Micronecking and fracture in cavitated superplastic materials
- PDF / 312,916 Bytes
- 4 Pages / 594 x 774 pts Page_size
- 71 Downloads / 193 Views
I.
INTRODUCTION
SUPER_PLASTIC materials are considered as a very important class of materials for metal forming processes because of their high ductilities, v-q Cavitation occurs during hot plastic deformation, where the deformation is terminated at an early stage in the process due to nucleation, growth, and coalescence of cavities, v~l In the case of superplastic deformation, materials are able to tolerate very large volume fractions before fracture occurs owing to their very high strain-rate sensitivities, t41 Jonas and Baudelet[61 and, more recently, Ragab and Zaki t71 demonstrated that generation of spherical cavities during deformation increases the tendency toward tensile instability by reducing the effective values of the strain-rate sensitivity and the work-hardening coefficient. Another approach is proposed by Stowell, I81who correlates superplastic elongation in uniaxial tension to cavity growth by considering an arbitrary criterion for specimen failure based on cavity growth rate and geometrical coalescence without taking the effect of strain-rate sensitivity into consideration. Two main mechanisms of cavity growth are now firmly established: vacancy diffusion controlled growth and plasticity controlled growth. These two mechanisms, which are not wholly independent, are microscopically modeled in several works, t9.~~ The latter mechanism dominates the deformation under most superplastic conditions, except for very small cavities and low strain rates, t'~ The basic relationship for plasticity controlled growth is
dV/dt = RVi~
[11
where V is the volume of the cavity (V = 7rr3/4, r is the cavity radius), R is the cavity growth rate parameter, and is the remote strain rate. Values of the parameter R were determined theoretically by several investigatorsY ~.~3.141Based on the slab model illustrated by Cocks and Ashby, ~3] Stowell ]j~ predicted for uniaxial tension and for small volume fraction (i.e., noninteracting voids) of spherical voids, the following expression for R: R = 3/2 (m+l/m) sinh [2(2-m)3(2+m)]
The parameter R thus decreases as the strain-rate sensitivity index, m, increases, yielding a value of 1.85 for a value of m = 0.5. Other data are available in the literature in which void growth is treated as a problem in continuum plasticity. One example is that of Rice and TraceyV41 for a rigid perfectly plastic matrix with 1/m tending toward infinity. They predict for a spherical isolated void in a perfectly plastic material obeying von Mises criterion R = 3[0.558 sinh (30-m/20"~) +0.008 /X cosh (30-m/2~.)
where o m is the mean stress, ~ is the effective stress, and /x = -3/~/(~i - 4) knowing that ~i > ~ > 4. The value of R is evaluated as 0.9 for uniaxial tension. Experimental values of R may depend on strain, strain rate, grain size, and temperature, and for two-phase alloys, R is a function of the harder phase volume fraction.t3,15J These values are found to be close to 2 for most superplastic alloysJ ~ 5,s~ Lian and SuerytS] investigate the effect of both strain-rate sensitivity and cavity
Data Loading...
