle and a low one for a negative angle. It transpires that the mechanisms of pulsed laser forming are dependent mainly upon the laser power, the heating time, the clamping arrangement, as well as the geometry, the thermal properties and the original stress states of the specimen.     

Residual stress delaying phase transformation in Y-TZP bio-restorations

Engineering favorable residual stress for the complex geometry of bi-layer porcelain-zirconia crowns potentially prevents crack initiation and improves the mechanical performance and lifetime of the dental restoration. In addition to external load, the stress field depends on initial residual stress before loading. Residual stress is the result of factors such as the thermal expansion mismatch of layers and compliance anisotropy of zirconia grains in the process of sintering and cooling. Stress induced phase transformation in zirconia extensively relaxes the residual stress and changes the stress state. The objective of this study is to investigate the coupling between tetragonal to monoclinic phase transformations and residual stress. Residual stress, on the surface of the sectioned single load to failure crown, at 23 points starting from the pure tetragonal and ending at a fully monoclinic region were measured using the micro X-ray diffraction sin² ψ method. An important observation is the significant range in measured residual stress from a compressive stress of ?400?MPa up to tensile stress of 400?MPa and up to 100% tetragonal to monoclinic phase transformation.     

内应力对Mn2NiGa铁磁形状记忆合金的结构、相变和磁性能的影响

通过施加压应力的方法,在铁磁形状记忆合金Mn₂NiGa中引入残留内应力,研究了内应力对 Mn₂NiGa材料的结构、相变和磁性能的影响.研究发现,加压过程使材料发生了塑性形变,在材料内部引入了大量的位错缺陷.卸载后保留的位错缺陷在材料中造成了残留的内应力,导致了马氏体相变温度大幅度提高, 使原本室温下的母相转变成了马氏体相.测量到导致样品转变成马氏体的阈值压应力为1.0 GPa.加压形成的马氏体中的残留内应力将矫顽力从低于50 Oe提高到350 Oe.残留内应力在730 K的热处理中由于位错缺陷的消失而得以消除,样品实现了马氏体逆相变.如此高的逆相变温度使得 Mn₂NiGa马氏体的居里温度测量成为可能,获得了530K的数值.     

Ni52Mn24Ga24单晶中取向内应力的热动力学计算

测量了Ni₅₂Mn₂₄Ga₂₄单晶样品在磁场加载和未加载情 况下马氏体相变时的相变应变.分析结果表明：用提拉法生长单晶时在晶体内部引入了单一取向的内应力，该取向内应力可诱导马氏体变体择优取向，从而导致马氏体相变时产生大的相变应变.从理论上计算了该内应力的大小.另外，对样品在马氏体态单纯磁诱导应变的热动力学研究，表明取向内应力在马氏体态依然存在. 关键词： 马氏体相变 磁感生应变 内应力     

Influences of Y2O3 dopant content on residual stress,structure, and optical properties of ZrO2 thin films

Four kinds of Y2O3 stabilized ZrO2 （YSZ） thin films with different Y2O3 contents （from 0 to 12 mol%） are deposited on BK7 glass substrates by electron-beam evaporation method. The effects of different Y2O3 dopant contents on residual stress, structure, and optical properties of ZrO2 thin films are investigated. The results show that residual stress in YSZ thin films varies from tensile to compressive with the increase of Y2O3 molar content. The addition of Y2O3 is beneficial to the crystallization of YSZ thin film and transformation from amorphous to high temperature phase, and the refractive index decreases with the increase of Y2O3 molar content. Moreover, the variations of residual stress and the shifts of refractive index correspond to the evolution of structures induced by the addition of Y2O3.