Elasto-Plastic Bilinear Material Subjected to Thermal Loadexamples|products|Murata Software Co., Ltd.

Example35 Elasto-Plastic Bilinear Material Subjected to Thermal Load

General 

  • In this exercise, 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.
     

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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

Mechanical 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 125[deg] to the ambient temperature -40[deg] and then back to the reference temperature 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 “Include the unloading process”, 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 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 Expansion

21.7×10^-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 component.

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 kinematic hardening while the other is based on the isotropic 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 kinematic hardening than with the isotropic hardening.