A series of experiments is conducted in which a thin plate is subjected to biaxial tension/compression, σ1, σ2 , the plane surfaces of the plate being traction-free (i. e. σ 3-O) Unbeknown to the experimenter, the material contains microscopic defects which can be idealized as a sparse distribution of small circular holes through the thickness of the plate. The hoop stress around the circumference of one of these holes when the plate is loaded in uniaxial tension σ is known to be σ 0-o(1-cos 2θ), where the angle θ is measured from the direction of the applied stress. Show graphically the relation that will hold at yield between the stresses ' σ2 applied to the defective plate if the Tresca criterion applies for the undamaged material (Hint: The hoop stress due to biaxial stress can be constructed by superposition. The maximum must occur at either θ = 0 or θ-m2, depending on the relative magnitude of σ, σ2 .)