PSI - Issue 52

Vinit Vijay Deshpande et al. / Procedia Structural Integrity 52 (2024) 391–400 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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the results. The results fared well with the experimental measurements investigated in Schukraft et al. (2020). The present work adopts the same numerical procedure to study biaxial compression failure of alumina foam. The objective in this work is to apply macroscopic strain loading on a reconstructed foam volume element as shown in Fig. 2a.

Fig. 2. (a) Boundary conditions for biaxial compression of foam; (b) Proportional monotonic strain loading defined by the angle . The loading is applied in the form of proportional monotonic macroscopic strains 11 and 22 and the ratio between them is defined by tan = 22 11 ⁄ . Note that, 11 and 22 in Fig. 2b indicate compressive strains even though they are shown in the first quadrant. Johnson Holmquist model is selected as a constitutive model for the alumina base material. In Deshpande and Piat (2022), a size effect study was conducted to determine appropriate size of a statistical volume element to be used for finite element (FE) simulations. The selected volume element had an edge length of 150 pixels (0.39 mm and size factor = 5). The same size is selected in the present study. A quasi-static FE simulation is conducted to determine effective stress-strain behavior along the two selected orthogonal directions. The results of effective stress-strain curves averaged on four equivalent volume elements along the two directions for a selected few values of 25˚, 45˚ and 65˚ (approximate tan values of 0.5, 1 and 2) along with two cases of uniaxial compression along 1 and 2-directions are shown in Fig. 3a-b. It can be seen that for cases = 25˚ and 65˚, the smaller macrostrain is half of that of the larger macrostrain. Also, 11 and 22 are the effective compressive stresses along 1 and 2 - direction. The finite element simulations are conducted using ABAQUS software by Simulia (2022).

Fig. 3. Effective compressive stress - strain curves for load cases = 25˚, 45˚ and 65˚ along (a) 1- and (b) 2-directions and two uniaxial compression cases. It can be seen in Fig. 3 that the maximum stress increases in biaxial compression cases as compared to the uniaxial case. The loss of strength is also abrupt in the case of biaxial compression. To gain deeper insight into the nature of