Three-Parameter Twin τ2 Strength Theory for Brittle Materials under Multiaxial Stress State and Its Application

The strength failure of brittle materials under complex stress is an important problem. Herein, we propose a novel three-parameter twin τ2 strength theory considering the influence of hydrostatic pressure and normal stress on the principal shear-stress surface, derive a mathematical expression for the strength theory, and compare the theoretical predictions under several stress states with existing experimental data. The results show that different ultimate stress ratios, α and β, correspond to different strength theories for brittle materials. The principal stress σ1 increases gradually with an increase in σ2 (=σ3) under the stress state σ1 > σ2 = σ3; σ1 (=σ2) increases gradually with an increase in σ3 under the stress state σ1 = σ2 > σ3. Furthermore, the biaxial compressive strength is considerably higher than the uniaxial compressive strength under the biaxial compressive stress for σ1 > 0, σ2 > 0, and σ3 = 0. When σ3 is fixed and σ2 is relatively small under the stress states of σ1 > 0, σ2 > 0, and σ3 > 0, the maximum principal stress σ1 increases with the increasing σ2. When σ2 is relatively large and as σ1 gradually decreases with the increasing σ2, the effect law of intermediate principal stress σ2 is obtained.