Download AHMED-DISSERTATION

Texas Tech University, H. S. Tanvir Ahmed, December 2010
stress σ for bow-out of an edge dislocation from Frank-Read source in the slip planes
is expressed as [59]:
σ=
0.36Gb   L 

ln   − 1.653 

L  b

(1.22a)
σ=
0.36Gb  L  0.59508Gb
ln   −
L
L
b
(1.22b)
where, G is the shear modulus of rigidity and b is the Burger’s vector. The constant
1.653 at the end of expression arose following the assumptions of edge dislocation and
a Poisson ratio of 0.33. Activation volume V equals Lb2 for dislocation based
deformation [26]. Relationship between activation volume and strain rate sensitivity is
originally proposed by Cahn and Nabarro [60] and is given by:
m=
3kT
V ⋅σ f
(1.23)
where, k is Boltzman constant (8.62×10-5 eV/K), T is temperature (K) and σ f is the
flow stress. The constant of
3 originates from assuming Von Mises criterion for
yielding and hence, converting the original expression of shear mode of deformation
to tensile mode of deformation. Using equation (1.22) and (1.23), the final relationship
between m and V is given as below:
0.5
1.5

3kT  L    L3 
m=
ln
−
1.653


 
 
0.36G  V    V 


The general relationship can be given as:
26
−1
(1.24)