Home / Examples / Stress Analysis [Galileo] / Example 35: Elasto-Plastic Bilinear Material Subjected to Thermal Load

Example 35: Elasto-Plastic Bilinear Material Subjected to Thermal Load

General 

• In this example, the solder defined as a temperature-dependent elasto-plastic material is subjected to thermal load.
   

• The plastic strain and the accumulated equivalent plastic strain at the reached temperature are solved.
   

• Unless specified in the list below, the default conditions will be applied.
   

• Obtain this session's project file. (Right-click and choose 'Save link as')
  
  

• Results will vary depending on Femtet version and the PC environment.

 

• Elasto-plastic analysis is available in an optional package.

 

Analysis Space

Item	Settings
Analysis Space	2D
Model Unit	mm

 

Analysis Conditions

To simplify the analysis, the 2-D 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
Step/Thermal Load	Reference Temperature	125 [deg]
	Step/Reached Temperature Setting	Step Substeps Reached Temperature [deg] 1 10 -40
	Options for the Nonlinear Analysis	Save the results of substeps : Select Add unloading step : Select

 

The temperature changes from the reference temperature of 125 [deg] to the ambient temperature of -40 [deg] and then back to the reference temperature of 125 [deg] .The plastic deformation is analyzed

To shorten the calculation time, Number of Substeps is set to be smaller than the default value, 20.

By selecting [Add unloading step], the unloading process of -40 [deg] back to 125 [deg] is added to the loading process of 125 [deg] to -40 [deg].

By selecting [Save the results of substeps], the results at the intermediate temperatures can be output.

 

Model

A silicon chip is to be soldered on a glass-epoxy PCB.

Select [Reflective] on the Symmetry/Continuity tab for the face of symmetry.

The mesh size of the solder ball is set to 0.1.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Sheet	PCB	006_Glass_epoxy
1/Sheet	CHIP	301_Silicon(single-crystal)
3/Sheet	SB	SOLDER

 

The material properties of SOLDER are set up as follows:

Material Name	Tab	Properties
SOLDER	Elasticity	Material Type: Elasto-plastic/Bilinear Hardening Law: Kinematic Hardening * Material Property: as listed below   Stress - Strain Graph:
	Coefficient of Linear Thermal Expansion	21.7X10-6 [1/deg]

* Isotropic hardening model is also included in the project file.

 

Boundary Conditions

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
Fix/Edge	Mechanical	Displacement	Select the XZ components. UX=0, UZ=0
Sym_x/Edge	Symmetry/Continuity	Symmetry	Reflective

Results

The principal strains of the plastic strain at step 1 (reached temperature of -40 [deg]) are shown below.

The full model can be viewed.

 

High strains are exhibited at the border of SB and CHIP.

 

The contour diagram below shows the accumulated equivalent plastic strains at step 1.

Strains are concentrated at the top right corner of the right solder ball.

 

The plots below indicate the accumulated equivalent plastic strain at the highly concentrated points over the steps.

One plot is based on the kinetic hardening while the other is based on the isotropic hardening.

For your reference: Isotropic Hardening and Kinetic Hardening

Steps 0 through 1 are the 10 steps starting from 125 [deg] down to -40 [deg].
Steps 1 through 2 are the 10 steps returning from -40 [deg] back to 125 [deg]. This is the unloading process.

 

The accumulated equivalent plastic strain increases even in the unloading process. The increase rate is higher with the kinetic hardening than with the isotropic hardening.