John Goldak

A new finite element model for welding heat sources

A mathematical model for weld heat sources based on a Gaussian distribution of power density in space is presented. In particular a double ellipsoidal geometry is proposed so that the size and shape of the heat source can be easily changed to model both the shallow penetration arc welding processes and the deeper penetration laser and electron beam processes. In addition, it has the versatility and flexibility to handle non-axisymmetric cases such as strip electrodes or dissimilar metal joining. Previous models assumed circular or spherical symmetry. The computations are performed with ASGARD, a nonlinear transient finite element (FEM) heat flow program developed for the thermal stress analysis of welds.* Computed temperature distributions for submerged arc welds in thick workpieces are compared to the measured values reported by Christensen1 and the FEM calculated values (surface heat source model) of Krutz and Segerlind.2 In addition the computed thermal history of deep penetration electron beam welds are compared to measured values reported by Chong.3 The agreement between the computed and measured values is shown to be excellent.

Computer modeling of heat flow in welds

This paper summarizes progress in the development of methods, models, and software for analyzing or simulating the flow of heat in welds as realistically and accurately as possible. First the fundamental equations for heat transfer are presented and then a formulation for a nonlinear transient finite element analysis (FEA) to solve them is described. Next the magnetohydrodynamics of the arc and the fluid mechanics of the weld pool are approximated by a flux or power density distribution selected to predict the temperature field as accurately as possible. To assess the accuracy of a model, the computed and experimentally determined fusion zone boundaries are compared. For arc welds, accurate results are obtained with a power density distribution in which surfaces of constant power density are ellipsoids and on radial lines the power density obeys a Gaussian distribution. Three dimensional, in-plane and cross-sectional kinematic models for heat flow are defined. Guidelines for spatial and time discretization are discussed. The FEA computed and experimentally measured temperature field,T(x, y, z, t), for several welding situations is used to demonstrate the effect of temperature dependent thermal properties, radiation, convection, and the distribution of energy in the arc.

CONSTRUCTING DISCRETE MEDIAL AXIS OF 3-D OBJECTS

In this paper, an algorithm to construct the approximate medial axis of an object is proposed. The algorithm is based on the Delaunay triangulation of points on the object boundaries. Because the medial axis constructed by this algorithm consists of a set of discrete points, we call it the discrete medial axis. Based on the classification of these discrete points, the structure of the medial axis surfaces of a three-dimensional object are discussed in detail. The correctness of the algorithm is substantiated by a brief theoretical analysis.

Coupling Heat Transfer, Microstructure Evolution and Thermal Stress Analysis in Weld Mechanics

The mechanical behavior of welds is sensitive to the close coupling between heat transfer, microstructure evolution and thermal stress analysis. Since the temperature field computed from a heat transfer analysis can be considered to drive the mechanics of the welding process, the first step is to solve the energy equation usually with FEM. The research issue is decoupling the physics of the arc and weld pool from the energy equation. This is done by modeling the heating effect of the arc. Although the effects of microstructure and stress-strain evolution on heat transfer are not large, the effect of temperature on the microstructure and thermal stress is dominant. In addition, the coupling between microstructure and thermal stress can be strong and subtle. The microstructure evolution is modeled with algebraic equations for thermodynamics and ordinary differential equations for kinetics. The thermal stress analysis involves large strains and large rotations. The most popular constitutive equation has been elasto-plastic. Phase transformations such as the austenite to martensite transformation, can dominate the stress analysis. Since realistic welding problems tend to be truly three dimensional with complex geometry, transient and nonlinear, numerical methods have advantages. However, the computational demands have limited the size of welds that can be analyzed. In the past five years considerable progress has been made in developing numerical methods to solve this coupled problem with increasing speed and accuracy. Major gains have been made with better mesh grading and more efficient solvers. In addition, software engineering has played a major role in managing the complexity of software.

Constructing 3-D discrete medial axis

In solid modeling, each represent~ tion scheme is suitable for some operations and applications. Some modeling systems work on two or more different representation schemes in order to perform every operation in the most suitable scheme. The problem of conversion between different representation schemes arises. There exists another option for a solid modeling system, however, That is to use one representation, say boundary representation, and create an associated structure which can remedy the weakness of the representation. This is the motivation of the work presented in this paper: we propose the medial axis of the object to associate with its B~ep to improve the applicability of solid modeler and reduce the computation complexity of certain algorithms. *Department of Mechanical and Aerospace Engineering tDepartment of Computer Science Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing M=hinery. To copy otherwise, or to sepublish, requires a fee and/or specific permission. In this paper, an algorithm to construct the approximate medial axis of an object is proposed. The algorithm is based on the Delaunay triangulation of the pointa on the object boundaries. Because the medial axis constructed by this algorithm consists of a set of discrete points, we call it discrete medial axis. Bssed on the classification of these discrete points, the structure of the medial axis surfaces of a threedimensional object are discussed in detail. The correctness of the algorithm is substantiated by a brief theoretical analysis.

Combining Variation Simulation With Welding Simulation for Prediction of Deformation and Variation of a Final Assembly

In most variation simulations, i.e., simulations of geometric variations in assemblies, the influence from heating and cooling processes, generated when two parts are welded together, is not taken into consideration. In most welding simulations, the influence from geometric tolerances on parts is not taken into consideration, i.e., the simulations are based on nominal parts. In this paper, these two aspects, both crucial for predicting the final outcome of an assembly, are combined. Monte Carlo simulation is used to generate a number of different non-nominal parts in a software for variation simulation. The translation and rotation matrices, representing the deviations from the nominal geometry due to positioning error, are exported to a software for welding simulation, where the effects from welding are applied. The final results are then analyzed with respect to both deviation and variation. The method is applied on a simple case, a T-weld joint, with available measurements of residual stresses and deformations. The effect of the different sources of deviation on the final outcome is analyzed and the difference between welding simulations applied to nominal parts and to disturbed (non-nominal) parts is investigated. The study shows that, in order to achieve realistic results, variation simulations should be combined with welding simulations. It does also show that welding simulations should be applied to a set of non-nominal parts since the difference between deviation of a nominal part and deviation of a non-nominal part due to influence of welding can be quite large.

Finite element analysis of weld distortion in carbon and stainless steels

Welding creates residual stresses and distortion through the elasto-plastic response of the object to the transient, localized thermal expansion and contraction. The volume of plastically deformed material can be quite large, roughly the size of the region experiencing temperature changes greater than 100°C. Fabricators must allow for distortion during design, or resort to expensive post-weld treatments. Various strategies minimize distortion, but a basic understanding of the deformation is required. Distortion depends on the geometry and welding conditions as well as the material properties of the object being welded. A qualitative understanding of the role played by the thermal and mechanical properties would be instructive. Welding. stainless steels causes approximately three times the distortion experienced in low carbon steels for the same arc current, voltage, speed, etc. Differences in thermal properties (1)t such as the thermal conductivity, k, and volumetric specific heat, C, , as well as mechanical properties such as the yield strength, oy, coefficient of thermal expansion, a, and Young’s modulus, E, are responsible. At temperatures below SOOT, k for AISI 304 stainless steel is lower than that of low carbon steel. Thus, for a given heat flux, thermal gradients will be higher in the stainless steel. C, is also lower for AISI 304 stainless steel, leading to higher temperatures for a given energy input. The isotherm pattern seen in stainless steel welds might be expected to be narrower, enclosing higher temperatures and showing steeper thermal gradients and lower cooling rates. The effect of this on welding distortion is not clear. The difference in the yield strength of the two materials is of little importance. Lower yield strengths cause larger regions of plastic deformation. This is offset by the lower level of residual stress present in the larger

Error estimates for finite element solutions of elliptic boundary value problems

Abstract A error estimate for the finite element solutions of elliptic boundary value problems is introduced. The error measure is defined by the energy-norm distance between the kinematically admissible stress field computed by the displacement finite element method, and a quasi-statically admissible stress field. The error estimate is defined using this distance normalized by the total strain energy of the deformed body. The element contribution to the above error estimate is used to define an error indicator and a local error measure which can be used in adaptive finite element method as a criteria for mesh refinement. This method of error estimate can be implemented in existing finite element programs in a straightforward manner.

Heat and Fluid Flow in Welds

The current state and future directions of numerical modeling of heat and fluid flow in welds are presented. Weld pool models have evolved rapidly in the past decade and full 3D analyses are now possible for short welds. In two dimensions, modeling the formation of defects has begun. Outside of the weld pool, computational heat flow analyses are now able to analyze welds of medium length with useful resolution and accuracy. Prescribed flux and power density functions or prescribed temperature functions are used to model the heating effect of the arc. Kinematic models have evolved from 2D cross-sectional to 2D in-plane to full 3D and shell-3D composite models. The coupling of heat flow models to the evolution of microstructure and thermal stress analysis has resolved the effect of transformations on the residual stress in high strength steels. The paper closes with a discussion of future opportunities and challenges.

A METHOD TO IMPROVE EFFICIENCY IN WELDING SIMULATIONS FOR SIMULATION DRIVEN DESIGN

Welding is one of the most commonly used methods of joining metal pieces. In product development it is often desirable to predict residual stresses and distortions to verify that e.g., alignment tolerances, strength demands, fatigue requirements, stress corrosion cracking, etc. are fulfilled. The objective of this paper is to derive a strategy to improve the efficiency of welding simulations aiming at a (future) simulation-driven design methodology. In this paper, a weld bead deposition technique called block dumping has been applied to improve the efficiency. The proposed strategy is divided into seven steps, where the first four steps are verified by two welding simulation cases (a benchmark problem for a single weld bead-on-plate specimen and a T-welded structure). This study shows that by use of the block dumping technique, the computation time can be reduced by as much as 93% compared to moving heat source, still with acceptable accuracy of the model.Copyright