Home / Examples / Stress Analysis [Galileo] / Example 38: Elasto-Plastic Material Subjected to Repetitive Thermal Loading
This is an example of multi-step thermal load analysis.
In this example, the solder as a temperature-dependent elasto-plastic material is subjected to the thermal load of temperature cycles.
The plastic strains accumulate over time.
Unless specified in the list below, the default conditions will be applied.
Elasto-plastic analysis is available in an optional package.
Item |
Settings |
Analysis Space |
Axisymmetric |
Model Unit |
mm |
To simplify the analysis, the axisymmetric model is analyzed.
Select the thermal load option.
Item |
Settings |
Solver |
Stress Analysis [Galileo] |
Analysis Type |
Static Analysis |
Options |
Select Thermal Load |
The Step/Thermal Load tab is set as follows.
Tab |
Setting Item |
Settings |
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Step/Thermal Load |
Step Setting |
Multi-step Thermal Load Analysis |
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Time Setting |
Set up |
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Reference temperature |
25 [deg] |
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Step/Reached Temperature Setting |
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Options for the Multi-Step Analysis |
Save the results of substeps : Select |
The reference temperature (non-stress temperature) is 25 [deg]
Select [Multiple steps] for the step setting and [Set up] for the time setting,
and set the time, substeps, and reached temperature for the step/reached temperature setting.
The duration of the temperature-rise/fall steps is 300 [s] = 5 [min] each and the number of substeps is 10.
The duration of the temperature-keep steps is 3300 [s] = 55 [min] and the number of substeps is 1.
The time setting is the same as that of Example 39 for easy comparison.
The absolute time has no meaning when analyzing elasto-plastic materials.
The number of substeps is minimized to 1 during the temperature-keep steps as there is no change expected.
The absolute time is a physical parameter required for the creep materials analysis. See Example 39 for more information.
By selecting [Save results of substeps], the results at each substep can be output.
A silicon chip is to be soldered on a glass-epoxy PCB.
The mesh size of the solder ball is set to 0.2.
Body Number/Type |
Body Attribute Name |
Material Name |
0/Sheet |
PCB |
006_Glass_epoxy |
1/Sheet |
SB |
SOLDER |
2/Sheet |
CHIP |
301_Silicon(single-crystal) |
The material properties of SOLDER are set up as follows:
Material Name |
Tab |
Properties |
SOLDER |
Elasticity |
Material Type: Elasto-plastic/Multilinear Hardening Law: Kinematic Hardening Temperature Dependency: Yes Material Property:
[Young's Modulus Poison's Ratio Temperature] Table:
[Plastic strain-Stress] Multilinear: See graphs below.
Stress-Strain Graph, Stress-Plastic strain Graph
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Coefficient of Linear Thermal Expansion |
23X10-6 [1/deg] |
Boundary Condition Name/Topology |
Tab |
Boundary Condition Type |
Settings |
Fix_z/Vertex |
Mechanical |
Displacement |
Select the Z-direction component. UZ=0 |
The accumulated equivalent plastic strain at the final time of 14400 [s] is shown below.
High strains are exhibited at the border of SB and CHIP.
Strains are concentrated at the top right corner of the solder.
The accumulated equivalent plastic strain over time is shown below.
The plastic strains accumulate over time.
There is no change while the temperature remains the same.
The von Mises equivalent stress at the border of SB and CHIP over time is shown below.
The stress is higher at the low-temperature period than at the high-temperature period.
This is because the temperature difference from the reference is larger and the solder's yield stress is higher at low temperature.
