Final answer:
The critical resolved shear stress for a metal is the stress needed to cause plastic deformation by initiating slippage along a crystallographic plane, and is related to the shear modulus 'S'.
Step-by-step explanation:
The critical resolved shear stress for a metal is the stress required to initiate slippage along a crystallographic plane, which leads to plastic deformation. This shear stress is related to the shear modulus, denoted as 'S', which is a measure of a material's rigidity or resilience to shear deformations. The shear modulus 'S' can be found by using the relationship where S equals the force applied (F) divided by the cross-sectional area (A) and multiplied by the initial length (Lo). Breaking stress, or ultimate stress, is another concept that refers to the stress at the fracture point, which varies for different materials.
It is important to note that static equilibrium plays a role in these calculations, as the body must be at rest or moving at a constant velocity within an inertial frame of reference. By comparing equations and values from Equation 12.34 and Table 5.3, we can understand that different materials will have different values for S, consequently affecting their critical resolved shear stress and breaking load capacity.