PSI - Issue 17

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

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Fig. 5. Comparison of Ramberg-Osgood constants calculated from experimental data vs. estimated values.

3.1 Inverse analysis In the previous section, N values were estimated using S u and S y and ε̃ − . Some materials with low ductility show a monotonically increasing engineering stress-strain curve till failure. These materials fail at stress S F before reaching the peak stress with zero slope which conventionally defies the ultimate tensile strength value, S u . For such materials the maximum ultimate strength, S u , coincides with failure stress, S F , i.e. S u = S F . In such cases, it is difficult to predict the true stress strain curve without knowing the ultimate stress at point of zero slope value. Hence, in this section an inverse approach for the apparent ultimate stress, S u app , estimation is suggested. The apparent S u app is estimated from Eq. (11) using experimental values of N , S y and corresponding 0.2% plastic offset strain. Figure 6 shows three materials, A, B and C, with low ductility that has been chosen to demonstrate this inverse approach [12].

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 Normalized True stress/S y Normalized True stress/S y 0.2 0.4 0.6 0.8 1.0 1.2

Normalized True stress/S y

Experimental epsilon (p)=0.002 R-O relation Experimental Ramberg-Osgood fit Estimated (  p =0.002) Material B [12]

Material A [12] Experimental

Experimental epsilon (p)=0.02 R-O relation

Ramberg-Osgood fit Estimated (  p =0.002)

0

0.002

0.004

0.006

0.008

0.01

0.005

0.01

0.015

True strain

True strain

Material C [12]

Experimental epsilon (p)=0.002 R-O relation

Experimental Ramberg-Osgood fit Estimated (  p =0.002)

0.0

0

0.002

0.004

0.006

0.008

True strain

Fig. 6. Comparison of Ramberg-Osgood constants calculated from experimental data vs. estimated values.

Table 1 summarizes the inverse analysis of estimated normalized apparent ultimate strength, S u app /S y , for these steels.