PSI - Issue 17

Pranav S. Patwardhan et al. / Procedia Structural Integrity 17 (2019) 750–757 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

3

752

where H and n are obtained by the best fit line in log- log coordinated of ̃ vs. ε̃ . The H can be also estimated from the following relationship as = ̃ where ̃ = 0.002 is the true offset plastic strain corresponding to the yield stress S y . 2. Background 2.1 Non-dimensional form of the Ramberg-Osgood relationship The Ramberg-Osgood relationship can also be represented in its non-dimensional form = + ( )

(8)

(9)

where N = 1/n = strain hardening exponent,  = − = non-dimensional material constant. By comparing the plastic part of the strain given by Eqs. (5) and (9), the true plastic strain can be expressed as = ( ) (10) 2.2 Approach proposed by Kamaya [1] Recently, Kamaya [1] proposed equations to calculate N values in non-dimensional Ramberg-Osgood relationship using yield and ultimate strengths and a specific value of the plastic yield strain, . Using this procedure Kamaya [1] obtained the following relations for N as: = 3.93 × ( ( ⁄ )) − . for = . (11) = 3.27 × ( ( ⁄ )) − . for = . (12) = . ( ( ⁄ )) − . for = . (13) Such estimated N values were then used for predicting true stress versus true strain curves of the Ramberg -Osgood relationship. In his analysis Kamaya didn’t specify what value for should be used. Kamaya applied his estimation procedure to four ferrite steels materials using three values of . Kamaya’s analysis shown to be successful in relating N if of 0.2%, 0.5% or 1% has been properly selected. However, how this value of needs to be selected for different material was not specified. 3. Proposed method

In subsequent analysis Eqs. (11-13) are generalized to the following form: = [ln ( )] −

(14)