Stress-strain state

Normal stress in simple tension is given by s=Force/Area. If we cut the section at an angle j, there are two stress components perpendicular (s_n) and parallel (t) to the incline plane.

The maximum shear stress occuring at j=45^o is equal to half of maximum axial stress s.

For a bi-axial state of stress, normal stress s_n and shear stress t on an inclined plane depend on the two shown stress components.

For common plane stress state there are two perpendicular planes (principle planes) where there is no shear stress and normal stresses are a minimum and maximum. The two components are known as the principle stresses.

Maximum shear stress acts at the planes inclined 45^o to principle planes.

Hooke's law generally includes two constants of the material: Young's modulus E and Poisson's ratio m.

In the general case, maximum shear stress depends on two principle stresses only - maximum and minimum.

According to the first theory of strength fracture occurs if the maximum principle stress exceeds its critical value.

According to the second theory of strength fracture occurs if the maximum tensile strain exceeds its critical value. This can be transformed into an equation with the equivalent stress depending on all three stress components and Poisson's ratio.