Meso-Macro Modelling of Coated Forming Tools under Thermal Shock Conditions

In hybrid-forming processes workpieces are heated up before forming in order to reduce the forming forces. They are innovative methods for the production of components with graded properties, particularly with regard to tailored material properties and geometrical shape. During service life the forming tools are subjected to cyclic thermal shock loading conditions which can result into damage and failure. For improvement of the tool durability in the hybrid-forming process coated forming tools with multilayered coating systems are considered to be applied in future. This contribution shows the actual state of work for the development of a twoscale FE model for the simulation of the multilayered coated forming tool. Within this model the three-dimensional model of the forming tool builds the macromodel. On the macrolevel the multilayered coating is discretized with one element over the coating thickness. The mesomodel of the coating considers the actual layer design with metallic and ceramic layers. The macro-meso transition is realized with a Taylor-assumption. As the microscale is not considered in our model, the constitutive equations are formulated on the mesoscale. The meso-macro transition is done using volume averaging procedures. Furthermore, a damage model is included for particular layers. The scalar damage variable is used in a thermo-mechanical coupled model for simulation of a reduced heat transfer through a partially damaged layer. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

ALE-based 3D FE simulation of electromagnetic forming

Electromagnetic forming is a contact-free high-speed forming process. The deformation of the work piece is driven by the Lorentz force which results from the interaction of a pulsed magnetic field with eddy currents induced in the work piece by the field itself. The purpose of this work is to present a fully-coupled three-dimensional simulation of this process. For the mechanical structure, a thermoelastic, viscoplastic, electromagnetic material model is relevant, which is incorporated in a large-deformation dynamic formulation. The electromagnetic fields are governed by Maxwell's equations under quasistatic conditions. To consider their reduced regularity at material interfaces Nédélec elements are applied. Coupling takes the form of the Lorentz force, the electromotive intensity and the current geometry of the work piece. A staggered solution scheme based on a Lagrangian mesh for the work piece and an ALE formulation for the electromagnetic field is employed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deformation and Damage Analysis of a Hybrid-Forming Tool under Thermal Shock Conditions

In the hybrid–forming process for gradient structures [1] inhomogeneous cyclic thermo–mechanical stresses and strains lead to higher risks of failure of the forming tool. The main topic of this paper is the validation of finite element calculations for a tool–like specimen under complex thermo–mechanical loadings in order to predict the material behaviour [3]. To this end thermal shock experiments of tool–like specimens are performed. Optical measuring systems are used for three–dimensional digitalisation of the specimens to get a sufficient amount of data. Results of experimental optical measurings and results of finite element calculations are compared. Additionally, damage analysis using the eddy current method is performed to characterize the surface state of the cyclically thermal shocked specimens. This damage analysis provides data for lifetime prediction models under thermal shock conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and Simulation of Curing Processes of Epoxy Resin

During the curing reaction, the adhesive changes its thermomechanical material behaviour from a viscous fluid to a viscoelastic solid. This phase transition is an exothermal chemical reaction which is accompanied by thermal expansion, chemical shrinkage and changes in temperature. In this work the numerical simulation of the curing process will be presented. The material model for the implementation is presented in [1]. For the implementation of the material model the consistent tangent operator has been derived. In the presentation, experimental data and simulation are shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bifurcation and chaos of thin circular functionally graded plate in thermal environment

A ceramic/metal functionally graded circular plate under one-term and two-term transversal excitations in the thermal environment is investigated, respectively. The effects of geometric nonlinearity and temperature-dependent material properties are both taken into account. The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power law distribution of the volume fraction of the constituents. Using the principle of virtual work, the nonlinear partial differential equations of FGM plate subjected to transverse harmonic forcing excitation and thermal load are derived. For the circular plate with clamped immovable edge, the Duffing nonlinear forced vibration equation is deduced using Galerkin method. The criteria for existence of chaos under one-term and two-term periodic perturbations are given with Melnikov method. Numerical simulations are carried out to plot the bifurcation curves for the homolinic orbits. Effects of the material volume fraction index and temperature on the criterions are discussed and the existences of chaos are validated by plotting phase portraits, Poincare maps. Also, the bifurcation diagrams and corresponding maximum Lyapunov exponents are plotted. It was found that periodic, multiple periodic solutions and chaotic motions exist for the FGM plate under certain conditions.     

Characterization of short fiber reinforced polymers

This contribution presents ideas, how composite materials can be characterized with respect to experimental testing. The material properties of the investigated short glass fiber reinforced polymer are obtained by providing results from the experiment in order to seperate different material effects, such as elasticity, plasticity, damage, viscoelasticity, compressibility and anisotropy. Therefore, at first, linear uniaxial tensile tests with cyclic loadings have been realized. The application of the material in this work is the machining by a three-dimensional forming process. Hence, multiaxial loadings have to be additionally taken into account matching these conditions. In order to provide more information, biaxial tensile tests have to be realized using a testing device supplying the additional necessary experimental data [1, 2]. A final aim of this work is to develope a verification experiment representing the three-dimensional forming process as realistically as possible, e. g. a Nakajima test [4]. For this case, a three-dimensional optical analysis in order to get the necessary measurement data, is indispensable to realize an inverse method [3] by comparing the information of the complete deformation field as well as the force data of the experiment using a given material model. (© 2015 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)     

Microstructure evolution during rolling and annealing of mild steels

The process chain for components made of sheet metals consists of different forming techniques like hot rolling, cold rolling, and deep drawing as well as heat treatment operations like annealing. For the design and optimization of the whole manufacturing process and the final component behavior, a correct representation of the material behavior and the application of appropriate numerical simulation techniques are required. For our first investigations, a ferritic mild steel DC04, which is a typical steel grade for automotive applications, is analyzed. Therefore, specimens are taken out of a real manufacturing process after hot and cold rolling and after annealing. These specimens are intensively investigated in order to study the texture evolution and the development of other material properties, like yield function during the process chain. In this paper different homogenization methods are used to simulate the texture evolution during cold rolling. The results are compared concerning accuracy and efficiency of the considered models. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite strain contact model for mixed lubricated surfaces in forming processes

For an accurate simulation of forming processes, it is of paramount importance to model the different lubrication regimes that can develop at the contact interface. These might vary from zone to zone of the forming piece, and from one regime to another, resulting in forces of different nature and magnitude. In these cases, the use of the classical Coulomb friction law will be clearly not sufficient to capture, in a suitable manner, the variety of forces applied on the forming piece.     

Analytical solution for electromagnetothermoelastic behaviors of a functionally graded piezoelectric hollow cylinder

Analytical study for electromagnetothermoelastic behaviors of a hollow cylinder composed of functionally graded piezoelectric material (FGPM), placed in a uniform magnetic field, subjected to electric, thermal and mechanical loads are presented. For the case that the electric, magnetic, thermal and mechanical properties of the material obey an identical power law in the radial direction, exact solutions for electric displacement, stresses, electric potential and perturbation of magnetic field vector in the FGPM hollow cylinder are determined by using the infinitesimal theory of electromagnetothermoelasticity. Some useful discussions and numerical examples are presented to show the significant influence of material inhomogeneity, and adopting a certain value of the inhomogeneity parameter β and applying suitable electric, thermal and mechanical loads can optimize the FGPM hollow cylindrical structures. This will be of particular importance in modern engineering design.     

FE-simulation of spatially graded gelation during adhesive's curing

In this contribution main aspects of material characterization and modelling of a curing adhesive are denoted. It is pointed out how to deal with the exothermic heat generation during curing, both, how to obtain it experimentally as well as how to account for it in the continuum mechanical an FE-modelling framework. Furthermore, a strategy to simulate spatially graded gelation processes in ANSYS® is presented. An academic simulation example completes this work. By the help of this simulation tool a better understanding of a novel manufacturing process of smart semi-finished light weight structures is ensured. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal Residual Stresses and Triaxiality Measures

High performance ceramics have found their way into many highly challenging engineering tasks. For example silicon nitride is one of the best choices, if a material for demanding applications like metal forming and cutting is required. Due to the brittle nature of these hard and strong materials it is useful to know about thermal residual stresses, which can arise during the sintering process. In order to gain insight into the material behaviour, a single grain inclusion is exposed to thermal loads. Due to thermal mismatch, it undergoes a residual stress and strain field. The geometry of the model and the material data are motivated by the properties of silicon nitride. The stress fields are analyzed by three different measures for stress triaxiality. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

钛合金插铣过程温度场的数学建模与有限元分析

从金属切削理论出发分析了钛合金插铣过程的切削热产生机理,推导出工件的热传导方程式,并在此基础上建立钛合金插铣的数学模型,应用Galerkin有限元方法对工件的热传导方程进行推导计算,随后利用Matlab进行数值模拟,最终得到工件稳定后温度分布图.通过数值计算结果与实验结果对比,验证了有限元模型具有可靠和高精度优点.对钛合金插铣过程加工参数的优化和刀具的设计提供了重要参考依据.     

Nonlinear analysis of buckling,free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment

Employing Euler–Bernoulli beam theory and the physical neutral surface concept, the nonlinear governing equation for the functionally graded material beam with two clamped ends and surface-bonded piezoelectric actuators is derived by the Hamilton’s principle. The thermo-piezoelectric buckling, nonlinear free vibration and dynamic stability for the piezoelectric functionally graded beams, subjected to one-dimensional steady heat conduction in the thickness direction, are studied. The critical buckling loads for the beam are obtained by the existing methods in the analysis of thermo-piezoelectric buckling. The Galerkin’s procedure and elliptic function are adopted to obtain the analytical solution of the nonlinear free vibration, and the incremental harmonic balance method is applied to obtain the principle unstable regions of the piezoelectric functionally graded beam. In the numerical examples, the good agreements between the present results and existing solutions verify the validity and accuracy of the present analysis and solving method. Simultaneously, validation of the results achieved by rule of mixture against those obtained via the Mori–Tanaka scheme is carried out, and excellent agreements are reported. The effects of the thermal load, electric load, and thermal properties of the constituent materials on the thermo-piezoelectric buckling, nonlinear free vibration, and dynamic stability of the piezoelectric functionally graded beam are discussed, and some meaningful conclusions have been drawn.     

Analytical solution in transient thermo‐elasticity of functionally graded thick hollow cylinders (Pseudo‐dynamic analysis)

This work studies transient thermal stresses in a thick hollow cylinder made of a functionally graded material (FGM). Material properties are considered to be nonlinear with a power law distribution through the thickness. The cylinder is assumed to be of infinite length, and the plane strain condition is supposed. The displacement and the distribution of stresses are obtained by analytical solution of governing differential equations of the Navier type. The transient dynamic behavior of thermal stresses is determined and discussed for various power law exponents appearing in functions determining mechanical properties of FGMs. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic Modeling and Force Control of a Redundant Robot for Polishing Applications

For many robotic applications with tasks such as cutting, assembly or polishing, it is necessary to get in contact with the surrounding. In this paper a redundant robot with seven degrees of freedom in a metal polishing task is considered. For simulation as well as for the controller design a dynamic model of the robot and a contact model are required. The equations of motion of the robot are calculated with the Projection Equation in subsystem representation and the contact model contains linear tool elasticities and work piece elasticities. In the case of a polishing task, a constant contact force during the process is required even if the robot moves along a trajectory. Thus some degrees of freedom of the robot tool center point have to be position controlled while the other ones have to be force controlled. The redundant robot offers the possibility to avoid singular positions or to maximize the available end-effector forces within the inverse kinematics and is therefore best suited for polishing large objects. The actual process forces are measured with a six axis force-torque-sensor mounted at the tool center point. These forces are used in a parallel force/position control law to achieve the desired behavior. Results from measurements of a test arrangement are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of optimal metal flow in incremental sheet forming

Sheet metal forming processes are manufacturing processes in which a piece of sheet metal is shaped to a specified geometry, e.g. a car door. A promising new forming process is incremental sheet metal forming, in which the deformation is imposed by a progressive, localised plastic deformation induced by a pin-like forming tool that moves under numerical control along a pre-defined trajectory. This process offers the possibility to control the metal flow by adjusting the trajectory of the forming tool. Mathematically, sheet metal forming processes can be considered as a mapping between the initial, undeformed sheet metal and the final, deformed state. In most applications the surface area of the sheet metal is enlarged during the deformation. In this case, an ideal mapping would produce a homogeneous stretching of the sheet metal such that the final sheet thickness is the same everywhere. In this work, we analyze the following question: for each point in the initial configuration, what must be its location on the final geometry such that the thickness is the same everywhere? We construct a special type of surface evolution that combines flow along the surface normal with appropriate tangential velocity corrections, and show that the flow yields a constant sheet thinning on a sheet metal. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and numerical investigation of different types of articular cartilage replacement materials

The aim of the presented work is to characterize the mechanical properties of different types of articular cartilage replacement materials. For this propose an elastic-diffusion model is developed to identify the elastic and diffusion properties of the replacement materials. A set of unconfined compression tests were performed with several kinds of implants. By means of finite element simulation integrated with an user-defined material model, the material parameters were identified. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)