无铅焊料合金压入蠕变性能参数表征研究

微互连焊点高温下的服役可靠性很大程度上决定了电子产品性能的优劣，本文通过微纳米压入法开展了典型无铅焊料合金Sn-3.0Ag-0.5Cu 的高温蠕变性能研究，采用“快速加载–保载–快速卸载”的测试方式获取不同温度下完备的蠕变行为，分析发现温度升高焊料软化加剧、蠕变变形更为明显；得到了焊料合金不同温度下的稳态蠕变应力指数n 与不同硬度下的蠕变激活能Q，分析了温度与硬度对二者的影响并给出激活能Q 与lnH之间的关系．     

基于纳米压入法Sn-Ag-Cu无铅焊料高温力学性能的研究

无铅化和微型化已经成为电子封装的发展趋势,温度对无铅焊点的可靠性产生了不可忽视的影响。本文对Sn96.5Ag3Cu0.5无铅焊料进行回流处理,采用纳米压入法研究其在实际工况下的高温力学性能。结果表明,温度对焊料试样的力学性能影响显著。随着温度的升高,弹性模量和硬度逐渐降低,焊料发生软化;较高温度下的蠕变应力指数较小,焊料的蠕变抗力降低,其相应的蠕变激活能为76kJ/mol。由此可知,随温度的升高,焊料的蠕变机制由位错攀移逐渐转变为晶界滑移。     

Effect of Varying Test Parameters on Elastic–plastic Properties Extracted by Nanoindentation Tests

A systematic experiment was performed in an effort to investigate how the levels of certain test parameters affect the values of elastic modulus, hardness, yield stress, and strain hardening constant obtained using nanoindentation test. Maximum applied load, loading (unloading) rate, and hold time at maximum load were varied at three levels. The effects of these testing parameters were investigated through a three-level, full factorial design of experiment. The experiments were conducted on ultrafine Al-Mg specimens that were mechanically extruded. Both longitudinal and transverse extrusion directions were examined to investigate effects of anisotropy on mechanical properties and evaluate the persistence of observed variations due to test parameters on different materials orientations. An indentation size effect (ISE) was observed demonstrating that maximum load—and thereby maximum indentation depth—can have a significant effect on values of hardness and elastic modulus. Hardness values decreased with higher loading rates, and higher rates of unloading resulted in higher values of elastic modulus (5–10 GPa increases). Strain-hardening exponent showed a decreasing trend with increasing loading rate while yield stress exhibited a consistent correlation to hardness across all studied parameters. The material exhibited very little creep during the hold period, and values of the calculated properties were not significantly altered by varying the length of the hold time. Anisotropy effect was observed, particularly in the values of yield strength. This is attributed to the preferred grain orientation due to extrusion.     

High Temperature Nanoindentation of PMR-15 Polyimide

This paper presents the high temperature nanoindentation experiments performed on an aerospace polymer resin–PMR-15 polyimide. The sharp-tipped Berkovich nanoindenter equipped with a hot-stage heating system was used. The indentation experiments were performed using the “hold-at-the-peak” method at various indenter holding times and unloading rates. The creep effect was seen to decrease with increasing holding time and/or unloading rate. Procedures used to minimize the creep effect are investigated at both ambient and elevated temperatures so that the correct contact depth (together with modulus and hardness) can be determined from nanoindentation load-depth curve. The temperature dependent mechanical properties of PMR-15 are measured through the current nanoindenter and results are consistent with those obtained from macroscopic tests.     

Nanocharacterization of creep behavior of multiwall carbon nanotubes/epoxy nanocomposite

High temperature instrumented indentation testing was used to evaluate the mechanical properties of multiwall carbon nanotubes/epoxy nanocomposite system. Reference neat epoxy samples were also tested and compared with the results obtained for the nanocomposite. The nanoindentation creep tests were utilized to provide the creep strain rate sensitivity parameter, the contact creep compliance and the time-dependent deformation under constant loads. Different thermo-mechanical conditions comprising three temperatures of 25, 40 and 55 °C and three loads of 1, 2 and 3 mN were utilized. The improvements in the properties were not as high as anticipated through the use of mixture rule, indicating insufficient dispersion. However, variations in modulus, hardness and creep strain rate sensitivity parameter obtained using nanoindentation showed quantifiable differences between the MWCNTs nanocomposite and epoxy specimens.The comparison of the creep strain rate sensitivity A/d(0) from short term, 60 s, creep tests and the creep compliance J(t) from the long term, 1800 s, creep tests suggests that former parameter is a more useful comparative creep parameter than the creep compliance. The analysis of the creep strain rate sensitivity clearly revealed that the addition of MWCNTs to a commercial epoxy reduced the creep rate. This reduction of creep rate sensitivity parameter was observed particularly at thermal environments just below the glass transition temperature.     

Extraction of Mechanical Properties with Second Harmonic Detection for Dynamic Nanoindentation Testing

In this article, a new method based on the detection of the second harmonic of the displacement signal to determine mechanical properties of materials from dynamic nanoindentation testing, is presented. With this technique, the Young’s modulus and hardness of homogeneous materials can be obtained at small penetration depths from the measurement of the second harmonic amplitude. With this innovative method, the measurement of the normal displacement is indirectly used, avoiding the need for very precise contact detection. Moreover, the influence of the tip defect and thermal drift on the measurements are reduced. This method was used for dynamic nanoindentation tests performed on fused silica and on an amorphous polymer (PMMA) because these materials are supposed not to exhibit an indentation size effect at small penetration depths. The amplitude of the second harmonic of the displacement signal was correctly measured at small depths, allowing to calculate the Young’s modulus and the hardness of the tested materials. The mechanical properties calculated with this method are in good agreement with values obtained from classical nanoindentation tests.     

纳米硬度技术的发展和应用

近二十年来,主要用于检测材料表面微米和亚微米尺度力学性质的纳米硬度技术发展迅速.首先,概述硬度的定义、分类及其适用范围.然后,系统地总结纳米硬度技术的发展,重点介绍纳米压痕硬度的测量原理及其影响因素,连续刚度测量原理,高分辨率的载荷位移测量原理,几种常用压头的几何形状,试样表面的准备和确定,相关的测试方法,仪器校准和显微观察等问题.通过压痕实验可获得硬度、弹性模量、断裂韧性、存储模量和损耗模量、蠕变应力指数等.最后,简要介绍纳米划痕硬度测量技术的发展和应用.      

Development of High Temperature Nanoindentation Methodology and its Application in the Nanoindentation of Polycrystalline Tungsten in Vacuum to 950 °C

The capability for high temperature nanoindentation measurements to 950 °C in high vacuum has been demonstrated on polycrystalline tungsten, a material of great importance for nuclear fusion and spallation applications and as a potential high temperature nanomechanics reference sample. It was possible to produce measurements with minimal thermal drift (typically ~0.05 nm/s at 750–950 °C) and no visible oxidative damage. The temperature dependence of the hardness, elastic modulus, plasticity index, creep, creep strain, and creep recovery were investigated over the temperature range, testing at 25, 750, 800, 850, 900 and 950 °C. The nanoindentation hardness measurements were found to be consistent with previous determinations by hot microhardness. Above 800 °C the hardness changes relatively little but more pronounced time-dependent deformation and plasticity were observed from 850 °C. Plasticity index, indentation creep and creep recovery all increase with temperature. The importance of increased time-dependent deformation and pile-up on the accuracy of the elastic modulus measurements are discussed. Elastic modulus measurements determined from elastic analysis of the unloading curves at 750–800 °C are close to literature bulk values (to within ~11 %). The high temperature modulus measurements deviate more from bulk values determined taking account of the high temperature properties of the indenter material at the point (850 °C) at which more significant time-dependent deformation is observed. This is thought to be due to the dual influence of increased time-dependency and pile-up that are not being accounted for in the elastic unloading analysis. Accounting for this time-dependency by applying a viscoelastic compliance correction developed by G. Feng and A.H.W. Ngan (J. Mater. Res. (2002) 17:660–668) greatly reduces the values of the elastic modulus, so they are agree to within 6 % of literature values at 950 °C.     

微米/纳米尺度的材料力学性能测试

针对如何定量测定纳米、微米尺度及低维材料的力学性能,叙述了采用当今先进观测手段,结合设备特点和力学分析技术来评价材料的硬度、弹性模量、屈服应力、抗蠕变及抗疲劳性等力学性能的测试方法．     

分级加载条件下紫色泥岩三轴蠕变特性研究

流变性质是岩石材料的重要力学特性,以紫色泥岩为例,在分级加载条件下研究了其三轴蠕变特性。采用自行研制的重力杠杆式岩石蠕变实验机,并配备三轴压力室,对紫色泥岩实施分级加载三轴蠕变实验。实验结果表明,紫色泥岩在相同轴压条件下,围压越大,瞬时弹性变形和蠕变变形越小;在相同围压条件下,轴压越大,二者变形越大。紫色泥岩的蠕变速率具有相同的变化趋势,且在相同轴压条件下,围压越大,稳定蠕变阶段的蠕变速率越不明显。另外,应力与瞬时应变线性拟合结果表明,瞬时轴向应变与轴向荷载近似成比例增长。通过分析紫色泥岩蠕变曲线变化趋势,认为采用H/M模型进行模拟较为合理。并且采用MATLAB软件非线性回归分析进行模型参数拟合,最后得到实验曲线与理论曲线的最大误差在2e-5左右。证明采用的H/M模型能较好地描述紫色泥岩的蠕变特性。     

Characterization of the Grain-Level Mechanical Behavior of Eglin Sand by Nanoindentation

Characterization was made on the structure and grain-level mechanical behavior of Eglin sand (Quikrete #1961 sand quarried in Pensacola, FL). The as-received assorted sand was sorted to six grain sizes: 0.60 mm, 0.50 mm, 0.42 mm, 0.30 mm, 0.212 mm, and 0.15 mm. The sand chemical constituents and crystalline structures were determined using energy dispersive X-ray spectroscopy, X-ray diffraction and transmission electron microscopy. The Young’s modulus and hardness were determined using nanoindentation with a Berkovich tip, and the fracture toughness was measured using a cube-corner tip. The median Young’s modulus, hardness and fracture toughness were determined as 90.4 GPa, 12.8 GPa and 2.32 MPa?m^0.5, respectively. The mechanical properties were analyzed statistically and the parameters of the Weibull distribution were determined. The grains show highly ductile behavior under nanoindentation due to confinement by high pressure induced by Berkovich tip. An inverse problem solving approach using finite element method (FEM) with the consideration of the Ramberg-Osgood model was used to determine the stress–strain relationship for individual sand grains.     

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.      

Influence of Vickers tip imperfection on depth sensing indentation tests

In the last decade, the development of depth sensing indentation equipment has permitted two of the most conventional mechanical properties of materials to be easily determined: hardness and Young’s modulus. Some care is needed to accurate results from the experimental determination of the aforementioned mechanical properties. In this study, numerical simulations were performed on two well-known materials (Bk7 glass, AISI M2 steel) and on fictitious materials with a wide range of mechanical properties, using Vickers indenters with different sizes of tip imperfections. The purpose is to estimate the influence of the size of the defect on the hardness and Young’s modulus results obtained by ultramicro and nanoindentation tests.     

岩石蠕变特性试验研究

针对大安山煤矿+550水平西二石门围岩蠕变变形严重的问题,采用室内蠕变试验与理论分析相结合的方法研究岩石蠕变特性。选取泥质粉砂岩作为软岩试样,通过自制三轴蠕变仪对所取岩样进行恒围压分级增轴压的三轴压缩蠕变试验,结果表明:随应力水平的提高,起始蠕变速率增大,进入稳态蠕变阶段用时延长,稳态蠕变速率从0h-1增大到3.12e-4·h-1,瞬时应变以线性关系增加,围压9MPa条件下的起始蠕变应力阈值为6MPa,当应力水平超过岩石长期强度时出现加速蠕变。基于蠕变试验规律,考虑起始蠕变应力阈值,将一种可用阶跃函数表示的开关元件与广义K体并联,并引入损伤元件对CVISC蠕变模型进行改进。采用1st-Opt中的Levenberg-Marquardt+通用全局优化法计算蠕变参数并进行反演。反演结果表明理论曲线与试验曲线的吻合效果较好,证明了所建模型的合理性。上述研究成果可为岩石工程的长期稳定性分析提供试验和理论依据。     

Determination of Asphalt Binder Creep Compliance Using Depth-Sensing Indentation

Asphalt binders are common construction materials, however due to time- and temperature- dependence, their mechanical properties are often difficult to characterize. Several standard tests methods exist to describe their complex behavior. This paper presents an exploratory feasibility study of a flat-tip indentation testing to analyze the linear viscoelastic properties of asphalt binders. Depth-sensing indentation testing has been extensively used to characterize the properties of many engineering materials, however the applications to asphalt binders are very limited. This paper presents a simple solution for the creep compliance in tension derived for flat-tipped indenter. This solution was verified with the Finite Element Analysis and then applied to the experimental results from the indentation testing performed on one typical unmodified asphalt binder. The testing was conducted at three different low temperatures and under three different creep load levels to verity the linearity of the response, and to evaluate the robustness and applicability of the indentation method. Furthermore, the creep compliance functions determined from the indentation testing were compared with a more traditional 3-point bending experiments. The results show that there is a non-uniform discrepancy between the two testing methods, most likely due to nonlinear behavior of the asphalt binder at higher temperatures and micro-damage of the binder samples at lower temperatures. Other possible sources of error between indentation and 3-point bending are problems determining the initial tip-specimen contact surface and possible tip-specimen adhesion. It is concluded that flat-tipped indentation at low temperatures should be performed at lower load levels to avoid excessive stress concentrations that leads to micro-damage and nonlinear response of asphalt binders. Alternatively, asphalt binders at low temperatures could be evaluated using different indenter geometries, such as spherical or pyramidal, using corresponding parameter interpretation procedures.     

Testing methods for nanoindentation property of the cuticle of bovine hoof wall and dung beetle’s foreleg femur

Natural biomaterials have extensively been researched since their distinguished properties adapting to their living surroundings. The cuticle surfaces of bovine hoof and dung beetle directly contact soil when they move on soft ground or in soil. Their surface materials and structures can provide some information for designing soil-engaging components of soft terrain-machines. While, it is difficult to measure their mechanical properties since the cuticle of the bovine hoof wall and dung beetle are very thin. Nanoindenter provides a powerful tool for examining the mechanical properties such as reduced modulus and hardness in nano-scale. The testing methods for nanoindentation properties of the cuticle of the bovine hoof wall and dung beetle (Copris ochus Motschulsky) were discussed in this work.     

Local mechanical properties of the 6061-T6 aluminium weld using micro-traction and instrumented indentation

The local mechanical properties of a weld zone, in a 6061-T6 aluminium alloy subjected to the modified indirect electric arc technique have been studied. The mechanical properties of the base metal, the weld metal and the heat affected zone were determined by means of usual and instrumented indentation testing, as well as micro-traction testing. To analyse the heat input effect resulting from the welding process, the evolution of the weld zone size was evaluated by means of classical indentation under a constant applied load. The results were presented using a Vickers hardness map representation. This allows monitoring exact hardness variation while leading to the identification of the different zones of the welded joint. Instrumented indentation testing was carried out to determine the local mechanical properties, such as the yield stress, the bulk modulus and the strain-hardening exponent. Obtained results are compared to those derived from tensile tests conducted on micro-specimen cuts taken from the weld zone. It was observed that yield stress values are directly comparable for indentation and micro-traction experiments. As for the elastic properties, no comparison was possible since the bulk modulus is measured by indentation, whereas it is the Young’s modulus by tensile test. The micro-traction testing seems to be more sensitive to represent the work hardening of a material since the corresponding exponent is found to be constant by instrumented indentation.     

Quick assessment methodology for reliability of solder joints in ball grid array (BGA) assembly—Part II: Reliability experiment and numerical simulation

In the present study, a facility, i.e., a mechanical deflection system (MDS), was established and applied to assess the long-term reliability of the solder joints in plastic ball grid array (BGA) assembly. It was found that the MDS not only quickly assesses the long-term reliability of solder joints within days, but can also mimic similar failure mechanisms in accelerated thermal cycling (ATC) tests. Based on the MDS and ATC reliability experiments, the acceleration factors (AF) were obtained for different reliability testing conditions. Furthermore, by using the creep constitutive relation and fatigue life model developed in part I, a numerical approach was established for the purpose of virtual life prediction of solder joints. The simulation results were found to be in good agreement with the test results from the MDS. As a result, a new reliability assessment methodology was established as an alternative to ATC for the evaluation of long-term reliability of plastic BGA assembly. The project supported by the National Natural Science Foundation of China (59705008)     

Measurement of Temperature-Dependent Young’s Modulus at a Strain Rate for a Molding Compound by Nanoindentation

The mechanical properties of a molding compound on a packaged integrated circuit (IC) were measured by spherical nanoindentation using a 50 μm radius diamond tip. The molding compound is a heterogeneous material, consisting of assorted diameters of glass beads embedded in an epoxy. Statistical analysis was conducted to determine the representative volume element (RVE) size for a nanoindentation grid. Nanoindentation was made on the RVE to determine the effective viscoelastic properties. The relaxation functions were converted to temperature-dependent Young’s modulus at a given strain rate at several elevated temperatures. The Young’s modulus values at a given strain rate from nanoindentation were found to be in a good agreement with the corresponding data obtained from tensile samples at or below 90 °C. However, the values from nanoindentation were significantly lower than the data obtained from tensile samples when the temperature was near or higher than 110 °C, which is near the glass transition. The spatial distribution of the Young’s modulus at a given strain rate was determined using nanoindentation with a Berkovich tip. The spatial variation of the Young’s modulus at a given strain rate is due to the difference in nanoindentation sites (glass beads, epoxy or the interphase region). A graphical map made from an optical micrograph agrees reasonably well with the nanoindentation results.     

Characterization of viscoelastic properties of polymeric materials through nanoindentation

Nanoindentation testing was used to determine the dynamic viscoelastic properties of eight polymer materials, which include three high-performance polymers and five densities of high-density polyethylene. It was determined that varying the harmonic frequency of nanoindentation does not have a significant effect on the measured storage and loss moduli of the polymers. Agreement was found between these nanoindentation results and data from bulk dynamic mechanical testing of the same materials. Varying the harmonic amplitude of the nanoindentation had a limited effect on the measured viscoelastic properties of the resins. However, storage and loss moduli from nanoindentation were shown to be sensitive to changes in the density of the polyethylene.