Finite volume methods applied to the computational modelling of welding phenomena

This paper presents the computational modelling of welding phenomena within a versatile numerical framework. The framework embraces models from both the fields of computational fluid dynamics (CFD) and computational solid mechanics (CSM). With regard to the CFD modelling of the weld pool fluid dynamics, heat transfer and phase change, cell-centred finite volume (FV) methods are employed. Additionally, novel vertex-based FV methods are employed with regard to the elasto-plastic deformation associated with the CSM. The FV methods are included within an integrated modelling framework, PHYSICA, which can be readily applied to unstructured meshes. The modelling techniques are validated against a variety of reference solutions.

Characterisation of weldpool shapes in the laser welding of thick plates

We consider the problem of finding the heat distribution and the shape of the liquid fraction during laser welding of a thick steel plate using the finite volume CFD package PHYSICA. Since the shape of the keyhole is not known in advance, the following two-step approach to handling this problem has been employed. In the first stage, we determine the geometry of the keyhole for the steady-state case and form an appropriate mesh that includes both the workpiece and the keyhole. In the second stage, we impose the boundary conditions by assigning temperature to the walls of the keyhole and find the heat distribution and the shape of the liquid fraction for a given welding speed and material properties. We construct a fairly accurate approximation of the keyhole as a sequence of include sliced cones. A formula for finding the initial radius of the keyhole is derived by determining the radius of the vaporisation isotherm for the line heat source. We report on the results of a series of computational experiments for various heat input values and welding velocities.

A domain decomposition algorithm for inverse welding problems

A mathematical model and a numerical scheme for the inverse determination of heat sources generated by means of a welding process is presented in this paper. The accuracy of the heat source retrieval is discussed.

Domain decomposition methods for welding problems

This paper, a 2-D non-linear electric arc-welding problem is considered. It is assumed that the moving arc generates an unknown quantity of energy which makes the problem an inverse problem with an unknown source. Robust algorithms to solve such problems e#ciently, and in certain circumstances in real-time, are of great technological and industrial interest. There are other types of inverse problems which involve inverse determination of heat conductivity or material properties [CDJ63][TE98], inverse problems in material cutting [ILPP98], and retrieval of parameters containing discontinuities [IK90]. As in the metal cutting problem, the temperature of a very hot surface is required and it relies on the use of thermocouples. Here, the solution scheme requires temperature measurements lied in the neighbourhood of the weld line in order to retrieve the unknown heat source. The size of this neighbourhood is not considered in this paper, but rather a domain decomposition concept is presented and an examination of the accuracy of the retrieved source are presented. This paper is organised as follows. The inverse problem is formulated and a method for the source retrieval is presented in the second section. The source retrieval method is based on an extension of the 1-D source retrieval method as proposed in [ILP].

Minimising the risk of defects in nano-imprint forming

Nano-imprint forming (NIF) is among the most attractive manufacturing technologies offering high yield and low-cost fabrication of three-dimensional fine structures and patterns with resolution of few nanometres. Optimising NIF process is critical for achieving high quality products and minimising the risk of commonly observed defects. Using finite element analysis, the effect of various process parameters is evaluated and design rules for safe and reliable NIF fabrication formulated. This work is part of a major UK Grand Challenge project - 3D-Mintegration - for design, simulation, fabrication, assembly and test of next generation 3D-miniaturised systems.

Three-dimensional simulation of the influence of convection on dendritic solidification

Bulk and interdendritic flow during solidification alters the microstructure development, potentially leading to the formation of defects. In this paper, a 3D numerical model is presented for the simulation of dendritic growth in the presence of fluid flow in both liquid and semi-solid zones during solidification. The dendritic growth was solved by the combination of a stochastic nucleation approach with a finite difference solution of the solute diffusion equation and. a projection method solution of the Navier-Stokes equations. The technique was applied first to simulate the growth of a single dendrite in 2D and 3D in an isothermal environment with forced fluid flow. Significant differences were found in the evolution of dendritic morphology when comparing the 2D and 3D results. In 3D the upstream arm has a faster growth velocity due to easier flow around the perpendicular arms. This also promotes secondary arm formation on the upstream arm. The effect of fluid flow on columnar dendritic growth and micro-segregation in constrained solidification conditions is then simulated. For constrained growth, 2D simulations lead to even greater inaccuracies as compared to 3D.

Modelling the tilt-casting process for the tranquil filling of titanium alloy turbine blades

The tilt-casting method is used to achieve tranquil filling of gamma-TiAl turbine blades. The reactive alloy is melted in a cold crucible using an induction coil and then the complete crucible-mould- running system assembly is rotated through 180degrees to transfer the metal into the mould. The induction current is ramped down gradually as the rotation starts and the mould is preheated to maintain superheat. The liquid metal then enters the mould and the gas within it (argon) escapes through the inlet aperture and through auxiliary vents. Solidification starts as soon the metal enters the mould and it is important to account for this effect to predict and prevent misruns. The rotation rate has to be controlled carefully to allow sufficient time for gas evacuation, but at the same time preserve superheat. This 3-phase system is modelled using the FV method, with a fast implicit numerical scheme used to capture the transient liquid free surface. The enthalpy method is used to model solidification and predict defects such as trapped bubbles, macro-porosity or surface connected porosity. Modeling is used to support an experimental program for the development of a production method for gamma-TiAl blades, with a target length of 40cm. The experiments provide validation for the model and the model in turn optimizes the tilt-casting process. The work is part of the EU project IMPRESS.