基于有限变形单晶塑性滑移的微观热-力耦合模型及其有限元计算

基于率相关的晶体塑性滑移理论,论文考虑晶体内部塑性变形产生的热以及快速热冲击作用下温度急剧变化产生热应力的热-力双向耦合效应,建立起微观单晶的瞬态热-弹-塑性耦合模型,推导出与温度有关的剪应变率和弹塑性切模量公式.根据论文建立的模型,对ABAQUS软件进行二次开发[1],数值模拟出<001>/{100}单晶Cu在单轴拉伸状态下的应力、应变与温度的关系和弹性模量的变化,结果如下:轴向应力随温度升高先呈线性增加再呈非线性减小,轴向应变随温度增加而增加;弹性模量随塑性变形的增加而降低,与分子动力学模拟的趋势[2]是一致的.数值实验表明,论文建立的模型和算法是正确合理的,且计算量远远小于分子动力学模拟.     

基于J-C模型的Q235钢的失效准则

使用Instron材料试验机、霍普金森拉杆（SHTB）对Q235钢试件进行了不同温度下的准静态和动态拉伸实验,研究了温度、应变率及应力三轴度对Q235钢失效应变的影响,结果表明:Q235钢失效应变随温度的升高而增加,随应变率的增加而减小,随应力三轴度的增加先减小后增加再减小。基于实验结果对Q235钢J-C失效模型中的温度项进行了修正,并结合数值模拟提出了基于J-C失效模型的应力三轴度三分段式失效准则,通过Taylor撞击实验和数值模拟对给出的模型相关参量进行了验证,实验与模拟结果吻合较好。     

高氮奥氏体不锈钢高温动态响应特性及本构关系

在293~873 K的环境下,采用分离式霍普金森杆装置对高氮钢试样进行了102~103 s-1应变率下的动态加载实验。结合准静态实验结果,分析了应变率和温度对材料塑性流动特性的影响。结果表明:高氮钢的动态力学行为具有很强的应变率敏感性和温度敏感性。当应变率达到400 s-1或更高时,流动应力随应变率的增加显著升高;在同一应变率下,流动应力随温度的降低明显升高。研究了温度和应变率耦合效应对材料塑性行为的影响,得出温度软化效应在高氮钢高温动态塑性变形中起主导作用。基于经典的Johnson-Cook（J-C）模型,通过对实验数据的分析,得出了高氮钢材料的修正J-C本构方程,经验证修正J-C方程预测结果与实验结果吻合。     

冷质部件支撑结构中压杆的热过屈曲分析

以圆杆式冷质量支撑结构中的压杆为研究对象,考虑了材料线膨胀系数α随温度非线性变化的特性及材料本构关系的非线性,基于轴线可伸长原理建立了压杆的热过屈曲数学模型;利用打靶法分别分析了材料本构关系取线性模型和非线性模型时的压杆热屈曲过程,并对二者进行了对比。研究结果表明:无论材料本构关系采用线性模型还是非线性模型,当α取常数时临界屈曲温度与柔度无关;而当α随温度非线性变化时,柔度则对临界屈曲温度产生影响;在同一柔度下,考察α对屈曲特性参数的影响规律时材料本构关系的非线性特性不可忽略;在非线性本构关系下线膨胀系数随温度非线性变化时可得到最大轴向载荷、最小横向支座反力、最小轴线总伸长量;较小的横向支座反力可以有效减小支撑结构中心收缩位移,较小的轴线总伸长量可以有效减小压杆周向固定端连接处应力。     

一维非线性黏弹体和黏塑性体中的最优应变路径

得出了一维非线性黏弹体和黏塑性体中最优应变路径方程，并揭示了它们的某些特性，如：（１）当非线性黏弹本构方程中的黏性部分与应变的关系具有上凸形式时，相应的最优应变路径具有下凸性质；（２）对于过应力和Ｂｏｄｎｅｒ－Ｐａｒｔｏｎ黏塑性体，它们的最优应变路径是塑性应变为线性形式，即塑性应变率为常数，而弹－黏塑性体的最优应变路径则不同。     

超临界CO_2作用下煤体膨胀变形规律试验研究

为解决采用应变片对超临界CO_2作用下煤体膨胀变形进行点测量时,试验结果离散性大、超临界CO_2作用导致应变片易脱离破损等问题,自主研发了具有施加热流力载荷功能的膨胀体积应变测量装置,对不同温度、压力的超临界CO_2作用下,煤体膨胀体积变形规律进行研究。结果表明:煤体膨胀体积应变随超临界CO_2作用时间增加呈现先增大后趋于稳定的变化规律;当孔隙压力不变时,膨胀体积应变随超临界温度的升高而增加,温度越高,达到稳定膨胀变形所需时间越长;当温度不变时,随着超临界孔隙压力增加,膨胀体积应变也随之增大,但达到稳定膨胀变形所需时间随孔隙压力的升高呈先增加后减少的趋势;超临界CO_2作用下,煤体体积应变随温度和孔隙压力均呈"S型"Logistic函数规律变化;膨胀体积应变对超临界温度和孔隙压力的变化率具有分区性,其变化率大小排序依次为:近临界区跨临界区高临界区。     

力-电-初始取向对液晶凝胶薄膜均匀变形行为影响分析

针对液晶凝胶在电场作用下的多场耦合多尺度力学行为,基于小应变假设,通过反逆法获得了有不同初始液晶指向方向的液晶凝胶薄膜在力-电耦合作用下均匀变形的解析模型.分析表明,电场与拉应力都可使液晶指向转动到与其平行的方向,当施加电场的方向与液晶初始取向垂直时,指向矢仅在超过一个临界电场强度后方会失稳转动,指向矢方向施加拉应力将增大所需阈值;而当液晶初始取向不与外加电场垂直时,电致指向矢转动将立即发生,其在力-电耦合下的指向矢转动和宏观变形行为与初始取向密切相关.因此,液晶凝胶的变形行为不仅可以通过力-电载荷进行控制,也可通过设计所需的初始液晶取向加以调节.     

钛合金TB-2在高应变率下的动态应力应变关系

用分离式Hopkinson压杆对国产型钛合金TB-2的动态应力应变关系在高达3103S-1的高应变率下作了实验研究。试验结果表明TB2对应变率高度敏感,其本构关系可用Malvern粘塑性方程来表达。从高速变形下热-力学耦合的观点讨论了其应变硬化模量随应变率的增加而降低,从而有应变率敏感系数随应变增大而降低的特性。     

一种改进的金属材料的高温动态拉伸实验技术

在旋转盘冲击拉伸实验装置上,利用金属材料自身的导电特性,对试样施加电流.使其在电流作用下发热,实现自加热,形成了试件快速加热而波导杆温升很小的金属材料的动态高温高应变率拉伸实验技术.应用该实验技术获取了45 #钢从室温到1000℃温度范围和应变率650s-1时的材料动态拉伸应力—应变曲线.实验结果表明,45 #钢具有明显的热软化效应,其流动应力和屈服应力随温度的升高而降低.     

Cr15Mn9Cu2Ni1N不锈钢的高温拉伸变形特性分析

利用热/力模拟试验机,对Cr15Mn9Cu2Ni1N不锈钢进行了950℃~1200℃高温范围内的拉伸试验;采用有限元方法对试样的均匀变形过程进行了分析。高温拉伸过程中,试样在达到最大应力后并不立即颈缩,而是还要经历一段宏观均匀变形后才颈缩。分析结果表明:最大应力之后,试样端部区域等效应力降低,横截面积收缩量减小,而中心区域横截面积收缩量增大,形成了潜在颈缩区;在应变速率敏感性的作用下,潜在颈缩区的变形抗力随应变速率的增大而增加,使变形不能在该区域集中,而转向其它位置,保持了试样的宏观均匀变形,且颈缩未在最大应力后立即发生;在高温拉伸条件下,材料应变速率敏感性的增大是颈缩延迟发生的主要原因,随着变形温度升高,应变速率敏感性增大,也使得试样颈缩前的均匀变形量增大。     

Thermomechanical modeling of the thermo-order-mechanical coupling behaviors in liquid crystal elastomers

Liquid crystal elastomer is a kind of anisotropic polymeric material, with complicated micro-structures and thermo-order-mechanical coupling behaviors. In this paper, we propose a method to systematically model these coupling behaviors. We derive the constitutive model in full tensor structure according to the Clausius-Duhem inequality. Two of the constitutive equations represent the mechanical equilibrium and the other two represent the phase equilibrium. Choosing the total free energy as the combination of the neo-classical free energy and the Landau-de Gennes nematic free energy, we obtain the Cauchy stress-deformation gradient relation and the order-mechanical coupling equations. We find the analytical homogeneous solutions of the deformation for the typical mechanical loadings, such as uniaxial stretch, and simple shear in any directions. We also compare the compression behavior of prolate liquid crystal elastomers with the stretch behavior of oblate liquid crystal elastomers. As a result, the stress, strain, temperature, order parameter, biaxiality and the direction of the director of liquid crystal elastomers couple with each other. When the prolate liquid crystal elastomer sample is stretched in the direction parallel to its director, the deviatoric stress makes the mesogens more order and increase the transition temperature. When the sample is sheared or stretched in the direction non-parallel to the director, the director of the liquid crystal elastomer will rotate, and the biaxiality will be induced. Because of the order-mechanical coupling, under infinitesimal deformation, liquid crystal elastomer has anisotropic Young’s modulus and zero shear modulus in the direction parallel or perpendicular to the director. While for the oblate liquid crystal elastomers, the stretch parallel to the director will cause the rotation of the director and induce the biaxiality.     

液晶高弹体的光致变形与弯曲行为研究

本文研究了一类光敏液晶高弹体在紫外光照射下的变形和弯曲行为。在分析了近年发现的光敏液晶高弹体中光致变形的机理和规律的基础上,给出了该材料一维变形本构关系,研究其变形行为,进而利用铁木辛科双金属片弯曲的思想建立了梁的光致弯曲模型。     

BIAXIAL LOADING OF NEO-CLASSICAL LIQUID CRYSTAL ELASTOMERS:CONSTITUTIVE RELATIONS AND SOFT BEHAVIOR

The thermo-order-mechanical behaviors of liquid crystal elastomers(LCEs) under biaxial loading are studied in this paper.Inverse method for nonlinear elastic problems is utilized by imposing biaxial stretching to thin rectangular samples.Neo-classical elastic energy is used together with the Landau-de Gennes nematic free energy.Under plane stress assumptions,the constitutive equations are derived.Due to the possible reorientations of the liquid crystal molecules induced by the imposed biaxial loading,the in-plane nonlinear stress-strain relations can have different expressions depending on which loading axis will have the largest effective principal strain.And the free energy is a multi-well non-convex potential function.As shown by some typical loading paths,the LCE samples will exhibit an anisotropic nonlinear elastic behavior,as long as the loading has not induced a reorientation of the liquid crystal molecules.When this did occur,jumps of stresses could take place for dead loadings due to the losing of stability.     

A gradient model of light-induced bending in photochromic liquid crystal elastomer and its nonlinear behaviors

Photochromic liquid crystal elastomer was recently reported to be able to deform largely and bend under illumination. In this paper, considering the opto-chemical process and the nematic-isotropic phase transition, we introduce the light and temperature into the constitutive relation of the liquid crystal elastomers, and propose a model for the light-induced bending. The dynamic deflection curve equation of the light-induced bending is derived based on the Hamilton principle. In the equation, the effect of light is introduced as an effective optical bending moment, which is caused by the inhomogeneous light-induced strain and Young's modulus. Several simulation examples are given to show the light-induced bending under different boundary conditions and various illumination or temperature controlling. Under the condition of deep nematic phase and weak enough illumination, the approximate analytical expression of the effective moment and the stress distribution can be obtained. Rich nonlinear behaviors are found in this model. The effective moment is a non-monotonic function of time, thickness ratio, and light intensity when the thickness ratio is not very large. The stress distribution through the thickness is nonlinear with two or three zero-stress planes.     

Sub-stripe pattern formation in liquid crystal elastomers: Experimental observations and numerical simulations

We report on some new experimental observations of pattern formation during stretching experiments of nematic liquid crystal elastomers (LCEs).     

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。     

Stress-free layers in photoinduced deformations of photoelastomer beams

Nematic liquid crystals combined with long molecular chains to form liquid crystal elastomers are capable of large extension. When such liquid crystal elastomers contain azo dyes to constitute photoelastomers, illumination can trigger large contraction. Beams made from such photoelastomers possess a non-uniform illumination and hence photostrain across their cross-section, resulting in bending and highly non-linear stress distribution. Due to the non-linear stress distribution, there can be more than one stress-free layers within the beam. In this paper, we present a dimensionless parametric study of nematic photoelastomer beams under the combined effects of light and mechanical loads. We show how the number of stress-free layers depends on three dimensionless parameters. The paths traced out by the system in the space of dimensionless parameters by varying the different real parameters are investigated, showing how the number of stress-free layers changes when e.g. the thickness or the mechanical load of the elastomer beam is varied. These results are important if the strain induced director rotation is not negligible.     

A Local and Global Well-Posedness Results for the General Stress-Assisted Diffusion Systems

We prove the local and global in time existence of the classical solutions to two general classes of the stress-assisted diffusion systems. Our results are applicable in the context of the non-Euclidean elasticity and liquid crystal elastomers.     

有限变形下多晶晶体塑性模型算法及应用

用Sanna和Zacharia^[1]所提出的延性单晶本构模型的积分算法和Taylor多晶模型假设研究了时间步长和硬化模型的选取对多晶集合体的应力应变响应和织构演化的影响。该算法是利用变形梯度乘法分解获得弹性变形梯度演化方程，用增量迭代法积分该方程，显式更新各滑移上的临界分切剪应力。算例的结果表明该算法具有时间步大，计算效率高的特点，另外，不同硬化模型的选取对多晶集合体应力应变响应的预测有明显的影响但对织构演化的预测影响不大。     

Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications

We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments. Analytical formulas characterizing the stress-strain response in pure shear are derived, providing an easily testable benchmark for future numerical and experimental investigations on the mechanics of nematic elastomers.