Thermomechanical finite element simulations of selective electron beam melting processes: performance considerations

The present contribution is concerned with the macroscopic modelling of the selective electron beam melting process by using the finite element method. The modelling and simulation of the selective electron beam melting process involves various challenges: complex material behaviour, phase changes, thermomechanical coupling, high temperature gradients, different time and length scales etc. The present contribution focuses on performance considerations of solution approaches for thermomechanically coupled problems, i.e. the monolithic and the adiabatic split approach. The material model is restricted to nonlinear thermoelasticity with temperature-dependent material parameters. As a numerical example a straight scanning path is simulated, the predicted temperatures and stresses are analysed and the performance of the two algorithms is compared. The adiabatic split approach turned out to be much more efficient for linear thermomechanical problems, i.e. the solution time is three times less than with the monolithic approach. For nonlinear problems, stability issues necessitated the use of the Euler backward integration scheme, and therefore, the adiabatic split approach required small time steps for reasonable accuracy. Thus, for nonlinear problems and in combination with the Euler backward integration scheme, the monolithic solver turned out to be more efficient.     

A mesh re-zoning technique for finite element simulations of metal forming processes

Based on some fundamental properties of finite element approximations, a mesh re-zoning scheme is proposed for finite element simulations of metal forming problems. It is demonstrated that this technique is indispensable in analysing many difficult forming processes, especially when there exist corners or very irregular shapes on the boundaries. The algorithm is tested by a backward extrusion process and direct extrusion through a square die.     

Solid-mechanics finite element simulations of the draping of fabrics: a sensitivity analysis

This paper covers numerical investigations of the draping of woven fabrics into a “hat” shape, combining a hemispherical cup with a wide flat rim. A mechanical approach is adopted using finite element analysis (FEA) methodology. In this, the fabric is considered as a solid sheet with mechanical properties and friction properties. In this study, a linear elastic anisotropic material model describes the deformation of fabrics. An explicit dynamic finite element analysis is applied and systematic parametric numerical studies are presented, which incorporate investigations of the effects of numerical parameters, material properties and processing conditions on the draping of fabrics. More specifically, the effects of the following variables and parameters are included: number of elements, number of time increments in the dynamic FEA analysis, punch speed, shear and tensile moduli of fabric, coefficient of friction for all interfaces and level of load on the fabric holder.     

Towards parallel I/O in finite element simulations

I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY-2 system. Performance results are reported.     

Vectorized 3D microstructure for finite element simulations

Microstructure based forming models using statistically representative microstructural input provide the most accurate predictions for early localization and failure during complex forming operations. However, the sheer size and complexity of the three dimensional (3D) microstructural data from real materials makes it hard to implement that data in current finite element models. In this report, a technique to create a vectorized 3D microstructure suitable for input into finite element codes is developed and applied to represent the distribution of particles of different phases found in continuous cast (CC) AA5754 sheets, which tend to have heterogeneous particle distributions with particles of several phases in different shapes and sizes (from 0.2 μm to 10 μm) and distributed at random, in stringers and along the “centerline”. The technique consists of a 3D reconstruction of the true microstructure by performing serial sections and conversion of the 3D raster image to the vector image. A 3D mesh is generated automatically using Unigraphics and Hypermesh from real particle field measurements, which can be imported to any FE code. The vectorized microstructure is validated by comparison with the reconstructed images of particle distribution data.     

Thermomechanical finite element simulations of ultrasonically assisted turning

Ultrasonically assisted turning (UAT) is studied with finite element (FE) simulations and compared with conventional turning (CT) using both computational results and infrared thermography experiments. The two-dimensional thermomechanically coupled FE model of both UAT and CT utilizes MSC MARC general FE code and incorporates temperature dependent material properties, strain rate effects, heat generated due to plastic flow, contact interaction and friction at the cutter/workpiece interface. Material separation in front of a cutting edge and automatic remeshing of distorted elements are implemented in the developed computational scheme. Influence of friction on resultant temperatures and chip shapes in turning for both UAT and CT is discussed. Temperature fields in the cutting region and in the cutting tool for CT and UAT are studied and compared with the experimental data. A role of various heat transfer parameters on thermal processes in UAT and CT is investigated.     

Multipass rolling of aluminium alloys: finite element simulations and microstructural evolution

Abstract

Use of numerical predictive methods such as finite element analysis is becoming progressively more common for modelling industrial hot metal working and forming processes. These tools are used not only to predict the thermomechanical behaviour of metals but increasingly to predict microstructural changes by linking them to physical models of recrystallisation and textural evolution. This paper describes the development and application of a fully integrated model for the prediction of thermomechanical and microstructural behaviour during multipass hot rolling of aluminium alloy AA 3104. Finite element code ABAQUS/standard has been used in the work and the process is modelled assuming plane strain conditions. It is shown that for this alloy the static recrystallisation which occurs during interpass cooling does not significantly influence the thermomechanical response during subsequent rolling passes.     

Coarse grain parallel finite element simulations for incompressible flows

Parallel simulation of incompressible fluid flows is considered on networks of homogeneous workstations. Coarse-grain parallelization of a Taylor–Galerkin/pressure-correction finite element algorithm are discussed, taking into account network communication costs. The main issues include the parallelization of system assembly, and iterative and direct solvers, that are of common interest to finite element and general numerical computation. The parallelization strategies are implemented on a Sun workstation cluster using the Parallel Virtual Machine (PVM) message passing library. Test results are obtained with a maximum of nineteen workstations and various PVM configurations are exhibited. Parallel efficiency close to ideal has been achieved for some strategies adopted. It is suggested that load balancing may not always be beneficial on distributed platforms with broadcasting communication connection. © 1998 John Wiley & Sons, Ltd.     

Cross-type optical particle separation in a microchannel

A continuous, real-time optical particle separation, which was previously delineated theoretically, is successfully implemented experimentally for the first time. In this method, particles suspended in a flowing fluid are irradiated with a laser beam propagating in a direction perpendicular to direction of fluid flow. Upstream of the laser beam, the particles move parallel to the direction of fluid flow. When the particles pass through the laser beam, the scattering force pushes them in the direction of laser beam propagation, causing the particles to be displaced perpendicular to the fluid flow direction. This displacement, known as the retention distance, depends on the particle size and the laser beam parameters. Finally, the particles escape from the laser beam and maintain their retention distances as they move downstream. In the present work, the trajectories and retention distances of polystyrene latex microspheres with three distinct diameters were monitored and measured using cross-type optical particle separation. The measured retention distances for different-sized particles were in good agreement with theoretical predictions.     

Adaptive mesh refinement processes for finite element solutions

The nature of adaptive processes is reviewed using as an example a specific finite element problem. Several possible formulations for the objective of mesh refinement processes are given. For the most natural of these objectives the A*-algorithms of artificial intelligence turn out to provide a solution process which is known to be optimal in a certain sense. But practically, there is insufficient information and these processes tend to be inefficient. On the other hand, if the objective is replaced by a strictly local objective based on Pareto-optimality, the error estimates of the resulting mesh sequence are shown to exhibit the order of convergence which is known to be best possible for the type of elements used.     

Optimization under adaptive error control for finite element based simulations

Optimization problems constrained by complex dynamics can lead to computationally challenging problems especially when high accuracy and efficiency are required. We present an approach to adaptively control numerical errors in optimization problems approximated using the finite element method. The discrete adjoint equation serves as a key tool to efficiently compute both parameter sensitivities and goal-oriented error estimates at the same discretized levels. By using a recovery method for the error estimators, we avoid expensive higher order adjoint calculations. We nest the adaptivity of the mesh within the optimization algorithm, which is responsible for converging both the state and optimization algorithms and thereby allowing the reuse of state, parameters, and reduced Hessian in subsequent optimization iterations. Our approach is demonstrated on a parameter estimation problem for contamination transport in a contact tank reactor. Significant efficiency and accuracy improvements are realized in comparison to uniform grid refinement strategies and black-box optimization methods. A flexible and maintainable software interface was developed to provide access between the underlying linear algebra of a production simulator and advanced numerical algorithms such as optimization and error estimation.     

An object-oriented finite element framework for multiphysics phase field simulations

The phase field approach is a powerful and popular method for modeling microstructure evolution. In this work, advanced numerical tools are used to create a framework that facilitates rapid model development. This framework, called MARMOT, is based on Idaho National Laboratory’s finite element Multiphysics Object-Oriented Simulation Environment. In MARMOT, the system of phase field partial differential equations (PDEs) are solved simultaneously together with PDEs describing additional physics, such as solid mechanics and heat conduction, using the Jacobian-Free Newton Krylov Method. An object-oriented architecture is created by taking advantage of commonalities in the phase field PDEs to facilitate development of new models with very little effort. In addition, MARMOT provides access to mesh and time step adaptivity, reducing the cost for performing simulations with large disparities in both spatial and temporal scales. In this work, phase separation simulations are used to show the numerical performance of MARMOT. Deformation-induced grain growth and void growth simulations are also included to demonstrate the muliphysics capability.     

Design and characterization of a microchannel optical interconnect for optical backplanes

The design, modeling, and experimental characterization of a microchannel-based free-space optical interconnect is described. The microchannel interconnect was used to implement a representative portion of an optical backplane that was based on field-effect transistor, self-electro-optic device smart-pixel transceivers. Telecentric relays were used to form the optical interconnect, and two modes based on two different optical window clusterings were implemented. The optical system design, including the optical geometry for different degrees of clustering of windows supported by a lenslet relay and the image mapping associated with a free-space optical system, is described. A comparison of the optical beam properties at the device planes, including the spot size and power uniformity of the spot array, as well as the effects of clipping and misalignment for the different operating modes, is presented. In addition, the effects of beam clipping and misalignment for the different operating modes is presented. We show that microchannel free-space optical interconnects based on a window-clustering scheme significantly increase the connection density. A connection density of 2222 connections/cm(2) was achieved for this prototype system with 2 x 2 window clustering.     

Modelling convection in solidification processes using stabilized finite element techniques

Solidification of dendritic alloys is modelled using stabilized finite element techniques to study convection and macrosegregation driven by buoyancy and shrinkage. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume‐averaging method. A single domain model is considered with a fixed numerical grid and without boundary conditions applied explicitly on the freezing front. The mushy zone is modelled here as a porous medium with either an isotropic or an anisotropic permeability. The stabilized finite‐element scheme, previously developed by authors for modelling flows with phase change, is extended here to include effects of shrinkage, density changes and anisotropic permeability during solidification. The fluid flow scheme developed includes streamline‐upwind/Petrov–Galerkin (SUPG), pressure stabilizing/Petrov–Galerkin, Darcy stabilizing/Petrov–Galerkin and other stabilizing terms arising from changes in density in the mushy zone. For the energy and species equations a classical SUPG‐based finite element method is employed with minor modifications. The developed algorithms are first tested for a reference problem involving solidification of lead–tin alloy where the mushy zone is characterized by an isotropic permeability. Convergence studies are performed to validate the simulation results. Solidification of the same alloy in the absence of shrinkage is studied to observe differences in macrosegregation. Vertical solidification of a lead–tin alloy, where the mushy zone is characterized by an anisotropic permeability, is then simulated. The main aim here is to study convection and demonstrate formation of freckles and channels due to macrosegregation. The ability of stabilized finite element methods to model a wide variety of solidification problems with varying underlying phenomena in two and three dimensions is demonstrated through these examples. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficient implicit finite element analysis of sheet forming processes

The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time‐savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton–Raphson iterations. This also applies to quasi‐static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd.     

Dual boundary element method and finite element method for mixed‐mode crack propagation simulations in a cracked hollow shaft

Three‐dimensional mixed‐mode crack propagation simulations were performed by means of the dual boundary element method code BEASY and 2 finite element method‐based crack propagation codes: ZENCRACK (ZC) and CRACKTRACER3D (CT3D). The stress intensity factors (SIFs) along the front of an initial semielliptical crack, initiated from the external surface of a shaft, were calculated for 4 different load cases: bending, press fit, shear, and torsion. The methods used for the SIF assessment along the crack front were the J‐integral for BEASY and ZC and the quarter point element stress method for CT3D. Subsequently, crack propagation simulations were performed, with the crack growth rate evaluated by using Paris' law, calibrated for the material at stake (American Society for Testing and Materials A469 steel). The kink angles were evaluated by using the minimum strain energy density and maximum tangential stress criteria for BEASY, the maximum energy release rate and maximum tangential stress for ZC, and the maximum principal asymptotic stress for CT3D. The results obtained in terms of SIFs and crack propagation life show very good agreement among the 3 codes. Also, the shape of the propagated crack, which is significantly out‐of‐plane for the shear and torsion loading, matched very well.     

Refining constitutive relation by integration of finite element simulations and Gleeble experiments

Thermo-mechanical coupled finite element calculations were carried out to simulate the Gleeble compression of the samples of a titanium alloy (Ti60), and the results are analyzed and compared with the actual compression tests conducted on a Gleeble 3800 thermo-mechanical simulator. The changes in temperature, stress and strain distribution in the samples and the source of error on the constitutive relations from Gleeble hot compression test were analyzed in detail. Both simulations and experiments showed that the temperature distribution in the specimen is not uniform during hot compression, resulting in significant deformation inhomogeneity and non-ignorable error in the flow stress strain relation, invalidating the uniform strain assumption commonly assumed when extracting the constitutive relation from Gleeble tests. Based on the finite element simulations with iterative corrections, we propose a scheme to refine the constitutive relations from Gleeble tests.