Problem 7: Fracture of Silicon Carbide

An engineering component is made of silicon carbide (SiC) ceramic that has out = 350 MPa. The

most severely stressed point is subjected to the following state of stress:

- 40-50 0

0-50 100 12

0 12 30

MPa

Determine the following:

a. Principal normal stresses (01, 02, 03) and principal shear stresses (T1/2, T1/3, T2/3).

b. Maximum normal stress (max) and maximum shear stress (Tmax).

c. Safety factor against fracture using the maximum normal stress criterion.

Note: For part (a), determine the roots (eigenvalues) of the stress tensor to evaluate 01, 02, and 03.