Modelling of heat flow has become a standard practice in many solidification processes. Effort is currently being made to couple heat flow calculations to related macroscopic phenomena such as mould filling, fluid flow, macrosegregation, or thermal stresses. If these macroscopic aspects are important in predicting formation of macroscopic defects or optimising process conditions, then microstructural features such as phase appearance, morphology, grain size, spacings, or microdefects are certainly no less important in determining the ultimate mechanical properties of the solidified product. The aim of the present paper is to introduce the basic concepts of macroscopic and microscopic phenomena which enter normally into any solidification process. At the macroscopic level, i.e. at the scale of the whole process (casting, weldment, … ), the latest developments in numerical techniques which are used to solve the continuity equations are briefly presented together with the advantages and inconvenience...

Modelling of microstructure formation in solidification processes

A numerical model combining the methods of enthalpy, effective-viscosity and volume-of-fluid is developed to simulate the metal transfer process in gas metal arc welding. The model describes not only the influence on droplet profile and transfer frequency of electromagnetic force, surface tension, and gravity, but it can also model the nonisothermal phenomena such as heat transfer and phase change. The model has been used to study the shape of the melting interface on the welding wire, the droplet oscillation at wire tip, the characteristics of relevant physical variables and their roles in metal transfer. We find that the taper formation in spray transfer is closely related to the heat input on the unmelted portion of the welding wire, and the taper formation affects the globular–spray transition by decelerating the transfer process. The formation of satellite drops during the metal transfer process is also considered. High-speed photography, laser-shadow imaging, and metallographic analysis validate the numerical model, and recommendations are made on the topics that require further consideration for a more accurate metal transfer model.

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Modelling and analysis of metal transfer in gas metal arc welding

By developing mathematical models for the arc and the weld pool in the GTAW process, the effect of the electrode tip angle on both arc and weld pool was studied. The present paper is concerned with the model for the arc. By applying a variable cathode surface area, the effect of the electrode tip angle (in the range of 10 to ) on the arc properties, especially on the anode current density, heat flux and gas shear stress over the weld pool, was investigated. Comparison of the calculated results with the available experimental data for 200 A arcs of different lengths showed that the model predictions for temperatures higher than 10 000 K are in very good agreement. For temperatures less than 10 000 K, some modifications were necessary to take into account the absorption of heat by the cooler parts of the arc. It was found that by increasing the electrode tip angle, the anode spot at the weld pool surface tended to be more localized. This led to a higher maximum heat flux and anode current density. On the other hand, the gas shear stress increased on decreasing the electrode tip angle.

https://iopscience.iop.org/article/10.1088/0022-3727/30/19/013/pdf

The effect of the cathode tip angle on the GTAW arc and weld pool: I. Mathematical model of the arc

A thermomechanical three-dimensional (3-D) finite element analysis of solidification is presented. The heat transfer model is based on a multidomain analysis accounting for noncoincident meshes for the cast part and the different mold components. In each subdomain, a preconditioned conjugate gradient solver is used. The mechanical analysis assumes the mold is rigid. A thermoelastic-viscoplastic rheological model is used to compute the constrained shrinkage of the part, resulting in an effective local air gap width computation. At each time increment, a weak coupling of the heat transfer and mechanical analyses is performed. Comparisons of experimental measurements and model predictions are given in the case of a hollow cylindrical aluminum alloy part, showing a good quantitative agreement. An application to an industrial aluminum casting is presented, illustrating the practical interest of thermomechanical computations in solidification analysis.

Thermomechanics of the cooling stage in casting processes : three-dimensional finite element analysis and experimental validation

The optimal design of a casting rigging system is considered. The casting geometry is systematically modified to minimize the gate and riser volume, while simultaneously ensuring that no porosity appears in the product. In this approach, we combine finite-element analysis of the solidification heat-transfer process with design sensitivity analysis and numerical optimization to systematically improve the casting design. Methods are presented for performing the sensitivity analysis, including the sensitivity of important solidification parameters such as freezing time, temperature gradient, and cooling rate. We also present methods for performing Newton-Raphson iteration for solidification models that use the boundary-curvature method to represent the sand mold. Finally, the methods are applied to design risers for an L-shaped steel plate to control microporosity and for a steel hammer to control macroporosity. It is demonstrated that the size of a conventionally designed riser can be reduced by a significant amount while retaining the quality of the cast product.

Optimal riser design for metal castings

A method has been developed to predict stress development in gray iron foundry castings. A new yield function, based on theoretical developments by Frishmuth and McLaughlin,9 and on experiments by Coffin10 was implemented as a user-written element in a commercial finite element package. The yield function takes into account the strong dependence of the yield stress in cast irons on the loading path. Stresses resulting from thermal displacements in the cooling casting are computed using the new yield function in an elastic-viscoplastic stress analysis. In earlier work, techniques were developed to represent the mold in the thermal analysis by sets of boundary conditions on the surface of the part. For this work, a second user-written element was used to apply force-displacement boundary conditions on the surface of the casting to represent the mechanical constraint of the mold. The properties for this element were based on soil mechanics considerations. Example problems are given, showing a substantial difference in the computed stresses when using the present formulation, in comparison to results obtained with the more usual von Mises yield function.

Modeling stress development during the solidification of gray iron castings

An energy absorbing beam construction for use in vehicle seat belt restraining systems includes an energy absorbing beam which is mounted or fastened to a vehicle frame or vehicle seat frame. The seat belt retracting mechanism or belt buckle end of the seat belt restraining system can then be mounted to the energy absorbing beam. In use, when the vehicle is subjected to a head-on collision, the energy absorbing beam deforms elastically at collision speeds less than a target speed and deforms plastically at speeds greater than this to minimize injury to a vehicle occupant that may occur as a result of seat belt restraint.

Energy absorbing beam construction for use with vehicle seat belt restraining systems

In Part I of this paper, a new method was presented for modeling heat flow in sand castings. In this paper, the method is used to simulate the solidification of parts of varying complexities. Comparisons are made between conventional calculations (with the mold enmeshed), calculations using the boundary curvature method, and experimental results. The results are shown to agree well with each other. Reductions in cpu time up to 96 pct are found by adopting the new method.

Modeling of heat flow in sand castings: Part II. Applications of the boundary curvature method

SPIDER and the boundary curvature method: simulating the solidification of foundry castings

A comprehensive technique is described for performing the simulation of the solidification of foundry castings. A finite element method (FEM) mesh is produced for the pattern of the part, using geometric modeling techniques. Results are presented to demonstrate selection rules for the mesh size. The size of the heat transfer problem is reduced by replacing the FEM mesh in the mold material by appropriate boundary conditions on the surface of the casting. The boundary conditions are found automatically by a program which relates local surface curvature on the part to a pre-calculated library of solutions. Methods for ensuring that all of the latent heat of fusion is included are presented, and comparisons are made between different solution methods.

J. W. Wiese

Papers

Modeling stress development during the solidification of gray iron castings

Energy absorbing beam construction for use with vehicle seat belt restraining systems

Modeling of heat flow in sand castings: Part II. Applications of the boundary curvature method

SPIDER and the boundary curvature method: simulating the solidification of foundry castings

Modeling the solidification of foundry castings