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• Introduction  
• Sn-Pb Properties and Models  
• Sn-Ag Properties and Creep Data  
• Sn-Ag-Cu Properties and Creep Data  
• General Conclusions/ Recommendations  
• Acknowledgements  
• References  
     
  For more information contact:  
  metallurgy@nist.gov  
 
Sn-Ag Properties and Creep Data
 
  Overview and Conclusions  
  Bulk Sn-3.5Ag Tensile Creep  
  • Source and Plot of Data  
  • Specimens  
  • Microstructures  
  • Data Analysis  
  • Discussion  
  • Comparison to Sn-4Ag Tensile Creep Data  
  Sn-3.5Ag Compression Creep  
  • Raw Data  
  • Data Analysis  
  • Comparison of Tensile and Compressive Creep  
  Creep of Sn-3.5Ag Lap Shear and Plug & Ring Joints  
  • Shear Joint Sizes  
  • Sn-3.5Ag Lap Joint and Plug & Ring Shear Data  
  • Analysis of Sn-3.5Ag Lap Joint and Plug & Ring Shear Data  
  • Comparison to Sn-3.65Ag and Sn-4Ag Data  
  Creep of Sn-3.5Ag CCC Solder Joints in Shear  
  • Darveaux's Sn-3.5Ag Data  
  • Fit of Darveaux's Data to Lap Shear and Plug & Ring Correlation Band  
  • Regression of Darveaux's CCC Shear Data  
  Creep of Sn-3.5Ag Flip-Chip Solder Joints in Shear  
  • Flip-Chip Sn-3.5Ag Shear Data  
  • Comparison of Flip-Chip and CCC Solder Joint Shear Data  
  Other Properties of Sn-3.5Ag  
  • Young's Modulus vs. Temperature  
  • Poisson's Ratio  
  • Coefficients of Thermal Expansion (CTE)  
  • Other Physical Properties  
  Discussion  
  • Data Scatter  
  • Multiaxial Conditions  
  • Constitutive Modeling  
  • Recommendations  
 

Discussion

Data Scatter

The scatter of the Sn-3.5Ag literature data is better described as erratic rather than random since none of the reported studies was statistical in nature. There are many possible reasons for this, including differences in specimen size and geometry, specimen preparation and treatment, interfacial metallurgical effects in the case of shear specimens, test and loading conditions (e.g., tensile test at constant strain rate versus loadcontrolled creep test), possible specimen misalignment and other experimental differences and errors. Also, load-controlled creep tests are not exactly constant-stress tests although the data is often treated as if they were. Last, the initial loading rate has an impact on the entire deformation history but, often, this initial loading rate is not reported.

The various tests that were investigated did not follow a unique standard and the reports that were examined had variable levels of completeness. For example, the microstructural features of solder joints or specimens were not always available and, when they were, representative dimensions (such as the length and distribution density of intermetallic precipitates) were not given and were difficult to evaluate on micrograph reproductions.

Multiaxial Conditions

The Sn-3.5Ag compression, bulk solder data suggests higher strength or creep resistance in compression than in tension. However, we were not able to find a correlation between shear and tensile test results.

The often-used Von Mises yield criterion leads to a simple (and useful) transformation between tensile (sigma, epsilon) and shear (tau, gamma) stresses and strains: sigma = tausquare root 3, an = gamma / square root3. This criterion has been validated at strain rates above 10-4/sec for near-eutectic SnPb based on mechanical testing of bulk tensile and torsion specimens (Low and Fields, 1991).

To our knowledge, the Von Mises criterion, and the resulting stress / strain transformations, remain to be investigated before they can be applied to Sn-3.5Ag.

Constitutive Modeling

The data that was analyzed was fitted to simplified hyperbolic sine creep models. These do not constitute a full-fledge constitutive model per se but provide a simple equation that allows for some consolidation of secondary creep data. The hyperbolic sine models have been found to work well for engineering metals that exhibit significant creep deformations and they are easily implemented in commercial finite element models.

The reviewed data does not allow for the development of a complete constitutive model since mostly secondary or steady state creep was reported on. However, it is noteworthy that the study by Darveaux et al. (1995) provides a tentative constitutive model for Sn3.5Ag solder joints. The Darveaux model is of the additive type whereby strains are broken up in their elastic, plastic, primary and secondary creep components. The reader is referred to the original work by Darveaux et al. (1995) for pertinent details of this model. Yang, H. et al. (1996) also stressed the need to investigate primary creep for Sn3.5Ag solder.

Given the parallelism between Darveaux's CCC and Wiese et al.'s flip chip data, it is worthwhile applying the Darveaux model to the stress/strain analysis of Sn-3.5Ag solder assemblies. As always, such an analysis would have further merit if it were validated against independent experimental data.

More advanced constituve models have been proposed for Sn-3.5Ag and Sn-4Ag, such as Unified Creep Plasticity (UCP) models (see Wen, 2001, and Neu et al., 2001, for example). These models treat plastic and creep strains as a single visco-plastic or inelastic strain. In the formulation of inelastic strain rates, applied stresses are reduced by an internal back-stress that reflects the resistance of intermetallic precipitates, or other obstacles, to dislocation motions. Back-stresses are state variables that follow their own evolution equations. The latter are semi-empirical and may call for a large number of fitting constants depending on the complexity of the back-stress model.

One advantage of the UCP models is that they allow for the simulation of entire stress/strain histories, prior to and after initiation of cumulative damage. However, to this author's knowledge, the user implementation of UCP models in commercial finite element codes is not readily available.

Recommendations

Based on our review of Sn-3.5Ag properties, further analysis is warranted before the full range of deformations can be characterized accurately and before a workable constitutive model can be used in engineering / design applications. Whatever type of constitutive model is developed, it is important that the model be validated against independent data. Often, model constants are obtained from a set of test results from a single source and the model is validated (when it is) against other or similar results from the same test matrix.

Three types of stress/strain measurements are useful for model validation:

  • Graphs of entire stress/strain curves that are acquired in isothermal, constant strain rate tests. Many reports only publish the ultimate strength (e.g. the Ultimate Tensile Strength or UTS from a tensile test) for a given strain rate and temperature. The entire stress/strain curve would be of use as the portion of it prior to reaching the ultimate strength captures a more complete history of inelastic deformations. An appropriate constitutive model should be capable of simulating this initial portion of the stress/strain curve.
  • Similarly, few creep test reports include plots of deformations versus time. Again, these would be useful for the investigation of initial deformations (plastic flow, primary creep) as well as for the validation of constitutive models. See Villain et al., 2000, for such examples of Sn3.5Ag deformation curves.
  • Last, since one major goal of alloy testing is to develop models for the analysis of solder joints of electronic assemblies under thermal cycling conditions, histories or cyclic hysteresis loops of average shear stresses and strains in actual solder joints are needed. Such hysteresis loops will provide for the ultimate validation of solder alloy constitutive models. Guidelines and test procedures for acquiring such hysteresis loops are available in Hall (1984), Lau and Pao (1997) and Pao et al. (1992-93).
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