Abstract: I₁ fracture criterion assumption is a newly developed fracture criterion based on atomic force model and fracture process analysis. In this criterion, material begins to fracture when first stress invariant I₁ of material local region reaches critical value I_b which is defined as fracture strength. Based on this fracture criterion and Mises yield criterion, four basic mechanical behaviors criterions are proposed, including elastic deformation, plastic deformation, brittle fracture and ductile fracture. To confirm the validity of the newly developed I₁ fracture criterion assumption under biaxial stress condition, internal hydraulic pressure-axial mechanical tension combined loading experiment with thin-walled tube specimen is designed. Test results of 304 austenite stainless steel, 10Ni5CrMo V steel and EH50 steel show that for the same material, a linear relationship exists between first principal stress and second principal stress. The first stress invariant I₁ remains almost constant when fracture occurs in different biaxial stress states, indicating the presence of fracture strength I_b. Therefore, the validity of I₁ fracture criterion assumption in description of fracture process of material under approximate biaxial stress condition is confirmed.