Influence of hydrostatic pressure and multiaxial straining on cavitating superplastic materials
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f 5 f0 exp (R«Me)
INTRODUCTION
SUPERPLASTIC materials have many potential applications, particularly in the aerospace industry.[1,2] The cavitation phenomenon, in which nucleation, growth, and coalescence of cavities occurs during deformation, can terminate the forming process.[3,4] These materials are able to tolerate quite large volume fractions of cavities before fracture, owing to their very high strain-rate sensitivities.[3,4,5] On the other hand, the superposition of a hydrostatic pressure during the forming process would appear to have the greatest potential for keeping the levels of cavitation low, by inhibiting the cavity nucleation and growth processes.[1,2,3] The constitutive equation for flow stress can usually be written as se 5 s0 « en «z em
[1] z where s0 is a material constant and se, εe, and εe are the effective flow stress, effective strain, and effective strain rate, respectively. The strain-hardening parameter n is essentially zero under superplastic conditions, and m is the strain-rate–sensitivity parameter. The flow stress-strain curves of cavitated superplastic materials are characterized by a strain softening up to strains corresponding to a 10 pct cavitation level; after that, the strain hardening that occurs is accomodated by a complex mechanism of cavity coalescence.[3,6] These flow curves may be looked upon as apparent ones, since their determination is based on the outside dimensions of the test specimen without any reference to the presence of the growing voids in the deforming material. Cavity growth during superplastic deformation is controlled by the effective plastic strain of the matrix material (εMe) surrounding the cavity.[4,7] For a given material tested under specific conditions, the basic relationship governing plasticity-controlled growth is[2–5,7]
MOHAMED ZAKI, Assistant Professor, is with the Department of Mechanical Design and Production, Faculty of Engineering, Cairo University, Giza, 12316 Egypt. Manuscript submitted March 18, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS A
[2]
in which the term f0 is the initial cavity volume fraction in the range between 2.5 3 1024 and 1.6 3 1022 for most superplastic materials,[8] and the term f is the total cavity volume fraction. The term R is the cavity growth rate, given by.[2] R 5 3/2
$ m m1 1 % sinh M
M
@~ 2
!{
2 2 mM 2 1 mM
#
[3]
Q/3 2 P/se}
where mM is the strain-rate–sensitivity parameter for the matrix material, P is the superimposed gas pressure, and Q is a geometric factor which equals 1 for uniaxial applied stress,[2] 2 for equibiaxial stress,[9] and =3 for plane strain.[9] Equation [3] clearly predicts that the cavity growth rate, for example, in uniaxial tension (Q 5 1), can be entirely prevented by superimposing a hydrostatic pressure equal to 1/3 of the applied stress. However, this prediction is not satisfied experimentally for most materials.[1,3,9] For a/b brass (63 pct a), Zaki[3] showed that superimposing a pressure greater than 0.4 of the flow stress is not sufficient to supress cavitation. Expe
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