A moving crack is a crack that propagates with some speed due to loading and unloading of a metal work material. When loading and unloading is being done, a large fraction of irreversible energy associated with those actions is eventually dissipated as heat and other part is being stored in the work material due to change in material structure and constraints caused dislocation pile-ups, etc. The fraction of heat dissipated in material (
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Heat generation and temperature increment
In general, the amount of loading and unloading energy which is converted into heat is for unit volume having high value. So this large value of heat generation per unit of volume results in substantial rise in temperature of the tip of the moving crack. This temperature rise can be of several hundred degrees Celsius as found in experiment done by Mason and Rosakis and others. The process region near tip of moving crack is the zone for maximum temperature.
Temperature measurement
Mostly, for measurement of temperature at tip of moving crack mode-I of fracture is being preferred. But maximum temperatures are expected for other two modes-(I, II)of fracture due large deformations with shear banding, particularly with high confining pressure, where impact generated shear bands is due to the impact load itself. According to a study by Zhou et al. and Rosakis et al.(1997) on impact produced shear bands of mode-II gives a result of temperature rises of over 1650 K for C-300 steel. These temperatures are being measured by special purpose high precision thermocouple.
Mathematical formulation of temperature of moving crack tip
If one applies the cell model of material and given total energy supply as
where
Revising this for conduction using the moving crack tip governing equation for heat conduction for the upper half of the crack (
where
where,
Using the final equation of