Thermo-mechanical Model for WAAM
Date: 13.05.2025
Mukul
M. Tech, IIT Bombay
(Corrosion Science & Engineering)
Contents
• Introduction
• Assigning Interaction
• Model Details
• Load: Thermal Load and Boundary
Conditions
• Part Design: Sketching and Modelling
• Meshing
• Material Properties: Ti-6Al-4V and IN718
• Creating and Assigning Section
• Results: Von-Mises Stress, Temperature
Distribution, Temperature Gradient, and
Heat Flux
• Assembly Drawing
• Conclusion
• Creating Step
2
Introduction
• 3-D transient coupled temperature-displacement thermo-mechanical model is
attributed for WAAM model using ABAQUS™ in order to understand the
deposition methodology and process
• A solution domain of Ti-6Al-4V and IN 718 for 100 mm length (X-axis) , 9 mm
high (Y-axis), and 100 mm thick (Z-axis) was used as a substrate and a single heat
source is applied
• The primary objective is to monitor temperature variations within the built part
and precisely analyze the temperature distributions and stress within the melt
and compare the results between Ti-6Al-4V and IN 718
3
Model Details
Fig: Substrate of 100 mm long, 9 mm high, and 100 mm thick
Source: https://www.youtube.com/watch?v=R7b3psTrhWs
• Single heating source is used to heat the material and layers are deposited over
the substrate
4
Part Design: Sketching
Fig: Sketch of solution domain
Source: https://www.youtube.com/watch?v=R7b3psTrhWs
• Substrate and layers are sketched two-dimensionally on XY plane with proper
dimensions (in mm)
5
Part Design: Modelling
Fig: Model of solution domain
Source: https://www.youtube.com/watch?v=R7b3psTrhWs
• Part modelling is 3-D deformable type and base features are solid extrusion type
6
Ti-6Al-4V Mechanical Properties
Temp (K)
Young’s Modulus (MPa)
Temp (K)
Yield Stress (MPa)
Temp (K)
Expansion Co-efficient (/K)
300
125000
300
955
300
8.78E-6
533
110000
573
836
533
9.83E-6
589
100000
773
732
589
1E-5
700
93000
1023
581
700
1.07E-5
755
80000
1073
547
755
1.11E-5
811
74000
1173
480
811
1.12E-5
923
55000
1273
405
923
1.17E-5
1073
27000
1373
330
1073
1.22E-5
1098
22000
1098
1.23E-5
1123
18000
1123
1.24E-5
1573
12000
1573
1.3E-5
1873
9000
1873
1.63E-5
Table: Temperature-dependent mechanical properties
Source: http://dx.doi.org/10.1016/j.commatsci.2016.10.003
• In our case, yield strength, elastic modulus, and expansion co-efficient is considered
7
Ti-6Al-4V Thermo-physical Properties
T (K)
Specific Heat (N-mm/kg-K)
T (K)
Specific Heat (N-mm/kg-K)
T (K)
Conductivity (W/mm-K)
T (K)
Conductivity (W/mm-K)
300
499523.8
1023
513600.5088
300
6.28
1023
16.891471
533
504537.508
1073
514412.4448
533
9.813911
1073
17.586671
573
505352.5848
1098
514810.5753
573
10.409671
1098
17.932396
589
505674.8702
1123
515203.4808
589
10.647079
1123
18.276871
700
507851.8
1173
515973.6168
700
12.28
1173
18.962071
755
508892.2955
1273
517451.1888
755
13.079975
1273
20.317471
773
509227.3288
1373
518845.1608
773
13.340471
1373
21.652871
811
509925.7262
1573
521382.3048
811
13.888279
1573
24.263671
923
511913.9368
1873
524561.0208
923
15.486071
1873
28.029871
Density (kg/𝐦𝐦𝟑 )
Solidus Temperature (K)
Liquidus Temperature (K)
4E-6
1878
1928
Table: Temperature-dependent thermal properties and physical properties
Source: http://dx.doi.org/10.1016/j.commatsci.2016.10.003
• In our case, specific heat, thermal conductivity, and general property i.e. density,
solidus and liquidus temperature is considered
8
IN 718 Mechanical Properties
Temp (K)
Young’s Modulus (MPa)
Temp (K)
Yield Stress (MPa)
Temp (K)
Expansion Co-efficient (/K)
300
156300
300
308.9
300
1.17E-5
366.5
151800
588.7
246.3
477.6
1.28E-5
477.6
144900
810.9
226.1
588.7
1.34E-5
588.7
138000
1033.2
207.7
922
1.46E-5
699.8
131400
1255.4
114
1033.2
1.51E-5
810.9
124700
1144.3
1.57E-5
922
124000
1366.5
1.66E-5
1033.2
123400
1672
1.66E-5
1144.3
107700
1900
1.42E-5
1255.4
92050
2400
1.08E-5
1366.5
68950
2700
9.47E-6
1672
23790
3200
7.84E-6
Table: Temperature-dependent mechanical properties
Source: http://dx.doi.org/10.1016/j.commatsci.2016.10.003
• In our case, yield strength, elastic modulus, and expansion co-efficient is considered
9
IN 718 Thermo-physical Properties
T (K)
Specific Heat (N-mm/kg-K)
T (K)
Specific Heat (N-mm/kg-K)
T (K)
Conductivity (W/mm-K)
T (K)
Conductivity (W/mm-K)
300
367680
1144.3
384754.11
300
8.63
1144.3
24.57874257
366.5
369231.711
1255.4
386576.2834
366.5
10.24824425
1255.4
25.93439588
477.6
371745.193
1366.5
388299.711
477.6
12.81368768
1366.5
27.11724425
588.7
374159.9292
1672
392529.664
588.7
15.20632617
1672
29.478912
699.8
376475.9198
1900
395200
699.8
17.42615972
1900
30.39
810.9
378693.1648
2400
399600
810.9
19.47318833
2400
29.84
922
380811.664
2700
401280
922
21.347412
2700
27.83
1033.2
382833.191
3200
402480
1033.2
23.05028432
3200
21.68
Density (kg/𝐦𝐦𝟑 )
Solidus Temperature (K)
Liquidus Temperature (K)
8.1E-6
1533
1609
Table: Temperature-dependent thermal properties and physical properties
Source: http://dx.doi.org/10.1016/j.commatsci.2016.10.003
• In our case, specific heat, thermal conductivity, and general property i.e. density,
solidus and liquidus temperature is considered
10
Creating and Assigning Section
Fig: Solid homogeneous section
11
Assembly Drawing
Fig: Assembly of solution domain
• Dependent instance part is created for which the mesh will be operated on part
12
Step
• Coupled temperature-displacement type transient analysis is done for all the
steps
• Increment size = 0.1 unit for time period = 1 unit
• NLGEOM = YES is considered for geometric non-linearity
• Step-1 is deactivated the part region
• Step-2 is reactivated the part region
13
Interaction
• Defines mechanical contact between the part instances of an assembly or
between part region and its surroundings
• Attributes, such as contact properties and surface properties are assigned as
part of the contact interaction definition but independently of the contact
domain definition, which allows use one set of surfaces for the domain
definition and another set of surfaces for the attribute assignments
• In our case, model change type is implemented for coupled temperaturedisplacement analysis
• The solution domain is a base plate with layer deposition on the central part of
the substrate
• First of all, the interaction of all the part region is deactivated, after that the
interaction of part region is activated
14
Interaction (Cont.)
Fig: Deactivation and reactivation of part region
15
Load
• Define the loads and boundary conditions
• In our case, thermal load is surface heat flux and boundary condition is the fixed
bottom surface i.e. displacement of all nodes of the surface along the global x, y,
and z axes respectively is zero and no rotation was allowed in any direction
• Elements only become activated with the stepwise movement of the heat
source. The heat source was applied as surface heat flux on newly activated
elements and previous elements
• Thermal loading, in our case, surface heat flux is implemented independently
• When thermal loading is activated in one step, the other step is kept deactivated
i.e. new elements are activated in each step
16
Boundary Conditions
Fig: Boundary condition at the bottom of part region
• U1, U2, and U3 is zero i.e. no displacement or rotation along the global x, y, and
z axes respectively for the substrate and layers
17
Thermal Load: Surface Heat Flux
Fig: Surface heat flux for part region
18
Meshing
Fig: Mesh of solution domain
• Mesh refinement was done for all the elements at the interface and in the
deposit to ensure accurate spatial resolution in the analysis.
• The mesh size = 1 unit is considered
19
Results
• Von-Mises Stress Distribution: To investigate the mechanical behaviour, the
stress distribution within the layer at various time steps was simulated using ‘S’
field output variable
• Temperature Distribution: To investigate the thermal behaviour, the temperature
distribution within the layer at various time steps was simulated using ‘NT11’
field output variable
• Heat Flux Distribution: To know about the amount of heat transferred across a
surface, the temperature distribution at various time steps was simulated using
‘HFL’ field output variable
• Temperature Gradient: To analyse the rate of change of temperature with
respect to spatial coordinates during heat transfer and thermal stress, the
simulation was done at various time steps using ‘GRADT’ field output variable
20
Mises Stress Distribution for Ti-6Al-4V at t = 0.1, 0.4, 0.7, 1 sec
t = 0.1 sec
t = 0.4 sec
t = 0.7 sec
t = 1 sec
21
Mises Stress Distribution for IN 718 at t = 0.1, 0.4, 0.7, and 1 sec
t = 0.1 sec
t = 0.4 sec
t = 0.7 sec
t = 1 sec
22
Inference
2
Variation of Mises Stress Distribution
−2
Min Stress
(MPa)
Log
Value
Max Stress
(MPa)
Log
Value
Ti-6Al-4V
1.55E-03
-2.81
1.48E+01
1.17
IN 718
1.96E-08
-7.71
2.94E-01
-0.53
1.16879
1
−4
0
−6
−0.53195
−7.70863
−1
Ti-6Al-4V
Log Minimun Von-Mises Stress (MPa)
Material
Log Maximum Von-Mises Stress (MPa)
−2.81051
−8
IN 718
• The stress increases with the interaction of loading, there is more increment in IN 718
than Ti-6Al-4V
23
Temperature Distribution for Ti-6Al-4V at t = 0.1, 0.4, 0.7, 1 sec
t = 0.1 sec
t = 0.4 sec
t = 0.7 sec
t = 1 sec
24
Temperature Distribution for IN 718 at t = 0.1, 0.4, 0.7, and 1 sec
t = 0.1 sec
t = 0.4 sec
t = 0.7 sec
t = 1 sec
25
Inference
Variation of Temperature Distribution
Min
7
Max
Material
Min Temp (K)
Max Temp (K)
Ti-6Al-4V
1.20E-01
7.11E+00
IN 718
0.00E+00
2.15E-01
Temperature (K)
6
5
4
3
2
1
0
Ti-6Al-4V
IN 718
• As the time progresses, the temperature increases significantly in Ti-6Al-4V and there is
not much change in IN 718 during the deposition
26
Temperature Gradient for Ti-6Al-4V at t = 0.1, 0.4, 0.7, and 1 sec
t = 0.1 sec
t = 0.4 sec
t = 0.7 sec
t = 1 sec
27
Temperature Gradient for IN 718 at t = 0.1, 0.4, 0.7, and 1 sec
t = 0.1 sec
t = 0.4 sec
t = 0.7 sec
t = 1 sec
28
Inference
200
Variation of Temperature Gradient
Material
Minimum
Temperature
Gradient (K/m)
Maximum
Temperature
Gradient (K/m)
Ti-6Al-4V
0.19
185.3
IN 718
0
95.31
Temperature Gradient (K/m)
185.3
Min
Max
150
100
95.31
50
0
0.188
Ti-6Al-4V
0
IN 718
• The temperature gradient during deposition is high in Ti-6Al-4V, this could be potential
for residual stresses and other defects during the process
29
Heat Flux Distribution for Ti-6Al-4V at t = 0.1, 0.4, 0.7, and 1 sec
t = 0.1 sec
t = 0.4 sec
t = 0.7 sec
t = 1 sec
30
Heat Flux Distribution for IN 718 at t = 0.1, 0.4, 0.7, and 1 sec
t = 0.1 sec
t = 0.4 sec
t = 0.7 sec
t = 1 sec
31
Minimum
Heat Flux
(W/𝐦𝟐 )
Maximum
Heat Flux
(W/𝐦𝟐 )
Ti-6Al-4V
1180
1164000
IN 718
0
822500
Material
Maximum Heat Flux (W/m2)
1200000
Variation of Heat Flux
1250
1125000
1000
1050000
750
975000
500
900000
250
825000
0
Ti-6Al-4V
Minimum Heat Flux (W/m2)
Inference
IN 718
• Heat flux per unit area increases more in Ti-6Al-4V than IN 718 during the deposition
32
Conclusion
• A solution domain of 100 mm length (X-axis) , 9 mm high (Y-axis), and 100 mm
thick (Z-axis) was modelled successfully using 3-D transient coupled
temperature-displacement thermo-mechanical model in ABAQUS™
• Simulation done successfully for the deposition of one layer over the substrate
for WAAM process
• Temperature and stress distribution of Ti-6Al-4V and IN 718 within the melt is
analyzed precisely
• Finally, understood the deposition methodology and process
33