Microstructure transformation due to thermo-mechanical processing have an acute effect the macroscopic properties of low carbon steels. This effect includes visco-plastic deformation and phase transformations. Hot forming processes such as press hardening are particularly affected. Most engineering applications require a combination of high strength and sufficient residual ductility, which can be achieved by the development of graded microstructures. In the present work, the evolution of phase transformations is investigated by linking experiments and simulations to produce graded microstructures. For this purpose, an extended material model is proposed to represent the evolution of phase transformations under inhomogeneous heating and cooling strategies. On the experimental side, phase transformations are identified during thermo-mechanical treatment of flat steel specimens using digital image correlation and thermal imaging. Based on the experimental results, the material parameters are identified, and the simulation model is validated. On the numerical side an algorithm for the finite-element simulation of phase transformations in low carbon steels is proposed. The evolution of phase transformations is presented for the simulation of tensile specimen employing the finite-element-method.

As an effective and accurate method for modelling composite materials, mean-field homogenization is still not well studied in modelling non-linear and damage behaviours of UD composites. Investigated micro FE-simulations show that the matrix of UD composites exhibits different average plastic behaviour, named as average asymmetric matrix plasticity (AAMP), when the composite behaves different under shear, longitudinal and transverse loadings. In this study, a non-linear mean-field debonding model (NMFDM) combining a mean-field model and a fibre–matrix interface debonding model, is developed to simulate UD composites under consideration of AAMP, fibre–matrix interface damage and progressive failure. AAMP is considered by using so-called stress mode factor, which is expressed in terms of basic invariants of the matrix deviatoric stress tensor and is used as an indicator for detection of differences in the loading mode. The material behaviour of UD composites with imperfect interface is assumed identical as for perfect interface and stiffness reduced fibres. Progressive failure criteria are established with consideration of fibre breakage and matrix crack for different fibre orientations. As a representative example for the NMFDM, a C30/E201 UD composite is studied. To verify the model, experiments are conducted on polymers, carbon fibres and UD CFRPs. Finally, the model is applied to simulate a perforated CFRP laminate, which shows excellent prediction ability on deformation, debonding and progressive failure.

This paper presents a numerical method for solution of a stochastic partial differential equation (SPDE) for a linear elastic body with stochastic coefficients (random variables and/or random fields). To this end the stochastic finite element method (SFEM) is employed, which uses W IENER’S polynomial chaos expansion in order to decompose the coefficients into deterministic and stochastic parts. As a special case, we consider isotropic material behavior with two fluctuating parameters. Computational approaches involving GALERKIN projection are applied to reduce the SPDE into a system of deterministic PDEs. Furthermore, we consider normally distributed random variables, which are assumed to be stochastically independent, and which establish the number of stochastic dimensions. Subsequently, the resulting finite element equation is solved iteratively. Finally, in a representative example for a plate with a ring hole we study the influence of different variances for material parameters on the variances for the finite element results.

<jats:title>Abstract</jats:title> <jats:p>The alignment of polymer chains is a well known microstructural evolution effect due to straining of polymers. This has a drastic influence on the macroscopic properties of the initially isotropic material. In this work, cold forming is performed at room temperature on a tensile testing machine. Polycarbonate films are examined in two loading phases. In the first phase, the specimen is loaded to induce anisotropy, and in the second, it is re-loaded, while the material direction is varied. The investigations are supported by an optical measurement system to gain knowledge about the inhomogeneous material behavior in the initial loading phase and about the anisotropic homogeneous behavior during the re-loading phase. Two dimensional strain contours are obtained from the test data. Additionally, we propose a method for approximation of the macroscopic true stress and compare the results with a common approach based on volume consistency. In the future, the test data will set a basis for parameter identification of constitutive equations taking into account a combination of inhomogenous and homogenous material behavior, exhibiting strain induced anisotropy.</jats:p>

<jats:p>The prime aim of this paper is to investigate, with the help of experiments, the induced anisotropy of mechanical properties in polycarbonate films. It is known that a molecular orientation in polymer materials occurs through cold-forming. In this study, cold forming is performed at room temperature on a tensile testing machine. The polycarbonate films are examined in two phases. In the first phase, the specimen is loaded, while the prestrain is varied, and in the second, it is loaded, while the material direction is varied. The main findings are that the prestrain has virtually no influence on the anisotropy and that the material direction does exert a major influence. Furthermore, this paper summarizes comparisons of anisotropic characteristic data, maximum stresses, elasticity moduli and failure strain.</jats:p>