given a brittle material has an ultimate

Question

Given:  A brittle material has an ultimate tensile strength of 300 MPa and an ultimate compressive strength of  -1000MPa.  Assume that failure can be represented by the Modified Mohr fracture criterion.  Biaxial data show σ_i = -400 MPa.

a) Sketch, at least approximately to scale, the failure envelope for this material when loaded under biaxial stress (σ_x and σ_y exist, but all other components are zero.

b) Determine whether or not brittle failure is expected for each of the following biaxial stress states.  Justify your work.

• σ_x = 500 MPa, σ_y = 100 MPa
• σ_x = 250 MPa, σ_y = -300 MPa
• σ_x = 250 MPa, σ_y = -700 MPa

c) Suppose the material is loaded in a biaxial tension-compression state where σ_x = 200MPa, σ_y = -C, C>0.  Determine the maximum value of the C before brittle failure.