形状记忆合金结构拓扑优化设计方法研究

形状记忆合金由于其优良的力学特性得到了广泛关注,并形成了一系列具有变革性的创新应用.为了充分提升形状记忆合金结构的力学性能,提出了一种基于实体各向同性材料惩罚模型SIMP (Solid Isotropic Materi-al with Penalization)的形状记忆合金结构拓扑优化方法.基于ZM宏观唯象本构模型,考虑形状记忆合金材料特性,对拓扑优化过程中引入的中间密度材料的奥氏体和马氏体弹性模量以及相变转变应力进行插值.同时,考虑形状记忆合金本身的材料非线性和结构在大变形下的几何非线性效应,以获得准确的力学响应.采用三密度场法来避免最终设计结果出现的棋盘格现象、网格依赖性和大量中间密度单元.利用超单元法来改善由于低密度单元引起的非线性有限元分析过程的数值不稳定问题.利用伴随法对优化模型中的响应函数进行灵敏度分析.最后,通过二维和三维的数值算例验证了本文的优化设计方法,结果表明本文提出的拓扑优化框架能够对预期性能的形状记忆合金结构方案进行求解.     

基于自适应网格的材料渗透系数设计

采用基于单元(结点)密度为设计变量进行结构和材料的拓扑优化设计时,有限元网格的密度对优化设计有很大影响. 在以渗透系数为目标进行材料微结构设计时,为了较好地描述单胞中的流固边界,需要将单胞划分为很小的网格,进一步增加了有限元计算和优化分析的规模. 为了降低计算规模, 研究了基于自适应网格的逆均匀化方法,以最大化各向同性等效渗透系数为目标,进行材料微结构设计. 优化迭代过程中,对单胞中流固界面处的网格进行自适应加密,降低优化问题的计算规模. 采用这一算法,对不同初始密度分布得到的单胞优化结果虽然不同,但具有相同的材料微结构,一定程度上说明了该方法的有效性.      

耐磨TiNi形状记忆合金设计准则的有限元研究

采用有限元方法模拟微突体在TiNi形状记忆合金表面的压入过程，研究了伪弹性应变、伪弹性模量和相变启动应力等参数对TiNi合金抗磨性能的影响，并初步确立了TiNi形状记忆合金耐磨材料设计准则．结果表明：伪弹性应变对TiNi形状记忆合金摩擦学性能的影响最显著；就TiNi形状记忆合金耐磨材料的设计而言，应当强调提高伪弹性应变、降低伪弹性模量、增加相变启动应力；同时满足上述3方面要求的TiNi形状记忆合金的耐磨特性最优．     

OPTIMAL SPECIMEN DESIGN FOR LAP SHEAR TEST

在采用搭接剪切试件进行的剪切强度实验中,试件失效往往是由于试件两端的剥离应力过大,而不是切应力造成的,这往往造成错误的实验结果. 通过有限元和光弹实验相结合的方法研究在搭接结构中引入凹槽以使试件所受的切应力均匀分布并减少两端的剥离应力,从而提高实验精度的可行性. 研究表明,只要凹槽的形状和位置合适,完全可以达到上述效果,从而实现了搭接剪切试件的优化设计.     

横观各向同性轴对称界面端奇异性研究

套筒模型是复合材料中常用的进行纤维、基体间应力传递分析的轴对称模型.在套筒模型中,中心为纤维,纤维外包裹的"套筒"有假设为各向同性基体材料的,也有假设为横观各向同性复合材料的.不失一般性,本文将纤维和基体均视作横观各向同性材料,建立了任意楔形角的横观各向同性复合材料基体包裹横观各向同性纤维的轴对称模型,采用两次坐标变换、逐次渐近等求解方法,得到了求解该模型界面端应力奇异性指数的特征方程.考虑常见的碳纤维/环氧树脂复合材料制成的压入和拔出试件,根据得到的特征方程计算了两种试件的界面端奇异性指数随碳纤维体积百分含量的变化情况,结果发现,随纤维体积百分含量的增加,两种试件界端的奇异性均呈减弱趋势.     

正交各向异性韧性材料应力-应变关系

采用大变形弹塑性有限元方法分析了各向同性和正交各向异性韧性材料光滑圆棒拉伸试件的颈缩问题．首先给出了采用计算机模拟确定各向同性韧性材料真实应力-应变曲线的具体方法；对正交各向异性韧性材料的分析表明，颈缩截面呈椭圆形，其长短轴方向的等效塑性应变基本上均匀分布，与Bridgman假设一致；轴向拉伸载荷-位移曲线与其它两方向的各向异性参数关系不大．在此基础上，建议了一种确定正交各向异性韧性材料真实应力-应变曲线的方法．     

SiC/Al梯度功能材料紧凑拉伸试件裂纹扩展分析

SiC/Al梯度功能材料各梯度层由不同体积浓度的陶瓷和金属组成,由于材料组分梯度变化,克服了双材料界面的应力突变问题,获得了优异的使用性能.本文首先采用激光云纹干涉法,对具有四个梯度层的SiC/Al梯度功能材料紧凑拉伸试件在机械荷载作用下的拉伸实验位移场进行记录,进而获得紧凑拉伸试件裂纹口位移P-V曲线以及材料断裂韧度实验值;然后根据层合梯度功能材料理论分析模型,建立FGM紧凑拉伸试件的渐近分网有限元平面应变模型,采用通用有限元软件的单元删除模块对试件模型进行裂纹扩展单元的应变模拟分析,从计算所得的裂纹尖端应变图像分析得出梯度材料试件的裂纹扩展规律.     

SMA智能混凝土材料裂缝监测与修复机理和试验研究

混凝土材料的裂缝产生与扩张一直是土木工程领域亟待解决的难点问题之一.论文将形状记忆合金(SMA)材料植入混凝土材料中,构成一种基于SMA驱动的智能混凝土材料.通过对SMA材料的电阻变化和混凝土裂缝大小的关系进行讨论,建立了SMA智能混凝土材料的裂缝监测理论模型;对SMA试件在初始状态为奥氏体情况下所展示的形状记忆效应进行理论和试验分析,给出了SMA智能混凝土材料的裂缝修复理论模型;最后通过试验测试,讨论了不同尺寸试件的裂缝修复过程和裂缝修复程度.论文研究可为形状记忆合金智能混凝土材料的进一步优化设计和工程应用提供理论指导.     

航空发动机叶片抗冲击动力学拓扑优化研究

本文运用了结合混合元胞自动机(Hybrid Cellular Automaton, HCA)方法和基于LS-DYNA显式有限元算法的动力学拓扑优化方法来解决非线性动力学拓扑优化问题,并形成了该方法迭代过程的数学模型．运用该方法,对某航空发动机叶片进行了动力学拓扑优化设计,给出了优化后结构的材料分布,并与优化前结构进行了对比分析．结果表明,优化后结构相比于优化前在材料分布上更加合理,在减少质量的同时降低了结构在冲击过程中的最大应力,实现了航空发动机的抗冲击优化,为航空发动机动态优化设计提供了有效分析方法．     

受面内双向荷载蜂窝材料的弹性屈曲模式及其影响因素

基于压弯耦合梁柱稳定理论,分析了蜂窝材料在面内双轴应力作用下的弹性屈曲行为,得到了蜂窝材料在不同应力荷载作用下发生两种屈曲模式转换的临界条件和对应的屈曲临界荷载.讨论了孔穴几何参数对此转换条件和临界荷载的影响,并用ANSYS软件进行了有限元模拟.结果表明理论分析与数值模拟吻合很好.     

滑轨导向式静/动态双轴拉伸实验技术

基于液压伺服高速加载系统,发展了一种材料双轴拉伸力学性能测试技术。利用锥面接触导向驱动方法,把加载锤竖直方向的驱动力转化为水平方向的双轴驱动力,从而实现对十字形试样平面双轴加载。借助有限元数值模拟手段优化了锥面接触角和十字形试样尺寸。当接触锥角为45°时,既有较好的水平驱动转化效率,同时又保持较小的接触力,确保水平驱动加载各组件在弹性变形范围内,可多次重复使用。确定了加载臂狭缝个数、狭缝与减薄区边缘长度和标距段厚度等试样设计关键参数,在十字形试样测试标距段内实现了均匀变形。设计了测力夹持一体化导杆和非接触光学全场应变测试系统,准确获得了试样的应力和应变。利用此平面双轴拉伸加载装置,开展2024-T351铝合金板单轴拉伸实验和激光探测同步性验证实验,验证装置设计的可行性;开展铝合金板材在不同加载速率下的双轴拉伸实验,得到在双轴加载下铝合金板材应力应变曲线,并与单轴加载下实验结果进行了对比分析。     

Experimental study of the plastic yielding of rolled sheet metals with the cruciform plate specimen

In the current paper, an experimental technique for the evaluation of the in-plane yield loci of sheet metals with the cruciform plate specimen is presented. The measurement system is shown to conform to the optimized design concept proposed by other researchers. Finite element analysis demonstrates a reasonably wide area of uniform stress distribution in the center of the cruciform specimen, which allows the measurement of in-plane strain field by using a stacked strain rosette. Based on the designed apparatus, the yield loci of the 1100-F aluminum sheets corresponding to the as-received condition, and 25% and 50% thickness reductions by further rolling, were constructed, respectively, by applying biaxial loadings along the two principal axes of the cruciform specimen. A set of uniaxial tension tests were also performed to determine the plastic properties of the aluminum sheet along different directions with respect to the rolling direction. Finally, Hill's 1990 yield criterion is examined based on the experimental data from both biaxial and uniaxial tension tests.     

Influence of Specimen Geometry on the Estimation of the Planar Biaxial Mechanical Properties of Cruciform Specimens

It is in general challenging to characterize planar mechanical properties of extremely soft tissues such as cell-seeded collagen gels. One of the difficulties is related to premature failure of specimens. This issue may be resolved by employing fillets on stress-concentrated spots of the specimen. The existence of fillets, however, complicates the estimation of stress at the center of the specimen where stiffness data are collected. In this study, cruciform rubber specimens with two types of fillets (general vs. cut-in fillets) at the intersections of perpendicular arms were prepared and subjected to planar biaxial mechanical testing, aiming at investigating how the fillets affect the estimation of mechanical properties of cruciform specimens. Digital image correlation was used to analyze full-field deformation in the central region of the specimens. Finite element analysis with a Neo-Hookean model was performed to simulate the full-field deformation under the same experimental boundary conditions. The strain distribution for each specimen geometry obtained by finite element analysis was found to be in good agreement with that analyzed by digital image correlation, validating the finite element models. Finite element simulation showed that the greatest value of the maximum principal strain decreased with increasing the fillet radius regardless of the fillet type. Increasing the fillet radius, in general, also reduced the strain field uniformity in the central region. Compared with general fillets, however, the use of cut-in fillets provided greater strain field uniformity given the same fillet radius. Finite element analysis was also used to estimate effective transverse length required to convert tensile force at the boundary to local stress at the center. It was found that the effective transverse length for each specimen geometry remained relatively constant if the specimen was not excessively deformed (i.e., global equibiaxial stretch ≤ 1.2). We suggest using cut-in fillets at the intersections of perpendicular arms when preparing cruciform specimens for testing extremely soft tissues.     

Novel Design of Cruciform Specimens for Planar Biaxial Testing of Soft Materials

Cruciform specimens have long been used in planar biaxial testing of inanimate materials such as metals and composite materials. The efforts to improve the geometric design of cruciform specimens have focused on maximizing the degree of uniformity of stress and strain in the gage section. The standardization of the procedure for the determination of the mean stress in the gage section is lacking, however, because the exact load transferred from the grippers to the gage section during testing is unknown. Here, we introduce a novel split-arm design for cruciform specimens by taking into account three important factors: i) the effectiveness of load transfer from the grippers to the gage section, ii) the uniformity of normal stress (in the loading direction) over the symmetry line, and iii) the compatibility between the nominal stress and the true stress. By ensuring these conditions, one can estimate more accurately the mean stress in the gage section based on the measured force at the grippers and the deformed configuration of a reference length. A genetic algorithm coupled with finite element analysis was utilized to optimize the geometric shape of the novel cruciform design. The identified optimum design provides a load transfer effectiveness of 100 %. The calculated nominal stress deviates from the true stress at the center of the specimen by only ?0.49 %. A numerical experiment was conducted to validate the substantially improved performance of the optimized new design. Experiments were also conducted for natural latex rubber to demonstrate the application of the proposed design.     

A new direct biaxial testing machine for anisotropic materials

A screw-driven new biaxial testing machine for the realization of experimental investigations on anisotropic sheet materials, such as composite plates or rolled sheet metals, is presented. The described mechanical concept and servocontrol system allow cruciform specimens to be subjected to large strain biaxial tensile and compressive tests without kinematic incompatibilities. Moreover, for the proper implementation of biaxial tensile tests, the specific problems linked to the anisotropic properties of the investigated materials are taken into account; therefore, for the first time, the biaxial machine is supplied with the original ‘off-axes testing device,’ consisting of hinged fixtures with knife-edges at each arm of the cruciform specimen. A recently developed optimization method for the optimal design of flat tensile cruciform specimens is shortly reviewed. Numerical simulations illustrate the decisive superiority of the optimized specimen compared with specimen designs proposed in the literature, as well as the necessity to use the ‘off-axes’ testing technique in biaxial tests on anisotropic materials.     

Development of an apparatus for biaxial testing using cruciform specimens

A testing apparatus has been developed to study the behavior of sheet metals and composite materials under monotonic and cyclic biaxial loading conditions. This test facility employs cruciform specimens that are loaded in their plane. Problems encountered while developing the test system are discussed.We also discuss the difficulties common to test methods employing cruciform specimens. These relate to the design of a suitable specimen geometry and to the determination of the stresses throughout the specimen. A method for designing an optimal geometry for these specimens is presented. This method is based on the statistical tools of factorial and response surface designs. The statistical method, coupled with a finite-element analysis of the specimen, was successfully applied to optimize the geometry of a cruciform specimen with a circular reduced central region.Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 8.     

Determination of Yield Surfaces in Accordance With ISO 16842 Using an Optimized Cruciform Test Specimen

Background: For the standard ISO 16842 cruciform test specimen, stresses obtained from the gauge area are far below the ultimate tensile strength due to high stress concentrations at the slit ends which lead to premature failure. Objective: To introduce a new cruciform specimen design which has been optimized with respect to the determination of yield surfaces. Methods: The proposed design differs from the ISO standard by an additional thinning of the gauge area and wider slits in the arms to avoid stress singularities. Compared to other cruciform test piece designs found in the literature, the stress distribution is still homogeneous and there is no need to reduce the size of the gauge area, thanks to the specimen’s well-balanced proportions. Results: Biaxial tensile tests have been conducted with aluminium 5754 alloy samples of different thicknesses. For the standard cruciform test piece, the maximum strain achieved at the gauge area is only 25% of the fracture strain. The optimized cruciform test piece can attain about 66% of the fracture strain before breaking. Conclusions: The optimized specimen design enables the measurement of yield surfaces at higher stress levels. In case of other materials such as elastomers, the slit length has be to adjusted accordingly.

     

复合材料后压力框加筋元件双轴拉伸试验与模拟

试验针对应用在飞机后压力框上的碳纤维织物复合材料的力学特性和设计压力框壳体加强筋的刚度匹配问题,本文设计了十字形的试件,并开展了双轴拉伸试验,测试分析了试件中心位置含有不同尺寸加强筋时对刚度和强度的影响。依照试验条件,建立有限元模型,以中心位置未加筋试件为基准,探讨了两种尺寸筋条增强效果的差异。试验与模拟结果表明:在双轴拉伸载荷作用下,帽型加强筋明显提高了试件刚度和强度;两种筋条尺寸的差异对于试件刚度和强度的影响不明显;根据重量最小的原则,在同等条件下使用较小尺寸加强筋更为合适;有限元模拟与试验结果吻合良好,验证了本文提出的试验和模拟方法可用于复杂应力条件下织物复合材料结构的力学性能分析。     

基于试验与有限元耦合技术的延性材料全程单轴本构关系获取方法

摘 要: 材料拉伸直至断裂的全程单轴本构关系对材料大变形和断裂机理研究具有重要意义。传统拉伸试验获取的材料真应力-真应变曲线在试样颈缩后不可测。借助可以精确测量三维变形的DIC(Digital image correlate) 技术和有限元分析技术(Finite element analysis),本文提出了基于漏斗试样拉伸试验获取材料全程单轴本构关系的新方法,即TF(Test and FEA)方法。该方法将TF方法获取的材料全程单轴应力应变关系曲线作为有限元软件中的材料本构关系对漏斗试样拉伸变形过程进行模拟,其模拟载荷-位移曲线、漏斗根部直径-位移曲线和漏斗变形轮廓线等均与试验结果吻合良好,试样表面模拟应变也与DIC测试结果吻合, 根据不同半径漏斗试样模拟获得的全程真应力-真应变曲线保持良好一致性。最后,还对试样颈缩断面的力学行为进行了讨论,并给出了304不锈钢、汽轮机叶片材料2Cr12Ni4Mo3VNBN和 1Gr12Ni3Mo2VN、汽轮机转子材料30Cr2Ni4MoV的全程单轴本构关系模型参数、破断应力和破断应变。     

Modeling single crystals: time integration,tangent operators,sensitivity analysis and shape optimization

In this paper, a comprehensive overview of the numerical analysis of single crystalline materials at high temperatures is presented, including implicit higher order time integration, consistent linearization and respective sensitivity analysis. Both a phenomenological and a crystallographic model are employed to simulate the mechanical isothermal behavior of the nickel-based superalloy CMSX-4 at 950°C in a finite element environment. A shape optimization methodology for testing specimen design based on extensive finite element computations is presented. The sensitivity analysis according to the chosen time integration scheme is performed leading to an algorithm for simultaneous analysis and design (SAND). Examples for the shape optimization of a cruciform specimen for biaxial tensile experiments at high temperatures are given and discussed in detail.