Temperature Dependent Material Properties
John Selverian, Jahm Software Inc., MA, USA
While setting up the governing equations, geometry, and mesh consumes the most simulation time, usually little time or effort is devoted to obtaining accurate material properties. Frequently, scientists and engineers obtain material data from a handbook or web site, which often provide limited data. For example, these resources typically do not specify the test and material conditions, and a reference to the original data source is not provided. It is common to use data at room temperature in a simulation because elevated temperature data could not be found. However, the effects of temperature on a given material property can be quite large and ignoring the temperature effects can lead to erroneous and misleading simulation results.
Faster Model Set-up Using the Material Library
Finding the right material properties to use in simulations can be time-consuming and expensive. The best method is to measure the properties you need on an actual sample of the material. Often, however, this is not possible, as material tests can cost tens of thousands of dollars and take several weeks if not longer to complete.
In light of these practical limitations, users of COMSOL can now turn to the Material Library for access to 2,500 materials, all of which fully integrate into the COMSOL Multiphysics modeling and simulation environment. This new product provides a database of temperature dependant material properties that can be added to your models at a click of a button. Even if the material is not available at the exact conditions you are using it, physical properties can be estimated from similar materials. For example, if your copper alloy does not match a material in the database exactly, you can select one that is as close as possible in composition, its heat treatment, or some other relevant aspect.
A Thermal Stress Study
Figure 1. Depiction of the surface resistor problem. The resistor is made from aluminum oxide (Al2O3).
An example of a surface mounted resistor (Figure 1) demonstrates the importance of temperature dependence and material plasticity on analysis results. Electrical current flowing through the resistor leads to energy dissipation which results in an increase in temperature. Electrical and therefore thermal cycling can lead to cracks propagating through the solder joints, resulting in premature failure. The failure is caused by the difference in thermal expansion coefficient between neighboring materials. A multiphysics simulation would consider heat transport, along with structural stresses and deformations. In this case, the resistor body is modeled using aluminum oxide (Al2O3) as the material, while the termination is made from silver, the solder from the Sn-4Ag alloy, and the circuit board from FR-4. Four different simulations are performed using combinations of room temperature versus temperature dependant material data with elastic versus elastic-plastic deformation.
Figure 2. Temperature dependence of the yield strength of the materials.
The model consists of 78,000 degrees of freedom and 3,732 elements. The same mesh and boundary conditions were used for all four analyses, where only the material properties and the plasticity model were changed: plastic deformation was defined to be perfectly plastic. Figure 2 shows the temperature dependence of the yield strength from 20°C to 160°C. The yield strength of Sn-4Ag is a factor of 2 lower at 160°C than at 20°C. This effect must be accounted for in any realistic simulation.
Three main conclusions can be drawn. First, plasticity must be included in the material model for realistic results. Second, over the temperature range of this problem, the temperature dependence of the thermal properties is not significant. The only material with substantial dependency on the thermal conductivity is Al2O3. However, this simulation applies a volumetric thermal load so that the thermal conductivity of Al2O3 does not influence the results. Third, the temperature dependence of the yield strength of the Sn-4Ag solder is very significant.
Results from the simulation show the maximum effective plastic strain in the solder increasing from 0.0194 to 0.0563, and the maximum tensile stress in the resistor decreasing from 341 MPa to 221 MPa, when the temperature dependency of the yield strength is taken into account (Table 1). Since many of the solder-reliability predictive equations use the plastic strain as a critical parameter, including temperature effects is very important when developing predictive correlations. Basing a design decision on the model performed using the room temperature data would result in a non-conservative design; i.e., the actual part would perform worse than the simulation predicts. Whenever possible, any uncertainty should lead to overdesign of the component, not underdesign.
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Figure 3. Plot of the effective plastic strain in the solder (above gure). The left-bottom figure is a close-up of the area of the joint from the simulation using room temperature properties. The right-bottom figure is from the simulation using the temperature-dependent properties. |
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The new Material Library database is designed to give more accurate simulation results from which better design decisions can be made. The ease at which the data can be imported into COMSOL makes the database as important tool for improved simulations with faster turnaround time.
| SIMULATION TYPE | MAXIMUM TEMPERATURE (°C) | MAXIMUM PRINCIPAL STRESS IN RESISTOR (MPa) | MAXIMUM EFFECTIVE PLASTIC STRAIN IN SOLDER |
|---|---|---|---|
| Room temperature material data and elastic deformation | 160 | 749 | - |
| Room temperature material data and elastic-plastic deformation* | 160 | 341 | 0.0194 |
| Temperature dependent material data and elastic deformation | 161 | 711 | - |
| Temperature dependent material data and elastic-plastic deformation* | 160 | 221 | 0.0563 |
* plastic deformation was defined to be perfectly plastic
Author Information
John Selverian, JAHM Software, Inc., has been involved in materials science for almost thirty years. He received his B.Sc. in Metallurgy in 1983, and then his M.Sc. (1985) and Ph.D (1988) in Materials Science and Engineering from Lehigh University in Bethlehem, PA. Dr Selverian started building his Material Properties Databases (MPDB) in 1998 when he was involved in high-temperature materials research. During the subsequent years, he has produced more than 20 papers and other publications, two US patents and one European patent.