Quadric Surfaces Criterion for Composite Materials

Abstract

A new criterion, which is named the quadric surfaces criterion for composite materials, is proposed based on the form of quadratic surface associated with a second-degree polynomial. The three interaction terms (i.e., σ_Iσ_j, σ_Iτ_ij, and σ_jτ_ij) are included in the quadric surfaces criterion completely. However, no more biaxial tests are required for the determination of those coefficients of the three stress interaction terms.

Since the quadric surfaces criterion requires three yield strengths from simple tension, compression, and torsion tests, respectively, this criterion is applicable for ductile materials as well as brittle materials with different strengths in tension and compression. One unique feature of the quadric surfaces criterion is the ability to change its format depending upon what types of stresses are applied and what types of material strengths are considered. Thus, it is shown that the entire closed failure envelope of the quadric surfaces criterion is composed of piecewise quadric surfaces. For example, when a material is deformed in compression, the compressive strength should be the dominant critical strength, not the tensile strength. Accordingly, the failure function must be adjusted so that it can accommodate the compressive strength.

The validity of the quadric surfaces failure criterion is examined with experimental results from off-axis uniaxial strength tests of unidirectional fiber composites, and angle-ply laminated composites. Comparisons were made with other well-known an isotropic strength theories as well.