Please answer the following question for part (b), thank you!
Recall the Tsai-Wu yield criterion where failure occurs when
F + F + F + F + 2F0 + F2 - 10
and the material is elastic if
F0 + F + F + F + 2F0 + F - 1 < 0
Assume the Tsai-Wu constants in the principal coordinate system have the values F1 MPa, F2 MPa, F3 MPa, F4 MPa, F5 MPa, F6 MPa: 0.021, 0.0036, 0.052, 0.021, 0.0, 0.143
For an applied shear stress (Ï„xy = Ï„yx = 0) in the x-y coordinate system, write an algebraic expression for the resulting stresses in the Ï„1-Ï„2 coordinate system.
If the x-y coordinate system is at an angle of 45° from the material coordinate system, what is the lowest magnitude of shear stress, τ, that can be applied in the x-y coordinate system to cause failure?
The stress transformation relationship is:
cos^2θ sin^2θ sin2θ sinθ cosθ -sin2θ -sinθ cosθ
τ12 = τxy cos^2θ + τyx sin^2θ + 2τxy sinθ cosθ
where θ and θ are the axial stresses along the 1 and 2 directions, τ is the shear stress in the 1-2 plane, and θ is measured positive counter-clockwise from the x axis to the y axis. The inverse relationship is found by replacing θ by -θ.
