Description of Mechanics of composite materials

Question 1: An orthotropic lamina with a fiber orientation of 45 degrees is subjected to stresses sigma_x = 0, sigma_y > 0, and tau_xy.

Determine the failure envelope and the non-failure region in the sigma_y - tau_xy plane using Tsai-Hill theory for the following cases:

i) tau_xy > 0
ii) tau_xy < 0

Take y axis as sigma_y and x axis as tau_xy.

DATA

sigma_1T = 250 MPa
sigma_1C = 200 MPa
sigma_2T = 20 MPa
sigma_2C = 40 MPa
tau_12 = 10 MPa

Question 2: A unidirectional lamina with a fibre orientation of 0 degrees is subjected to stresses sigma_1 and sigma_2 in the 1 (fibre) and 2 (transverse) directions as well as a shear stress of tau_12 = 25 MPa. Determine the non-failure region in the sigma_1 - sigma_2 plane using Tsai-Hill criterion.

Note that sigma_1 and sigma_2 can be tensile or compressive.

DATA

sigma_1T = 250 MPA
sigma_1C = 150 MPa
sigma_2T = 30 MPa
sigma_2C = 90 MPa
tau_12 = 50 MPa