Analysis of stresses during the freezing of solid spherical foods

An analytical model is presented to calculate thermal stresses and strains during the freezing of a spherical food, taking into account both the expansion during phase change and subsequent thermal contraction due to temperature decrease. The Young modulus and Poisson ratio are assumed to undergo a step change at the freezing point. The expansion due to phase change cause a uniform and virtually constant isotropic tensile stress in the unfrozen core. In the frozen shell, this expansion gives rise to tensile radial stress and compressive tangential stress. The thermal contraction subsequent to phase change causes reverse effects, i.e. uniform compressive stress in the unfrozen core and compressive radial stress in the frozen shell, while tangential stress is tensile on the outside and compressive on the inside of the frozen shell. The effect of thermal contraction is noticeable only at cryogenic temperatures.