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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1. Introduction Porous ceramics are highly sought after materials in applications that demand temperature, corrosion and wear resistance along with high strength and lightness in weight. The examples of such applications include molten metal filtration, high temperature insulation, light weight construction materials, artificial bone implants, etc. Compression is the most common type of loading condition in such applications and the understanding of how the microstructure of these materials respond to such loading is a critical aspect of product design. Experimental investigations into the compressive failure of porous ceramics are scarce in literature with most of them focusing on uniaxial compression and a limited range of volume fraction (volume fraction of solid content). Colombo and Modesti (1999) and Colombo et al. (2001) studied compression strength of silicon oxycarbide foams having volume fraction in the range of 0.13-0.3. Seeber et al. (2013) studied compressive behavior of alumina foams with volume fraction 0.05 and 0.1. Voigt et al. (2013) studied alumina, ZrO 2 , SiC and fused silica foams with the focus on effect of loaded area, rate of loading and pore size on compression strength. Meille et al. (2012) focused on alumina foams with volume fraction in the range of 0.25-0.7. These works attempt to correlate effective compression strength of the materials with design parameters like volume fraction, ambient temperature, loading conditions etc. Since it is very difficult to experimentally study the crack propagation mechanisms with respect to loading, analytical theories and numerical simulations play a vital role in understanding these materials. The material studied in the present work is an alumina foam described in Horny et al. (2020). It was manufactured by mechanical stirring of alumina slurry and had a homogeneous microstructure with almost spherical shaped pores. Schukraft et al. (2022) experimentally measured the uniaxial compression stress-strain behavior of the foam and described the nature of crack propagation and mode of sample failure. This material was studied in Deshpande et al. (2021) by performing numerical microstructure characterization, reconstruction and determination of effective elastic properties. A novel microstructure reconstruction algorithm was developed to numerically recreate this material that is statistically equivalent to the real one. This allowed us to create as many realizations as needed and of different sizes so as to determine appropriate volume element size to conduct finite element simulations. Effective stiffness was calculated numerically that was in agreement with that of the real foam that was calculated numerically as well as experimentally as reported in Horny et al. (2020). Further, the same reconstructed microstructures were utilized to study uniaxial compression failure behavior of alumina foam in Deshpande and Piat (2023). The effective compression stress-strain behavior of a foam volume element was studied through finite element simulations and compared successfully with the experimental investigations in Schukraft et al. (2020). Further, the same reconstruction algorithm was used to generate artificial microstructures of foam with different volume fractions. A correlation study was performed to determine volume fraction – compression strength relationships in alumina foams. Change in failure mode of the material as the volume fraction is increased was also studied. The results matched the experimental measurements in Meille et al. (2012) as well as the theoretical predictions in Gibson and Ashby (1997). The present research aims to study the biaxial compression behavior of alumina foam and understand the failure mechanisms involved. The biaxial loading is in the form of macroscopic strains applied at different ratios. The effective macroscopic stress-strain behavior in the two orthogonal directions is calculated through finite element simulations. Tracking the creation of damaged regions as the loading is increased gives useful insights into the damage mechanisms involved. Lastly, the paper introduces a neural network based surrogate model to predict the macroscopic stress-strain behavior of the foam material subjected to biaxial compression loading. The proposed neural network is based upon the idea that any neural network that is infused with a physical model is better equipped in making accurate predictions. Physics enriched neural network models have been explored recently in literature. Haghighat et al. (2021) and Arora et al. (2022) modified the loss function to incorporate physical constraints. Vlassis and Sun (2021) imposed thermodynamic consistency by incorporating derivatives of predictions into the loss function. Maia et al. (2023) proposed to add a material layer composed of constitutive model of the matrix phase within a neural network. In the present work, it is proposed to first create a neural network trained on data from a volume element of a smaller size. Then this neural network is used as part of a transfer learning strategy to create another neural network to be trained on data of a larger volume element (a representative volume element). The idea behind such a modelling is to infuse the outer neural network (the one trained on larger volume element) with some informed model of the foam