Flow lines are defined by a set of points. The points can be element nodes or Gauss quadrature points inside elements. Because the velocity is chosen parallel to the x-axis in this example, the flow lines are always parallel to the x-axis. The first step in constructing flow lines loops over all points. The layered […]

The most time-consuming part of the flow line construction is in locating the elements that contain points on the flow line, since there may be several such searches required for each flow line. These searches are required to establish the starting conditions. At each layer, Gu et al [2] isolate the intervals in the direction […]

Some functionality will be required in the process to build up the flow lines. Since there are some similarities among all requirements, the required functionality will be implemented in one data structure. The data structure provides the functionality to: 1. loop over elements in the order from upstream to downstream; 2. find an element containing […]

The computation of microstructures at a spatial point requires that the thermal history be deduced from a set of elements or nodes in a steady state temperature field. The correct history of a material point at a downstream spatial point can be revealed only by following a flow line from its upstream origin to its […]

The microstructure algorithm used here was motivated by the work of Kirkaldy [16], and originally developed for welding by Watt et al.[21], Henwood et al.[22] and enhanced by Khoral [4]. The various microstructural transformation temperatures are a function of carbon and alloy content of the low alloy steel. For low alloy steel, the liquidus and […]

4.1 Introduction and Synopsis One of the most widely used methods for joining metal in engineering is fusion welding. The progress made in the chemical and oil industry, aerospace, shipbuilding, structures, etc. heavily relies on reliable welds. Potential losses and risk to human life involved in weld failure have resulted in stringent material and welding […]

Two test cases, of butt welds, have been analyzed on the same mesh structure, shown in Figure 3-17. The characteristics of this mesh are that the liquid metal in the weld pool is excluded and the weld bead can be seen on the plate after the weld pool to account for the added filler material. […]

Complex Weld Pool Shape Computational results are presented for the experiments described by Barlow [5]. It is a weld deposited on a low carbon steel plate of thickness 19 mm. The weld length is about 250 mm. In order to minimize end effects, the length and width of the plate are chosen to be 1224 […]

Of the three strong candidate numerical methods; finite difference, boundary element and finite element analysis, the finite element method have been chosen for its capability for nonlinear analysis and dealing with complex geometry. In addition, it is most compatible with modem CAD/CAM software systems. For thermal analysis alone, a strong argument can be made in […]

On the boundary of the domain Q either the essential (prescribed temperature) or natural (prescribed flux) boundary conditions must be satisfied. The essential boundary condition can be defined as: T(x, y,z, t) T|(x, y,z, t) on the boundary Sj, i. e., (x, y,z)^ S]. t ^ 0 (3-16) The natural boundary condition can be defined […]