Question

Questions

(a) Determine the critical resolved shear stress for an iron crystal which deforms by simultaneous slip on (110) [-1 1 1]; (110) [-1 1 -1]; (110) [1 1 1] and (110)[1 1 -1] when the tensile stress along [0 1 0] is 95.2 MPa

(b) If the critical resolved shear stress for yielding in aluminum is 240x10^3 Pa. Caclulate the tensile stress required to cause yielding when the tensile axis is [001].

(c) Along which crystallographic orientation in an fcc crystal must the tensile axis be oriented to give multiple slip on four (4) slip systems, six (6) slip systems and eight (8) slip systems.

Answer 1

Calculate one angle between the tensile axis (a long (001) direction) and the slip direction (110) lambda = cos^1 - 1[u_1u_2 + v_1v_2 + w_1w_2/ squareroot (u^2_1 + v^2_1 +w^2_1)(u^2_2 + v^2_2 + w^2_2)] = cos^- 1[0 + 0 + 1/ squareroot (0 + 0 + 1^2)((- 1)^2 + 1^2 + 0^2] = cos^- 1(1/ squareroot 2) = 45 calculate the angle between the tensile axis (along (001)direction: and the normal to the step plane (111) pi = cos^- 1[u_1u_2 + v_1v_2 +w_1w_2/ squareroot (u_1^2 + v^2_1 + w^2_1)(v^2_2 + u^2_2 + w^2_2)] = cos^- 1[0 + 0 + 1/ squareroot (0^2 + 0^2 + 1^2)(1^2 + 1^2 + 1^2) = cos^- 1(1/ squareroot 3) = 54.7 calculate the tensile stress required to cause yielding tau_etss = sigma_y(cos pi cos lambda)_max 240 = sigma_y (cos 54.7)(cos 45 degree) sigma = 587.36 k pa