Jesper Thorborg

An integrated numerical model of the spray forming process

Abstract In this paper, an integrated approach for modelling the entire spray forming process is presented. The basis for the analysis is a recently developed model which extents previous studies and includes the interaction between an array of droplets and the enveloping gas. The formulation of the deposition model is accomplished using a 2D cylindrical heat flow model. This model is now coupled with an atomization model via a log-normal droplet size distribution. The coupling between the atomization and the deposition is accomplished by ensuring that the total droplet size distribution of the spray is in fact the summation of ‘local’ droplet size distributions along the r-axis. A key parameter, which determines the yield and the shape of the deposit material, is the sticking efficiency. The sticking phenomenon is therefore incorporated into the deposition model.

A numerical model for predicting the thermomechanical conditions during hydration of early-age concrete

Abstract In the present study, a macroscopic numerical model for the thermomechanical conditions during hydration of early-age concrete is presented. The formulation is based on a semi-coupled, incremental thermomechanical model where the heat production from the hydration process is expressed in terms of the maturity and the thermal activation is expressed by the Arrhenius principle. The material properties are assumed to depend on the hydration process via the maturity. The discretization of the governing equations is accomplished by a control volume formulation involving a time-splitting scheme for the heat conduction equation. Non-linear phenomena such as sequential casting, maturity dependent material properties, creep and non-linear thermal boundary conditions are all taken into account. Different rheological models describing the viscoelastic behaviour have been implemented. Validations of the model against analytical solutions are carried out as well as examples of analysis of real concrete structures.

A quasi-stationary numerical model of atomized metal droplets. II: Prediction and assessment

A new model which extends previous studies and includes the interaction between enveloping gas and an array of droplets has been developed and presented in a previous paper. The model incorporates the probability density function of atomized metallic droplets into heat transfer equations. The main thrust of the model is that the gas temperature was not predetermined and calculated empirically but calculated numerically based on heat balance considerations. In this paper, the accuracy of the numerical model and the applicability of the model as a predictive tool have been investigated by comparing experimental and calculated results for the powder particles of 12Cr-Mo-V steel. The study also focuses on some aspects of the process which are not available experimentally, for example the effect of undercooling and the gas/metal ratio on the solidification. The important effects of these parameters are illustrated. A comparison between the numerical model and the experimental results shows an excellent agreement and demonstrates the validity of the present model, for example the calculated gas temperature which has an important influence on the droplet solidification behaviour as well as the calculated cooling rate of the droplets is found to be in good agreement with the experimentally determined value. The fact that the present approach of modelling is more general than previous studies opens up new possibilities for a deeper understanding of such a process without the limitation of experimental input parameters, for example gas temperature. Finally, the present approach of modelling and its predication illustrate the fact that quantitative results and guidelines can be drawn from this model which can then be used as a tool for the optimization of the process.

A quasi-stationary numerical model of atomized metal droplets. I: Model formulation

A mathematical model for accelerating powder particles by a gas and for their thermal behaviour during flight has been developed. Usually, dealing with the solidification of metal droplets, the interaction between an array of droplets and the surrounding gas is not integrated into the modelling of such a process, for example, in the literature the gas temperature is often modelled by an empirical expression. In this model, however, the interaction between the enveloping gas and an array of droplets has been coupled and calculated numerically. The applicability of the empirical relation of the gas temperature proposed in the literature has been discussed in relation to the model. One of the major advantages of this modelling is that it provides a tool to predict the thermal behaviour of droplets during flight without the need for experimental parameters, i.e. gas temperature. Furthermore, the model predicts the effect of process parameters on the size distribution, temperature, velocity histories, fraction-solid and cooling rate for all droplet sizes characterizing the complete droplet size distribution.

A micro-mechanical analysis of thermo-elastic properties and local residual stresses in ductile iron based on a new anisotropic model for the graphite nodules

In this paper, the thermo-elastic behavior of the graphite nodules contained in ductile iron is derived on the basis of recent transmission electron microscopy investigations of their real internal structure. The proposed model is initially validated by performing a finite element homogenization analysis to verify its consistency with the room-temperature elastic properties of ductile iron measured at the macro scale. Subsequently, it is used to investigate the formation of local residual stresses around the graphite particles by simulating the manufacturing process of a typical ferritic ductile iron grade, and the results are compared with preliminary measurements using synchrotron x-rays. Finally, the obtained accurate description of the stress & strain field at the micro scale is used to shed light on common failure modes reported for the nodules and on some peculiar properties observed in ductile iron at both micro and macro scale.

Thermo-mechanical modelling of aluminium cast parts during solution treatment

The increasing interest of the automotive industry in reducing the weight of cars has resulted in increasing replacement of steel with aluminium parts as well as in an optimization of the design of the components, through structural analysis by FE-codes. The design and manufacturing of these components are important for the lifetime and reliability of the final parts. It is common practice to do load analyses in order to evaluate component lifetime and to do design optimization. However, in order to improve these structural analyses it is important to include the full load history of the material including the influence of the casting process and the subsequent solution treatment phase, quenching and artificial ageing. These manufacturing stages can have a high influence on the deformation and development of residual stresses which are important as initial conditions for subsequent load analysis during service.This paper presents a 3D numerical procedure capable of modelling the development of deformations and stresses from the full thermal history starting from mould filling through solidification to cooling and subsequent reheating for solution treatment, quenching and artificial ageing. However, in the present work the focus is on the modelling of the solution treatment only. The mechanical material model is described by a unified creep model to include rate effects and inelastic behaviour. An industrial component is used as an example to present the influence of creep at high temperature and calculated results with regard to deformations are compared with measurements.

A Casting Yield Optimization Case Study: Forging Ram

This work summarizes the findings of multi-objective optimization of a gravity sand-cast steel part for which an increase of casting yield via riser optimization was considered. This was accomplished by coupling a casting simulation software package with an optimization module. The benefits of this approach, recently adopted in the foundry industry worldwide and based on fully automated computer optimization, were demonstrated. First, analyses of filling and solidification of the original casting design were conducted in the standard simulation environment to determine potential flaws and inadequacies. Based on the initial assessment, the gating system was redesigned and the chills rearranged to improve the solidification pattern. After these two cases were evaluated, the adequate optimization targets and constraints were defined. One multi-objective optimization case with conflicting objectives was considered in which minimization of the riser volume together with minimization of shrinkage porosity and limitation of centerline porosity were performed.

Prediction of the Impact of Flow-Induced Inhomogeneities in Self-Compacting Concrete (SCC)

SCC is nowadays a worldwide used construction material. However, heterogeneities induced by casting may lead to variations of local properties and hence to a potential decrease of the structure’s load carrying capacity. The heterogeneities in SCC are primarily caused by static and dynamic segregation. The present paper reports property maps for a beam based on particle distributions at the end of casting derived from numerical flow simulations. A finite volume based numerical model is used to predict particle distributions at the end of casting, which are then converted into property maps using semi-empirical relations from the literature.

Modeling of damage in ductile cast iron - The effect of including plasticity in the graphite nodules

In the present paper a micro-mechanical model for investigating the stress-strain relation of ductile cast iron subjected to simple loading conditions is presented. The model is based on a unit cell containing a single spherical graphite nodule embedded in a uniform ferritic matrix, under the assumption of infinitesimal strains and plane-stress conditions. Despite the latter being a limitation with respect to full 3D models, it allows a direct comparison with experimental investigations of damage evolution on the surface of ductile cast iron components, where the stress state is biaxial in nature. In contrast to previous works on the subject, the material behaviour in both matrix and nodule is assumed to be elasto-plastic, described by the classical J2-flow theory of plasticity, and damage evolution in the matrix is taken into account via Lemaitres isotropic model. The effects of residual stresses due to the cooling process during manufacturing are also considered. Numerical solutions are obtained using an in-house developed finite element code; proper comparison with literature in the field is given.

Elimination of Hot Tears in Steel Castings by Means of Solidification Pattern Optimization

A methodology of how to exploit the Niyama criterion for the elimination of various defects such as centerline porosity, macrosegregation, and hot tearing in steel castings is presented. The tendency of forming centerline porosity is governed by the temperature distribution close to the end of the solidification interval, specifically by thermal gradients and cooling rates. The physics behind macrosegregation and hot tears indicate that these two defects also are dependent heavily on thermal gradients and pressure drop in the mushy zone. The objective of this work is to show that by optimizing the solidification pattern, i.e., establishing directional and progressive solidification with the help of the Niyama criterion, macrosegregation and hot tearing issues can be both minimized or eliminated entirely. An original casting layout was simulated using a transient three-dimensional (3-D) thermal fluid model incorporated in a commercial simulation software package to determine potential flaws and inadequacies. Based on the initial casting process assessment, multiobjective optimization of the solidification pattern of the considered steel part followed. That is, the multiobjective optimization problem of choosing the proper riser and chill designs has been investigated using genetic algorithms while simultaneously considering their impact on centerline porosity, the macrosegregation pattern, and primarily on hot tear formation.