The material parameters for two isothermal viscoplastic models with deliberately limited sets of material parameters have been estimated. The models are to describe the behaviour of the nickel based superalloy IN792 in a gas turbine hot part application. The models are based on a power law flow equation and the state variable used is backstress. The model calibration is done by least-squares optimization using non-standard constitutive tests that are aimed at describing relevant component conditions. The constitutive tests give information about the kinematic hardening effects for the backstress evolution equations, while secondary creep data provides stress versus inelastic strain rate information for the flow equation. All tests are uniaxial and isothermal. With the estimated parameter sets the models give relatively good fits to the data. The results suggest that the models can be used to describe the high temperature behaviour of IN792. ⌐ 2002 Elsevier Science B.V. All rights reserved.

This paper presents a method where a multi objective optimization techniqueis used together with response surface methods in order to support crashworthiness design. As in most engineering design problems thereare several conflicting objectives that have to be considered when formulating a design problem as an optimization problem. Here this is exemplified by the desire to minimize the intrusion into the passenger compartment area and simultaneously obtain low maximum acceleration during vehicle impact. These two objectives are naturally conflicting, since low maximum acceleration implies large intrusion. The contribution of thispaper is to show a successful application of a set of existing methods to solve a real world engineering problem.The paper also presents methods of illustrating the results obtained from the multi-objective optimization.

Delamination initiation and growth are analyzed by using a discrete cohesive crack model. The model is derived by postulating the existence of a maximum load surface which limits the adhesive forces in the process zone of the crack. The size of the maximum load surface is made dependent on the amount of dissipated crack opening work such that the maximum load surface shrinks to zero as a predefined amount of work is consumed. Mode I, II, III loading or any combined loading is possible. The delamination model is implemented in the explicit finite-element code LS-DYNA and simulation results are found to be in agreement with experimental results. ⌐ 2001 Elsevier Science Ltd. All rights reserved.

A delamination model for shell elements is presented. It consists of an adhesive penalty contact formulation for initially tying shells together and a cohesive zone model for degrading the adhesive forces. An adhesive contact used between shell elements has to account for the thickness offset, such that the rotational degrees of freedom in the shell elements are included in the algorithm. This is considered in the present contact model and the complete delamination model is implemented in the explicit Finite Element code LS-DYNA. By preventing delamination growth the delamination model can be turned into a tied contact. As such it is used in two FE-models, where plates are bonded together and subjected to various loads. The adhesive penalty contact performs well. The complete delamination is validated by simulating the Double Cantilever Beam, End-Notch Flexural and Mixed Mode Bending setups, and the results are shown to be in agreement with experimental data.

An existing delamination model is further developed for use in transverse impact simulations. An algorithm is developed making it possible to determine the propagation direction of the delamination front. Using this it is possible to determine relative orientation of the delamination front with respect to the fibers above and below the interface. In a qualitative evaluation it is shown that the present delamination model can be used for modeling delamination initiation and growth in transverse impact simulations.

The common manufacturing procedure for components of cemented carbide is a closed die cold compaction of a powder and a subsequent sintering of the compact to full density and strength.

Major problems with the manufacturing process are the possible fracturing on ejection from the tooling and the distortion in the final shape. It is beneficial to perform the design iterations in the form of computer simulations, provided such simulations predict at least the final shape with good accuracy. This thesis concerns the development of computer simulation tools for both the compaction and the sintering.

A constitutive model for the compaction based on elasto-plasticity has been developed. The model has a compactness tensor that measures the directionality of the deformation history and a two-dimensional hardening parameter set. The model represents the deformation induced anisotropy in the form ofa kinematic hardening combined with an isotropic hardening, and uses a flow rule that emanates from a non-associated flow potential.

Furthermore, a continuum model of the sintering with and without loading has been developed, based on a micromechanical model of the sintering without loading. The model is visco-elastic with the capillary forces represented bya sintering stress. The model parameters evolve with temperature, relative density and rate of temperature. The author presented a rationale for deciding, in which mechanism the rate of temperature influence belongs.

The models were implemented in the explicit FE-program LS-DYNA2D and verified against several experimental compaction and sintering tests. Finally, the models have been verified by the simulation of the complete compaction and sintering process of an industrial tool piece. The agreement between simulation and measurement in final shape is good. The convergence of the simulation concept is also demonstrated.

Using modal analysis, the deflection of a beam subjected to an axial tensile force N and a moving vertical force P , has been determined. This solution was exploited in a study of deflection and wave propagation in the contact wire of a railway overhead catenary system. For moderate values of speed c of the moving force P ( i.e ., c less than half the lowest critical speed c crit ) travelling waves reflect at the boundaries of the contact wire so that the waves meet and catch up with the moving force several times. In practice, when a pantograph (here modelled by the force P ) touches the contact wire some distance from the end of the wire, waves are sent out both in the forward and backward direction, giving even more reflections and wave interactions with the contact force. These waves will add or subtract to the wire deflection at the point of force application. The stress in the wire due to bending is estimated and it appears to be moderate for the speeds investigated here ( i.e ., for c < 0.5ccrit). Close to the critical speed, however, bending stresses will be significant.

Contact searching is an important and time-consuming part of computer simulation of certain deformation processes. Contact searching can be facilitated by orthogonal range searching. We have experimentally evaluated four methods for orthogonal range searching: the projection method, the cell method, the k-d tree method, and the range tree method.

The results of our experiments indicate that two of these methods, the cell and k-d tree methods, have practical significance. The cell method is in most cases faster than the k-d tree method.

This thesis concerns the optimization of structures subjected to impact loading. Major applications can be found in the crashworthiness design of vehicles. There is an industrial interest in using optimization methods in the crashworthiness design process. However, strongly nonlinear responses, including high frequency components, make the Finite Element (FE) simulations computationally demanding. This fact restricts the number of possible optimization methods that can be applied.

In this work two optimization methods have been investigated: Response Surface Methodology (RSM) and Kriging. In both these methods the number of functional evaluations, i.e. here FE simulations, depends at least linearly on the number of design parameters. Thus, the number of design parameters is limited due to the computational effort. One objective of this work has been to reduce the total computational cost of the optimization process, or alternatively the possibility to use more design parameters at the same computational cost. When using RSM and Kriging, the number of functional evaluations in each iteration can be reduced, and/or the convergence of the optimization process can be improved. In many applications, RSM has been used with linear approximating response surfaces for robustness and efficiency reasons. Linear RSM may suffer from iterative oscillations, since the optimal design is often found on the boundary of the feasible design region. This oscillatory behaviour can be reduced if Kriging is used for the approximating response surfaces. However, it has been found that Kriging may have problems in fulfilling the constraints. In the initial design process of a structure very many alternative designs exist. At these early stages topology optimization is a mean of finding a structure that is optimal for the objective at hand. In this work a topology optimization approach is proposed for the design of crashworthiness structures. The resulting structure must still be subjected to an interpretation by engineers and also be improved by further optimization.

This thesis is concerned with the use of optimization methods in the vehicle industry. Numerical optimization has been used with limited extend in the vehicle industry. However, great potential of using optimization methods has been identified during the development process of vehicle body structures. One driving force in this direction is the increased focus on building lighter and cheaper vehicles with better crashworthiness. There is also an interest, from an academic point of view in the area of optimization research, to establish the use of optimization methods in the industry.

This thesis presents a method that introduces optimization as a tool to be used during the design procedure of vehicle body structures. The three included papers introduces a way of including optimization methods during the development of vehicle body structures.

The goal is reliable creep-fatigue lifing methodology for industrial gas turbines.

A literature study on high temperature materials used in gas turbines reveals that:

• Most testing/modelling work has focused on characterisation and modelling of material response in isothermal standard tests, i.e. creep, tensile and LCF tests. This is not applicable to creep-fatigue lifing of industrial gas turbines. The difference between test and component conditions implies that models calibrated with standard data would be used far outside their domain of confidence.

• A limited amount of testing/modelling work has included TMF testing. TMF test conditions are reasonably close to component conditions in aero turbines but the results are still not applicable for industrial gas turbines which, unlike TMF tests and aero gas turbines, are run at full load and therefore at maximum temperature, for extended times, typically in the order of 40000h.

• A small amount of tests on aged material can be found in literature. It provides valuable but

insufficient insight into the effects of long temperature exposure.

The conclusion is that methodology improvement requires more appropriate testing. Testing/modelling work based on this has been done. Results so far:

• Constitutive and life models have been developed for the carbide precipitating material Haynes 230. We have been limited to 'what can be done' in existing test rigs but the resulting methodology constitutes a definite step forward.

• Constitutive models for the gamma prime strengthened material IN792 have been evaluated and calibrated using creep and 'step relaxation' data. This is a step forward compared to use of standard data but we have yet to perform tests on aged material and anisothermal verification tests to finalise the modelling.

• We are developing a prototype for a new class of TMF rigs. Heating, cooling and insulation is used to reproduce local conditions at critical points in components under controlled laboratory conditions. The rigs will be designed for long term testing at a reasonable cost. The drawback is that the test conditions, e.g. strain ranges, must be calculated by FE simulation rather than measured.

• Tests on virgin and aged specimen are ongoing to characterise the embrittling effect of long term exposure as a basis for a rational ranking of materials, i.e. on the basis of tests on appropriately aged rather than virgin material.

Most of the results of the testing/modelling work should be of generic value for the material classes

represented by Haynes 230 and IN792.

In recent years, the automotive industry has shown increased interest in reducing weight and improving environmental effects of cars. This has lead to an increased use of lightweight parts. The exchange to lighter materials is however not a simple task since all demands on driving performance, crashworthiness, driving economy etc should still be fulfilled. One attractive concept is the spaceframe, which uses extruded aluminium profiles. The profiles are formed by bending and/or hydroforming and are connected by different types of joints. By using hydroforming several advantages can be found compared to traditional forming methods, including better tolerances, a decreased number of parts and an increased range of forming options.

The aim of this project is to study the effect from the forming and assembling processes on the crashworthiness of the spaceframe. In this work, the focus is on the bending and hydroforming processes of extruded aluminium tubes. The objective is to accurately and efficiently predict the final product properties by the use of Finite Element (FE) simulations.

The present study accentuates the need for improved anisotropic constitutive models. It is shown that a material model, which accurately describes the anisotropic behaviour of aluminium tubes, can be obtained by using simple and robust experiments.

Since the hydroforming often is preceded by a bending operation this yields a demand on history dependent failure criteria. A selected number of known failure indicators are studied, including Forming Limit Diagram (FLD), Forming Limit Stress Diagram (FLSD), bulk forming criteria and the Continuum Damage Approach (CDM). If an accurate constitutive model is used, a strain path independent failure indicator is shown to be an efficient tool to determine the remaining formability of hydroformed parts.

The potential of using simulation and optimization techniques in the design of sheet metal forming processes has been investigated. Optimization has been used in a variety of sheet metal forming applications. This usage has given ideas and guidelines on how to formulate an optimization problems, how to ensure its rapid convergence and how to reach a feasible process design. Furthermore one method to include the uncertainty and variation in the governing parameters has been evaluated.

For each forming process many formability problems exist which usually are associated with fracture, wrinkling and springback. The aim of a good process design is to avoid these problems. By the use of simulation based design the physical trial- and error iterations can to a large extent be replaced by virtual iterations. When optimization techniques are used in the design process the number of iterations can be very large. In this work effort has been made to develop an optimization method, Space Mapping (SM), which is less computing intensive. It has been shown that SM can drastically reduce the required computing time and that its optimal solution is close to the optimal solution obtained by the more computing intensive Response Surface Methodology (RSM). The drawback of SM is that the method is less robust compared to RSM, and that it requires a better initial design for convergence.

Each industrial sheet metal forming process exhibits a certain degree of stochastic behavior due to uncertainties and variations in material properties, geometry and other process parameters. The forming process must be designed such that it is insensitive to these uncertainties and variations, i.e. the process must be robust. One possibility to consider uncer tainties and variations in a simulation and optimization based design process is to use the Monte Carlo method, in particular in combination with response surfaces as metamodels. It has been shown in this work that a linear response surface can successfully be used to identify the important design variables and to give an estimate of the probabilistic response. It has also been found that quadratic surfaces are required for a more accurate evaluation of the response.

The aim of the present work is to find a stable and effective optimization algorithm that can be used to determine the location and size of drawbeads in sheet metal forming processes. The result from the optimization will be the restraining force that each drawbead applies to the blank. In addition, optimization has been used to determine the physical dimensions of the drawbead.

The study in Paper I is limited to two structures in crashworthiness design, each with two design variables and three responses. The conclusion is that 1.5 times the minimum number of function evaluation should be used to fit the surface approximations. The conclusion of this study gives an indication on how many evaluations that are needed in order to efficiently construct the response surface approximations.

Paper II shows that the optimization algorithm using Space Mapping is well suited for optimization problems in crashworthiness design and in the design of sheet metal forming processes. All optimization applications converged to the correct optimum and the computing time was decreased with a maximum of 63% relative to the traditional RSM optimization.

The Space Mapping algorithm presented in Paper III converged to an optimum value that is lower than the optimum value from the traditional RSM, when the approximated surfaces from the first RSM iteration were used as the coarse model. The Space Mapping algorithm, however, reached a higher value compared to RSM, when surfaces from the third RSM iteration was used as the coarse model. Hence, the Space Mapping algorithm converged to a better objective value compared to RSM with less evaluations.

This thesis has shown that it is possible to apply optimization on the design of sheet metal forming processes. For the problem used in the last paper both the traditional Response Surface Methodology and the Space Mapping technique were successful in avoiding failure due to necking and to decrease the risk of wrinkles. The Response Surface Methodology is robust enough to be used in the industrial tool design process. The Space Mapping technique using linear response surfaces as coarse model needs further research before it can be used efficiently in industry.

In the present paper, an optimization of the draw-in of an automotive sheet metal part has been carried out using response surface methodology (RSM) and space mapping technique. The optimization adjusts the draw bead restraining force in the model such that the draw-in in the FE-model corresponds to the draw-in in the physical process. The conclusion of this study is that space mapping is a very effective and accurate method to use when calibrating the draw-in of a sheet metal process. In order to establish draw bead geometry from the draw bead restraining force a 2D-model was utilized. The draw bead geometry found showed good agreement with the physical draw bead geometry.

The aim of the present paper is to evaluate the use of linear and quadratic approximating response surfaces as metamodels in a reliability assessment of a sheet metal forming process using the Monte Carlo simulation technique. Monte Carlo simulation was used to determine the probability for springback and thickness variation in a sheet metal part. The conclusions of this study is that Monte Carlo analysis can be used to identify the most important variables and to estimate the range of the studied responses. Linear metamodels can be used to identify the important variables and to give an estimate of the probabilistic response. But quadratic surfaces are required for a more accurate analysis.

In the present paper optimization has been used to evaluate alternative sheet metal forming processes. Six process set-ups were first defined in a hierarchy of designs and optimization was then used to evaluate each forming process of these designs. The challenge in designing the forming process was to avoid failure in the material and at the same time reach an acceptable through thickness strain. The conclusions of this study is that there may exist a different process that can give an improved product for the desired geometry. This process might be impossible for the optimization algorithm to reach due to either a poor starting point or a not so wise process set-up.

Thermal barrier coatings, TBCs, are used in gas turbines as a thermal shield resulting in lower temperature in coated components. The decrease of temperature allows higher gas temperatures in the turbine, which increase the efficiency. The bimaterial construction with an outer ceramic layer applied onto a metallic material give rice to problems during thermal cycling. Thermal induced stresses will gradually break down the coating. The ceramic layer will delaminate from the substrate, resulting in spallation, and the component will break down due to overheating.

The delamination process is investigated in this thesis by finite element simulations. The growth of an internal alumina layer in the top/bond coat interface is investigated by 3D finite element simulations which show that the local stress state change in such way that the alumina growth help nucleation and growth of small delamination cracks. Finite element simulations, in which t he energy release rate and stress intensity factors are calculated, investigate the growth of small delamination cracks in or close to the top/bond coat interface. Experiments show that these cracks grow parallel to or in the sinusoidal top/bond coat interface and the results of the simulations show that the mode mixity changes as the delamination cracks grow.

A new delamination life model is proposed which is based on results of the fracture mechanical simulations and experimental observations. The model predicts the growth of small cracks in the TBC before they form a large delamination crack. The model is based on a modified Paris law where a mode mixity dependence on the crack growth rate is included, meaning lower crack growth rate in mode 2 load compared with mode 1. Parameters of the model are obtained by optimisation of the model against experimental data, describing the delamination damage evolution in the TBC. The data are obtained from interrupted thermal cycling tests and the prediction of the model corresponds well with these data.

In the present paper failure mechanisms in air plasma sprayed thermal barrier coatings for land-based gas turbines have been studied. This has been done by finite element simulations and fractographic investigations of low cycle fatigue (LCF) tested material, here chosen as an 350 μm thick partially stabilised zirconia top coat (TC) together with a 150 μm thick Ni-Co-Cr-Al-Y bond coat (BC) on a nickel base substrate (Haynes 230). Both LCF testing, modelling results and fractographic investigations point in the same direction. An increased thickness of the thermally grown oxide (TGO) does decrease the LCF life of a coated structural alloy. Several points of crack initiation were found, in the TGO at the TC/BC interface, at the oxide network within the BC and at oxide inclusions between BC and substrate. During LCF tests the initiated cracks will grow radially into the substrate material. The behaviour is explained by increased TC/BC delamination stresses and changed oxidation behaviour with increased oxidation times.

This master thesis studies GPU-enabled parallel implementations of the 3D Parallel Marching Method (PMM). 3D PMM is aimed at solving the non-linear static Jacobi-Hamilton equations, which has real world applications such as in the study of geological foldings, where each layer of the Earth’s crust is considered as a front propagating over time. Using the parallel computer architectures, fast simulationscan be achieved, leading to less time consumption, quicker understanding of the inner Earth and enables early exploration of oil and gas reserves. Currently 3D PMM is implemented in shared memory architecture using OpenMP Application Programming Interface (API) and the MINT programming model, which translates C code into Compute Unified Device Architecture (CUDA) code for a single Graphical Process Unit (GPU). Parallel architectures have seen rapid growth in recent years, especially GPUs, allowing us to do faster simulations. In this thesis work, a new parallel implementation for 3D PMM has been done to exploit multicore CPU architectures as well as single and multiple GPUs. In a multiple GPU implementation, 3D data isdecomposed into 1D data for each GPU. CUDA streams are used to overlap the computation and communication within the single GPU. Part of the decomposed 3D volume data is kept in the respective GPU to avoid complete data transfer between the GPUs over a number of iterations. In total, there are two kinds of datatransfers that are involved while doing computation in the multiple GPUs: boundary value data transfer and decomposed 3D volume data transfer. The decomposed 3D volume data transfer is optimized between the multiple GPUs by using the peer to peer memory transfer in CUDA. The speedup is shown and compared between shared memory CPUs (E5-2660, 16cores), single GPU (GTX-590, C2050 and K20m) and multiple GPUs. Hand coded CUDA has shown slightly better performance than the Mint translated CUDA, and the multiple GPU implementation showed promising speedup compared to shared memory multicore CPUs and single GPU implementations.

Two-mesh refinement indicators based on the gradients of effective stresses and effective plastic strains, respectively, are proposed for adaptive finite element analysis of the large deformation, materially non-linear dynamic response of shells. The refinement strategy consists of equi-distributing the variation of stresses or plastic strains over the elements of the mesh. A program module for implementing these refinement indicators has been developed and coupled with the general non-linear finite element explicit code LS-DYNA. Numerical examples including both material and geometric non-linearities are presented. It is shown that these indicators can effectively identify those finite elements, which have high gradients of stresses and strains so that the mesh is refined in the region's undergoing the most severe deformations.

Trains have been operating on ballasted tracks for over 150 years. During this time demands from the railway organisations and from the industry to increase axle loads and train speeds on the existing railway lines have increased. The reasons for this are both economial and environmental.

Both higher axle loads and train speeds will increase the deterioration rate of the track and cause permanent settlements in the ballast and the underlaying soil. When the track quality decreases beyond certain limits maintenance for relevelling and realignment of the track is necessary, and this is expensive.

The aim of the work presented in this thesis, and of the work performed within the EU project SUstained PErformance of Railway TRACK (SUPERTRACK), is to investigate the dynamic train/track interaction and its effect on track degradation. Less degradation will reduce the maintenance costs regarding track settlement.

The work presented in this thesis focuses on different factors affecting the differential track settlement. By using the finite element method, the dynamic behaviour of a railway track subjected to a moving load has been studied. Dynamic effects of unsupported sleepers and their effect on track settlement have been investigated. Also track stiffness irregularities along the track have been studied, and an optimazation of the track stiffness at a transition zone has been performed.

A ballasted railway track exposed to train traffic will degenerate. Track alignment and track level will deteriorate. Settlements of the track (loss of track level and alignment) require maintenance; the track is lifted and aligned, and new ballast material is injected under the sleepers. This paper presents a computer model by which the dynamic train/track interaction can be simulated and the permanent deformation of the track (i.e. track settlements) can be calculated. The voided sleepers ("hanging" sleepers) phenomenon will also be discussed.

The track stiffness experienced by a train will vary along the track. Sometimes the stiffness variation can be very large whitin short distances. These changes in track stiffness will cause variations in the train/track interaction forces, and force variations will normaly imply settlements of the track as a result of permanent deformation in the ballast and in the underlying structure.

Since the behaviour of the ballast and subground material is not exactly the same under all sleepers. and since the loading of the track is irregular. the amount of settlement will differ from one sleeper to another. As soon as the track geometry starts to deteriorate, the variations of the train/track interaction force increase, and this speeds up the track deterioration rate.

This paper discusses how the transition zone between two track stiffnesses should be designed to reduce the track settlement. The transition from one track stiffness to another is optimized to obtain a wheel/rail contact force with as small variations as possible. A smooth wheel/rail contact force at the transition area will minimize the track settlement.

This paper gives a bibliographical review of the finite element methods applied to the analysis and simulation of coatings, their mechanical and material properties from the theoretical and application points of view. The surface modification technologies in the context of coatings are also included. The added bibliography at the end of this paper contains 1032 references to papers and conference proceedings on the subject that were published in 1995-2005. The following topics are included: coating property simulations, surface modification process simulations and practical coating applications. © 2005 IOP Publishing Ltd.

The paper gives a bibliographical review of finite element methods applied to creep and creep fracture/damage of engineering materials and structures from the theoretical as well as practical points of view. It is a continuation of the author's bibliography published in Int. J. Pressure Vessels Piping 2000, 77: 53-77, where 964 references were listed for the period 1980-1999. This addendum lists more than 400 references to papers, conference proceedings and theses/dissertations on the subject that were published between 1999 and 2003. These references are classified in the following categories: materials, topics, and areas of applications. Each category is further divided into specific subcategories for a more effective and faster reference retrieval. © 2004 Elsevier Ltd. All rights reserved.