The most favored slip direction in a tensile test is the one whose angle with the tensile axis is closest to 45°, which is 48° in this case. The critical resolved shear stress (CRSS) for the metal can be calculated using the applied stress and the angles of the slip direction and plane normal to the tensile axis.
The question deals with the selection of a favorable slip direction in a crystal during a tensile test and the determination of the critical resolved shear stress (CRSS).
To identify the most favored slip direction, we must consider the angles these directions make with the tensile axis.
According to Schmid's law, the slip system with the highest value of resolved shear stress, which is a product of the applied stress and the cosine of both the angle between the slip direction and the tensile axis, and the angle between the slip plane normal and the tensile axis, will be the most favored.
(a) The most favored slip direction among 30°, 48°, and 78° with respect to the tensile axis would be the one with the angle closest to 45°, as this will provide the maximum resolved shear stress.
In this scenario, the angle of 48° would be most favored because it is closest to 45°.
(b) To calculate the critical resolved shear stress (CRSS), we would use the formula:
CRSS = Applied Stress × cos(λ) × cos(φ)
Where λ is the angle between the slip direction and the tensile axis, and φ is the angle between the slip plane normal and the tensile axis.
For the most favored slip direction (48°), and the given angle of the slip plane normal (64.2°), the CRSS can then be calculated using the given applied tensile stress of 1.6 MPa.