Exercise Mohr's Circle

 Mechanical Behavior of Materials

HW-1

1.  A body is loaded under a stress state σ_x = 400, σ_y = 100, τ_xy = 120, τ_yz = τ_zx = σ_z = 0.

a. Sketch the Mohr’s circle diagram.

b. Calculate the principal stresses.

• What is the largest shear stress in the body?

    2.      A state of stress is given by

σ₁₁ = −500 MPa,

σ₂₂ = 300 MPa,

σ₁₂ = 150 MPa.

Determine the principal stresses and the maximum shear stress, as well as their   orientation, using the Mohr circle construction.

3.  Consider an aluminum single crystal under a stress state σ_x = 250 MPa, σ_y =−50 MPa, τ_yz = τ_zx = τ_xy = σ_z = 0, where x = [100], y = [010], and z = [001].

a. What is the resolved shear stress, τ_nd, on the (111) plane in the [1-10] direction, that is, with n = [111], d = [1-10]?

b. What is the resolved shear stress on the (11-1) plane in the [101] direction?