Effects of the Laplace pressure during sintering of cylindrical specimens

In the last decades, powder technology has become one of the most important technological processes for the production of metallic and ceramics components; free sintering, hot isostatic pressing and hot forging are different ways to realize a key-phase in which the primary mechanical properties of the final material are obtained. A theory of sintering is necessary in order to be able to predict the final structure of a body undergoing such a kind of process. In this respect, it is crucial to be able to follow the evolution of the mechanical properties of the material (determined by this structure) during sintering and to get the final features of the compound at the end of this process. In this thesis, the influence of the pressure called “sintering stress” or “Laplace pressure” produced by the gas employed during the process and which gets trapped into the pores is analyzed. This is done for pre-compacted (micro/nano)-powdered axially-symmetric samples undergoing (i) isostatic pressing (also covering the case of free sintering), (ii) "free" forging (i.e. axial compressive load acting at the top and bottom faces of the specimens, with no lateral confinement) and (iii) constrained forging (i.e. transverse compression of the samples in a rigid die). Such cases are among the ones suggested in Olevsky, E.A., Molinari, A., “Kinetics and stability in compressive and tensile loading of porous bodies”. The role of the Laplace pressure in all of the mentioned cases is twofold. First of all, such a pressure influences the evolution of the porosity and, for instance, its residual value for a given time duration of the process. It is worth emphasizing that threshold pressures below which the sintering stress is actually not negligible are determined in this thesis; the duration of the process is indeed heavily affected by such a stress. In turn, such a duration would be underestimated otherwise. Furthermore, industrial processes often entail loading pressures lower than the thresholds mentioned above, especially of "small" grain sizes. The second aspect is based on a common feature exhibited by the two modes mentioned above: the loading parameter may be tuned in such a way that, at some stage of the sintering process, its value may equate the Laplace pressure, leading to a constant value of the porosity. Whenever this is the case, for (i) there exists a whole range of the loading parameter for which the process is actually unstable. Henceforth, in order to have stability of sintering either the loading parameter must be high enough with respect to the Laplace pressure or zero, leading to (stable) free sintering. For (ii), the stability analysis shows that the results obtained by using the different models for the shear and bulk moduli do not agree for a restricted range of external load. This is of course an intrinsic pathology of his specific loading mode. Moreover, it is worth noting that large strains occur in such a mode. Thus, both the stress and the (infinitesimal) strain employed in this analysis should be replaced by appropriate (possibly work-conjugate) choices of the stress and strain measures, although this goes beyond the aim of this work. For (iii), a stability analysis allows us to conclude that such a value represents a critical threshold, below which the sintering process cannot proceed. In the second part of the present work, the mechanical behavior of sintered specimens are investigated. Such a behavior is strongly influenced by the stress state at the end of the process, which depends on the final value of the interstitial pressure and of the loading mode used during the process. For the sake of simplicity, only the two "realistic" cases of isostatic pressing (also covering free sintering) and constrained forging are considered. For such components, isostatic pressing may induce isotropy, whereas constrained forging processes may enforce a transverse isotropic behavior in the direction of forging. Although for prestresses isotropic material the explicit constitutive law is given by Man in “Hartig's law and linear elasticity with initial stress”, the analog for the case of transversely isotropic material is deduced here, for the first time, through a method, suggested by Weiyi , “Derivation of the general form of elasticity tensor of the transverse isotropic material by tensor derivate”, based upon the partial differentiation of the strain energy with respect to both the strain tensor and the residual stress. Finally, the residual stress tensor for specimens sintered through (i) and (iii) is obtained and the correspondent stress response is deduced. Equivalent material constants (two constant in the case of isotropy, five in the case of transverse isotropy) arising in the presence of prestress may be introduced; such constants take the place of the classical material moduli characterizing the response in the absence of residual stresses. Finally, an experimental procedure to determine the values of such constants is proposed.