An analytical model of thermal mechanical stress induced by through silicon via

We present an accurate through silicon via （TSV） thermal mechanical stress analytical model which is verified by using finite element method （FEM）. The results show only a very small error. By using the proposed analytical model, we also study the impacts of the TSV radius size, the thickness, the material of Cu diffusion barrier, and liner on the stress. It is found that the liner can absorb the stress effectively induced by coefficient of thermal expansion mismatch. The stress decreases with the increase of liner thickness. Benzocyclobutene （BCB） as a liner material is better than SiO2. However, the Cu diffusion barrier has little effect on the stress. The stress with a smaller TSV has a smaller value. Based on the analytical model, we explore and validate the linear superposition principle of stress tensors and demonstrate the accuracy of this method against detailed FEM simulations. The analytic solutions of stress of two TSVs and three TSVs have high precision against the finite element result.

Transient thermal cracking associated with non-classical heat conduction in cylindrical coordinate system

This paper studies the fracture behavior of a thermoelastic cylinder subjected to a sudden temperature change on its outer surface within the framework of non-classical heat conduction.The heat conduction equation is solved by separation of variable technique.Closed form solution for the temperature field and the associated thermal stress are established.The critical parameter governing the level of the transient thermal stress is identified.Exact expression for the transient stress intensity factor is obtained for a crack in the cylinder.The difference between the non-classical solutions and the classical solution are discussed.It is found that the traditional classical heat conduction considerably underestimates the transient thermal stress and thermal stress intensity factor.

Thermal characteristics and thermal stress analysis of solar thermochemical reactor under high-flux concentrated solar irradiation

Nowadays, using a solar-driven thermochemical reaction system to convert greenhouse gases into high-quality liquid fuels has been proven to be an effective way to address the growing depletion of traditional fossil fuels. However, the utilization of highlyconcentrated solar irradiation runs the high risk of reactor damage issues resulting from thermal stress concentration, which seriously threatens the security and reliability of the total reactor system. In this study, the thermal radiation distribution and thermo-mechanical process in a volumetric reactor were numerically investigated by combining Monte Carlo ray-tracing method with computational fluid dynamics method. Based on the experimental results and thermal characteristic analysis, the formation mechanism of thermal stress concentration and the strategies of improving thermal stress distribution were discussed in detail.The simulation results indicate a great possibility of reactor damage at about 1000℃ operating temperature and 9.0 k W lamp power, which is well-matched with related experimental results. The ceramic damage typically occurs at the inner edges of the through-holes, including the aperture, the gas inlet, and the thermocouple hole, then extends along the lines connecting these holes and finally causes brittle fracture. By reasonable control of the opening direction and the distance between the throughholes, the maximum compressive stress can be reduced by 21.78%.