PSI - Issue 17

First page Table of contents Previous page 61 Next page Last page

Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2019) 000 – 000 ScienceDirect

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 17 (2019) 750–757

ICSI 2019 The 3rd International Conference on Structural Integrity An Estimation of Ramberg-Osgood Constants for Materials with and without Luder’s Strain Using Yield and Ultimate Strengths Pranav S. Patwardhan a , Rajprasad A. Nalavde a and Daniel Kujawski* a ICSI 2019 The 3rd International Conference on Structural Integrity A Est mation of Ramberg-O good Constants for Materials with and without Luder’s Strain Using Yield and Ultimate Strengths Pranav S. Patwardhan a , Rajp asad A. Nalavde a nd Daniel Kujawski* a Abstract Tensile stress-strain curves for metallic materials typically show two different behaviors viz . with Luder’s strain and without Luder’s strain. Recently, Kamaya [1] proposed a method to estimate the true stress -true strain curve using a certain plastic strain together with yield and ultimate strengths. Kamaya’s method however, is not accurate enough for materials exhibiting Luder’s strain in their engineering stress-strain behavior. Hence, the aim of this paper is to propose a generalization of the Kamaya’s method for the materials with and without Luder’s strain s. This new generalized approach uses plastic strain value corresponding to the Luder’s strain along with engineering yield strength and ultimate tensile strength to estimate the strain hardening exponent in the Ramberg-Osgood type of true stress - true strain relationship. The new approach was applied to 16 different materials with and without Luder’s strain to validate the proposed estimation procedure. In addition, an inverse method for assessing an apparent ultimate tensile stress (stress at “ an apparent ” point of zero slope in an engineering stress-strain curve) for materials with low ductility due to quenching or carburizing is also suggested . Abstract Tensil stress-strain curves for metallic materials typically show two d fferent beh viors viz . with Luder’ stra n a d without Luder’s strain. Rec ntly, Kamaya [1] proposed a method to estimate the true s ress -tru strai curve using a cert in pl stic s rain t gether with yield and ultimate strengths. K maya’s method however, is not curate enough for materials exhibiting Luder’s strain in their engi eering stress-st ain behavio . Hence, the ai of hi pape is to pr pose a g neraliz tion of the Kamaya’s method for th materials with and without Luder’s s. Th s ew gen ralized a proach u es lastic strain valu corresponding to the Luder’s strain along wi h eng ne ring yield strength and ultimat tensile streng h to est mate the s rain ha dening expo ent in the Ra berg-O good type of true stress - true s rain relationship. Th new approach was applied to 16 different t i and without L der’s strain to validate the proposed estimation procedure. In addition, an inverse method for assessing an apparent ultimate tensile stress (stress at “ an apparent ” point of zero slope in an engineering stress-strain curve) for materials with low ductility due to quenching or carburizing is also suggested . a Western Michigan University, Mechanical and Aerospace Engineering 1903 W Michigan Av., Kalamazoo, MI, 49008-4353, USA a Western Michigan University, Mechanical and Aerospace Engineering 1903 W Michigan Av., Kalamazoo, MI, 49008-4353, USA

© 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. © 2019 The Authors. Published by Elsevier B.V. P er-review under re ponsibility of the ICSI 2019 org nize s.

Keywords: Ramberg-Osgood relationship; Luder’s strain; strain hardening exponent; stress -strain curves; yield and ultimate strengths.

1. Introduction

The tensile test is usually represented by a graph of engineering stress vs engineering strain, as illustrated in Fig. 1 from which, important mechanical properties such as: Young’ modulus, E, yield strength, S y , ultimate tensile strength, S u , strain hardening behavior, and stress and strain at fracture (F) can be determined. Relatively ductile materials undergo significant cross-sectional reduction due to necking of material after ultimate tensile strength (stress at point of zero slope in  -  curve). Hence, to study ductile materials behavior, true stress-true strain curves are often utilized. _______________ *Corresponding author. Tel.: +1-269-276-3428; fax: +1-269-276-3421. The tensile test is usually represented by a graph of engineering stress vs engineering strain, as illustrated in Fig. 1 from which, important mechanical properties such as: Young’ modulus, E, yield strength, S y , ultimate tensile strength, S u , strain hardening behavior, and stress and strain at fracture (F) can be determined. Rel tively ductile materials undergo significant cross-sectional reduction due to necking of material after ultimate tensile strength (stress at point of zero slope in  -  curve). Hence, to study ductile materials behavior, true stress-true strain curves are often utilized. _______________ *Corresponding author. Tel.: +1-269-276-3428; fax: +1-269-276-3421.

2452-3216 © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. 2452-3216 © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers.

2452-3216  2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. 10.1016/j.prostr.2019.08.100

Made with FlippingBook Digital Publishing Software