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)     

On physics-based crystal plasticity models: Application to virtual material testing of sheet metals

It is possible to pursue a multi-scale modeling approach for sheet forming simulations by applying the concept of virtual material testing to determine the yield surface from the microstructure of a given material. Full-field simulations with phenomenological crystal plasticity models are widely used for this kind of investigations. However, recent developments focus on incorporating physical quantities like dislocation density into these models. In this work, a dislocation density based crystal plasticity model is used to investigate the plastic anisotropy of the deep drawing steel DC04. In particular, we focus on the prediction of R-values, which can be used to calibrate macroscopic plasticity models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application and evaluation of hyper- and hypoelastic-based plasticity models in the FE simulation of metal forming processes

Metal forming processes are usually accompanied by large plastic strains and rotations of the material elements which emphasizes the need for reliable finite strain elastoplasticity models in corresponding FE simulations. In this work, two specific finite strain hyper- and hypoelastic-based plasticity models with combined nonlinear isotropic and kinematic hardening are presented and compared in numerical FE simulations. Although both models led to remarkably different results in a shear-dominated single element deformation test, the structural simulation of a standard deep drawing process delivered nearly congruent results which suggests that both models are equally well-suited for modeling metals in common forming processes. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Validation of Material Models in Grain Scale Simulation based on EBSD Experimental Data

A crystal plasticity model and a homogenization method are used to analyze the local and global mechanical behavior of a ferritic stainless steel. In the first step the material constants are determined based on tensile tests and used to simulate the local deformation behavior on the grain scale in the second step. For that 2D EBSD data are discretized by finite elements. The computed local grain reorientations of three different BCC slip systems are compared to experimental data at the state of 20% elongation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The integration of analysis and testing for the simulation of the response of hyperelastic materials

A family of hyperelastic finite elements capable of modeling arbitrarily large strains for axisymmetric and plane strain analyses has been developed. Constitutive behavior is determined by the selection of a strain energy density function for which user-supplied coefficients are required. Selective reduced integration for the volumetric strain energy terms allows for successful modeling of nearly incompressible materials. Available strain energy density functions are as follows: Mooney-Rivlin, Blatz-Ko, power law, and a nine-term Mooney expansion. The Ogden Strain Energy (OSE) law has also been implemented. The OSE law defines the strain energy relationship entirely in terms of the three principal components of stretch. This differs from the approach of other strain energy formulations, such as the Mooney law in which the strain energy is written as a function of strain invariants. The OSE law as implemented in this formulation is designed to facilitate the user's task of converting physical test data to the numerical (algebraic) form required for input. The family of hyperelastic finite elements has been integrated into ANSYS Revision 4.2 via the user element interface. Numerous verification solutions have been performed. As a representative example, a comparison with a closed-form solution for a Mooney-Rivlin type material is presented. Finally, the difficulties of obtaining test data in the form of user-supplied constants is discussed in the context of the comparison of experimental measurements and analytical simulation of an elastomeric test specimen.     

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)     

Martensitic transformations and damage: A combined phase field approach

A combined continuum phase field model for martensitic transformations and damage is introduced. The present approach considers the eigenstrain within the martensitic phase which leads in the surrounding material to both tensile and compressive stresses. The damage model needs to account for an appropriate differentiation thereof, since compressive stresses should not promote fracture. Interactions between micro crack propagation and the formation of the martensitic phases are studied in two dimensions. In agreement with experimental observations, martensite forms at the crack tip and influences the crack formation. For the numerical implementation finite elements are used while for the transient terms an implicit time integration scheme is employed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical Evaluation of EBSD Data

In this work, a short overview is given, how data resulting from Electron Backscatter Diffraction (EBSD) measurements can be used to obtain a discrete version of the Orientation Distribution Function (ODF). Discrete ODFs are necessary, e.g. for micromechanically based simulations of metal forming operations based on the finite element method. To use EBSD data for simulations several processing steps are necessary as conversion and segmentation of the EBSD measurement data [1], definition of a fundamental zone in Euler space and a procedure for the tesselation of this zone [2]. (© 2010 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)     

Strategies for the Computation of Configurational Forces in Dissipative Media

Configurational forces can be interpreted as driving forces on material inhomogeneities such as crack tips. In dissipative media the total configurational force on an inhomogeneity consists of an elastic contribution and a contribution due to the dissipative processes in the material. For the computation of discrete configurational forces acting at the nodes of a finite element mesh, the elastic and dissipative contributions must be evaluated at integration point level. While the evaluation of the elastic contribution is straightforward, the evaluation of the dissipative part is faced with certain difficulties. This is because gradients of internal variables are necessary in order to compute the dissipative part of the configurational force. For the sake of efficiency, these internal variables are usually treated as local history data at integration point level in finite element (FE) implementations. Thus, the history data needs to be projected to the nodes of the FE mesh in order to compute the gradients by means of shape function interpolations of nodal data as it is standard practice. However, this is a rather cumbersome method which does not easily integrate into standard finite element frameworks. An alternative approach which facilitates the computation of gradients of local history data is investigated in this work. This approach is based on the definition of subelements within the elements of the FE mesh and allows for a straightforward integration of the configurational force computation into standard finite element software. The suitability and the numerical accuracy of different projection approaches and the subelement technique are discussed and analyzed exemplarily within the context of a crystal plasticity model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anisotropic multiplicative elastoplasticity for the prediction of earings in sheet forming

In this work, the simulation of earings in cup drawing by means of a recently developed anisotropic combined hardening material model is discussed. The model represents a multiplicative formulation of anisotropic elastoplasticity in the finite strain regime with nonlinear kinematic and isotropic hardening. Plastic anisotropy is described by the use of second-order structure tensors as additional arguments in the representation of the yield function and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that preserves the plastic volume and the symmetry of the internal variables. Finite element simulations of cylindrical cup drawing processes are performed by means of ABAQUS/Standard where the discussed material model has been implemented into a user-defined reduced integration solid-shell element. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and Simulation of the Portevin-Le Chatelier Effect

During deformation of an Al-Mg alloy (AA5754) dynamic strain aging occurs in a certain range of temperatures and strainrates. An extreme manifestation of this phenomenon, usually referred to as the Portevin-Le Chatelier (PLC) effect, consists in the occurrence of strain localisation bands accompanied with discontinuous yielding. The PLC effect stems from dynamic dislocation-solute interactions and results in negative strain-rate sensitivity of the flow stress. The PLC effect is detrimental to the surface quality of sheet metals and also affects the ductility of the material. Since the appearance of the effect strongly depends on the triaxiality of the stress state, three-dimensional finite element simulations are necessary in order to optimize metal forming operations. We present a geometrically nonlinear material model which reproduces the main features of the PLC effect. The material parameters were identified based on experimental data from tensile tests. Special emphasis was put on the critical strain for the onset of PLC effect, ε _c , and the statistical characteristics of the stress drop distribution. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

MPM simulations of high-speed machining of Ti6Al4V titanium alloy considering dynamic recrystallization phenomenon and thermal conductivity

Ti6Al4V titanium alloy is often used in the aircraft industry due to its good strength and toughness etc. However, it is very difficult to simulate high speed machining of titanium alloy using the finite element method (FEM). The reason is that the high speed, large deformation and high strain rate of metal material at high temperature etc. will lead to the element distortions and other numerical difficulties. In contrast with FEM, material point method (MPM) has the advantage of simulating extreme large deformation, fracture and impact problems. Therefore, it is specially suitable for dealing with high speed cutting process. In many existing researches about the high speed cutting process using Johnson−Cook constitutive model, the material dynamic recrystallization softening effect under high pressure and high temperature has not been considered. For this, three modified Johnson−Cook constitutive models for Ti6Al4V titanium alloy are adopted and the parameters for these models were obtained by the split Hopkinson pressure bar (SHPB) test considering the critical strain values, high-temperature range and dynamic recrystallization phenomenon. Furthermore, to ensure the numerical accuracy, the transient heat conduction algorithm is employed in MPM implementation. Finally, comparison and discussion are carried out between the experimental and the simulation data, which show that the high speed cutting process can be better simulated using the modified Johnson−Cook constitutive models.     

压电弯曲元的夹层梁解析模型

压电弯曲元是一类传感和作动器件,已得到广泛的应用．基于一阶剪切变形理论发展了压电弯曲元夹层梁解析模型,对梁截面采用统一转角并将耦合电势沿厚度的分布假设为二次函数,进一步修正了横向剪应变对电位移的影响．以弯曲元简支梁自由振动为例进行数值分析,解析模型解与二维精确解相比具有良好的精度,为分析弯曲元动力机电响应提供了良好的解析模型．     

Application of a Viscoelastic Material Model in Electro-Mechanics

In this contribution, the numerical modeling of electro-viscoelastic material is considered. The electro-mechanical problem formulated in terms of a symmetrized stress tensor is extended to a viscoelastic material model. For the incorporation of the viscosity model, the logarithmic strain space setting is utilized which mimics the small strain setting. Therefore a rheological model for viscosity from the geometrically linear theory can be used. Numerical examples for a typical uniaxial tensile test show the capability of the method to demonstrate typical relaxation and creep behavior. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of Viscoelastic Properties and Damaging Effects of Highly Extensible Polyurea

The present work aims particular at the experimental identification of the viscoelastic properties of polyurea as well as on the onset of the damage. For the viscoelastic part, several relaxation experiments are performed. From the measured data a general viscoelastic model is derived where we use two different approaches. At first we identify a general Maxwell model (combining spring and damping elements for finite deformations) to use a prony series with N elements, which requires the identification of 2N + 1 parameters. At second, a model of generalized fractional elements [3] is employed. Both approaches are studied in detail and are compared to data from literature; furthermore a comparison concerning the effort is presented. Damaging effects of Polyurea are investigated using tensile tests with and without cyclic loading. In particular we focus on the the onset of damage by cavitation. To this end the recovered specimens were analyzed using a laser microscope; the surfaces of the ruptured areas are compared in terms of quantity and size of voids. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An elastic-plastic finite element solution for a cracked plate

In this paper, the finite element method is applied to a center-cracked plate subject to opening mode tensile loading. A complete elastic-plastic plane-stress solution for strain hardening materials obeying a Von Mises yield condition and Prandtl-Reuss stress-strain relations is obtained using only constant strain elements. An accurate representation of the stress-strain field even at distances very close to the crack-tip, is achieved by the use of a mesh arrangement in which the size of the elements decreases in a geometric series as the crack tip is approached. The numerical solution is compared with and used to discuss the range of validity of the well-known HRR (Hutchinson-Rice-Rosengren) crack tip solution valid for small scale yielding. The influence of different amounts of hardening and the effect of changes in the mesh arrangements are also considered. Features of the finite element algorithm which reduce the total computing time are discussed. The finite element program is executed on a CRAY-1 computer and the effect of vectorization on computational speed is discussed for this problem.     

Towards data driven selection of a penalty function for data driven Neyman tests

The data driven Neyman statistic consists of two elements: a score statistic in a finite dimensional submodel and a selection rule to determine the best fitted submodel. For instance, Schwarz BIC and Akaike AIC rules are often applied in such constructions. For moderate sample sizes AIC is sensitive in detecting complex models, while BIC works well for relatively simple structures. When the sample size is moderate, the choice of selection rule for determining a best fitted model from a number of models has a substantial influence on the power of the related data driven Neyman test. This paper proposes a new solution, in which the type of penalty (AIC or BIC) is chosen on the basis of the data. The resulting refined data driven test combines the advantages of these two selection rules.     

Isotropic softening model for high-cycle fatigue

As known the high cycle loading of structural elements above the fatigue limit results in catastrophic propagation of macroscopic fatigue crack(s). Therefore it is in demand to find a method, which would allow for early prediction of the fatigue life-time of particular structural element. The series of force-driven tests carried on 30CrNiMo8 steel have shown that, although the stresses by high-cycle fatigue do not reach the tensile stress, the material strength (measured indirectly from the strain-stress loop) decreases from the begin of the test, hence the damage nucleates and propagates from the very begin of the loading history. In this study we propose a thermodynamically consistent, strain driven constitutive model for isotropic damage accumulation by high-cycle fatigue of a homogeneous isotropic material, which should be capable to account for the above-mentioned experimental results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)