Modelling of deformation and fracture for a model quasi-brittle material with controlled porosity: Synthetic versus real microstructure

Deformation and fracture of materials are usually considered in terms of brittle and ductile modes. However, there is an intermediate class between these limits that is termed quasi-brittle where there is measurable inelastic deformation prior to final graceful ‘brittle’ failure. In previous work, we presented deformation and fracture data obtained tests conducted using a model material containing different known amounts of up to about 30% surrogate porosity. The model material is a hemi-hydrate gypsum plaster with additions of expanded polystyrene beads in the size range 1.5–2.0 mm dia. Use of gypsum plaster and artificial “pores” enabled creating a simple brittle model material with isolated pores randomly distributed and their size and geometry controlled. Herein, a comparison between two ways of generating microstructures for computer modelling of deformation and fracture of the model material is presented. The predictions for the computer model have been based upon two microstructure inputs (i) a synthetic 3-D pore model and (ii) measurements of porosity obtained from computed X-ray tomography images of the test material. Predictions of the elastic modulus and tensile strength for the different amount of porosity are compared between the two computer models and the experimental flexural data. The predicted deformation and fracture characteristics that describe the observed quasi- brittle response measured for the model material are discussed