Simulation of a Hybrid-Forming Process using Temperature- and Rate-Dependent Viscoplastic Material Models

Hybrid-forming processes for graded structures are quite innovative methods for the production of components with tailored properties, particularly tailored material properties and geometrical shape. In this contribution a hybrid-forming process based on the utilization of locally varying thermo-mechanical effects is investigated [1]. For process optimization and improvement of the resulting work piece the simulation of the entire forming process is necessary in modern engineering. The main topics of this contribution are the simulation of the cyclic thermal loaded forming tool and the simulation of the work piece treated at large deformations with phase transformations. For both materials temperature- and rate-dependent viscoplastic material models are applied and parameter identification using cyclic tensile-compression tests for the forming tool material and phase transformation tests for a low-alloy steel similar to the work piece material is presented. For validation of finite-element-calculations for the forming tool thermal shock experiments are performed with optical deformation measurements. For validation of finite-element-calculations for the work piece numerical results of geometry and structure after heating, forming and cooling are compared to experimental micro sections. Results concerning the forming tool will be used for future lifetime prediction and results concerning the work piece will be used for future specific setting of graded material properties. (© 2009 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)     

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)     

Characterisation of filled rubber with a pronounced non-linear viscoelasticity

This contribution presents the characterisation of an incompressible carbon black-filled elastomer as one characteristical example for highly filled rubber. It shows a strongly pronounced non-linear viscoelastic behaviour and the most important characteristic is the extremely long relaxation time which has to be taken into account. The material model is developed with respect to uniaxial tension data. The basis in the development of a phenomenological model is given by the basic elasticity. For this evaluation the long term relaxation behaviour results in a complex experimental procedure. Therefore, special attention has to be paid according to an optimised experimental process in order to get the necessary reference data in an adequate and reproduceable way [1]. With this model basis further investigations are taken into account concerning the time-dependent viscoelasticity. Therefore, cyclic deformations from zero up to a maximum of deformation are considered for different strain rates. Furthermore, the relaxation behaviour is investigated for multiple strain levels. The phenomena which are observed in the experimental results yield in a purely viscoelastic model, based on a rheological analogous model consisting of an equilibrium spring and several Maxwell-elements which contain nonlinear relations for the relaxation times of the dashpot elements [1,2]. The material model's numerical realisation is accomplished in two ways. Because of its numerical simplicity especially according to the parameter identification the model is restricted only to the simple case of uniaxial tension. A second, alternative implementation is executed providing the benefit that more complex deformation conditions can also be taken into account. Therefore, the general, three-dimensional finite model is implemented in an open-source Finite Element library [3]. (© 2015 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)     

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)     

Nonparametric Methods for Checking the Validity of Prior Order Information

A large number of statistical procedures have been proposed in the literature to explicitly utilize available information about the ordering of treatment effects at increasing treatment levels. These procedures are generally more efficient than those ignoring the order information. However, when the assumed order information is incorrect, order restricted procedures are inferior and, strictly speaking, invalid. Just as any statistical model needs to be validated by data, order information to be used in a statistical analysis should also be justified by data first. A common statistical format for checking the validity of order information is to test the null hypothesis of the ordering representing the order information. Parametric tests for ordered null hypotheses have been extensively studied in the literature. These tests are not suitable for data with nonnormal or unknown underlying distributions. The objective of this study is to develop a general distribution-free testing theory for ordered null hypotheses based on rank order statistics and score generating functions. Sufficient and necessary conditions for the consistency of the proposed general tests are rigorously established.     

Experimental and Numerical Study of the Open-Hole Tensile Strength of Carbon/Epoxy Composites

Open-hole tension tests are a part of the qualification process for composite parts that need to be joined to other parts in aircraft structures [1]. With each new material, a new set of tests is required. To reduce costs, it is desirable to develop analysis tools for the prediction of damage and failure in such tests, so that the amount of testing can be reduced and predictions can be made about material behaviour early in the design process. In this paper, an experimental and numerical study is presented on the notched (open-hole) strength of high-strength carbon/epoxy composites (HTA/6376). Open-hole tension tests have been performed on specimens with three different lay-ups — quasi-isotropic, zero-dominated, and cross-ply — in accordance with procedures in available standards. The data observed are being used to develop several methods for predicting the notched strength, and results from one such method using a progressive damage analysis are presented with comparisons with experiments. The predictions of specimen stiffness and failure load were found to agree well with experiments. To gain insight into the failure process, damage progression maps are shown.     

Material parameter identification using model reduction to uniaxial tensile test

Material parameter identification is the necessary link between constitutive modeling and application of material models in complex simulations of real world problems. We present an approach to make use of already developed stress algorithms for three-dimensional finite-element computations in terms of a reduction to uniaxial tensile tests for material parameter identification. Strain-driven stress algorithms lead to the approach of solving differential-algebraic equations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling the moisture dependent material behavior of adhesive bonds close to the glass transition temperature

In the presented work, a viscoelastic cross-linked polyurethane is investigated. Environmental influences lead to an inhomogeneous spatial distribution of the mechanical properties in polymer adhesives. Diffusive transport mechanisms transfer water from the environment into the polymer. Further effects like temperature, also have an influence on the mechanical behavior of adhesives. The model respects these influences and takes the incompressibility of the material into account. Viscoelastic behavior can be observed, especially close to the glass transition temperature [3]. Additional to these general effects on polymers, adhesive bonds show a dependency of the mechanical behavior on the thickness of the layer. For numerical investigations, all necessary balance and constitutive equations are implemented in the open-source C++ finite element code deal.II [1, 2]. With the help of this implementation and by comparing experimental results and results gained from simulations, material parameters of the used polymer can be identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameter Identification by Inverse Modelling of Biaxial Tensile Tests for Discontinous Fiber Reinforced Polymers

In the present article we discuss the characterization of the mechanical properties of long fiber reinforced thermoplastics (LFT) and sheet molding compounds (SMC) with biaxial tensile tests and the inverse parameter identification. The full 3D strain field is measured via digital image correlation (DIC). The anisotropic viscoelastic material properties are identified through inverse modelling by comparison of the heterogeneous experimental and simulated strain fields. A Gauss-Newton type algorithm is used to identify the optimal parameter set [1]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A material model of nonlinear fractional viscoelasticity

Multiscale methods are frequently used in the design process of textile reinforced composites. In addition to the models for the local material structure it is necessary to formulate appropriate material models for the constituents. While experiments have shown that the reinforcing fibers can be assumed as linear elastic, the material behavior of the polymer matrix shows certain nonlinearities. These effects are mainly due to strain rate dependent material behavior. Fractional order models have been found to be appropriate to model this behavior. Based on experimental observations of Polypropylene a one-dimensional nonlinear fractional viscoelastic material model has been formulated. Its parameters can be determined from uniaxial, monotonic tensile tests at different strain rates, relaxation experiments and deformation controlled processes with intermediate holding times at different load levels. The presence of a process dependent function for the viscosity leads to constitutive equations which form nonlinear fractional differential equations. Since no analytical solution can be derived for these equations, a numerical handling has been developed. After all, the stress-strain curves obtained from a numerical analysis are compared to experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation and Experimental Study of a Two-Way Reinforced Rubber-Cord Composite in Tension

A rubber-cord composite, reinforced in two directions with fibers of polyamide cord, under large tensile deformations is investigated based on calculations of a rubber-cord composite material and on tensile tests of specimens made of the casing of a diagonal truck tire. A method of the experimental tensile testing of rubber-cord composite specimens is described. The calculations are based on the carcass theory of composite materials. The calculated and experimental parameters of the macroscopic strains of the rubber tire cord and of its structure in a deformed configuration are given. The manifestation of edge effects in relation to the reinforcement angle is described.     

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)     

Experimental investigation and approximation of the temperature-dependent stiffness of short-fiber reinforced polymers

In order to predict the effective material properties of a short-fiber reinforced polymer (SFRP), homogenization of elastic properties with the self-consistent (SC) scheme and the interaction direct derivative (IDD) method is performed by means of µCT data describing the microstructure of the composite material. Using dynamic mechanical analysis (DMA), the material properties of both, polypropylene and fiber reinforced polypropylene are investigated by tensile tests under thermal load. The measured storage modulus of the matrix material is used as input parameter for the homogenization scheme. The effective properties of SFRP are compared to experimental results from DMA. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental investigations on PP-PE foil specimens

In the present work, we present an experimental characterization of a thermoplastic copolymer made out of Polypropylene and Polyethylene (PP-PE); a polymer that is, for example, used as a core material for layered sandwich composites. The rate-dependence and the temperature-dependence were investigated by means of tensile tests within the large deformation range and by shear tests. The experiments were monitored using a Digital Image Correlation (DIC) system. The main goal of the experimental campaign is related to the development of a constitutive model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonparametric tests based on N-distances

This paper is devoted to goodness-of-fit and homogeneity tests based on N-distances. The work is a continuation of our research started in [2]. The power of the proposed criteria is compared with classical tests using Monte Carlo simulations. Different alternatives both in one-and multidimensional cases are investigated. Applications of N-distance statistics for testing hypotheses of symmetry (univariate case) and independence (bivariate case) are provided.     

Three-dimensional continuum mechanical modeling of the Portevin-Le Châtelier effect

In many Al, Cu, Fe and Ni based alloys jerky flow associated with the Portevin-Le Châtelier (PLC) effect occurs within a specific range of temperatures and strain-rates. This effect which reduces the ductility and the surface quality of sheet materials is caused by dynamic interaction of mobile dislocations with solute atoms [1]. A three-dimensional continuum mechanical model of this effect, also known as dynamic strain ageing, is presented. Furthermore, the predictions of the three-dimensional model are compared with experimental data. Special emphasis is put on the determination of the instability region in the strain and strain-rate space [2]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)