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)     

Application of a viscoplastic material model on a combined quasi-static-electromagnetic forming process

The prediction and simulation of material behavior by finite element methods has become indispensable. Furthermore, various phenomena in forming processes lead to highly differing results. In this work, we have investigated the process chain on a cross-shaped cup in cooperation between the Institute of Applied Mechanics (IFAM) of the RWTH Aachen and the Institute of Forming Technology and Lightweight Construction (IUL) of the TU Dortmund. A viscoplastic material model based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity has been used [1,2]. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. This anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package LS-DYNA with the electromagnetical module. The aim of the work is to show the increasing formability of the sheet by combining quasi-static deep drawing processes with high speed electromagnetic forming. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Virtual process design on combined quasi-static and high-speed forming

Sheet metal forming processes play a key role in a vast number of manufacturing cycles. The pursuit of novel approaches and enhancements of process chains is limited by the tremendous cost of experimental investigations. Hence, virtual process design is a suitable tool to overcome this limitation and to investigate new aspects of the processes via computer aided design. This work focuses on the optimization of a class of triggering pulses utilized in combined quasi-static and electromagnetic high-speed forming that avoid reverse currents. As typical example double exponential pulses are treated. Non-linear, constrained optimization exploiting a LSDYNA simulation of the forming process is used to determine parameters defining a triggering current pulse, yielding an enhanced forming result, in terms of sharper drawing radii. A more detailed discussion of the method is presented in [1]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Coupled Process-Structure-Model to Simulate Robot Based In-cremental Sheet Metal Forming

A coupled process-structure model to predict path deviations in robot based sheet metal forming is presented. The model consists of a finite element (FE) approach to simulate the sheet forming and a multibody system (MBS) modelling the robot. By coupling both models a path prediction tool is provided. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale modeling of multiphase "in situ" composite

The elastic-plastic behaviour of rapidly solidified Al based (FeSi)-enriched alloys containing intermetallic compounds is considered. A new multilevel mechanical model for the “in situ” composite is proposed considering the aluminium matrix as a micropolar elastic plastic Cosserat material and the hardening phases as pure elastic ones. A two steps homogenization procedure is applied to obtain the overall properties of the multiphase “in situ“ composite, taking into account the existence of different sizes of intermetallic inclusions. A variational approach is applied to evaluate the equivalent stress on macro level at the transition from micro to macro scale. The model is developed using information provided by microstructural investigations and EDX analysis. The multistage bulk material manufacturing process from rapid solidified powders or ribbons is simulated using the Finite Element Method. The model is implemented as user subroutines into the FE code MARC. Numerical simulations are provided, corresponding to different values of metal forming parameters. The influence of the different inclusions sizes on the hardening behavior is discussed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deep Drawing Simulations Based on Microstructural Data

For the optimization of process chains in sheet metal forming it is required to accurately describe each partial process of the chain, e.g. rolling, press hardening and deep drawing. The prediction of the thickness distribution and the residual stresses in the blank has to be of high reliability, since the subsequent behavior of the semi-finished product in the following subprocesses strongly depends on the process history. Therefore, high-quality simulations have to be carried out which incorporate real microstructural data [1,2,3]. In this contribution, the ferritic steel DC04 is analyzed. A finite strain crystal plasticity model is used, for the application of which micro pillar compression tests were carried out experimentally and numerically to identify the material parameters of DC04. For the validation of the model, a two-dimensional EBSD data set has been discretized by finite elements and subjected to homogeneous displacement boundary conditions describing a large strain uniaxial tensile test. The results have been compared to experimental measurements of the specimen after the tensile test. Furthermore, a deep drawing process is simulated, which is based on a two-scale Taylor-type model at the integration points of the finite elements. At each integration point, the initial texture data given by the aforementioned EBSD measurements is assigned to the model. By applying this method, we predict the earing profiles of differently textured sheet metals. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling Metals At Finite Deformation

During metal forming processes, substantial microstructural changes occur in the material due to large plastic deformations leading to different mechanical properties. It is of great interest to predict the behaviour of these materials at different fabriction stages and of the final product. At first glance, the behaviour of metals can be approached by an elastoplastic isotropic material model with a volumetric-deviatoric split and isotropic hardening. In order to perform the calculations, a logarithmic strain is considered in the principal directions of stress and strain space, allowing to make predictions even at finite deformations. Because of the actual nature of metals, the crystalline structure, the deformation at the microstructural level is much more complex. Due to the mathematically algorithmic form of an elastic predictor and a plastic corrector, the elastoplastic model can be extended to crystal plasticity which is similarly handled in terms of a critical resolved shear stress on defined slip planes in the crystal. Hardening can be modelled through a viscoplastic power law. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formulation and application of models for anisotropic hardening in sheet metals subject to complex loading-path changes

In this work material models for the simulation of forming processes involving non-uniform loading path changes are investigated. Materials exhibiting an evolution of the yield surface due to the formation and interaction of dislocation structures on the micro structural level are modeled by employing evolving structural tensors. These account for the evolution of anisotropy and hardening behavior known from technical alloys on a phenomenological basis. In a first step material parameters are identified from experiments for non-uniform loading conditions. In a second step, the evolution of structural tensors for varying loading conditions is investigated and related to the evolution of kinematic quantities. Finally applications relevant to the simulation of sheet metal forming processes are presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Surface Deformation due to Shear and Ploughing in a Halfspace

Sheet and bulk metal forming are widely used manufacturing methods. The interaction between worktool and workpiece in such a process causes friction which has a remarkable impact on the expended energy of the process. Therefore the influence of friction is important. Friction can be split into shearing and ploughing [1]. Ploughing is the plastic deformation of a soft surface by a hard contact partner. Shear forces are only transferred in the real contact area where material contact occurs. The investigation of the contribution of both ploughing and shearing to the total friction resistance is done with the use of an elasto-plastic halfspace model. The multiscale character of surfaces demands a fine discretization, which results in numerical effort. While a finite element method takes into account both surface and bulk of the contact partners, the halfspace model only regards the contact surfaces and thereby consumes less computing capacity. In order to identify the friction resistance, two rough surfaces get into contact. After full application of the normal load, the surfaces are moved relatively to each other. New asperities of the contact surfaces get into contact and are plastically deformed. These deformations are used to estimate the ploughing effect in dependency on the relative displacement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extension of SPH to predict feeding,freezing and defect creation in low pressure die casting

Low pressure die casting is used to manufacture complex metal components where there is a need for high structural integrity. In this process, liquid metal is fed from below into the die used to form the component under a positive pressure. Smoothed particle hydrodynamics (SPH) is a meshfree Lagrangian method that has specific advantages for modelling such material forming applications. This paper describes extensions to the SPH method for predicting shrinkage of the cooling metal, tracking of oxide formation, prediction of feeding, solidification front dynamics and finally direct prediction of the residual pressure distribution in the solidified metal and of cavity defect formation. These are demonstrated using a simple two dimensional example which contains the essential features of an engine block.     

A rheological model for arbitrary symmetric distortion of the yield surface

A phenomenological model of metal viscoplasticity, which takes combined isotropic, kinematic, and distortional hardening into account, is motivated by a new rheological model. The distinctive advantage of the material model is that any smooth convex saturated form of the yield surface which is symmetric with respect to the recent loading direction can be captured. In particular, an arbitrary sharpening of the saturated yield locus in the loading direction combined with a flattening on the opposite side can be covered. Moreover, the yield locus evolves smoothly and its convexity is guaranteed at each hardening stage. The underlying two-dimensional rheological analogy can be used to provide insight into the main constitutive assumptions. This rheological model is utilized as a guideline for the construction of phenomenological constitutive relations. The distortion of the yield surface is described with the help of a so-called distortional backstress. Thus, 2nd rank tensors are utilized only. The resulting material model is thermodynamically consistent. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bayesian corporate bond pricing and credit default swap premium models for deriving default probabilities and recovery rates

This paper develops a Bayesian method by jointly formulating a corporate bond (CB) pricing model and credit default swap (CDS) premium pricing models to estimate the term structure of default probabilities and the recovery rate. These parameters are formulated by incorporating firm characteristics such as industry, credit rating and Balance Sheet/Profit and Loss information. A cross-sectional model valuing all given CB prices and CDS premiums is considered. The quantities derived are regarded as what market participants infer in forming CB prices and CDS premiums. We also develop a statistical significance test procedure without any distributional assumptions for the specified model. An empirical analysis is conducted using Japanese CB and CDS market data.     

About the Microstructural Effects of Polycrystalline Materials and their Macroscopic Representation at Finite Deformation

In the sheet bulk metal forming field, the strict geometrical requirements of the workpieces result in a need of a precise prediction of the material behaviour. The simulation of such forming processes requires a valid material model, performing well for a huge variety of different geometrical characteristics and finite deformation. Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. The validation on the macroscopic scale is performed through the reproduction of the experimentally calculated initial yield surface. Additionally, homogenised stress-strain curves from the microstructure build the outcome for a suitable effective material model. Through optimisation techniques, effective material parameters can be determined and compared to results from real forming processes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Material-based process-chain optimization in metal forming

The characteristics of a manufacturing product are influenced by a variety of different factors, such as the material properties of the base product. The prediction of properties that give optimal results in metal forming applications is a complex task but of high interest for the manufacturer. To realize such a prediction scheme, the process chain is split up into individual process steps and for each of them an inverse modeling is required. The specific aim of this work is to present an approach for the inverse problem formulation of a process step and to solve it using methods of machine learning. Moreover, the challenges that often arise due to the ill-posed nature of inverse problems will be discussed. The main focus is on the crystallographic texture of metals, which strongly affects the deformation behavior during a process step and highly influences the characteristics of the final product. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于改进的基因表达式编程在重金属形态获取中的应用

本文研究了基因表达式编程在重金属形态获取中的应用问题.利用改进的基因表达式编程和Shannon信息熵方法,验证了算法的高效性,获得了重金属形态预测模型并从该模型中获取了重金属的形态知识的结果.该新模型方法还可广泛用于其他时间序列预测问题的研究.     

一种基于无屈服概念的粘塑性模型

结合位错运动的热激活理论,基于无屈服概念,提出了一组描述金属材料变形规律的弹/粘塑性本构方程.方程从总体上考虑了应变率、应变历史、应率变历史、硬化和温度等效应,具有较强的物理基础.恒温单轴条件下商业纯钛的力学性能的理论预测与实验结果相比较,存在着良好的一致性.     

Selective proper orthogonal decomposition model reduction for forming simulations

Robot-based incremental sheet metal forming is a cost-effective and flexible method for prototype and low batch size production. The simulation of such processes is very challenging and elaborate from the computational point of view. To reduce the computational effort model reduction techniques such as proper orthogonal decomposition (POD) can be applied. But the reduction of highly non-linear models in solid mechanics for example forming simulation still leads to problems of efficiency and accuracy. Therefore, the aim of this paper is to present an alternative way to use POD for forming processes. The presented selective POD (SPOD) method is used to split the model into two domains depending on the degree of plastic strain. Only the domain with approximately linear elastic behavior will be reduced by using POD. Utilizing the SPOD method for the example of forming a horizontal flute reduces the computational time up to around 30 per cent. High accuracy with approximation errors smaller than one per mill is achieved. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermomechanical modeling and simulation of aluminum alloys during extrusion process

The purpose of this work is to simulate the microstructure development of aluminum alloys during hot metal forming processes such as extrusion with the help of the Finite Element Method (FEM). To model the thermomechanical coupled behavior of the material during the extrusion process an appropriate material model is required. In the current work a Johnson–Cook like thermoelastic viscoplastic material model is used. To overcome the numerical difficulties during simulation of extrusion such as contact problem and element distortion an adaptive meshing system is developed and applied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A micromechanical model for the transformation induced plasticity in polycrystalline steels

Due to the effect of transformation induced plasticity (TRIP) , TRIP-steels are very promising materials, e.g. for the automobile industry. The material behavior is characterized by very complex inner processes, namely phase transformation coupled with plastic deformation and kinematic hardening. We establish a micromechanical model which uses the volume fractions of the single phases, the plastic strain and the hardening parameter in every grain of the polycrystalline material as internal variables. Furthermore, we apply the Principle of the Minimum of the Dissipation Potential to derive the associated evolution equations. The use of a coupled dissipation functional and a combined Voigt/Reuss bound directly results in coupled evolution equations for the internal variables and in one combined yield function. Additionally, we show numerical results which prove our model's ability to give a first prediction of the TRIP-steels' complex material behavior. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)