Strength is a parameter reflecting the failure of materials such as fracture, tensile strength, compressive strength, etc., is the amount of material failure when the stress reaches how much, the unit of strength is generally trillion pa.

Damage type

Brittle fracture: sudden fracture that occurs without apparent plastic deformation. For example, cast iron specimens fracture along the cross section during tensile and round section cast iron specimens fracture along the oblique section during torsion.

Plastic yield: material produces significant plastic deformation resulting in the incapacity of the member, such as low carbon steel samples will undergo significant plastic deformation during tensile or torsion.

Strength theory

Maximum tensile stress theory: as long as the maximum tensile stress σ1 at a point in the component reaches the ultimate stress σ B under unidirectional stress state, brittle fracture will occur in the material. Therefore, the condition of brittle fracture failure of the component with the dangerous point in the complex stress state is: σ1=σ B. Therefore, the strength condition established according to the first strength theory is: σ1≤[σ].

Maximum tensile strain theory: as long as the maximum tensile strain ε1 reaches the limit value ε U under unidirectional stress state, the material will be brittle fracture, ε1=ε U. From the generalized Hooke’s law, ε1=[σ1-u(σ2+σ3)]/E, so σ1-u(σ2+σ3)=σb. According to the second strength theory, the strength condition is as follows: σ1-u(σ2+σ3)≤[σ].

Maximum shear stress theory: as long as the maximum shear stress τ Max reaches the ultimate shear stress τ0 under unidirectional stress state, the material will yield failure. Tau tau=0 Max. τ Max=(σ1-σ3)/2, τ Max=(σ1-σ3)/2, τ Max=(σ1-σ3)/2, τ Max=(σ1-σ3)/2. So the failure condition is rewritten as σ1-σ3=σs. According to the third strength theory, the strength condition is: σ1-σ3≤[σ].