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.
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.