Mechanical threshold stress

Two examples of path-dependent micromechanical effects are models of Swegle and Grady [13] for thermal trapping in shear bands and Follansbee and Kocks [14] for path-dependent evolution of the mechanical threshold stress in copper. 

The mechanical threshold stress has a straightforward micromechanical interpretation for pure materials... 

The mechanical threshold stress determines the applied stress necessary for substantial thermal activation. The quantity = 7.0 eV for OFE... 

The variation of r and f through 3.0 GPa and 5.4 GPa shock waves is shown in Fig. 7.7 [38]. This figure shows clearly that the shock-wave path is in the dislocation drag regime (r > f). The mechanical threshold stress f increases from 10 MPa to 80 MPa in the 5.4 GPa shock thus from (7.37)... 

Figure 7.7. Shear stress and mechanical threshold stress for 3.0 GPa and 5.4 GPa shock waves in copper.

The lone remaining aspect of this topic that requires additional discussion is the fact that the mechanical threshold stress evolution is path-dependent. The fact that (df/dy)o in (7.41) is a function of y means that computations of material behavior must follow the actual high-rate deformational path to obtain the material strength f. This becomes a practical problem only in dealing with shock-wave compression. 

P.S. Follansbee and U.F. Kocks, A Constitutive Description of the Deformation of Copper Based on the Use of the Mechanical Threshold Stress as an Internal State Variable, Acta Metall. 36, 81-93 (1988). 

D.L. Tonks and J.N. Johnson, Shock-Wave Evolution of the Mechanical Threshold Stress in Copper, in Shock Compression of Condensed Matter (edited by S.C. Schmidt, J.N. Johnson, and L.W. Davison), Elsevier Science, Amsterdam, 1990, pp. 333-336. 

P.S. Follansbee, U.F. Kocks A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable. Acta Mater. 36(1) 81-93 (1988)... 

Probably the most plausible explanation for the scatter of the creep parameters is based on a single mechanism involving GBS with a threshold stress (Oq).7,10,13 When a threshold stress is introduced into the creep equation (16.1), all the creep parameters in YTZP become n = 2, p= 2 and Q= 460 kJ/mol whatever the stress or temperature of the test. The value of this ct0 was found experimentally 13... 

To construct such a map (see Worked Example 12.4), SCG and creep rupture data must be known for various temperatures. The temperature dependence of the stress levels required to result in a given lifetime are then calculated from Eqs. (12.45) and (12.46). The mechanism that results in the lowest failure stress at a given temperature thus defines the threshold stress or highest applicable stress for the survival of a part for a given time. In other words, the lifetime of the part is determined by the fastest possible path. Such maps are best understood by actually plotting them. 

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