Question

A single crystal of a metal is oriented for a tensile test such that its slip plane normal makes an angle of 64.2° with the tensile axis. Three possible slip directions make angles of 30°, 48°, and 78° with the same tensile axis.

(a) Which of these three slip directions is most favored?

(b) If plastic deformation begins at a tensile stress of 1.6 MPa (232.1 psi), determine the critical resolved shear stress for this metal

Answer 1

We are asked to compute the critical resolved shear stress for the metal. As stipulated in the problem = 64.2^o , while possible values for are 30^o,48^o,and 78^o .

(a) slip will occur along that direction for which (cos cos ) is maximum . cosines for the possible values are given below:

                                         cos(30^o) = 0.87

                                         cos(48^o) = 0.67

                                         cos(78^o) = 0.21

Thus, the slip direction is at angle of 30^o with the tensile axis.

(b) From equation given, the critical resolved shear stress is just

                        _crss = _y(cos cos)_max

                       = (1.6MPa)[cos (64.2^o) cos (30^o)] = 0.61 MPa (88.5 psi)