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Fatigue Characterization and Cyclic Plasticity Modeling of Magnesium Spot-Welds
Fatigue Characterization and Cyclic Plasticity Modeling of Magnesium Spot-Welds by Seyed Behzad Behravesh A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Mechanical Engineering Waterloo, Ontario, Canada, 2013 © Seyed Behzad Behravesh 2013 AUTHOR'S DECLARATION I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Seyed Behzad Behravesh ii Abstract The automotive industry is adopting lightweight materials to improve emissions and fuel economy. Magnesium (Mg) alloys are the lightest of engineering metals, but work is required to assess their structural strength, especially for spot-welded applications. In the present research, fatigue behavior of magnesium spot-welds was characterized and compared with steel and aluminum spot-welds. A fatigue model was proposed to predict the failure location and crack initiation life in magnesium structures. The material under investigation, AZ31B-H24 Mg alloy, and its spot-welds were characterized from microstructural and mechanical points of view. Microstructure and hardness of the base metal (BM) and different regions in the spot-welds were studied. Monotonic testing of the BM demonstrated asymmetric hardening behavior under tension and compression. Under cyclic loading, the BM had an asymmetric hysteresis loop. Static behavior of spot-welds was studied with different specimen configurations. The effect of nugget size on the static peak load was similar to that of aluminum and less than steel. -
Engineering Mechanics 2020 Alternative Strain-Rate Dependent Hyperelastic- Plastic Material Model
26th International Conference ENGINEERING MECHANICS 2020 Brno, Czech Republic, November 24 – 25, 2020 ALTERNATIVE STRAIN-RATE DEPENDENT HYPERELASTIC- PLASTIC MATERIAL MODEL Jerábek R.*, Écsi L.** Abstract: At present, multiplicative plasticity-based models are used to model material degradation of hyperelastic materials within the framework of finite-strain elastoplasticity. The underlying theory assumes that the intermediate configuration of the body is locally unstressed, and as a result, no plastic deformation field exists that meets the conditions of compatibility. The assumption is; however, neither mathematically nor physically justified and the related material models are not continuum-based. In this paper, an alternative strain-rate dependent hyperelastic-plastic material model is presented. Based on the theory of nonlinear continuum mechanics for finite deformation of elastoplastic media, the model can describe the plastic flow in an objective and thermodynamically consistent manner. Therefore the strain-rate density of the model and the specimen from the uniaxial tensile test of the modelled material can be related. In this paper, the dynamic behaviour of a silicone cross-shaped specimen is studied numerically using a Mooney-Rivlin material model with internal damping. Keywords: Nonlinear continuum theory for finite deformations of elastoplastic media, Objective and thermodynamically consistent formulation, Hyperelastic-plastic material, Mooney-Rivlin material with internal damping. 1. Introduction Hyperelastic materials, such as natural and synthetic rubber, vulcanized elastomers, various types of polymers, biomaterials and many others are nonlinear elastic materials. The characteristic feature of hyperelastic materials is that they can undergo large elastic deformations without permanent deformations or being damaged. The materials are often considered to be isotropic, and their constitutive functions are derived from strain energy density functions (Hackett, 2018). -
A Numerical Investigation Into the Plastic Buckling Paradox for Circular Cylindrical Shells Under Axial Compression
A NUMERICAL INVESTIGATION INTO THE PLASTIC BUCKLING PARADOX FOR CIRCULAR CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION Rabee Shamass1, Giulio Alfano1, Federico Guarracino2 1 - School of Engineering and Design, Brunel University, UB8 3PH Uxbridge, UK 2 – University of Naples ‘Federico II’, Via Claudio 21, 80125 Napoli, Italy Abstract It is widely accepted that for many buckling problems of plates and shells in the plastic range the flow theory of plasticity leads to a significant overestimation of the buckling stress while the deformation theory provides much more accurate predictions and is therefore generally recommended for use in practical applications. The present work aims to contribute to further understanding of the seeming differences between these two theories with particular regards to circular cylindrical shells subjected to axial compression. A clearer understanding of the two theories is established using accurate numerical examples and comparisons with some widely cited accurate physical test results. It is found that, contrary to common perception, by using a geometrically nonlinear finite element formulation with carefully determined and validated constitutive laws very good agreement between numerical and test results can be obtained in the case of the physically more sound flow theory of plasticity. The reasons underlying the apparent buckling paradox found in the literature regarding the application of deformation and flow theories and the different conclusions reached in this work are investigated and discussed in detail. Keywords: shell buckling; shell instability; plastic buckling; deformation plasticity; flow plasticity; plastic paradox; non-linear FEA. 1. Introduction Plastic buckling of circular cylindrical shells has been the subject of active research for many decades due to its importance to the design of aerospace, submarine, offshore and civil engineering structures. -
Experimental Characterization and Modeling of High Strength Martensitic Steels Based on a New Distortional Hardening Model
EXPERIMENTAL CHARACTERIZATION AND MODELING OF HIGH STRENGTH MARTENSITIC STEELS BASED ON A NEW DISTORTIONAL HARDENING MODEL BY ELIZABETH K BARTLETT A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2018 © 2018 Elizabeth K Bartlett 2 To my daughter, Gwyneth Webb, who helps me to have fun, laugh, and love through the most difficult times in my life. 3 ACKNOWLEDGEMENTS First, I would like to thank all the members of my supervisory committee for their support. I would especially like to thank my committee chair, Prof. Oana Cazacu, for her support and constructive criticisms. It was an honor and a privilege to study her research. I would also like to thank Dr. Benoit Revil- Baudard for his expertise in numerical methods. I am so grateful for the support of the 96th Test Wing, my sponsoring facility in the Science, Mathematics, and Research for Transformation (SMART) scholarship program. Specifically, I would like to thank my commanders and supervisor, Mr. Ron Lutz, as well as, Mrs. Linda Busch and Dr. Betta Jerome. I also greatly appreciate the support of the Air Force Research Laboratory (AFRL) in the experimental characterization of Eglin steel: Dr. Geremy Kleiser and Dr. Philip Flater for their training in quasi-static testing, Dr. Brad Martin and Dr. Xu Nie for their expertise in dynamic split Hopkinson pressure bar (SHPB) testing, Dr. Rachel Abrahams and Dr. Sean Gibbons for their instruction in microscopy and material science, and Mr. Richard Harris for his expertise in material characterization at the Advanced Weapons Effects Facility (AWEF). -
An Alternative Material Model Using a Generalized J2 Finite-Strain Flow Plasticity Theory with Isotropic Hardening
Int. J. of Applied Mechanics and Engineering, 2018, vol.23, No.2, pp.339-353 DOI: 10.2478/ijame-2018-0019 AN ALTERNATIVE MATERIAL MODEL USING A GENERALIZED J2 FINITE-STRAIN FLOW PLASTICITY THEORY WITH ISOTROPIC HARDENING L. ÉCSI* and P. ÉLESZTŐS Slovak University of Technology in Bratislava Námestie slobody 17, 812 31 Bratislava, SLOVAKIA E-mail: [email protected] In this paper an alternative material model using a generalized J2 finite-strain flow plasticity theory with isotropic hardening is presented. The model is based on a new nonlinear continuum mechanical theory of finite deformations of elasto-plastic media which allows for the development of objective and thermodynamically consistent material models. As a result, the constitutive equation, the evolution equation and even the ‘normality rule’, characterising the plastic flow in the material during return mapping, can be expressed in various forms, using several instances of the yield surface and corresponding pairs of stress measures and strain rates, respectively, which are conjugate with respect to the internal mechanical power and its arbitrary higher order time derivative. Therefore the results of the material model when used in numerical analyses are not affected by the description and particularities of the material model formulation. Here, we briefly outline the nonlinear continuum theory along with a detailed description of the material model and finally present the model in a numerical example using a cross-shaped specimen in biaxial tension. Key words: nonlinear continuum theory of finite deformations of elasto-plastic media, generalized J2 flow plasticity theory with isotropic hardening, objective and thermodynamically consistent formulation. -
Plastic and Creep Deformation in Terms of the Synthetic Theory
dc_1366_16 Hungarian Academy of Sciences - Dissertation Plastic and creep deformation in terms of the synthetic theory Endre Ruszinkó Budapest 2017 Powered by TCPDF (www.tcpdf.org) dc_1366_16 Dedication To my father. 2 Powered by TCPDF (www.tcpdf.org) dc_1366_16 Abstract This dissertation deals with irrecoverable deformation of polycrystalline materials subjected to different types of mechanical and thermal impacts. This study has three major purposes: (1) to describe analytically the peculiarities of plastic and creep deformation due to the stepwise change in acting stresses (2) to model the steady-state creep of metals as a function of the parameters of preliminary mechanical-thermal treatment (3) to investigate and model the effect of ultrasound on the strength properties of metals such as ultrasonic hardening and softening as well as the influence of preliminary ultrasonic treatment upon the steady-state creep of metals. The implementation of the tasks listed above takes place in terms of the synthetic theory of irrecoverable deformation, which manifests itself as an effective mathematical apparatus to model numerous non-classical problems in the field of plastic and creep deformation. 3 Powered by TCPDF (www.tcpdf.org) dc_1366_16 Content Chapter I. Introduction ....................................................................................................................................... 6 1.1 Objectives .................................................................................................................................................... -
Mechanical Models in Nonparametric Regression
IMS Collections From Probability to Statistics and Back: High-Dimensional Models and Processes Vol. 9 (2013) 5–19 c Institute of Mathematical Statistics,2013 DOI:⃝ 10.1214/12-IMSCOLL902 Mechanical models in nonparametric regression 1, 2, Vladim´ır Balek ∗ and Ivan Mizera † Comenius University and University of Alberta This note is devoted to an extrapolation of a solid-mechanic motif from nonparamet- ric regression (or, as it is often referred to, smoothing) and numerical interpolation, athemeoriginatingintheexpositionofspline-basedmethods.Theattentionis turned to the fact that a mechanical analogy, akin to that from elasticity theory for quadratic spline penalties, can be elucidated in plasticity theory for certain penal- ties of different type. It is this—in the (slightly altered) words of a referee, “what would happen if the metaphor underlying splines were replaced by a metaphor of plastic energy”—what is the objective of what follows; everything else, in particular discussion of the origins of (certain types of) splines, or an exhaustive bibliograph- ical account, is outside our scope. To give an idea what mechanical analogies we have in mind, let us start by the quote from the Oxford English Dictionary, referencing (univariate) “draftsman spline” as “a flexible strip of wood or hard rubber used by draftsmen in laying out broad sweeping curves”.Bivariatecasebringsmoresophistication:thedesignation “thin-plate spline” is regularly explained by a story about the deformation of an elastic flat thin plate—see page 139 of Green and Silverman [12]orpage108ofSmall [31]: if the plate is deformed to the shape of the function ϵf,andϵ is small, then the bending energy is (up to the first order) proportional to the smoothing penalty. -
An Alternative Neo-Hookean Material Model with Internal Damping for Finite-Strain Elastoplasticity JERÁBEK Róbert1,A and ÉCSI
An alternative neo-Hookean material model with internal damping for finite-strain elastoplasticity JERÁBEK Róbert1,a and ÉCSI Ladislav1,b 1Institute of Applied Mechanics and Mechatronics; Faculty of Mechanical Engineering; Slovak University of Technology in Bratislava; Námestie slobody 17, 812 31 Bratislava 1, Slovak Republic [email protected], [email protected] Keywords: Nonlinear continuum theory for finite deformation of elastoplastic media, objective and thermodynamically consistent material model, Neo-Hookean material with internal damping Abstract. At present, multiplicative plasticity theories are used to model material degradation of hyperelastic materials within the framework of finite-strain elastoplasticity. The theories assume that the intermediate configuration of the body is locally unstressed, for which no deformation exists that meets the conditions of compatibility. The assumption, however; is in contradiction to the theory of nonlinear continuum mechanics, as it violates proper stress transformations, resulting from the invariance of the internal mechanical power. As a result, the theories and their related material models are not continuum based. In this paper, an alternative neo-Hookean material model with internal damping for finite-strain elastoplasticity is presented. The model, based on the first nonlinear continuum theory of finite deformations of elastoplastic media, can imitate material degradation of the neo-Hookean material under excessive dynamic loading. Introduction Hyperelastic materials, -
Numerical and Analytical Investigation Into the Plastic Buckling Paradox for Metal Cylinders Rabee Shamass
Numerical and Analytical Investigation into the Plastic Buckling Paradox for Metal Cylinders A thesis submitted for the degree of Doctor of Philosophy By Rabee Shamass School of Engineering, Design and Physical Sciences Brunel University London March 2016 Declaration This thesis entitled “Numerical and Analytical Investigation into the Plastic Buckling Paradox of Metal Cylinder”, is submitted to the Department of Mechanical, Aerospace and Civil Engineering, School of Engineering, Design and Physical Sciences, Brunel University of London, Kingston Lane, Uxbridge, UB8 3PH, UK, for the degree of Doctor of Philosophy. The research has not formed the basis of a submission for any other degree. Publications based on this thesis: Conference papers Shamass, R., Alfano, G. and Guarracino, F. (2013) ‘A numerical investigation into the plastic buckling of circular cylinders’. Shell Structures: Theory and Application, 3, pp.441-444. Journal articles Shamass, R., Alfano, G. and Guarracino, F. (2014) ‘A numerical investigation into the plastic buckling paradox for circular cylindrical shells under axial compression’ Engineering Structures, 75, 429-447. Shamass, R., Alfano, G. and Guarracino, F. (2015) ‘An analytical insight into the buckling paradox for circular cylindrical shells under axial and lateral loading’, Mathematical problems in engineering, ID 514267:1-11. Shamass, R., Alfano, G. and Guarracino, F. (2015) ‘An investigation into the plastic buckling paradox for circular cylindrical shells under non-proportional loading’, Thin-Walled Structures, 95, 347-362. Shamass, R. Alfano, G. and Guarracino, F. (2016) ‘On the Elastoplastic Buckling Analysis of Cylinders under Non-proportional Loading via the Differential Quadrature Method’, International journal of Structural Stability and Dynamics, (online ready). -
Doctorat Paristech T H È S E L'école Nationale Supérieure Des Mines De
N°: 2009 ENAM XXXX École doctorale n° 364 : Sciences fondamentales et appliquées Doctorat ParisTech T H È S E pour obtenir le grade de docteur délivré par l’École nationale supérieure des mines de Paris Spécialité “ Mécanique Numérique ” présentée et soutenue publiquement par Zhigang LIU le 23 Avril 2012 Numerical and experimental study of AZ31-O magnesium alloy warm sheet forming Directeur de thèse : Michel BELLET Co-Directeur de thèse : Elisabeth MASSONI Jury Mme Salima BOUVIER , Professeur, Robertval , Université technologique de Compiégne Rapporteur T M.Tudor BALAN , Maître de conférences – HDR, LEM3, Arts et Métiers ParisTech Rapporteur M. Jean-Claude GELIN, Professeur, ENSMM Examinateur H M. Patrice LASNE, Ingénieur, Transvalor Examinateur Mme Elisabeth MASSONI, Maître de recherche, CEMEF, Mines ParisTech Co-Directeur de thèse È M. Michel BELLET, Professeur, CEMEF, Mines ParisTech Directeur de thèse S E MINES ParisTech Centre de Mise en Forme des Matériaux Rue Claude Daunesse B.P.207, 06904 Sophia Antipolis Cedex, France Abstract Lightweight materials have been studied widely at present. Because weight reduction while maintaining functional requirements is one of the major goals in industries in order to save materials, energy and costs, etc. As the lightest structural alloys, magnesium alloys offer great potential to displace the most commonly used materials, because its density is about 2/3 of aluminum and 1/4 of steel. However, due to HCP (Hexagonal Close-Packed) crystal structure, magnesium provides only limited ductility for cold forming operations. But its formability improved obviously at elevated temperature. In this project, the material is AZ31- O magnesium alloy sheet, including 3% aluminum and 1% zinc. -
An Alternative J2 Material Model with Isotropic Hardening for Coupled Thermal-Structural Finite- Strain Elastoplastic Analyses
MATEC Web of Conferences 157, 06003 (2018) https://doi.org/10.1051/matecconf/201815706003 MMS 2017 An alternative J2 material model with isotropic hardening for coupled thermal-structural finite- strain elastoplastic analyses Ladislav Écsi1,*, Pavel Élesztos1, Roland Jančo1 1Institute of Applied Mechanics and Mechatronics, Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava, Slovakia Abstract. In this paper an alternative J2 material model with isotropic hardening for finite-strain elastoplastic analyses is presented. The model is based on a new non- linear continuum mechanical theory of finite deformations of elastoplastic media which allows us to describe the plastic flow in terms of various instances of the yield surface and corresponding stress measures in the initial and current configurations of the body. The approach also allows us to develop thermodynamically consistent material models in every respect. Consequently, the models not only do comply with the principles of material modelling, but also use constitutive equations, evolution equations and even ‘normality rules’ during return mapping which can be expressed in terms of power conjugate stress and strain measures or their objective rates. Therefore, such models and the results of the analyses employing them no longer depend on the description and the particularities of the material model formulation. Here we briefly present an improved version of our former material model capable of modelling ductile-to brittle failure mode transition and demonstrate the model in a numerical example using a fully coupled thermal-structural analysis. Keywords: finite-strain formulation, thermodynamically consistent formulation, thermal-structural finite element analysis, strong coupling, generalized J2 plasticity, isotropic hardening, material damping, ductile-to-brittle failure mode transition 1 Introduction Modelling materials within the framework of finite-strain thermoelastoplasticity represents a challenging task in computational mechanics. -
Of Contemporary Multiplicative Plasicity Models
Strojnícky časopis – Journal of MECHANICAL ENGINEERING, VOL 69 (2019), NO 2, 15 - 26 A STUDY ON THE ‘COMPATIBLITY ASSUMPTION’ OF CONTEMPORARY MULTIPLICATIVE PLASICITY MODELS ÉCSI Ladislav1, JERÁBEK Róbert1, ÉLESZTŐS Pavel1 1Slovak University of Technology in Bratislava, Faculty of Mechanical Engineering, Institute of Applied Mechanics and Mechatronics, Nám. Slobody 17,812 31 Bratislava, Slovakia, e-mail: [email protected] Abstract: Contemporary multiplicative plasticity models are now generally accepted as “proper material models” for modelling plastic behaviour of deformable bodies within the framework of finite-strain elastoplasticity. The models are based on the assumptions that the intermediate configuration of the body is stress-free or locally unstressed, for which no plastic deformation exists that meets the conditions of compatibility. The assumption; however, has never really been questioned nor justified, but was rather taken as an axiom and therefore considered to be generally true. In this study, we take a critical look at the assumption from both, physical and mathematical points of view, in order to investigate whether contemporary multiplicative plasticity models are indeed continuum based and if there are alternatives to them. KEYWORDS: Multiplicative plasticity models, finite-strain elastoplasticity, continuum theory, compatibility 1 Introduction Contemporary multiplicative plasticity models are now generally accepted as “proper material models” for modelling plastic behaviour of deformable bodies within the framework