Failure Criteria for Sapphire Anvils
Photograph of sapphire ball bearings, courtesy of Bloesch.
|
Sapphire PropertiesThe mechanical properties of single crystal sapphire are very difficult to measure due to its extremely brittle nature. Sapphire exhibits very low fracture toughness and hence, lacks in ductility. This means when load is applied, only minimal plastic deformation can occur causing large stresses to build up around the microscopic flaws within the material’s lattice structure. This is a particular concern when trying to measure its tensile strength using traditional methods as catastrophic brittle failure readily ensues. Thus, a variety of less conventional methods have been used to find sapphire’s critical mechanical properties giving a wide range of values for each property – i.e. sapphire’s critical parameters are not well defined. Thus, for the purpose of this thesis, suitable and reliable values from these ranges have been chosen for single crystal sapphire’s following three properties: the ultimate tensile strength, ultimate compressive strength and critical shear strength (see table below).
|
|
Critical PropertiesAnvil FailureIt is assumed that once the tensile, compressive or tensile stress within the sapphire anvil exceeds its critical value then failure is more than likely occur. The appropriate stresses under working conditions can be accurately calculated using the Finite Element Analysis Method.
In practise, failure of the sapphire anvil may occur well before the critical stress values are reached due to the following reasons:
Failure may also occur due to other reasons not considered in this thesis' analysis:
However, this thesis study will be concerned only with the failure of pure single crystal sapphires under proper first-time working conditions. The criteria for failure is the exceeding of the critical value for tensile stress, compressive stress or shear stress presented above. |