Multi-Scale and Multi-Component Approach for Solidification Processes

This articel focuses on a thermo-mechanical model for numerical simulation of solidification processes considering two different scales, both in time and space. The macro-scale implies two phases (solid and liquid steel), and is described by use of the theory of porous media (TPM). Moreover, a strong thermal coupling is addressed as well as finite J₂ elastic-plastic solid behavior. The physics of solidification during heat dissipation is covered on the micro-scale in the framework of phase-field modeling. Therefore, a Ginzburg-Landau type free energy function is used. After discussing the main model details, a numerical example will demonstrate the principal performance of the presented model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A ternary phase bi-scale FE-model for diffusion-driven dendritic alloy solidification processes

It is of high interest to describe alloy solidification processes with numerical simulations. In order to predict the material behavior as precisely as possible, a ternary phase, bi-scale numerical model will be presented. This paper is based on a coupled thermo-mechanical, two-phase, two-scale finite element model developed by Moj et al. [2], where the theory of porous media (TPM) [1] has been used. Finite plasticity extended by secondary power-law creep is utilized to describe the solid phase and linear visco-elasticity with Darcy's law of permeability for the liquid phase, respectively. Here, the microscopic, temperature-driven phase transition approach is replaced by the diffusion-driven 0D model according to Wang and Beckermann [3]. The decisive material properties during solidification are captured by phenomenological formulations for dendritic growth and solute diffusion processes. A columnar as well as an equiaxial solidification example will be shown to demonstrate the principal performance of the presented model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards a finite element simulation of coating by means of thermal spraying

Metal sheet forming processes like deep drawing are applied in order to produce carriage parts in mass production. Therefore, forming tools are required that are well protected against wear. For such forming tools, wear resistant surfaces are, e.g., produced by thermal spraying of hard material coatings. The thermal spraying process itself is a highly transient thermo-mechanical process. In order to gain a better understanding of the heat input and transfer during thermal spraying, a simulation framework for thermal spraying processes is presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An anisotropic enhanced thermal conductivity approach for modelling laser melt pools for Ni-base super alloys

Ni-base super alloys are extensively used in high temperature gas turbine engines and energy industries. Due to the high replacement costs of these components, there are huge economic benefits of repairing these components. Laser direct metal deposition processes (LDMD) based on laser cladding, laser fusion welding, and laser surface melting are some of the processes which are used to repair these high value components. Precise control of these processes is important to achieve the desired microstructure, stress distribution, distortions due to thermal stresses and other important output variables. Modelling of these processes is therefore an extremely important activity for achieving any degree of control/optimisation. However, modelling of these processes is not straight-forward due to melt pool flows dominated by Marangoni and buoyancy driven convection. Detailed CFD models are required for accurate prediction of melt pool geometry. But these models are computationally expensive and require greater expertise. To simplify and speed up the modelling process, many researchers have used the isotropic enhanced thermal conductivity approach to account for melt pool convection. A recent study on mild steel has highlighted that isotropic enhanced thermal conductivity approach is not able to accurately predict the melt pool geometry. Based on these findings a new approach namely anisotropic enhanced thermal conductivity approach has been developed. This paper presents an analysis on the effectiveness of the isotropic and anisotropic enhanced thermal conductivity approaches for laser melting of Inconel 718 using numerical technique. Experimental melt pool geometry has been compared with modelling results. It has been found that the isotropic enhanced thermal conductivity approach is not able to accurately predict the melt pool geometry, whereas anisotropic enhanced thermal conductivity approach gives good agreement with the experimental results.     

Choosing norms in adaptive FSI calculations

The thermal coupling of a fluid and a structure is of great significance for many industrial processes. As a model for cooling processes in heat treatment of steel we consider the coupling of the compressible Navier-Stokes equations along a surface with the heat equation. A partitioned approach is considered, where different codes for the sub-problems are employed. We use a finite volume method (FVM) for the fluid and a finite element method (FEM) for the heat equation. The semi-discrete coupled system is solved using stiffly stable SDIRK methods, where on each stage an FSI problem is solved. This has a black box character, since a stage calculation corresponds to a specific Backward-Euler integration step. For the resulting method it was shown by numerical experiments in [1] that second order convergence rate is obtained. This property is used for a simple time-step control, which saves considerable computational time and guarantees a specified maximum error of time integration. Here, we will consider different norms for measuring the error. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Residual stress on the run out table accounting for multiphase transitions and transformation induced plasticity

The development of harder and thinner new steel grades requires computationally efficient numerical simulations of forming processes in order to optimize industrial conditions through parametric studies. Within this general framework, the present contribution deals with one particular process, namely the run out table. Thus, this paper focuses on the evolution of residual stresses of thin strips during cooling on the run out table. Due to the fact that the complete problem is a nonlinear multiphysics process, it is known that simulating such processes with fully coupled numerical procedures leads to high computational costs. Therefore, a simplified numerical strategy has been developed. This procedure consists of three steps: (i) solving the thermal problem coupled with multiphase transitions; (ii) computing thermal expansion, metallurgical deformation and transformation induced plasticity and (iii) solving the associated mechanical problem. Residual stress profiles through the strip thickness are also computed in order to evaluate classic flatness defects such as crossbow and longbow. A post-processing is also included in order to quantify out of plane displacements that would take place if the strip was cut off the production line. The post-processing consists in computing at finite strain the relaxation of residual stresses when the tension applied by the coiler is released. The proposed numerical strategy has been tested on common industrial conditions.     

Thermo-mechanical modelling of cellular hybrid refractories

Refractory materials are subjected to both quasi-static and dynamic thermal loading (thermal shock) causing damage up to mechanical failure. Typical refractories are magnesia carbon bricks consisting of periclase (MgO) and carbon inclusions. Recently, a significant improvement of the thermo-mechanical behaviour could be achieved by cellular hybrid composites made of periclase-filled carbon foams. The present contribution focuses on MgO-filled carbon foams and the investigation and optimisation of the structure-property relationship with respect to a reduction of thermally induced stresses and damage. It is a transient as well as static, fully coupled thermo-mechanical problem. According to the fact that, in general, refractories are brittle materials a linear elastic model, with a damage criterion was used. To optimise the structural morphology of the cellular refractories, the effect of micro structural changes has been determined. For the investigation of the thermal shock! behaviour, the results correlate very well with the experimentally motivated Hasselman relation. There is a significant size effect depending on the pore size. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale damage analyis for steel structures

An approach to model the deterioration of steel structures is presented by transferring the results of a continuum damage mechanics analysis to an extended beam model which can account for the loss of structural integrity. Damage starts at the microscopic level by the initiation, growth and coalescence of voids with decreasing material resistance followed by the formation of microcracks at the mesoscale. Nevertheless, the material behavior can be sufficiently modelled on a phenomenological basis taking into account viscoplasticity, hardening effects and damage evolution. The associated model parameters are identified with the help of an evolutionary algorithm adapting numerical to experimental results. Using the finite element method a nonlocal formulation of the damage variable is required to obtain mesh-independent results by structural analysis. The maximum element size is limited by the small magnitude of the internal length. Therefore, numerical analyses of large scale 3D steel structures are computationally expensive. To reduce the effort a beam element is proposed to account for the plastic hinges and the loss of resistance in the course of damage evolution. The corresponding relationship of bending moment and curvature bases on the continuum damage mechanics model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

C0 FE model based on HOZT for the analysis of laminated soft core skew sandwich plates: Bending and vibration

Bending and free vibration behaviour of laminated soft core skew sandwich plate with stiff laminate face sheets is investigated using a recently developed C₀ finite element (FE) model based on higher order zigzag theory (HOZT) in this paper. The in-plane displacement fields are assumed as a combination of a linear zigzag function with different slopes at each layer and a cubically varying function over the entire thickness. The out of plane displacement is considered to be quadratic within the core and constant in the face sheets. The plate theory ensures a shear stress-free condition at the top and bottom surfaces of the plate. Thus, the plate theory has all of the features required for accurate modelling of laminated skew sandwich plates. As very few element model based on this plate theory (HOZT) exist and they possess certain disadvantages, an attempt has been made to check the applicability of the refined element model. The nodal field variables are chosen in such a manner that there is no need to impose any penalty stiffness in the formulation. Refined C₀ finite element model has been utilized to study some interesting problems on static and free vibration analysis of laminated skew sandwich plates.     

Combined higher order finite volume and finite element scheme for double porosity and non-linear adsorption of transport problem in porous media

In this work, a dual porosity model of reactive solute transport in porous media is presented. This model consists of a nonlinear-degenerate advection-diffusion equation including equilibrium adsorption to the reaction combined with a first-order equation for the non-equilibrium adsorption interaction processes. The numerical scheme for solving this model involves a combined high order finite volume and finite element scheme for approximation of the advection-diffusion part and relaxation-regularized algorithm for nonlinearity-degeneracy. The combined finite volume-finite element scheme is based on a new formulation developed by Eymard et al. (2010) [10]. This formulation treats the advection and diffusion separately. The advection is approximated by a second-order local maximum principle preserving cell-vertex finite volume scheme that has been recently proposed whereas the diffusion is approximated by a finite element method. The result is a conservative, accurate and very flexible algorithm which allows the use of different mesh types such as unstructured meshes and is able to solve difficult problems. Robustness and accuracy of the method have been evaluated, particularly error analysis and the rate of convergence, by comparing the analytical and numerical solutions for first and second order upwind approaches. We also illustrate the performance of the discretization scheme through a variety of practical numerical examples. The discrete maximum principle has been proved.     

Non-isothermal,compressible gas flow for the simulation of an enhanced gas recovery application

In this work, we present a framework for numerical modeling of CO₂ injection into porous media for enhanced gas recovery (EGR) from depleted reservoirs. Physically, we have to deal with non-isothermal, compressible gas flows resulting in a system of coupled non-linear PDEs. We describe the mathematical framework for the underlying balance equations as well as the equations of state for mixing gases. We use an object-oriented finite element method implemented in C++. The numerical model has been tested against an analytical solution for a simplified problem and then applied to CO₂ injection into a real reservoir. Numerical modeling allows to investigate physical phenomena and to predict reservoir pressures as well as temperatures depending on injection scenarios and is therefore a useful tool for applied numerical analysis.     

Simulation of a Hybrid-Forming Process using Temperature- and Rate-Dependent Viscoplastic Material Models

Hybrid-forming processes for graded structures are quite innovative methods for the production of components with tailored properties, particularly tailored material properties and geometrical shape. In this contribution a hybrid-forming process based on the utilization of locally varying thermo-mechanical effects is investigated [1]. For process optimization and improvement of the resulting work piece the simulation of the entire forming process is necessary in modern engineering. The main topics of this contribution are the simulation of the cyclic thermal loaded forming tool and the simulation of the work piece treated at large deformations with phase transformations. For both materials temperature- and rate-dependent viscoplastic material models are applied and parameter identification using cyclic tensile-compression tests for the forming tool material and phase transformation tests for a low-alloy steel similar to the work piece material is presented. For validation of finite-element-calculations for the forming tool thermal shock experiments are performed with optical deformation measurements. For validation of finite-element-calculations for the work piece numerical results of geometry and structure after heating, forming and cooling are compared to experimental micro sections. Results concerning the forming tool will be used for future lifetime prediction and results concerning the work piece will be used for future specific setting of graded material properties. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of quenching – Heat conduction in metallic materials

Metallic materials present a complex behavior during heat treatment processes. In a certain temperature range, change of temperature induces a phase transformation of metallic structure, which alters physical properties of the material. Indeed, measurements of specific heat and conductivity show strong temperature-dependence during processes such as quenching of steel. Several mathematical models, as solid mixtures and thermal–mechanical coupling, for problems of heat conduction in metallic materials, have been proposed. In this work, we take a simpler approach without thermal–mechanical coupling of deformation, by considering the nonlinear temperature-dependence of thermal parameters as the sole effect due to those complex behaviors. The above discussion of phase transformation of metallic materials serves only as a motivation for the strong temperature-dependence as material properties. In general, thermal properties of materials do depend on the temperature, and the present formulation of heat conduction problem may be served as a mathematical model when the temperature-dependence of material parameters becomes important. For this mathematical model we present the error estimate using the finite element method for the continuous-time case.     

A multiphase finite element simulation of biological conversion processes in landfills

Worldwide, landfills are the most common way to dispose of waste, but have an impact on the environment as a result of harmful gas and leachate production. Estimating the long-term behaviour of a landfill in regard to this gas production and organic degrading, as well as to settlement and waste water production, is of high importance. Therefore, a model has been developed to simulate these processes. This constitutive model is based on the multiphase Theory of Porous Media. The body under investigation consists of an organic and an inorganic phase as well as a liquid and a gas phase. The equations of the model are developed on the basis of a consistent thermo-mechanical approach including the momentum balance for the solid phase and the mixture, the energy balance for the mixture and the mass balance for the gas phase. All interactions between the constituents such as mass transfers, interaction forces and energy fluxes are taken into consideration. The strongly coupled set of partial differential equations is implemented in the finite element code FEAP. The theoretical framework and the results of meantime successfully performed simulation of a real landfill body will be shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A microcrack-based continuum damage model with application towards refractories

The present work discusses numerical results of damage evolution due to thermoshock processes at refractory ceramics. Damage patterns have been generated using a two-scale approach for brittle materials, implemented into a finite element framework. For this purpose, a cell model has been employed, incorporating cracks on a microscopic level. The impact of these discontinuities on macroscopic material properties and damage evolution is determined with the help of analytical homogenization techniques. Finally, the potential of the numerical tool is demonstrated by means of refractory bricks, being imposed by thermomechanical loading. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear analysis of residual stresses in a rail manufacturing process by FEM

The aim of this paper is to study the residual stresses in an UIC-60 rail and their reduction by means of roller straightening. Both experimental and numerical investigations have been carried out in the past to reveal the formation of dominant longitudinal residual stresses. However, the agreement between both investigations was not particularly good. The finite element method (FEM) has also been used to simulate one, two and three-dimensional analyses of a rail during roller straightening processes. The present model considers the longitudinal movement of a rail through the straightening machine, contact conditions between rail and rollers and kinematic hardening so as to take into account the plastic behaviour of the rail material (steel). These results were compared with the experimental investigations and good agreement was observed. In this respect, this paper presents a novel, more realistic numerical simulation by FEM for the roller straightening process. Finally, an improvement of the straightening process in order to obtain smaller residual stress in the rail section is proposed.     

Bacterial methane oxidation in landfill cover layers - a coupled FE multiphase description

Landfill gas is composed of methane (CH₄) and (CO₂) at a ratio of about (60% – 40%), whereby the impact of methane on the greenhouse effect is about 25 times higher than that of carbon dioxide. Bacterial methane oxidation, taking place in the landfill cover layer, helps to reduce the climate active emissions from landfill sites. This contribution presents a theoretical and numerical approach to model the coupled processes of bacterial methane oxidation. An isothermal biphasic model based on the Theory of Porous Media (TPM) and Mixture Theory is introduced as well as the coupled finite element (FE) calculation concept. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupled Thermo-Mechanical and Wear Effects on the Analysis of High Speed Railway Brake Systems

The high speed railway brakes transfer a large amount of kinetic energy into heat. The temperature during a brake operation could reach values higher than 90 °C. The dynamics of the brake system is rather complicated with respect to the multiphysical phenomena. In this paper, the thermo-mechanical coupling are investigated combined with the loos of brake material due to wear. The coupled model is discretized by conventional finite element method. Different coupled algorithms have been tested. Various scenarios have been simulated and shown reasonable results. The temperature and deformation on pad and disc, especially the thermal deformation of disc the so–called coning effect can also be prescribed with this coupled multiphysics model. Furthermore, the tapered wear on brake pads is also discussed as a requirement of railway brake design in terms of durability. Thereby, the Ehlers's model is normally used to minimize tapered wear by selecting an adequate point of applied braking force. An extended Ehlers's model is also presented here, which concerns wear effect based on Archard's model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)