MICROCRACK TOUGHENING

The standard model of microcrack toughening by elastic shielding, where the discrete microcracked process zone is replaced by a continuum effective medium of reduced modulus, is argued to be invalid since (i) the modulus near the crack tip is that of the matrix, not the effective medium, and (ii) the fluctuations in the distribution of microcracks as the crack grows determine the measured toughness, which is the highest toughness environment encountered prior to unstable cracking rather than the average toughness. Here, a simple spring model for both continuum and discrete microcrack situations is used to quantitatively analyze these effects. The model reproduces the standard model results but retaining the matrix modulus near the crack tip yields much lower toughnesses, in agreement with exact first-order calculations. Furthermore, with a true distribution of microcracks the average toughness is close to the lower-toughness result, but with large fluctuations about the average. A statistical analysis of crack growth in such fluctuating environments shows that the measured toughness can be much larger than the average toughness. Hence, neither the standard nor modified continuum models of microcrack toughening by elastic-shielding are valid; a statistical approach incorporating the fluctuations in the microcrack distribution is required. © 1990.