Notched plates in mixed mode loading (I+II): a review based on the local strain energy density and the cohesive zone model

Abstract

Two procedures to evaluate fracture resistance of notched components are proposed in this contribution: the Strain Energy Density (SED) over a control volume and the Cohesive Zone Model (CZM). With the aim to simplify the application of the two fracture criteria, the concept of the 'equivalent local mode I' is presented. The control volume of the SED criterion and the cohesive crack of the CZM, have been rotated along the notch edge and centered with respect to the point where the elastic principal stress is maximum. Numerical predictions are compared with experimental results from U and V shaped notches under three point bending with notch root radius ranging from 0.2 to 4.0 mm. In parallel the loading conditions vary, from pure mode I to a prevailing mode II. All specimens were made of PMMA and tested at -60°C. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.

Aging effect on combined mode fracture resistance of bitumen

“…In addition to the experimental fracture toughness data, there are some fracture models and criteria for theoretical prediction of combined mode brittle fracture. The maximum tangential stress (MTS), minimum strain energy density (SED), maximum energy release rate (MERR), cohesive zone model, maximum tangential strain, and local strain energy density are some of the well‐known conventional fracture criteria that have been utilized in the past for theoretical assessment of combined mode fracture phenomena in different brittle materials like brittle polymers, ceramics, glasses, rocks, and geomaterials . These conventional fracture criteria are derived based on the singular terms of stress/strain field ahead of the crack tip.…”

“…The maximum tangential stress (MTS), 47 minimum strain energy density (SED), 48 maximum energy release rate (MERR), 49 cohesive zone model, 50 maximum tangential strain, 51 and local strain energy density [52][53][54][55][56] are some of the well-known conventional fracture criteria that have been utilized in the past for theoretical assessment of combined mode fracture phenomena in different brittle materials like brittle polymers, ceramics, glasses, rocks, and geomaterials. [57][58][59][60][61][62][63][64] These conventional fracture criteria are derived based on the singular terms of stress/strain field ahead of the crack tip. For example, the conventional MTS theory that was suggested by Erdogan and Sih 47 in 1963 uses mode I and II stress intensity factors (K I and K II ) in deriving a mixed mode curve for predicting the onset of fracture under general combined mode I + II problem.…”

Nonlinear fatigue crack propagation in a baffle module of Wendelstein 7‐X under cyclic bending loads

“…Equation resembles the plastic zone size correction proposed by Edmunds and Willis in which, instead of K I , ΔK tot is used. However, it is worth noting that for notched components, similar values of r c also are proposed in the literature . Moreover, in Equation , σ ys is used instead of σ yc because ΔK tot in the modified version of UniGrow model is expressed as function of R‐ratio that depends on the monotonic load.…”

Fatigue surface crack propagation and intersecting cracks in connection with welding residual stresses

“…In spite of significant progress in the study of the effect of welding residual stress on the fatigue crack growth rate, the interpretation of most results is given in terms of the stress intensity factor in the framework of the validity of linear elastic fracture mechanics. It should be noted that other failure theories such strain‐based criteria can also be used to predict the fatigue life of welded structures …”