# Tantalum Alloy Welding: Does the Thermal Cycle Influence the Microstructure?
## 2 Materials and Methods
### Finite Element Method Simulation  
For the design verification in this project, the finite element modeling was carried out using the ANSYS software (ANSYS(r) Academic Research Mechanical, Release 2015 R1 Washington County, PA, USA).  
The arc welding process encapsulates several coupled physical phenomena, including, but not limited to, fluid flow in the molten pool, heat flow, and microstructural evolution of the materials. These processes must be modeled as a multiphysics problem.  
Despite the fact that the thermomechanical coupling effects [16] are known to effect on the precision of the model (when considering the combined effect of temperature and mechanical stresses), it is preferred to opt for a purely thermal model. Other arc welding simulation techniques, such as the double ellipsoidal model, developed by [17], have been  
Figure 2: Standard sample of the tantalum alloy, extracted from the non-heat-affected zone.  
discarded to the difficulty of the determination of its geometric and energetic parameters. This mentioned author recommends determining the geometrical characteristics of the ellipsoid and calibrating the energy parameters experimentally.  
Commercial FEA packages (such as ANSYS) are not capable of directly correlating the effects of multi-phase or -domain structures when the transformation of heterogeneous microstructures takes place (if a thermal and/or mechanical load is applied). In recent years, the phase field method, based on the Ginzburg-Landau theory [18], or isothermal phase field models [19] (for shape memory alloys) have been applied. It is understood that these simplifications suppose a slight uncertainty about the precision of the model, but they are understood as sufficient for the given purpose.  
The physical properties of pure tantalum have been used to carry out the simulation, assuming that it is practically the same as that of the B 521 alloy (consider as high purity tantalum). For the boundary conditions, the actual temperatures were defined, and the restrictions considered applied, where, at the non-welded ends, the temperature is that of the environment. An orthohedral geometry was used on a square mesh configuration. Ten cells, of 0.2 mm, were used in the direction of the Z axis (parallel to the heat-affected zone). Elements of 0.2 mm were used in the remaining areas. Figure 3 shows the meshed model of the welded pipe. The melting temperature of the base metal was applied to the welded area, which will allow for to obtain its distribution in the analyzed model. This more densely discretized the region concerns, from the vicinity of the surface to 1.5 mm in depth. The mesh was structured with 14,988 nodes and 2414 elements. SOLID186 elements were used; these are a higher-order, 3D, 20-node solid element that exhibits quadratic displacement behavior. The element is defined by 20 nodes, having three degrees of freedom per node: translations in the nodal x, y, and z directions [20].  
For the boundary conditions, the actual temperatures were defined, and the restrictions considered were applied. Displacement in X- \"(direction transverse to the length of the weld bead), Y- (the outgoing direction of the weld plane), and Z-axis (direction parallel to the length of the weld bead) were suppressed. This is known as \"restraining\" the piece to be welded. For simplicity, a cylindrical projection with variation in the X-axis has been assumed.  
The high temperatures of the refractory metal welding process did not allow the validation of the thermal model with thermocouples. Infrared thermometers show a good correlation, but the high degree of uncertainty at these temperatures is not conclusive, and the thermometer was focused on the bead area during the welding process.  
Figure 3: Meshed model of the welded pipe.