PSI - Issue 68

Swastik Soni et al. / Procedia Structural Integrity 68 (2025) 513–519 S. Soni et al. / Structural Integrity Procedia 00 (2025) 000–000

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3.2. Strain hardening exponent in DBT region The stress strain behavior of the tested samples was analyzed by removing the elastic strains and machine compliance influence and were described in Ramberg-Osgood relation expressed as, = ! " + & ! " ' # , (1) where k is a constant and ‘n’ is known as strain hardening exponent, with E representing Elastic modulus. The elastic modulus of this grade is taken from Tiwari and Singh (2018). The engineering stress vs plastic strain behavior are shown in Fig. 4. The strain hardening exponent’s behavior with temperature is shown in Fig. 5(a), which shows a similar behavior as Fig. 3(c) where the ratio of σ o / σ UTS is plotted.

Fig. 5. (a) Temperature vs strain hardening exponent. (b) Log-Log Plot for Determining the Fractal Dimension

3.1. Quantitative Fractography in DBT region Fractal dimension is a parameter which has been so far inconclusive in fracture mechanics and has shown both increasing and decreasing trends with change in temperature and strain rate. However, conceptually, it is expected that the fractal dimension should increase with increase in tendency towards ductile fracture. Sahu et al. (2017), for instance, shows an increasing behavior fractal dimension with increase in impact energy. The reason for this is fractal dimension describes roughness of the fractograph and as the ductile nature of the material increases, the roughness should increase. The fractal dimension is calculated in this work using the SEM images of 5 specimens at different strain rates and temperatures and using box-count method. It is similar to measuring the length of a coast line with varying yard sticks. As the yard stick size changes, the length of the coast also changes (usually larger length for smaller yard sticks) but it scales in a particular proportion which is called the fractal dimension of the parameter being analyzed which in this example in the coast line. In box count method, the SEM images calculate the amount of dark and bright regions in different sizes of boxes and when the box size vs dark or bright regions are plotted on a log scale, the slope of that curve provides the fractal dimension; an example of this calculation is shown in Fig. 5(b), which was tested at -20 o C and the strain rate of 6.7x10 -3 s -1 . Another parameter which can be quantified and is more accurate than fractal dimension is the average dimple diameter. The SEM images analyzed for fractal and dimple diameter are shown in Fig. 6.