Modified Dugdale crack models - some easy crack relations

The Dugdale crack model is widely used in materials science to predict strength of defective (cracked) materials. A stable Dugdale crack in an elasto-plastic material is prevented from spreading by uniformly distributed cohesive stresses acting in narrow areas at the crack tips. These stresses are assumed to be self created by local materials flow. The strength sigma_CR predictid by the Dugdale model is sigma_CR =(E Gamma_CR/phi1)^½ where E and 1 are Young’s modulus and crack half-length respectively of the material considered. The so-called critical strain energy rate is Gamma_CR = sigma_Ldelta_CR where sigma_L is strength, and at the same time constant flow stress, of the uncracked material while delta_CR is flow limit (displacement).Obviously predictions by the Dugdale model are most reliable for materials with stress-strain relations where flow can actually be described (or well approximated) by a constant flow stress (sigma_L). A number of materials, however, do not at all exhibit this kind of flow. Such materials are considered in this paper by Modified Dugdale crack models which apply for any cohesive stress distribution in crack front areas. Formally modified Dugdale crack models exhibit the same strength as a plain Dugdale model. The critical energy release rates Gamma_CR, however, become different. Expressions (with easy computer algorithms) are presented in the paper which relate critical energy release rates and crack geometry to arbitrary cohesive stress distributions.For future lifetime analysis of viscoelastic materials strain energy release rates, crack geometries, and cohesive stress distributions are considered as related to sub-critical loads sigma <sigma_CR. Such information needed in viscoelastic analysis are not obtained from traditional stress-deformation tests on materials.Limitations of the expressions presented are discussed. They are the same as for the well-known Griffith load capacity, namely: predicted sigma_CR must be lower than sigma_L /3. The reason is that Gamma_CR looses its meaning of an independent material property at higher strengths. A more general strength expression applying at any strength predicted is suggested introducing a so-called characteristic microstructural dimension which captures the materials failure properties in a more efficient way than Gamma_CR does.Identification of a characteristic microstructural dimension will cause that the rationale behind traditional Gamma_CR-determination by stress-deformation tests has to be modified. It is therefore suggested that future research on strength should include characteristic microstructural dimensions as a separate topic.