What is the relationship between yield shear stress and uni axial in tension?

The yield shear stress and the uniaxial tensile strength are related through the von Mises yield criterion, which states that yielding occurs when the effective stress reaches a critical value.

For an isotropic material, the von Mises yield criterion can be expressed as:

σ_y = √(σ_x^2 - σ_x σ_y + σ_y^2 + 3τ_xy^2)

where:

σ_y is the yield shear stress

σ_x and σ_y are the normal stresses in the x and y directions, respectively

τ_xy is the shear stress in the xy plane

In the case of uniaxial tension, the normal stresses in the y and z directions are zero, and the shear stress is also zero. Therefore, the von Mises yield criterion simplifies to:

σ_y = σ_x

This means that the yield shear stress is equal to the uniaxial tensile strength.