Evolution of Microstructure Depending on Deformations

5.1 Introduction and Synopsis The thermal cycle imposed on any welded object causes thermal expansions and contractions to occur that vary with time and location. Since this expansion is not …

Hardness Calculation of the HAZ

The hardness of the HAZ is a very good indicator of its susceptibility to cracks and other problems. The hardness at any point in the HAZ can be calculated using …

Clipped transient temperature field

Sometimes an estimate of the steady state micro structures is desired in a temperature field computed by a transient time marching analysis. This kind of temperature field is frequently available …

Steady State Temperature Field

The Figures in this section show the state at the rear end of the mesh or flow lines. In the regular mesh next to the filler material, each element has …

Test Problems and Results

The microstructures were computed first for the temperature field, Figure 4-10, obtained from ref. [25]. The steady state temperature field was computed on a mesh with about 12,000 elements. The …

Creating flow lines

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 …

Locating elements

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 …

Functionality of the Data Structure

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 Structures Flow lines

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 …

Microstructure Model

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]. …

Evolution of Microstructure Depending on Temperature

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, …

Welds with Filler Metal Addition

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 …

Computational Results

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. …

Finite Element Solutions with Prescribed Temperature

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 …

Boundary Conditions

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, …

Starting Transient

When a real weld is started, the weld pool is not formed instantly. First, a Gaussian flux distribution heats the solid to the melting point, then a thin layer of …

Implementation of prescribed temperature model

The welding path is assumed as any valid geometric curve in space on which a local coordinate system moves. From the local coordinate system, a tangential vector and principal normal …

Power Input

The net power input for the weld, volt x amp x efficiency/speed, should equal the total thermal load reaction or sum of the Lagrange multipliers at the nodes connected to …

Heat Transfer in Welds

The most popular model for the heat input is double ellipsoid, because for many arc welds the double ellipsoid shape is a good approximation. It shows that a Gaussian distribution …

Hierarchical Weld Process Models

When analyzing a given weld, one is not required to remain faithful to a single model. Clearly, unless one wishes to analyze the interior of the weld pool, it is …

Fifth Generation Weld Heat Source Models

Fifth Generation models make a serious effort to include a model of the arc in the heat source model. This adds the equations of magneto - hydrodynamics to the equations …

Fourth Generation Weld Heat Source Models

Fourth Generation models are distinguished by adding the equations of fluid dynamics to the modeling of the weld heat source. Recall that the First, Second and Third Generation models have …

Third Generation Weld Heat Source Models

The next advance in weld heat source models, Third Generation models, was initiated by Ohji et al. [21]. They predicted the liquid weld pool shape. The distinguishing feature of Third …

Prescribed Temperature Heat Source Models

These models treat the weld heat source as a sub-domain in which the temperature or specific enthalpy in the weld pool is known as a function of (x, y,z, t). …

Distributed Heat Source Models

The first second Generation models define a distributed heat source function. The best known example of such a function is the double ellipsoid model, see Figure 2-9. Another example is …

Second Generation Weld Heat Source Models

Second Generation weld heat source models replace the point, line and plane models that mathematically are delta functions, with distribution functions. The first of these was a distributed flux model …

First Generation Weld Heat Source Models

First Generation weld heat source models are the point, line and plane heat source models of Rosenthal [18] and Rykalin [17]. They are the first and most famous of weld …

Modeling a Weld Heat Source

Having specified the data available to characterize the weld heat source, the next step is to decide how to use the available data to compute the transient temperature field of …

Data to characterize a Weld Heat Source

The best way of modeling a weld heat source depends on many factors. The first factor to consider is how accurately we want to model the heat source. Few if …

Weld Heat Source

What we know about a weld heat source either comes from experimental observation or more detailed models of the welding process. Experimentally, currents, voltages, frequency, wire feed rates, welding speeds, …

Heat Transfer Theory

For the moment we will assume that the velocity of the material points is zero. However, the arc is allowed to move with some velocity. Also an observer is allowed …

Thermal Analysis of Welds

3.1 Introduction and Synopsis The conservation of energy is the fundamental principle in thermal analysis. Therefore in heat transfer theory, we are concerned with energy and ignore stress, strain and …

Spatial Integration Schemes

Since the Finite Element Method (FEM) is primarily an exercise in numerical integration, it is not surprising that better integration schemes are being sought. Numerical integration schemes replace an integral …

Microstructure Modeling in Heat Affected Zone (HAZ)

Many failures of welds initiate in the heat affected zone adjacent to the weld metal, e. g., in the coarse grained HAZ. For this reason, welding engineers devote much of …

Modeling Thermal Stresses and Distortions in Welds

The thermal stress analysis of welds is more complex than the heat flow analysis because of the geometry changes and because of the complex stress-strain relationship. In designing a welding …