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Trip Steels: Constitutive Modeling and Computational Issues TRIP STEELS: CONSTITUTIVE MODELING AND COMPUTATIONAL ISSUES by IOANNIS CHRISTOU PAPATRIANTAFILLOU Submitted to the Department of Mechanical & Industrial Engineering of UNIVERSITY OF THESSALY In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY UNIVERSITY OF THESSALY JUNE 2005 Institutional Repository - Library & Information Centre - University of Thessaly 08/12/2017 08:18:44 EET - 137.108.70.7 Πανεπιστήμιο Θεσσαλίας ΒΙΒΛΙΟΘΗΚΗ & ΚΕΝΤΡΟ ΠΛΗΡΟΦΟΡΗΣΗΣ Ειδική Συλλογή «Γκρίζα Βιβλιογραφία» Αριθ. Εισ.: 4549/1 Ημερ. Εισ.: 20-07-2005 Δωρεά: Συγγραφέα Ταξιθετικός Κωδικός: _Δ________ 669.961 42 ΠΑΠ Institutional Repository - Library & Information Centre - University of Thessaly 08/12/2017 08:18:44 EET - 137.108.70.7 TRIP STEELS: CONSTITUTIVE MODELING AND COMPUTATIONAL ISSUES by IOANNIS CHRISTOU PAPATRIANTAFILLOU Submitted to the Department of Mechanical & Industrial Engineering of UNIVERSITY OF THESSALY In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY UNIVERSITY OF THESSALY JUNE 2005 Institutional Repository - Library & Information Centre - University of Thessaly 08/12/2017 08:18:44 EET - 137.108.70.7 ABSTRACT TRIP STEELS: CONSTITUTIVE MODELING AND COMPUTATIONAL ISSUES Abstract TRIP (TRansformation Induced Plasticity) of multi-phase steels is a new generation of low- alloy steels that exhibit an enhanced combination of strength and ductility. These steels make use of the TRIP phenomenon, i.e., the transformation of retained austenite to martensite with plastic deformation, which is responsible for the remarkable enhancement of properties. A constitutive model for the mechanical behavior of steels exhibiting “Transformation Induced Plasticity” during martensitic transformation is presented in the Thesis. Two categories of multiphase TRIP steels are examined. The first category is the two-phase TRIP steels, in which particles of martensite are isotropically dispersed in an austenitic matrix; the second includes the four-phase TRIP steels, in which particles of retained austenite, martensite and bainite are isotropically dispersed in a ferritic matrix. In both cases the retained austenite is metastable at room temperature and, under the effect of plastic deformation, transforms to martensite. TRIP steels are essentially composite materials with evolving volume fractions of the individual phases. The total strain is assumed to be the sum of elastic, plastic and transformation parts. No restriction is placed on the magnitude of the strains and appropriate “finite strain” constitutive equations are developed. Standard isotropic linear hypoelasticity of homogeneous solids is used in order to describe the elastic behavior of TRIP steels since the elastic properties of all individual phases are essentially the same. The plastic part is determined by using homogenization techniques for non-linear composites that have been developed recently by Ponte-Castaneda, Suquet, and co-workers (Ponte-Castaneda 1996, Suquet 1996a, Ponte-Castaneda and Suquet 1998). The constitutive equation for the plastic deformation rate is estimated in terms of the plastic properties of the individual phases. The transformation strain rate has both deviatoric and volumetric parts and is proportional to the rate of change of the volume fraction of martensite. The evolution of martensite due to martensitic transformation is described by a kinetic model, which takes into account temperature, plastic strain and stress state. A methodology for the numerical integration of the resulting non-linear constitutive equations for TRIP steels in the context of the finite element method is developed and the constitutive model is implemented in a general-purpose finite element program. A methodology for the 1 Institutional Repository - Library & Information Centre - University of Thessaly 08/12/2017 08:18:44 EET - 137.108.70.7 ABSTRACT TRIP STEELS: CONSTITUTIVE MODELING AND COMPUTATIONAL ISSUES numerical integration of the constitutive model under plane stress conditions is also developed. The constitutive model for the four-phase TRIP steels is calibrated by using experimental data of uniaxial tension tests of a specific TRIP steel. The model predictions fit the data reasonably well. The dependence on temperature and stress state is examined. The constitutive model is used for the simulation of necking in a uniaxial tension test using the finite element method. TRIP effect hardens the material and increases substantially the range of uniform elongation. The constitutive model is used also for the calculation of “forming limit diagrams” for sheets made of TRIP steel; it is found that the TRIP phenomenon increases the strain at which local necking results from a gradual localization of the strains at an initial thickness imperfection in the sheet. n Institutional Repository - Library & Information Centre - University of Thessaly 08/12/2017 08:18:44 EET - 137.108.70.7 ACKNOWLEDGMENTS TRIP STEELS: CONSTITUTIVE MODELING AND COMPUTATIONAL ISSUES Acknowledgments I wish to express my sincere thanks to my supervisor, Professor Nikolao Arava, for his guidance and support throughout the course of this research. His continuous and well-targeted advices were determinant in the completion of my Thesis. It was a real challenge and a great experience to work close to a scientist like him. His knowledge and personality was a source of inspiration for me all these years. I am grateful to him because as an excellent teacher he is, he managed not only to widen my scientific knowledge but also to influence my way of thinking. I would also like to thank Professor Gregory Haidemenopoulo, one of the three-member advisory committee, for his significant help and well-aimed advices over the years of the dissertation. Especially, I thank him for the plenty of time he devoted in many helpful discussions about TRIP steels. Furthermore, I thank the Assistant Professor Sp. Karamano, one of the three-member advisory committee, for his sincere interest and encouragement. The author is also grateful to the other members of the committee Professor A. Giannakopoulo, Professor K. Papadimitriou, Professor V. Kostopoulo and Assistant Professor G. Petropoulo for their sincere interest and useful advices. Moreover, I would like to thank ECSC and GSRT (ΓΓΕΤ) for their financial support through the projects “Optimization of microstructure in multiphase steels containing retained austenite” (ECSC, contract No 7210-PR/161), “Control and exploitation of the bake­ hardening effect in multi-phase high-strength steels”, (ECSC, contract No 7210-PR/370) and “Materials with Microstructure: Constitutive Modeling and Computational Issues” (ΓΓΕΤ/ΠΕΝΕΔ 1999). Many thanks to my colleagues Dr. A. Vasilako and Dr. A. Katsama for the excellent collaboration during the two ECSC research programs and the helpful conversations we had. Furthermore, I would like to thank M. Agoras for the use of his program concerning the Institutional Repository - Library & Information Centre - University of Thessaly 08/12/2017 08:18:44 EET - 137.108.70.7 ACKNOWLEDGMENTS TRIP STEELS: CONSTITUTIVE MODELING AND COMPUTATIONAL ISSUES solution of the forming limit diagrams problem and my colleagues K. Christodoulou and S. Houliara for their encouragement. Moreover, thanks to Mrs. M. Karanika, the secretary of the Laboratory of Mechanics and Strength of Materials, for her secretarial support. I would also like to thank Natassa for her patience, continuous support and encouragement during the years of the course. Finally, I would like to express my gratitude to my family; my brother Dimitri and my parents Christo and Evagellia for their unfailing support and continuous encouragement all over the years of my studies. They made the best they could for making my work much more easy. I am very grateful to them and the least I can do is to devote them this Thesis. IOANNIS CHRISTOU PAPA TRIANTAFILLOU UNIVERSITY OF THESSALY JUNE 2005 IV Institutional Repository - Library & Information Centre - University of Thessaly 08/12/2017 08:18:44 EET - 137.108.70.7 TABLE OF CONTENTS TRIP STEELS: CONSTITUTIVE MODELING AND COMPUTATIONAL ISSUES TABLE OF CONTENTS LIST OF FIGURES......................................................................................................................5 LIST OF TABLES........................................................................................................................16 1. INTRODUCTION....................................................................................................................17 2. HISTORICAL PERSPECTIVE........................................................................................... 22 2.1. Introduction.........................................................................................................................23 2.2. General aspects of martensitic transformation................................................................ 24 2.3. Driving force for martensitic transformation.................................................................. 26 2.4. Transformation Plasticity...................................................................................................27 2.5. Heat treatment of TRIP steels........................................................................................... 29 2.6. Modeling of the mechanical constitutive behavior......................................................... 30 3. VISCOPLASTICITY.............................................................................................................
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