mong the quantities of basic interest to the development of the theory of crushing are: the work input to the fractured material, the new area formed, and the change in thermodynamic state of the fractured material. The relationships between these variables were among the objectives of a research program at the University of Minnesota and were studied by crushing single and multiple particles of quartz and glass. Drop-weight (Heney,1 951; Johnson and others,1 949), slow compression (Axelson and Piret, 1950; Kenny,1957), and calorimeter-dual pendulum( Zeleny,1 957), devices were used to determine the work input to a sample. The new surface area was measured by the B.E.T. gas adsorption technique (Brunauer and others, 1938) using ethane. Since glass and quartz may be considered to be perfectly elastic, the thermodynamic state of the crushed material was determined by its temperature and surface area.One relation between the above mentioned variables was obtained by an energy balance about a sample for a crushing process in which the initial and final temperatures and external pressures were equal. By neglecting sound, electric, and other minor energy terms, the following equation was obtained: Equation (1) (Available in full paper)
The surface energy s8 is a non-equilibrium value because the surface was formed under non-equilibrium conditions. Due to the imposed conditions of equal initial and final temperatures and external pressures, the deformation energy change, ¿ D8, equals the internal energy change of the sample. In the case of quartz and glass, ¿ D8=0 and Equation1 simplifies to : Equation (2) (Available in full paper)
In the drop-weight studies, the relations between W8 ¿ A and were determined for single and multiple particle crushing. Estimates of Q8 were also obtained in some of the slow compression experiments. In the calorimeter dual pendulum studies Q8 and ¿ A were determined the, order of magnitude of s8 was established, and in addition, it was possible to calculate the energy lost to permanent plastic deformation of the metal crusher surfaces.
EXPERIMENTAL
Drop-weight CrusherThe drop-weight device consisted of a steel mortar with a close fitting plunger. A bed of particles or a single particle was placed in the mortar cavity and pressure was applied to the plunger by dropping a steel bail on the plunger top when the mortar rested on a steel base. The energy input, W8, was equal to the potential energy change of the steel ball minus corrections for energy losses within the steel parts of the crushing assembly.
Slow-compression CrusherIn Axelson's work (1950) the mortar-plunger device was used to contain the sample, and pressure was applied by placing the crusher assembly between the jaws of a hydraulic press. The energy input was calculated from force measurements on the piston and its movement with appropriate corrections for elastic deformation of the steel.In the experiments by Kenny (1957), the sample was simply placed between the jaws of the press, and a piece of plastic tubing around the sample prevented sample loss during fracture.
