PSI - Issue 60

S.K. Pandey et al. / Procedia Structural Integrity 60 (2024) 3–12

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S. K. Pandey/ Structural Integrity Procedia 00 (2023) 000–000

loading condition along the length) and axisymmetric model has been used for the specimen using 8-node biquadratic axisymmetric quadrilateral, reduced integration (CAX8R) element. The numbers of elements along minimum cross section radius are 25 and the aspect ratio of the elements have been maintained as ‘1’ in order to obtain better accuracy. It is the most critical zone of the FEA mesh with the element distortion point of view. The finite element mesh for smooth, notch-5 mm, notch-2.5 mm, notch-1.25 mm and notch-0.5 have been depicted in Fig.3. A typical experimental and FEA load-displacement curve is provided in Fig.4. Physical significance of Error is the average of deference between average load for FEA and average load for the experiment for all specimens taken for study, as provided in Fig.5. Error has been defined, in Eq.2, as the average of modulus (absolute) of difference between area ( ) under the load-displacement curve of experimental data and area ( ) under load displacement curve of FEA data divided by the maximum elongation ( δ ) of specimen at the rupture for the different types of specimens. Assume load-displacement data (experimental and FEA) are available for five specimens, viz., smooth, notch-5, notch-2.5, notch-1.25 and notch-0.5. The Error for each point (each RO parameter) is calculated as the sum of � � − � � for all type of specimen (smooth, notch-5, notch-2.5, notch-1.25 and notch-0.5) divided by the number of types of specimens as in Eq. 2. The basis for this equation (2) is as follows. The differences in load-displacement data between FE analysis and experiments occurs because of the error in the Ramberg-Osgood parameter set, which describe the true stress-strain curve of the material through Eq. (1). Hence the objective function is the same of the normalized area between the load-displacements curves of smooth and notched specimens as we want to optimize data for all types of specimens including the specimens with different notch radii (simulating different triaxial conditions). These areas scale according to specimen displacement which is very large for smooth specimen, when compared to the notched specimen. Hence, we scale the error in area by the total elongation (used as scaling factor in Eq. 2) in order to give equal weightage to smooth as well as notched specimen. If this scaling is not used, smooth specimen shall have more weightage (due to more elongation and hence, area under load-displacement curve) and it shall introduce error for notched specimens as their weightage becomes less in the objective function.

Fig 3. FE mesh for (a) smooth specimen (b) notch 5mm (c) notch 2.5mm (d) notch 1.25mm

Fig 4. Typical experimental and FEA load-displacement curve of smooth specimen

Fig 5. Schematic of error evaluation