Abstract
Under many conditions, hot isostatic pressing (HIP) of metallic or ceramic porous preforms occurs by the densification of a shell at the surface of the preform, which then thickens until the whole sample is fully densified.[2,4] The development of such a dense shell reduces the effective pressure acting to densify the remaining porosity. Furthermore, this pressure difference can lead to anisotropic creep of the shell, and this may be a contributary cause of shape change of samples during HIP. The stresses occurring during cooling of the sample and the residual stresses are calculated as a function of all of the various material and pressing parameters. It is found that, in many cases, the cooling stresses which are tensile at the surface may well be large enough to cause cracking in ceramic samples.
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Abbreviations
- A :
-
Dorn constant
- a s :
-
thermal diffusivity of solid (m2 s−1)
- b :
-
Burger’s vector (m)
- δD B :
-
boundary diffusion coefficient times boundary thickness (m3 s-1)
- D C :
-
core diffusion coefficient (m2/s)
- Di :
-
initial relative packing density
- D ν :
-
lattice diffusion coefficient (m2/s)
- D eff :
-
effective diffusion coefficient (m2/s)
- d :
-
grain size (m)
- E :
-
elastic modulus (Pa)
- K :
-
reducing rate of surface temperature (K/S)
- n :
-
creep exponent
- P :
-
HIP pressure (Pa)
- P i :
-
inner pressure (Pa)
- P s :
-
maximum HIP pressure (Pa)
- P o :
-
atmospheric pressure (Pa)
- Q b :
-
activation energy of boundary diffusion(J/mol)
- Q ν :
-
activation energy of volume diffusion(J/mol)
- R o :
-
outer radius (m)
- R j :
-
inner radius of solid shell (m)
- R mo :
-
initial radius of the cylinder (m)
- r :
-
radius coordinate (m)
- T :
-
temperature (K)
- T m :
-
melting temperature (K)
- Ts :
-
HIP temperature (K)
- T o :
-
room temperature (K)
- U r :
-
displacement in radial direction (m)
- έ Cr :
-
radial creep strain rate (s−1)
- έ dr :
-
radial densification strain rate (s−1)
- α s :
-
coefficient of linear thermal expansion of solid material
- α p :
-
coefficient of linear thermal expansion of porous material
- μ :
-
shear modulus (Pa)
- μ 0 :
-
shear modulus at 0 K (Pa)
- ν :
-
Poisson’s ratio
- σ *,έ * :
-
equivalent stress (Pa) and strain rate
- σ r,σ θ :
-
stresses (Pa)
- σ zέr, έθ έ j :
-
strain rate
- Ω:
-
atomic volume (m3)
References
J. Besson and M. Abouaf:Proc. Int. Conf. on Hot hostatic Pressing of Materials, The Royal Flemish Society of Engineers, Antwerp, Belgium, 1988, p. 17.
W.-B. Li, M.F. Ashby, and K.E. Easterling:Acta Metall., 1987, vol. 35 (12), pp. 2831–42.
R. McMeeking: Materials Program, University of California-Santa Barbara, private communication, 1990.
W.-B. Li and K.E. Easterling:1st Int. HIP Conf., Luleå, Sweden, 1987, pp. 97–105.
Raymond J. Roark and Warren C. Young:Formulas for Stress and Strain, 6th ed., McGraw International Book Company, New York, NY, 1989.
H.S. Carslow and J.C. Jaeger:Conduction of Heat in Solids, Oxford University Press, Oxford, United Kingdom, 1959, ch. 7.
H.J. Frost and M.F. Ashby:Deformation—Mechanism Maps, Pergamon Press, Oxford, U.K., 1982.
A.S. Helle, K.E. Easterling, and M.F. Ashby:Acta Metall., 1985, vol. 33 (12), pp. 2163–74.
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Li, W.B., Easterling, K.E. & Ashby, M.F. Instantaneous and residual stresses developed in hot isostatic pressing of metals and ceramics. Metall Trans A 22, 1071–1078 (1991). https://doi.org/10.1007/BF02661100
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DOI: https://doi.org/10.1007/BF02661100