无铅焊料的力学性能研究及ANAND本构参数确定

根据ASTM E8M-04标准,对两种无铅焊料91.5Sn8.5Sb和95.5Sn3.8AgO.7Cu分别在15℃、75℃、150℃温度下和10-5s～10-2s十种应变速率下进行了一系列恒定应变速率的拉伸试验.分析了这两种无铅焊料的粘塑性力学行为.实验表明这两种无铅焊料具有温度和应变速率相关性.采用统一型Ahand粘塑性本构式,描述了这两种无铅焊料的非弹性率相关的变形行为,并基于非线性拟合程序确定了Anand粘塑性本构式的九个材料常数.结果表明Ahand式能有效描述无铅焊料的粘塑性行为,可应用于电子封装无铅焊点的可靠性模拟和失效分析.     

焊锡材料的应变率效应及其材料模型

采用分离式霍普金森压杆和拉杆实验,研究了含铅Sn37Pb、无铅Sn3.5Ag和Sn3.0Ag0.5Cu3种焊锡材料在600~2200s^{-1}应变率下的力学性能,得到了它们在不同应变率下的应力应变曲线. 根据实验数据建立了3种焊锡材料的应变率无关弹塑性材料模型和率相关Johnson-Cook材料模型,并用于模拟板级电子封装在跌落冲击载荷下焊锡接点的力学行为. 结果表明,高应变率下无铅焊料比含铅焊料对应变率更敏感,其抗拉强度为含铅焊料的1.5倍,其韧性也明显高于含铅焊料;在跌落冲击过程中,焊锡接点经历的应变率可达到1000s^{ -1}左右;给出的率相关Johnson-Cook材料模型能预测出比率无关的弹塑性模型更合理的应力应变结果.      

基于应变率阶跃测试的晶体铜压入应变率敏感性研究

纳米压入测试可以原位获取材料的诸多力学性能,包括弹性模量,硬度,屈服应力,应变率敏感指数等。本文利用应变率阶跃测试技术对多晶铜试样的应变率敏感性进行测试分析,硬度-位移曲线表明压头下方所存在的变形梯度对各阶跃应变率下的硬度值存在明显影响;采用基于晶体细观机制的塑性应变梯度理论对压入变形梯度效应予以修正,比较了修正与未修正数据所得的应变率敏感指数,在有效剔除压入变形梯度影响的基础上,应变率阶跃测试可实现单次压入下材料应变率敏感性的测试表征。     

应变控制的热机械疲劳行为的数值模拟

根据高温合金材料的力学性能，以弹粘塑性本构模型为基础，用数值模拟方法研究材料的热机械疲劳循环特性，模型将应变分为弹性应变、温度应变和粘塑性应变三部分，认为材料在高温循环载荷下呈现明显的弹粘塑性特征，根据虚位移原理建立轴对称体的弹粘塑性计算有限元格式，对于循环机械载荷和循环温度载荷，程序中采用了增量法迭代求解，在非线性项中不仅考虑了机械载荷增量的影响，同时也考虑了温度增量的影响，根据应变控制热机械疲劳的特点，发展了应变增量法的有限元计算方法、通过数值模拟，得到材料在各种循环载荷下的应力—应变响应，数值模拟较好地反映了粘塑性变形过程以及温度变化的效应，所描述的不可逆系统在某一时刻的状态完全由当时的状态参数、内变量、承载时间及塑性应变累积量决定，对带缺口试件的模拟结果显示了程序对复杂轴对称结构进行热机械疲劳计算的有效性。     

软化Mohr-Coulomb材料强度参数的测定方法

为了得到试件的粘聚力和内摩擦角随轴向塑性压应变变化的曲线提出本方法。试件的弹塑性本构关系遵循相关联的Mohr-Coulomb强度准则;对常规三轴试验,试件受力进入塑性状态后,处在棱椎状屈服面的棱上,加载过程遵循Koiter流动法则。按经典塑性力学理论,推导得到轴向塑性压应变与轴向应力与轴向应变的关系;在常规三轴试验机上获得不同围压下试件的全程应力-应变曲线,进而可得到各自围压下轴向塑性压应变随加载过程的变化曲线;把来自不同围压下对应同一轴向塑性压应变的应力分别代入屈服面方程,即可求得对应的粘聚力和内摩擦角。结果表明,Mohr-Coulomb材料的两个强度参数的变化由轴向塑性压应变确定。轴向塑性压应变可以作为塑性变形的状态参数,它和试件的受力过程可以唯一确定试件的变形过程。     

薄膜材料微观力学行为的有限元分析

采用有限元法对材料表面改性层和薄膜材料在显微压入过程中的力学行为进行了计算机模拟。从所得的载荷与压入深度的关系曲线、压痕周围应力、应变场的大小和形状分布曲线等为依据，对在超显微硬度测试中基底材料及界面层的影响进行了详细的讨论，并得出：为排除基底材料的影响，通常规定压入深度（Ｄ）不得超过膜厚（ｔ）的１０～２０％的规则并不适用于所有薄膜系统。测试时，允许的Ｄ／ｔ的临界比值将随薄膜系统不同而异。对软膜硬基底系统而言，由于压头下的塑性应变区更多的是沿膜层的横向扩展，故Ｄｃ／ｔ允许大于上述规定值，而对硬膜软基底系统而言，则由于压头下的塑性应变区很容易扩展到基底材料中去，其Ｄｃ／ｔ值将小于上述规定值。     

铀铌合金层裂行为的数值模拟

采用一种唯象模型来模拟铀铌合金在高应变率条件下的变形行为,该模型包括了材料的非线性弹性（状态方程）、率相关塑性和孔洞的形核及生长等多种效应。并且采用一种对角隐式Runge-Kuta方法来求解本构率方程组,提高了热粘塑性本构关系计算的稳定性及精度。对D.L.Tonks等的铀铌合金平板撞击实验进行了数值模拟,并将计算结果同文献中的实验和数值模拟结果进行了比较。结果表明,本文的计算结果比文献中的数值模拟结果更接近有关实验数据。     

SnPb钎料合金的粘塑性Anand本构方程

采用统一型粘塑性本构 Anand方程描述了电子封装焊点 Sn Pb钎料合金的非弹性变形行为 ,基于 Sn Pb 合金的弹塑性蠕变本构方程和实验数据 ,确定了6 2 Sn36 Pb2 Ag、6 0 Sn40 Pb、96 .5 Sn3.5 Ag和 97.5 Pb2 .5 Sn四种钎料合金 Anand方程的材料参数 ,验证了粘塑性 Anand本构方程对 Sn Pb合金在恒应变速率和稳态塑性流动条件下应力应变行为的预测能力。结果表明 ,Anand方程能有效描述 Sn Pb钎料的粘塑性本构行为 ,并可应用于电子封装 Sn Pb焊点的可靠性模拟和失效分析     

Al基含能结构材料的Johnson-Cook本构模型及失效参数研究

利用万能实验机和Hopkinson杆装置测试了Al基含能结构材料在不同温度下的静动态力学性能，分析实验结果得到了温度效应和应变率效应对材料力学性能的影响及该合金的Johnson-Cook本构模型参数.结合二维数字图像相关(DIC)方法，研究了Al基含能结构材料的失效应变与应力三轴度及温度之间的关系，得到了该合金的Johnson-Cook失效模型参数.通过平面撞击实验获得了Al基含能结构材料粒子速度和应力波波速之间的经验线性关系和该合金的Grüneisen系数.基于实验获得的材料本构关系和状态方程参数，完成了Al基含能结构材料超高速撞击多层间隔薄钢板的数值模拟，结果表明，数值模拟中靶板的毁伤模式、破孔直径及弹坑主要散布区和实验结果吻合.     

基于能量密度等效的超弹性压入模型与双压试验方法

针对超弹性材料压入问题, 本文基于能量密度中值等效原理, 提出了描述球、平面、锥3类压头独立压入下载荷、深度、压头几何尺寸和Mooney-Rivlin本构关系参数之间关系的半解析超弹性压入模型(semi-theoretical hyperelastic-material indentation model, SHIM), 进而提出了球、平面、锥压入组合的双压试验方法(indentation method due to dual indenters, IMDI). 正向验证表明, 基于系列超弹性材料的本构关系参数, 由SHIM分别预测的球、平面、锥3类压入下的载荷-位移曲线与有限元分析(finite element analysis, FEA)结果之间密切吻合; 反向验证表明, 基于系列超弹性材料的FEA条件本构关系下3类压入的载荷-位移曲线, 由双压试验方法预测的Mooney-Rivlin本构关系与FEA条件本构关系密切吻合. 针对3种超弹性橡胶, 完成了球、平面、锥压入试验, 应用双压试验方法获得的3组Mooney-Rivlin本构关系均与单轴拉伸试验结果吻合良好.      

The equivalent axisymmetric model for Berkovich indenters in power-law hardening materials

Nix and Gio [Nix, W.D., Gao, H.J., 1998. Indentation size effects in crystalline materials: a law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids 46, 411–425] established an important relation between the micro-indentation hardness and indentation depth for axisymmetric indenters. For the Berkovich indenter, however, this relation requires an equivalent cone angle. Qin et al. [Qin, J., Huang, Y., Xiao, J., Hwang, K.C., 2009. The equivalence of axisymmetric indentation model for three-dimensional indentation hardness. Journal of Materials Research 24, 776–783] showed that the widely used equivalent cone angle from the criterion of equal base area leads to significant errors in micro-indentation, and proposed a new equivalence of equal cone angle for iridium. It is shown in this paper that this new equivalence holds for a wide range of plastic work hardening materials. In addition, the prior equal-base-area criterion does not hold because the Berkovich indenter gives much higher density of geometrically necessary dislocations than axisymmetric indenter. The equivalence of equal cone angle, however, does not hold for Vickers indenter.     

纳米压痕过程的三维有限元数值试验研究

采用有限元方法模拟了纳米压痕仪的加、卸载过程，三维有限元模型考虑了纳米压痕仪的标准Berkovich压头．介绍了有限元模型的几何参数、边界条件、材料特性与加载方式，讨论了摩擦、滑动机制、试件模型的大小对计算结果的影响，进行了计算结果与标准试样实验结果的比较，证实了模拟的可靠性．在此基础上，重点研究了压头尖端曲率半径对纳米压痕实验数据的影响．对比分析了尖端曲率半径r＝0与r＝100nm两种压头的材料压痕载荷—位移曲线．结果表明，当压头尖端曲率半径r≠0时，基于经典的均匀连续介质力学本构理论、传统的实验手段与数据处理方法，压痕硬度值会随着压痕深度的减小而升高．     

ANALYSIS ON PSEUDO-STEADY INDENTATION CREEP

Theoretical analysis and finite element （FE） simulation have been carried out for a constant specific load rate （CSLR） indentation creep test. Analytical results indicate that both the representative stress and the indentation strain rate become constant after a transient period. Moreover, the FE simulation reveals that both the contours of equivalent stress and equivalent plastic strain rate underneath the indenter evolve with geometrical self-similarity. This suggests that pseudo-steady indentation creep occurs in the region beneath the indenter. The representative points in the region are defined as the ones with the equivalent stress equal to the representative stress. In addition, it is revealed that the proportionality between indentation strain rate and equivalent plastic strain rate holds at the representative points during the pseudo-steady indentation creep of a power law material. A control volume （CV） beneath the indenter, which governs the indenter velocity, is identified. The size of the CV at the indented surface is approximately 2.5 times the size of the impression. The stress exponent for creep can be obtained from the pseudosteady indentation creep data. These results demonstrate that the CSLR testing technique can be used to evaluate creep parameters with the same accuracy as conventional uniaxial creep tests.     

Comparison between Berkovich,Vickers and conical indentation tests: A three-dimensional numerical simulation study

Three-dimensional numerical simulations of Berkovich, Vickers and conical indenter hardness tests were carried out to investigate the influence of indenter geometry on indentation test results of bulk and composite film/substrate materials. The strain distributions obtained from the three indenters tested were studied, in order to clarify the differences in the load–indentation depth curves and hardness values of both types of materials. For bulk materials, the differentiation between the results obtained with the three indenters is material sensitive. The indenter geometry shape factor, β, for evaluating Young’s modulus for each indenter, was also estimated. Depending on the indenter geometry, distinct mechanical behaviours are observed for composite materials, which are related to the size of the indentation region in the film. The indentation depth at which the substrate starts to deform plastically is sensitive to indenter geometry.     

On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials

Indentation is widely used to extract material elastoplastic properties from the measured force-displacement curves. One of the most well-established indentation techniques utilizes dual (or plural) sharp indenters (which have different apex angles) to deduce key parameters such as the elastic modulus, yield stress, and work-hardening exponent for materials that obey the power-law constitutive relationship. However, the uniqueness of such analysis is not yet systematically studied or challenged. Here we show the existence of “mystical materials”, which have distinct elastoplastic properties yet they yield almost identical indentation behaviors, even when the indenter angle is varied in a large range. These mystical materials are, therefore, indistinguishable by many existing indentation analyses unless extreme (and often impractical) indenter angles are used. Explicit procedures of deriving these mystical materials are established, and the general characteristics of the mystical materials are discussed. In many cases, for a given indenter angle range, a material would have infinite numbers of mystical siblings, and the existence maps of the mystical materials are also obtained. Furthermore, we propose two alternative techniques to effectively distinguish these mystical materials. The study in this paper addresses the important question of the uniqueness of indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material elastoplastic properties.     

Polymer indentation: Numerical analysis and comparison with a spherical cavity model

Three dimensional analyses of indentation of a polymer by a rigid indenter are carried out. The polymer is characterized by a finite strain elastic-viscoplastic constitutive relation and the calculations are carried out with a dynamic finite element program used to simulate quasi-static behavior. Two types of indenter are considered; a conical indenter and a pyramidal indenter. For each indenter type, different values of the sharpness of the indenter are considered and two rates of indentation are analyzed. Significant sink-in is found to occur in all cases considered. The amount of sink-in is found to be smaller for sharper indenters. The calculated values of both the nominal and true hardness do not differ significantly for the two indenter shapes. An expanding spherical cavity model is also considered and the predictions of this model are compared with the finite element results for various indenter shapes and indentation rates. The spherical cavity model is found to give fairly good agreement with the predictions of the finite element analyses for the nominal polymer hardness for both indenter shapes.     

A study on robust indentation techniques to evaluate elastic–plastic properties of metals

Spherical indentation is studied based on numerical analysis and experiment, to develop robust testing techniques to evaluate isotropic elastic–plastic material properties of metals. The representative stress and plastic strain concept is critically investigated via finite element analysis, and some conditions for the representative values are suggested. The representative values should also be a function of material properties, not only indenter angle for sharp indenter and indentation depth for spherical indenter. The pros and cons of shallow and deep spherical indentation techniques are also discussed. For an indentation depth of 20% of an indenter diameter, the relationships between normalized indentation parameters and load–depth data are characterized, and then numerical algorithm to estimate material elastic–plastic curve is presented. From the indentation load–depth curve, the new approach provides stress–strain curve and the values of elastic modulus, yield strength, and strain-hardening exponent with an average error of less than 5%. The method is confirmed to be valid for various elastic properties of indenter. Experimental validation of the approach then is performed by using developed micro-indentation system. For the material severely disobeying power law hardening, a modified method to reduce errors of predicted material properties is contrived. It is found that our method is robust enough to get ideal power law properties, and applicable to input of more complex physics.