| |
· For "hot forming," (T/ Tm) > 0.5, and there is little work hardening but a strong strain rate dependence of the required stress modeled by:
σ = C(dε/dt )m , where m is the strain rate sensitivity exponent.
· The exponent, m, is dependent on the homologous temperature. For many metals m has a value of 0.01 at (T/ Tm) = 0.2 and goes towards 1.0 as
(T/ Tm) -> 1.
· Neck formation during this high temperature deformation of fine grained alloys depends upon the value of m, and for 0.9 < m < 1.0 neck formation does not occur.
· In this deformation mode: σ= (F/ Ai) = C(dε/dt )m , where Ai is the instantaneous area, also: (dε/dt) = (1/L){dL/dt} = - (1/A){dA/dt} .
· This gives: {dA/dt} = - (F / C)(1/m){1/A[{1 - m}/ m ] }, which, for m = 1, is independent of A. No neck forms and Α0Λ0 = A1Λ1.
|
|
|
