PSI - Issue 57

Camilo Gonzalez Olier et al. / Procedia Structural Integrity 57 (2024) 658–669 Camilo Andres Gonzalez Olier/ Structural Integrity Procedia 00 (2019) 000 – 000

661

4

= ( ) + ( ) 1

(2) Where is the Young’s Modulus, is the true stress, is the hardening coefficient, and is the hardening exponent. This relationship is shown in Figure 2. The Ramberg Osgood model is commonly used to model the stress-strain curve under monotonic loading, but it has also been adapted to predict the cyclic response of various materials [23,27]. To simulate hysteresis loops, equation (2) is modified to an incremental form by replacing = ∆ , and = ∆ as follows: ∆ = ∆ + (∆ ) 1 (3) Where ∆ and ∆ε are the change in stress and change in strain, respectively. The parameters and in equation (3 are different as those used for fitting monotonic curves.





 (log)

K

 e

 p

1

f y

 e

n

E

 p







 e ,  p   (log)



Figure 2. the Ramberg – Osgood relationship.

The Ramberg Osgood model is advantageous for its simplicity in adjusting model parameters based on experimental data. Mostaghel et al [27] and Li. J et al [28] have successfully applied the Ramberg Osgood model to characterize the hysteresis loops of different steels. However, some studies have suggested that the Ramberg Osgood model predictions are not accurate enough for certain steels [30]. Additionally, the R – O model is not suitable for predicting hysteresis loops in buckling cases during cyclic strain [31]. Likewise, it is not appropriate to simulate the cyclic hardening or softening of the materials [25]. 4. Model calibration To obtain the actual stress-strain curves from the test results the engineering stress ( ) and strain ( ) are computed based on the initial cross section area and gauge length Lc, respectively. Hence, and are estimated as follows [23]: = (1+ ) (4) = (1 + ) (5) Equations (4) and (5) are applicable only until necking occurs. Hence, the various models are fitted up to f u . To find, K and n for every test, the Ramberg-Osgood equation should be linearized.