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Kinetic modelling of thermal de-binding and sintering of pure Cu, Fe12Cu and W8Ni2Cu
Wolfgang Hohenauer, Daniel Lager and Ijaz Ul Mohsin
The prediction of the final shape of sintered parts, the estimation of stress during the sintering process or the design of production relevant technological conditions is of great technological and economic concern. During the technological treatment chemical composition, morphology solid state phases, and sometimes even the state of aggregation change. Thus, it makes sense to emanate from a processing material, and to search for a method describing the sequence of material states and the correlated material properties as well.
Appropriate material laws to describe de-binding and sintering are still not known. However, thermo-kinetic modelling enables the mathematical description of a succession of process steps. Subsequently, consecutive reactions as well as branch reactions can be applied to formal kinetic models. Thus, based on the measurements of thermal mass and thermal expansion/ shrinkage, formal kinetic models for de-binding and sintering will be formulated. Model free data analysis (Friedman analysis) is used to classify reaction steps and reaction types, and to estimate initial kinetic parameters for subsequent kinetic modelling as well. The final optimum kinetic model is obtained iteratively from a non-linear, multivariate regression – fitting the measured curves by optimizing the specific parameters of the describing functions – but strictly related to the assigned reaction types and justified by stringent phenomenological assumptions.
The methodology shows how to construct, formulate and optimize thermo-kinetic models to describe de-binding and sintering of three different copper alloys. They represent three different variants of sintering technology: solid state sintering, transient liquid phase sintering, and persistent liquid phase sintering. The resulting thermo-kinetic models represent so called “implicit material laws”. The specific kinetic parameters are given. Correlation coefficients k > 0,9999 are achieved. The models are confirmed experimentally and technologically as well and they were successfully used to predict parameters for rate controlled production processes. In a follow up publication elsewhere in this issue (Hohenauer W, Lager D, Mohsin IU, Improvement of thermo-physical data od pure copper, Fe12Cu and W8Ni2Cu during and after sintering using kinetic modelling) these models are used to examine thermo-physical data from measurements under optimum laboratory conditions but mapped on the specific transient histories as materials will meet under production conditions.
Keywords: Kinetic modelling, de-binding, sintering, solid state, liquid state sintering, persistent liquid state sintering, rate controlled process.