Mobile dislocation density

Calculations of this type are carried out for fee, bcc, rock salt, and hep crystal structures and applied to precursor decay in single-crystal copper, tungsten, NaCl, and LiF [17]. The calculations show that the initial mobile dislocation densities necessary to obtain the measured rapid precursor decay in all cases are two or three orders of magnitude greater than initially present in the crystals. Herrmann et al. [18] show how dislocation multiplication combined with nonlinear elastic response can give some explanation for this effect. 

The shock-induced micromechanical response of <100>-loaded single crystal copper is investigated [18] for values of (WohL) from 0 to 10. The latter value results in W 10 Wg at y = 0.01. No distinction is made between total and mobile dislocation densities. These calculations show that rapid dislocation multiplication behind the elastic shock front results in a decrease in longitudinal stress, which is communicated to the shock front by nonlinear elastic effects [pc,/po > V, (7.20)]. While this is an important result, later recovery experiments by Vorthman and Duvall [19] show that shock compression does not result in a significant increase in residual dislocation density in LiF. Hence, the micromechanical interpretation of precursor decay provided by Herrmann et al. [18] remains unresolved with existing recovery experiments. 

The number of newly generated dislocation loops is directly proportional to the mobile dislocation density and also to the dislocation velocity. Hence the multiplication rate of mobile dislocations is given by... 

Assume the mobile dislocation density is and the Burgers vector is b. The plastic strain, according to Orowan s Law, may be given by ... 

Data from Choi et al. s [43] prior work on the same in situ CugSns composite solder joints showed substantially better creep resistance even under pre-aged conditions as shown in Fig. 10(a). These data points were obtained by unloading the specimen to obtain micrographs of a particular scratch placed on a solder joint to quantify the shear displacement. Recovery that can occur during these periods of interrupted unloading apparently reduces the mobile dislocation density available for deformation on reloading the sample. 

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