The Influence of Porosity on the Failure Behaviour of Foams
Authors: Theocaris Pericles S. 
Published: July 2008

Rigid closed-cell polyurethane forms are accepted as transversely isotropic materials with their symmetry axis as the strong one and the transverse isotropic plane as the weakest plane. Failure modes of a series of polyurethane foam (PUR) were studied by employing the failure tensor polynomial criteria, convenient to describe such materials, and as such criterion the elliptic paraboloid failure surface (EPFS) was used. In a previous paper by Theocaris (1992) it has been indicated by testing a series of three different samples of varying porosity that as the density of the materials is decreased, the failure mode of the foam changes drastically, from a compression-strong material to a tension-strong one. In this paper a series of several rigid polyurethane foams (PUR-foams) were tested to failure in tension and tension compression along the principal stress axes, thus yielding enough data for an accurate and reliable definition of their failure surfaces.

The range of materials tested was spanned from a material of very low density of dr = 58 kg/M3 to a material of high density equal to dr = 192 kg/M3, thus covering materials from a very high porosity, to ones of rather low porosity. Since most foams may be considered to a high approximation as transversely isotropic materials with their rise direction corresponding to their higher strength, it is reasonable to accept, as an appropriate failure criterion, one of the group based on failure tensor polynomials, and as such the elliptic paraboloid failure surface (EPFS) was judged the most appropriate (Theocaris, 1992a).

Thus, the series of groups of data defining failure in tension and compression along the three principal axes of anisotropy were used to define for each material its failure locus along its axisymmetric plane (the principal diagonal plane), as well as the principal (ax,, ar3) or (Cr2, a3)-stress planes (with the a3-stresses along the strong axis a3 of the material). These failure loci indicated clearly that, as the porosity of the foams is increased, their failure behaviour changed progressively from a strongly anisotropic compression-strong behaviour to a mild anisotropy, they passed through a transition region, where the materials were almost isotropic with their failure loci almost coinciding with the Mises failures. For some particular value of porosity, the mode of failure of the foams was reversed, thus indicating that the materials become tension-strong ones with their anisotropy starting again to increase for very porous materials.

Furthermore, from the respective (al, X3)-plane failure loci of the foams it was derived that, as the porosity is increased the position of each principal-plane failure locus is displaced and its center is angularly changed, while the shapes of the elliptic loci changed position and rotated according to definite movements, indicating clearly that there is, neither isotropic, nor kinematic type of variation of failure loci. Similar phenomena of displacements of the yield loci were already detected in previous papers, where the modes of hardening of elastic-plastic materials were studied (Theocaris and Panagiotopoulos, 1995).