Thermal Stresses From Large Volumetric Expansion During Freezing of Biomaterials

Abstract

Thermal stresses were studied in freezing of biomaterials containing significant amounts of water. An apparent specific heat formulation of the energy equation and a viscoelastic model for the mechanics problem were used to analyze the transient axi-symmetric freezing of a long cylinder. Viscoelastic properties were measured in an Instron machine. Results show that, before phase change occurs at any location, both radial and circumferential stresses are tensile and keep increasing until phase change begins. The maximum principal tensile stress during phase change increases with a decrease in boundary temperature (faster cooling). This is consistent with experimentally observed fractures at a lower boundary temperature. Large volumetric expansion during water to ice transformation was shown to be the primary contributor to large stress development. For very rapid freezing, relaxation may not be significant, and an elastic model may be sufficient.