CHAPTER 5 SIMULATION METHODS
5.2 Thermomechanical Inherent Strain Method
5.1.3 Cube Specimens Simulation
Using the strain values derived from the isotropic and orthotropic calibrations, cubes were simulated for 0°, 67° and 90° HR. A cut plane was specified at a height of 3.8 mm from the build plate, with the cutting procedure applied in three steps to incorporate the resultant directional stress relieving. Model input parameters were taken from the isotropic and orthotropic calibration results with the input inherent strains from the corresponding calibrations. Simulation of the cubes with the evolution of the equivalent stress throughout the process is shown in Figure 5-4 indicating the stress build up as the elemental layers are added.
Figure 5-4: Equivalent stress development during isotropic ISM.
The results for the isotropic and orthotropic ISM were analyzed after incorporating removal from the build plate and removal of the support structures in the FEM environment. Nodal values of the elements were extracted for the σxx, σyy and σzz stresses and compared to the experimentally measured RS as presented in following chapters, with full results of the XZ plane measurement region at center width shown in Appendix B.
as a result of thermal input. The complete method, calibration targets and results are presented as follows.
5.2.1 Material Thermal Properties
In the thermo-mechanical simulations types the same mechanical properties were taken as given for the mechanical ISM models. Thermal properties of the IN718 solid material were adjusted to take into consideration variation in emissivity and thermal conductivity at different temperatures with values as shown in Table 5-4 [72],[89].
Table 5-4: Thermal properties of solid IN718.
Temperature [K]
Thermal Conductivity
[W/mK]
Emissivity [-]
Temperature [K]
Thermal Conductivity
[W/mK]
Emissivity [-]
298 8.9 0.539 1173 25.8 0.537
373 10.8 0.533 1273 26.7 0.537
473 12.9 0.533 1373 28.3 0.538
573 15.2 0.534 1443 29.3 0.538
673 17.4 0.534 1609 444 0.329
773 18.7 0.535 1673 444 0.332
873 20.8 0.535 1773 444 0.337
973 21.9 0.536 1873 444 0.341
The thermal properties of the build plate and powder material are shown in Appendix A as a function of temperature. After defining the thermal and mechanical properties of the build plate, powder material and solid IN718, the model was further developed with build and simulation parameter inputs.
5.2.2 Simulation Setup
For the thermomechanical simulation, voxel sizes of 0.25 mm and 1 mm were used for the cantilever and build-plate respectively with no mesh coarsening. Build plate deformation was enabled in the simulation, with build plate release set as instant (the Coherent Creator™ only uses a single centered attachment point for the build plate). An initial build plate and feedstock temperature of 25 Co was specified with build volume temperature at 34.4 Co. The layers were
applied a bi-directional scanning strategy, with an 8 second cooling period between completion of a layer and scanning of the subsequent layer.
5.2.3 Calibration
In order to derive the energy exposure fraction, a cantilever is thermally modelled on the build plate with a peak temperature on the top center of the cantilever used as calibration target, this being the only calibration type that uses this location as target point (Figure 5-5).
Figure 5-5: Thermal calibration target point location.
The temperature was taken as 2000 oC correlating to a rule of thumb 1.5× melting temperature as prescribed by Simufact, which in theory is less than the maximum temperature described by Xia et al. at 2148oC [93], however this value may be decreased due to the increased hatch spacing used in this study, but would require further investigation which is beyond the scope of this work.
From the thermal calibration an exposure energy fraction of 33.501% was derived and used in the thermomechanical calibrations and simulations.
The thermomechanical calibration in Simufact Additive is similar to the isotropic calibration with regards to the displacement of single cantilevers with associated HR used as calibration target.
This method however also incorporates the material thermal properties and derived energy exposure fraction to determine the stress state resulting from the addition, heating and cooling of element layers. The calibration iteratively solves for a uniform volumetric expansion factor for the elements based on the thermal history of the cantilever.
For the thermo-mechanical calibration, thermal properties for the material were used as in the thermal calibration type, with mechanical properties being the same as specified in the mechanical ISM. Voxel sizes were again kept constant between the thermal and thermo- mechanical calibration types as the energy exposure fraction and volumetric expansion factor are
Thermal calibration target point
voxel size dependent. This thermomechanical approach was then used for three different instances of cantilever HR, namely, 0° longitudinal, 67° and 90° HR with volumetric expansion factors displayed in Table 5-5
Table 5-5: Thermomechanical calibration results.
Hatch rotation Volumetric expansion factor
Calibration result [mm]
Target difference [%]
0° longitudinal 0.9199 3.067 0.65
67° 0.60 2.220 0.18
90° 0.3250 2.231 0.67
The volumetric expansion factors were correlated well to the displacement of the cantilever, with all converged displacements being within 1% of the measured values.
5.2.4 Cube Specimens Simulation
To derive the stress state of the cubic specimens using the thermomechanical approach, the software solves for the thermal and mechanical state of the specimens by simulating the cycling that occurs with the addition and melting of each layer. This is then coupled to the mechanical FEM to show the stress state correlating to the thermal expansion of the newly deposited layer of elements (Figure 5-6).
Figure 5-6: Thermomechanical temperature and corresponding RS of a single layer thermal cycle
The single layer addition shows the tensile RS at a minimum while temperatures are highest, increasing as the component is cooled before the next layer addition.
Simulation of addition and heating of a new layer.
RS as a result of the simulated temperature field.
Temperature and corresponding stress state before addition of new layer of elements.
Cooling per time increment
The RS of the cubes upon cooling, removal from the build plate and removal of support structure is shown in Figure 5-7 for the 0° HR specimen central XZ plane.
Figure 5-7: Thermomechanical ISM stress results for 0° HR with A). σxx, B). σyy, and C). σzz RS on plane at Y = 7.5 mm.
The results of the plane at Y = 7.5 mm indicate large tensile RS on the outer regions of the plane, with compressive RS towards the central regions. RS results for the 67° and 90° HRs on the central plane (Y = 7.5 mm) are shown in Appendix B.