Abstract
Due to localized heating and cooling in the Selective Laser Melting based additive manufacturing process, a steep temperature gradient forms in the heat affected zone which induces unwanted thermal stresses in the component. In this work, a transient coupled thermo-mechanical model is developed to study the evolution of stresses at microscale on a spot during laser processing of Ti6Al4V powder layer in the heating and the subsequent cooling stage. The thermal model accounts for melting, solidification, fluid flow in the melt pool, variation of the material properties with different phases and volume reduction in the porous powder layer upon melting. The thermal model is validated by comparing the predicted melt pool size for different laser powers with the benchmark experimental data. The thermal model is fully coupled with the mechanical model, accounting plasticity, used to calculate the resulting stress field. The temporal evolution of temperature, various stress components and von Mises stress is described. During heating, compressive stresses are observed in the region below the melt pool. A zone of tensile stresses is developed in the surrounding region to balance these compressive stresses. During the cooling stage, tensile stresses are found in the solidified melt pool region and balancing compressive stresses are found in the region underneath. Determination of critical locations of excessive residual stress suggests that in the solidified melt pool and surrounding region in the solid substrate the residual stresses exceed the yield strength of the material. This implies yielding in that region which can cause material failure. It is quantified that the magnitude of residual stresses increases with laser power and laser interaction time and decreases with pre-heating of solid substrate.
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Abbreviations
- A :
-
Laser absorptivity of the powder material
- C p :
-
Specific heat capacity (J kg-1 K-1)
- E :
-
Young's Modulus (GPa)
- E T :
-
Tangent Modulus (GPa)
- \( \overrightarrow{g} \) :
-
Acceleration due to gravity (m s-2)
- h :
-
Convective heat transfer coefficient (W m-2K-1)
- k :
-
Thermal conductivity (W m-1K-1)
- L :
-
Latent heat of the fusion (J kg-1)
- P :
-
Laser power (W)
- p :
-
Pressure (Pa)
- q :
-
Heat energy from the laser beam (W m-2)
- R :
-
Laser beam radius (m)
- r :
-
Radial distance from the center of the laser beam (m)
- T :
-
Temperature (K)
- t x :
-
Traction component in x-direction (Pa)
- t y :
-
Traction component in y-direction (Pa)
- \( \overrightarrow{u} \) :
-
Continuum velocity vector (m s-1)
- u x :
-
Displacement in x-direction (m)
- u y :
-
Displacement in y-direction (m)
- V :
-
Volume of the domain (m3)
- V g :
-
Gaussian profile velocity for volume reduction (m s-1)
- ϕ :
-
Porosity of the powder layer
- ρ :
-
Density (kg m-3)
- β T :
-
Coefficient of thermal expansion of liquid (K-1)
- ε ′ :
-
Emissivity
- σ ′ :
-
Stefan Boltzmann constant (W m−2 K−4)
- β :
-
Volume fraction of liquid phase
- α m :
-
Mass fraction
- α:
-
Coefficient of thermal expansion of solid (K-1)
- μ :
-
Dynamic viscosity (kg m-1 s-1)
- τ:
-
Shear stress (Pa)
- γ:
-
Surface tension coefficient (N m-1 K-1)
- S ij :
-
Stress tensor (Pa)
- S ys :
-
Instantaneous yield strength (Pa)
- S ys0 :
-
Initial yield strength (Pa)
- ℇ ij :
-
Strain tensor
- l :
-
Liquid
- s :
-
Bulk solid
- p :
-
Powder
- solidus :
-
Solidus temperature
- liquidus :
-
Liquidus temperature
- ref :
-
Reference
- conv :
-
Convection
- rad :
-
Radiation
- el :
-
Elastic
- th :
-
Thermal
- σ :
-
Mechanical
- pl :
-
Plastic
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Saxena, S., Sharma, R. & Kumar, A. A Microscale Study of Thermal Field and Stresses during Processing of Ti6Al4V Powder Layer by Selective Laser Melting. Lasers Manuf. Mater. Process. 5, 335–365 (2018). https://doi.org/10.1007/s40516-018-0070-6
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DOI: https://doi.org/10.1007/s40516-018-0070-6