THE ONE-DIMENSIONAL CAR PARKING PROBLEM AND ITS APPLICATION TO THE DISTRIBUTION OF SPACINGS BETWEEN MATRIX CRACKS IN UNIDIRECTIONAL FIBER-REINFORCED BRITTLE MATERIALS

Experimental observations of the spacings between cracks formed in the matrix in unidirectional fiber-reinforced brittle materials in a situation where a tensile stress is applied parallel to the lengths of the fibers, and where the fibers have a longer elongation to failure than the matrix, suggest that the distribution of crack spacings does not follow the one expected on the basis of a model where the matrix cracks at a well-defined single-valued stress. A simple model which is able to account for this apparent discrepancy between theory and experiment is developed and discussed.