Characteristics at critical and sub-critical loading
A number of theories are presented in the literature on crack mechanics by which the strength of damaged materials can be predicted. Among these are theories based on the well-known Dugdale model of a crack prevented from spreading by self-created constant cohesive flow stressed acting in local areas, so-called fictitious cracks, in front of the crack.The Modified Dugdale theory presented in this paper is also based on the concept of Dugdale cracks. Any cohesive stress distribution, however, can be considered in front of the crack. Formally the strength of a material weakened by a modified Dugdale crack is the same as if it has been weakened by the well-known Griffith crack, namely sigma_CR = (EG_CR/phi)^1/2 where E and 1 are Young's modulus and crack half-length respectively, and G_CR is the so-called critical energy release rate. The physical significance of G_CR, however, is different.For brittle materials (considered by the Griffith theory )G_CR = 2 Gamma where Gamma is surface energy of material considered. For more tough materials (considered by the modified Dugdale theory) G_CR is a function f(sigma_L delta_CR) where sigma_L and delta_CR are theoretical strength and flow limit (displacement) respectively of material considered. The practical applicability of the two models is limited such that predicted strength sigma_CR must be less than sigma_L/3, which corresponds to an assumption that fictitious cracks are much smaller than real crack lengths considered. The reason for this limitation is that G_CR looses its meaning as an independent material property at higher strengths.Expressions are presented which relate critical energy release rate G_CR and fictitituous crack geometry of modified Dugdale cracks to arbitrary cohesive stress distributions. Examples are presented with cohesive stress distributions similar to such recently suggested in fracture analysis of cementitious materials. Other examples are presented whick demonstrate how fictitious cracks behave with respect to deformation and cohesive stress distribution when the material considered is subjected to sub-critical loads. Such information, which cannot be obtained experimentally, are needed in viscoelastic lifetime analysis.Finally, the question is considered whether or not fracture properties experimentally determined are real (genuine) material properties.