Material Behavior Of Steel Research Articles

Implementation of an algorithm for general material behavior of steel taking interaction between plasticity and transformation‐induced plasticity into account

AbstractIn this article a semi‐implicit algorithm (predictor–corrector approach) for incorporating the interaction between plasticity and transformation‐induced plasticity (TRIP) in steel is developed. Contrary to the usual elasto‐plasticity, the underlying model of material behavior of steel is far more complex. The interaction between plasticity and TRIP requires extensions of algorithms developed in Doghri (Int. J. Numer. Meth. Engng 1993; 36:3915–3932) and in Mahnken (Commun. Numer. Meth. Engng 1999; 15:745–754). A particular feature of the algorithm is that the inner iteration can be reduced to a single scalar equation. Numerical examples illustrate the algorithm's capabilities. Copyright © 2011 John Wiley & Sons, Ltd.

On The Distortional Buckling, Post-Buckling And Strength of Cold-Formed Steel Lipped Channel Columns Under Fire Conditions

This paper reports the available results of an ongoing shell finite element investigation on the distortional buckling, post-buckling and ultimate strength behaviour of cold-formed steel lipped channel columns (centrally compressed members) subjected to high temperatures typically caused by fire conditions. Two column collapse situations are dealt with, corresponding to different loading strategies: (i) application of an increasing compressive load to columns subjected to a constant (uniform) temperature distribution, in order to obtain failure loads, and (ii) application of a progressive temperature raise to axially compressed column, in order to obtain failure temperatures - the latter approach provides a more realistic simulation of fire conditions. The steel material behaviour at high temperatures is described by the constitutive model prescribed in Eurocode 3 for cold-formed steel. After validating the numerical model adopted, through the comparison with results of simulations reported in the literature and based on experimentally obtained stress-strain laws, the paper presents numerical results concerning lipped channel columns made of various steel grades under fire conditions - they consist of (i) non-linear equilibrium paths, yielded by steady state and transient column analyses, and (ii) the corresponding failure loads/stresses and temperatures.

Comparison of different approaches to transformation‐induced plasticity in steel

AbstractTransformation‐induced plasticity (TRIP) is an important phenomenon of material behaviour of steel. It may lead to distortion of work‐pieces. As there are open questions in modelling and simulation, TRIP is an important field of current research. There are different modelling approaches. The well‐known Leblond model is implemented in the commercial program SYSTUS (SYSWELD)®. New experiments and investigations show that there are interaction effects between TRIP and classical plasticity which cannot be described by the Leblond model. In this contribution, we compare the Leblond model with an alternative approach, discussing advantages and deficiencies. Moreover, we present some first comparative simulations in 3d settings.

Material behavior of steel – Modeling of complex phenomena and thermodynamic consistency

Steel has a complex material behavior. Stress- and strain-dependent phase transformations, transformation-induced plasticity (TRIP), and its interactions with plasticity are important phenomena of both theoretical and practical interest, as they may cause distortion of work-pieces. These phenomena continue to be intensively studied both experimentally and theoretically. In order to simulate real processes like heat treatment of work-pieces, one has to include the relevant phenomena in a suitable bulk model. It is the aim of the current paper to contribute to the formulation of such a model in the context of macroscopic continuum mechanics and to discuss the capabilities. Due to the possible interaction (coupling) of TRIP and plasticity, the usual approach in plasticity without phase transformations has to be modified substantially. We apply a general approach for non-linear hardening, allowing to model observable effects of interaction of plasticity and TRIP. Besides this, we prove the thermodynamic consistency under sufficient conditions.

Parameter identification for a TRIP model with backstress

The investigation of complex material behaviour of steel like transformation-induced plasticity (TRIP) is a large field of current research. The simulation of the material behaviour of work-pieces in complex situations requires a knowledge as deep as possible about phenomena like TRIP. In addition, there are effects in the case of non-constant stress which cannot be explained by the widely used Leblond model. Therefore, we consider a TRIP model taking into account backstress due to TRIP itself. Assuming a linear dependence of this backstress from the TRIP strain we derive formulas for calculation of the new TRIP parameters. Based on experimental data we calculate these parameters.

Strain-based approach to local buckling of steel sections subjected to fire

Local buckling under fire conditions needs to be considered in the context of a wider range of cross-sectional slenderness than in ambient temperatures design. This is due to the distinctly non-linear material behaviour of steel at elevated temperatures, and the large strains required for increasing cross-sectional capacity due to plastification. Stress-based design models, which are commonly used to explain local buckling at ambient temperatures, are not ideal for describing local buckling behaviour under fire conditions. Therefore a new strain-based approach has been developed which uses effective widths for stiffened and unstiffened elements at elevated temperatures. The resulting strain-based formulations avoid the use of section classes for fire design, and take into consideration the plastification effects, plastic stress distribution, and strain-dependent non-linear material behaviour of steel at high temperatures. The use of these formulations extends the application range of current state-of-the-art models for local buckling and non-linear material behaviour. They allow us to consider the decreasing branch of the load-carrying behaviour required during fires, in order to analyse sections with non-uniform temperature distribution. For unstiffened elements in compression at elevated temperatures, the load-carrying behaviour in the buckling and post-buckling ranges was analysed using temperature-dependent second-order linear elastic theory, taking into consideration initial imperfections and yield line theory, which allowed us to formulate a novel strength curve for these elements at elevated temperatures. In a parametric study, the resistance to compression and bending of stiffened and unstiffened elements during fire was calculated. The proposed design approach accords with results produced using the finite element approach.

Load-carrying Behavior Of Unstiffened Elements At Elevated Temperatures In Fire

Unstiffened elements affect markedly the resistance of commonly used open steel sections under fire conditions. The distinct non-linear material behavior of steel at elevated temperatures requires large strains to activate the increase of cross-sectional capacity due to plastification. The yield line theory in conjunction with temperaturedependent second order elastic theory including equivalent geometric imperfections has been used to describe the load-carrying behavior of unstiffened elements in compression and bending at elevated temperatures in fire. Using both theories, the complete loadcarrying behavior in the pre- and post-buckling range can be analyzed. In addition, the results obtained from these analytical solutions were compared to numerical results using a geometrical and physical non-linear finite element approach.

Micromechanical modeling of dual phase steels

Dual phase (DP) steels having a microstructure consisting of a Ferrite matrix, in which particles of Martensite are dispersed, have received a great deal of attention due to their useful combination of high strength, high work hardening rate and ductility, all of which are favorable properties for forming processes. Experimental investigation into the effect of the harder phase volume fraction, morphology and phase distribution on mechanical properties of the dual phase steels is well established and comprehensive in the literature. In the present work, a micromechanical model is developed to capture the mechanical behavior of such materials, adopting the constitutive behavior of the constituents from the literature. Analytical approaches have been used in the past to model the DP steel material behavior, but theoretical treatments are based on the assumption of uniform deformation throughout the constituents, neglecting the local strain gradients. This assumption contradicts experimental observations, reduces the understanding of the mechanics and mechanism of deformation of such materials. Based on the micromechanical modeling of cells, several idealizations are investigated out of which the axisymmetric model is shown to display intrinsic ability to capture the expected material behavior in terms of the trend of the stress–strain curves with increasing volume fraction of the second phase and in terms of the deformation fields of the constituents.

Design analysis of permanent magnet DC motors with differing armature, magnet and yoke lengths

A modified magnetic circuit method and a 2-D finite element procedure are presented here for the analysis of DC permanent magnet motors with differing armature, magnet and yoke lengths including nonlinear material behavior of steel and permanent magnet. A 12 V, 120 W motor is analyzed through these methods and compared with experimental results of a prototype sample. In case of finite element analysis, commutation effects and short chording of the armature winding are treated appropriately, and cogging torque and voltage ripple are predicted.