The relationship between the crushing strength of brittle materials and the size of cubical specimens tested

Cubes of coal have been tested in compression in the past, and it has been found. that the following formula, relating the compressive strength to the size of the cube can be applied:

P = k .a- n

Where P is the compressive strength in pounds per square inch. a is the edge dimension os specimens tested. n is a constant. k is a constant.

The value of n has been found by a majority of people working on coal to be 0.5, however, lower values have also been found.

In this study limestone shale and Plaster of Paris cubes, varying in size between one and three inches, and one and five inches in the case of shale, were tested in compression. The results were converted to logarithmic form, and the value of n determined for each material. It was found for the limestone and the Plaster of Paris that the value of n was close to zero over the range of sizes tested, indicating that the strength is independent of the size of the spec1men over the range one inch to three inch cubes. A value of 0.20 was found for the shale over the range one inch to five inches.

The Griffith crack theory of failure gives the following result:

P = k.c -0.5

Where P is the compressive strength in pounds per square inch. 2c is the length of cracks in the material. k is a constant.

Thus, depending upon the relationship between c and a, the Griffith theory predicts that the value of n should be 0.5 for cracked materials where the length of crack is directly proportional to the edge dimension of the specimen, and zero where the length of crack is independent of the edge dimension of the specimen, in relatively uncracked materials. The Griffith theory is supported both by the results of compression tests, and by the results of the tests in this study and those previously conducted on coal.