Equilibria in earthquakes and metal forming
Equilibrium is usually defined as a steady state in which a reversible chemical reaction is producing products (C and D) at the same rate that it is producing ‘reactants’ (A and B) such that the concentrations of all the components in solution remain constant. Chemical equilibrium applies equally to solids undergoing chemical changes such as rocks, the metals in car frames and semiconductor chips. Furthermore, in all these examples, the solid is simultaneously subjected to mechanical stresses. Although the fundamentals of equilibrium were described 150 years ago, the particular case of chemical equilibrium of solids under conditions of mechanical stress were problematic then and today continue to be an open area of research. European researchers initiated the ‘Precipitate elastic stress states’ (PRESS) project to investigate the special case of chemical reactions in which a precipitate (solid compound produced from a liquid) is formed on a non-hydrostatically stressed crystal in solution. Under these conditions, non-hydrostatic stress tends to deform a material and potentially change its properties without changing its volume (an elastic change). The scientists aimed to investigate whether or not the stress state of the precipitate and induced cracks could be used explicitly in modelling non-hydrostatically stressed crystals in contact with solution. The PRESS team confirmed that the stress state of the precipitate could be described by a single parameter (dc) representing critical thickness and that a non-hydrostatically stressed crystal, if sufficiently large, would always yield a smooth stress-free interface with the solution (a skin). A novel diffuse interface model incorporating chemical and mechanical equilibrium and their coupling was developed to study crack formations on length scales larger than dc during irreversible, coupled mechanical and chemical interface propagation in liquids and solids. PRESS project results are important to a wide variety of fields including physics, earth and geological science and materials science, and could enhance understanding of materials behaviour in diverse systems from those generating seismic events to electronic devices.
