Plastic Flow and Energy Dissipation

It is assumed that plastic flow occurs by the creation and motion of dislocations. The classical approach to dislocation motion holds that thermal fluctuations help carry the dislocations over the lattice potential barriers [13,14]. However, at normal temperatures the thermal fluctuations occur at rates of only lO rad/s to perhaps 10 rad/s while the dislocations responsible for the plastic wave due to shock or impact travel at speeds from about. 1 km/s to 10 km/s depending on the amplitude of the shock or impact. These dislocations must encounter and overcome the lattice potential barriers at rates often in excess of 10 rad/s [15]. Thus, energy transfer to the dislocations by thermal fluctuations occurs at rates at least two to three orders of magnitude slower than needed to overcome the lattice potential barriers and support the plastic wave component of a shock or impact. 

In order to overcome the difficulty that thermal processes cannot support the plastic wave due to a shock or severe impact, it has been suggested that dislocation motion occurs by quantum tunneling [15,16], The dislocation velocity, v(i, U), can be written as 

b is the Burgers length appropriate to the crystal, Pc(i) is the probability of creating a dislocation with the available shear stress energy and the quantity / o is the average thickness of the dislocation source. Ns is the number of active dislocation sources whose dislocations appear on the crystal surface and has dimensions of (length) l 

It is often convenient to let Ns = sAw-/) where s is the number of dislocation sources whose dislocations intercept the shear region of width w and length /. Equation (4) reduces to 

If the dislocations do not cross slip onto other slip systems but project directly onto the shear surface, then w = Z q. 

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