Calibration of a Constitutive Model from Tension and Nanoindentation for Lead-Free Solder.
Calibration of a Constitutive Model from Tension and Nanoindentation for Lead-Free Solder.
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无铅焊料张力和纳米压痕本构模型的校准
DOI：
10.3390/mi9110608
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发表时间：
2018-11-20
期刊：
影响因子：
3.4
通讯作者：
Chang C
中科院分区：
文献类型：
--
作者：
Long X;Zhang X;Tang W;Wang S;Feng Y;Chang C
考虑到电子设备中集成电路的小型化趋势，使用传统的单轴测试来评估有限尺寸材料的本构行为是具有挑战性的。仪器化的纳米压痕方法是有吸引力的，以获得作为渗透深度的函数的局部属性。在本文中，无论是传统的拉伸和纳米压痕实验进行无铅Sn-3.0Ag-0.5Cu（SAC 305）焊料合金的样品。为了调整材料的行为，在不同的温度和持续时间的所有标本进行热处理，拉伸实验和纳米压痕实验。基于布氏压头的自相似性，采用幂律模型描述其应力-应变关系，对纳米压痕实验中的载荷-穿透深度响应进行了无量纲分析。针对拉伸实验和纳米压痕实验中应变速率的显著差异，提出了两个“速率因子”，将所采用的解析模型中的代表应力和应力指数相乘，并以载荷-压痕深度关系的形式确定了相应的数值，以最佳预测纳米压痕响应。最后，当比较从拉伸实验测量的应力-应变响应和从纳米压痕实验的施加的载荷-压痕深度响应估计时，实现了良好的一致性。速率因子ε σ和ε n分别标定为0.52和0.10左右，这有利于有限尺寸材料样品的纳米压痕实验本构行为的转换。
It is challenging to evaluate constitutive behaviour by using conventional uniaxial tests for materials with limited sizes, considering the miniaturization trend of integrated circuits in electronic devices. An instrumented nanoindentation approach is appealing to obtain local properties as the function of penetration depth. In this paper, both conventional tensile and nanoindentation experiments are performed on samples of a lead-free Sn–3.0Ag–0.5Cu (SAC305) solder alloy. In order to align the material behaviour, thermal treatments were performed at different temperatures and durations for all specimens, for both tensile experiments and nanoindentation experiments. Based on the self-similarity of the used Berkovich indenter, a power-law model is adopted to describe the stress–strain relationship by means of analytical dimensionless analysis on the applied load-penetration depth responses from nanoindentation experiments. In light of the significant difference of applied strain rates in the tensile and nanoindentation experiments, two “rate factors” are proposed by multiplying the representative stress and stress exponent in the adopted analytical model, and the corresponding values are determined for the best predictions of nanoindentation responses in the form of an applied load–indentation depth relationship. Eventually, good agreement is achieved when comparing the stress–strain responses measured from tensile experiments and estimated from the applied load–indentation depth responses of nanoindentation experiments. The rate factors ψσ and ψn are calibrated to be about 0.52 and 0.10, respectively, which facilitate the conversion of constitutive behaviour from nanoindentation experiments for material sample with a limited size.
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DOI：
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