Computer simulation of low-temperature composites sintering processes for additive technologies

This is impact research of mixture raw components characteristics on the low-temperature composites structure formation during the sintering process. The obtained results showed that the structure determination of initial compacts obtained after thermal destruction of the polymer binder lets quantify the concentrations of main components and the refractory crystalline product of thermal destruction. Accounting for the distribution of thermal destruction refractory product allows us to refine the forecast of thermal stresses in the matrix of sintered composite. The presented results can be considered as a basis for optimization of initial compositions of multilayer low-temperature composites obtained by additive technologies.


Introduction
A relevant task is to research technological methods of sintering of multilayered low-temperature ceramic. Additive manufacturing technologies using these materials are distinguished by layer-bylayer material growth and subsequent sintering. The heterogeneity of particle sizes and the density of their packing during the formation of initial compacts are technological parameters of layers packing. And the formation of interlayer interfaces should be taken into account. The under study model structure of the initial compact should reflect the heterogeneity of concentrations and sizes of original powder components and pores in the consolidated layers and interlayer interfaces.
The computer modeling approach is developed to study the determining factors of low-temperature composites structure formation with considering the hierarchy of rheological processes in powder bodies and modification of hierarchically organized structures. The physical mesomechanic approach was taken in this research. It is combining the ideology and tools of solid state physics and mediums micromechanic with a structure. [1]. Local processes and materials characteristics are simulated based on the classical results.
The initial compact preparation regimes, low-temperature ceramics sintering, and the effect of structural-mechanical characteristics on residual strains in the sintered material are examined.
The initial compact of low-temperature ceramics is formed layer by layer from a mixture of components with certain porosity. Material matrix is forming during the composite sintering by the low-melting mixture raw components in a temperature lower than its melting point. The effective characteristics of the sintered ceramics are determined by the macroscopic structure of the initial compact, components and pores distribution and concentrations inhomogeneity of the phase and fractional initial components composition. The raw polydisperse mixture material of the initial compact refractory elements is presented by a set of particle sizes and volume fractions of each set in a mixture of refractory components. Coarse and microheterogeneous particles of the initial powder refractory components are different in sizes and referred as "large" particles because of ability to form the interacting particles power frame. Ultramicroheterogeneous refractory particles are attached to the dispersion phase forming and modifying its characteristics. The prediction of forming the refractory particles framework on macro-, meso-, or micro levels determines possibility to forecast the minimal sintered body porosity in accordance with the conditions for achieving mechanical contact of the fraction particles. It depends on the type of discrete distribution. The forming possibility of refractory components mixture frame at any structural level decreases with a local refractory components proportion decrease (and with increasing lowmelting component proportion). The forming possibility of refractory components frame at any indenture level makes a key contribution to the pore structure of the sintered sample formation [2].

Methods of modelling
Gas-phase decomposition products and a crystalline residue are forming during the binder's thermal destruction. The initial porosity of the green compact is increasing after removing the gasphase.
The crystalline residue of thermal destruction is an extra refractory phase in the sintered samples matrix. This leads to the appearance of thermal residual stresses in the matrix caused by the difference in the thermal expansion coefficients of the disperse compositions and the matrix. The following expression can be used from the position of thermo elasticity to estimate the residual thermal stresses in the sintered ceramic matrix: where Kglass(T) is the temperature dependence of the elastic bulk modulus of glass; βglass(T), βceramics(T), βSiO2(T) are the temperature coefficient dependences of thermal matrix and dispersed refractory components expansion; Cglass, Cceramics, CSiO2 are the volume concentrations of the matrix and dispersed refractory components; Tp is the temperature point of transition to an elastic stage, T0 is the initial temperature.
Calculation of residual thermal stresses should take into account the stage of viscoplastic stress relaxation when the sintered ceramics are cooled to laboratory temperature. In [3], it is proposed to introduce the temperature transition point of the material into the elastic state Tp in order to estimate the residual thermal stresses. The assumption is made of an abrupt transition to an elastic state, with allowance for which it can be assumed that in the temperature range from the sintering temperature to the temperature point of the transition, the temperature stresses relax to a negligible level. It is assumed that the transition to an elastic state stops the relaxation of residual stresses, and the evaluation of thermal stresses is possible from the position of thermoelasticity. For borosilicate glass we can use the temperature value Tp = 900 K, indicated in Figure 1 as the point of transition to the elastic state.
The type of the residual stresses (tensile or compressive) is determined by numerator signs in integrand in the temperature range Tp -T0. It is assumed that for temperature values T ≥ Tp the values of temperature stresses σT ≈ 0.

Results and discussion
Numeric evaluations were made using the component's material characteristics in [4][5][6][7]. The sintered ceramic sample model structure forming conditions were examined. The initial compact is formed by three successively applied layers. Two compositions of the initial mixture, differing in the mass content of components are considered to study the factors determining thermal stresses in the matrix of sintered composite.    The local tensile stresses are observed in interlayer interfaces (areas bounded by thin lines). The presence of significant tensile stresses exceeding the strength limit can cause defects and cracks in model composite matrix. As follows from the results shown in Figure 2, it is possible to change residual stresses ranges and to accomplish the strength criteria by varying the mass fraction balance. The tensile stresses for composition (b) in the interlayer interface are 2 times less than for the composition in (a). In addition, the significant local compressive thermal stresses in the ceramics sintered from composition (b) are predicted in the deposited (additive) layer, which prevent the development of defects.

Conclusion
The computer simulation of binder thermal destruction, which is the initial stage of composite sintering process, makes it possible to obtain a prediction of the sintered samples structure and residual thermal stresses.
Analysis of the results shows the possible appearance of both tensile and compressive quantities of residual stresses in the matrix of sintered ceramics. This can lead to destructive or hardening effects in the resulting products. Changing of value and residual stresses sign in the sintered material is possible by optimizing the concentration composition of initial compact components.