Download Numerical Analysis of Heat Distribution and Residual

By: Micah Bowen
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Experimental results for two thin plates being
welded together using a laser beam weld were
provided
The temperature, residual stress and strain, and
displacement of the workpiece will be replicated
using finite element analysis
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Reference [1] provided thermal, stress, and
displacement data to compare against.
Thermocouple
Locations
m
m
9 mm
7 mm
4 mm
0
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The experimental and FEA results from [1] will be
used.
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Laser
Path
5 mm
10 mm
15 mm
HAZ
1.5 mm
FEA Temperatrure
Locations
Jig
Clamps
200 mm
(1) Chukkan, Jazeel Rahman, M. Vasudevan, S. Muthukumaran, R. Ravi Kumar, and N. Chandrasekhar.
"Simulation of Laser Butt Welding of AISI 316L Stainless Steel Sheet Using Various Heat Sources and
Experimental Validation." Journal of Materials Processing Technology 219 (2015): 48-59. Web.
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The laser beam will be represented using a
conical heat source with a Gaussian distribution
shown below along with the equation
6 ∗ 𝜂 ∗ 𝑃 ∗ exp(3) −
𝑄 𝑥, 𝑦, 𝑧 =
∗𝑒
𝜋 ∗ (exp(3) − 1)
𝑥 2 +𝑦 2
𝑟𝑜 𝑧 2
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The material being analyzed in this project 316L stainless
steel
The workpiece temperatures are as high as 1,450.0°C during
welding. The melting temperature for 316L is 1,3751,400°C; therefore, the workpiece becomes molten around
the weld
This change to molten is
accounted for in the 316L
stainless steel properties
Kou, Sindo. Welding Metallurgy. Hoboken, NJ: Wiley-Interscience, 2003. Print.
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As the material heats up the yield stress decreased
When the workpiece heats up to molten temperatures, the
material begins to yield and goes from elastic to plastic.
Plasticity occurs when a material is stressed beyond its elastic
limit and yields resulting in large permanent deformations.
As the material stress goes into the plastic region up to point
A and is unloaded it returns
to point B. The distance
between the beginning
of the curve and point B
represents the permanent
deformation.
Digital image. Iron-Iron Carbide Phase Diagram Example., Web. 31 Oct. 2015.
<http://www.cyberphysics.co.uk/graphics/graphs/stress_strain2.gif> 6
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Finite element analysis will be used to
represent the laser beam experiment
Three steps to finite element analysis
◦ Pre-processing – The geometry of the system in
modeled in a computer automated design program
◦ Solution – The program derives the governing
matrix equations and solves for the displacement,
strains, and stresses
◦ Post-processing – The analyst obtains the desired
results of the analysis as well as checks the solution
for possible warnings and/or errors
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A 2D analysis of one of plates with symmetry
was modeled
The mesh density increased around the heat
affected zone (HAZ)
A transient thermal and structural run were
made
Applied Heat Source
Symmetry
Edge
Increasing Mesh Density
HAZ with Denser Mesh
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A transient thermal analysis was selected and the
thermal boundaries conditions were applied to
the model:
Symmetry Plane and
Perfectly Insulated
Conduction on Bottom
Surface
Convection and
Radiation
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The heat source was applied to the top of the
model
Heat was applied gradually to allow the model to
converge
Thermal probes were added to track the
temperature of the workpiece at specified
locations
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A transient structural analysis was selected
and the thermal time history was imported
into the structural run
A compression only support was added to the
bottom of the workpiece representing the jib
Three elastic supports representing the jig
clamps
Elastic Supports
Symmetry Compression Only
Support
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The FEA matched the HAZ from the experimental results
Since the temperature was applied more gradually, the overall
workpiece temperature was greater
The peaks of the temperature matched the experimental data
1.2 mm
1,600
Temperature (°C)
1,400
1,200
1,000
0.3 mm
800
FEA [1] 0 mm
600
FEA 0 mm
400
200
0
0
25
50
75
100
125
150
175
200
225
250
Time (s)
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In the FEA, the residual stress and strain are located at the interface
between the two plates and does not span the entire workpiece
There are multiple reasons this FEA did not capture the full residual
stress and strain across the entire workpiece including:
◦ Using elastic supports at the end of the workpiece over a clamped
constraint allowed the model to converge; however, these allowed for
more lateral displacement compared to a fixed support
◦ By applying the heat slowly, the steep gradient of a weld is lost and the
model does not plastically deform nearly as much as experiment in [1]
does
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The vertical displacement follows the
experimental trend but is lower in magnitude
This is due to the fact the heat was applied more
slowly compared to the actual experiment
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The FEA developed in this project could be
converted into three dimensional to capture the
structural affects along the length of the weld
This model could also adapt different types of
laser properties including different laser beam
shapes, continuous verse pulsed laser and
different laser welding patterns
Another addition to this project would be to track
the material phase as a function of heating and
cooling rates for materials such as AISI 1010
carbon steel
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When modeling a welding process using FEA, the
following aspects are important:
◦ Ensuring there the mesh around the HAZ area is
fine enough to properly predict the temperature
distribution to the surround material
◦ Inclusion of temperature dependent material
properties as well as thermal and structural
boundary conditions representing the actual
welding application
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