Constraining Effect in Presence of Vacancies Flux During Sintering of Biporous Bodies

摘要

The main object of paper - is the computational study of porous billets behaviour during the both free and constrained sintering. It is supposed that porous body analyzed below contains pores of two different sizes. The special attention in the given consideration is paid to evolution of different kinds of pores for cases: vacancies flux is ignored and taken into account. There is considered the behaviour of porous body in condition when the shrinkage in some directions is restricted (constraining). The analysis below is based on Theological model of biporous body created in [1]. The presence of external forces and kinematical constraints is known to change the passing of sintering essentially. In particular it causes a macroscopic non - homogeneity of shrinkage [2], [3]. As the result the distribution of density after the sintering is non - uniform even for cases when the non - uniformity of the given field after preliminary compaction can be neglected. Moreover, despite the increase of mean density, in some sections of billets one can see the growth of porosity. Attempts to explain these phenomena in the framework of well-known physical models appeared to be vain. They usually are aimed at the description of behavior of only some structural elements within the body, whereas such macroscopic aspects of sintering as non - uniformity of density fields are remained beyond the consideration. In turn, well - known continuum conceptions of the sintering, as a rule, are not sensitive to peculiarities of vacancies transfer and the nature of driving forces of shrinking. Meanwhile, they seem to be rather effective to describe such phenomenon as the density non - homogeneity caused, in particular, by constraining and external friction. Therefore the most preferable approach to the main problem declared above is the extension of continuum consideration to a sintering process developed particularly in [2], [6], [7], and [8]. It should be also remembered, that the main point of continual interpretation of the consolidation processes in Powder technologies - is the formulation of internal parameters of macroscopic model, which describe the current state of porous billet. The most widespread models are connected with the use of the only parameter - porosity. It can be interpreted on the local level within the framework of continual approach (namely is being connected with small volume of porous body, which, in turn, can be identified with some point of porous continuum).