Abstract: According to the physical process of material fracture, the theoretical assumption of fracture depending on the first stress invariant I₁ is proposed, and the corresponding facture criterion is also given. Material begins to fracture when first stress invariant I₁ of material local region reaches critical value I_b, I_bis defined as fracture strength. It can be determined by uniaxial tensile tests. Based on this fracture criterion and Mises yield criterion, four basic mechanical behavior criterions are given. The results are as follows, (1) elastic deformation:σ_mises< σ_y, I₁< I_b; (2) plastic deformation:σ_mises ≥ σ_y, I₁< I_b; (3) brittle fracture:σ_mises< σ_y, I₁ ≥ I_b; (4) plastic fracture:σ_mises ≥ σ_y, I₁ ≥ I_b.