PSI - Issue 40

I.Yu. Smolin et al. / Procedia Structural Integrity 40 (2022) 385–391

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I. Yu. Smolin et al./ Structural Integrity Procedia 00 (2022) 000 – 000

1. Introduction Internal thermal stresses are caused by volumetric changes in the material when the temperature decreases or increases. In homogeneous solid products, they can occur due to the uneven cooling of the external and internal zones, and in heterogeneous or composite materials, they can additionally appear due to the difference in the thermal expansion coefficients of the heterogeneities or the composite constituents. Thermal stress can play a positive and negative role, either leading to cracking of the material in the case of tensile stresses or restraining the growth of cracks in the case of compressive stress. Therefore, the analysis of internal thermal stress is very important both in the process of producing composites and in the process of their operation when the temperature changes. In recent years, ultra-high-temperature ceramic materials designed for the thermal protection of various products have attracted considerable interest. Such ceramics can act as components in layered composites or functionally graded materials. The presence of several layers in such materials with different values of thermal conductivity coefficients makes it possible to effectively solve not only the problem of thermal protection but also other problems, such as increasing the mechanical strength or chemical resistance (Bayati Chaleshtari et al., 2020; Bermejo et al., 2007). But the differences in the coefficients of thermal expansion that exist in this case can cause sufficiently large tensile internal stresses. According to the available estimates, the alternation of layers in layered composites leads to the appearance of compressive and tensile stresses on different sides of the interface (Bermejo et al., 2007; De Portu et al., 2005). As was noted above, compressive stresses perform a positive function, restraining the growth of the cracks, but negative stresses are dangerous for provoking the formation of new cracks and the growth of existing ones. The choice of the composite constituents and the shape of the products can significantly affect the quantitative values of the resulting internal stresses. So, in addition to qualitative results on the level and signs of thermal stresses, the quantitative assessment of internal thermal stresses in products made of composites of a particular composition is of great interest in engineering practice. The aim of this work is to analyze the internal stresses in a disk-shaped sample of a five-layered ceramic composite consisting of ZrB 2 – 20% SiC layers with various additives of ZrO 2 when it cools down from the sintering temperature to room temperature. The influence of taking into account the temperature dependence of the composite constituents' properties on the simulation results and the estimation of tensile stress dangerous for ceramics cracking is of particular interest.

Nomenclature E

Young's modulus bulk modulus

K T

temperature

the temperature of the undeformed state ambient temperature (room temperature) specific heat capacity at constant deformation

T 0 T r

c k q r

thermal conductivity coefficient

heat flux

radial coordinate

time

t

the component of the displacement vector along r -axis the component of the displacement vector along z -axis

u r u z

axial coordinate

z α β

linear coefficient of thermal expansion heat transfer (surface film) coefficient

δ ij ε ij

Kronecker delta

strain tensor components Lamé's first parameter

λ μ

Lamé's second parameter (shear modulus )