Theoretical critical resolved shear stress

For crystals of reasonably pure, well-annealed metals at a given temperature, slip begins when the resolved shear stress reaches a certain critical value, which is characteristic of each metal. In the case of aluminum, for example, the observed critical shear stress Uco is usually about 4x10 N/m ( 4 bars = 0.4 MPa). Theoretically, for a perfect crystal, the resolved shear stress is expected to vary periodically as the lattice planes slide over each other and to have a maximum value that is simply related to the elastic shear modulus /t. This was first pointed out in 1926 by Frenkel who, on the basis of a simple model, estimated that the critical resolved shear stress was approximately equal to h/Itt (see Kittel 1968). In the case of aluminum (which is approximately elastically isotropic), = C44 = 2.7x10 N/m, so the theoretical critical resolved shear stress is about lO wco for the slip system <100>(100). 

We will learn in the subsequent chapters that ductile metals yield by shearing, so now we will attempt to estimate their theoretical peld strength, or what will be called their critical resolved shear stress (erss). Shearing requires planes of atoms to slide over each other, rather like shearing a deck of cards as illustrated in Figure 7.7a. For cubic crystals. Equation 7.5 gives Sz = 446 = GQ y = Gxjd where G is the shear coefficient and x < d. 

The theoretical shear strength of ice is about 14 x lO psi, while glaciers deform at stresses as low as 2 psi. However, a number of non-metallic crystals with high or rather high melting points are ductile at room temperature. Examples are NaCl, AgCl, and MgO. The critical resolved shear stress of NaCl is about only 100 psi, while the theoretical strength is about 10 x lO" psi. 

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