Review of local strain energy density theory for the fracture assessment of V-notches under mixed mode loading

Abstract

The present work summarizes some recent experimental, theoretical and numerical results on brittle fracture of isostatic polycrystalline graphite. The analyses have been carried out on Vnotched samples under mixed mode (I+II), torsion and compression loading, considering various combinations of the notch tip radius, opening angle and notch tilt angle. The static strength of the considered specimens is assessed through an approach based on the strain energy density averaged over a control volume. The center of the control volume is located on the notch edge, where the principal stress reaches its maximum value. The correct orientation is obtained by a rigid rotation of the crescent-shaped volume while the size depends on the fracture toughness and the ultimate strength of the material. This methodology has been already used in the literature to analyze U-and V-shaped notches subject to mode I loading with very good results and advantages with respect to classic approaches. The results reported in this new work show, also under mixed mode loading conditions, good agreement between experimental data and theoretical predictions.

An experimental and theoretical comparison of CCNBD and CCNSCB specimens for determining mode I fracture toughness of rocks

“…The rock specimen for K Ic measurements usually has either a straight‐through notch or a chevron notch. The straight‐through notch is often regarded as the critical crack whose length is directly correlated to the fracture toughness calculation, so the notch tip must be machined to be very sharp, as the local stresses/strains/energies ahead of a blunt notch tip are quite different from those ahead of a crack tip . Otherwise, costly precracking procedures are needed for the straight‐notch specimens to generate a crack.…”

“…The straight-through notch is often regarded as the critical crack whose length is directly correlated to the fracture toughness calculation, so the notch tip must be machined to be very sharp, as the local stresses/strains/energies ahead of a blunt notch tip are quite different from those ahead of a crack tip. [45][46][47] Otherwise, costly precracking procedures are needed for the straight-notch specimens to generate a crack. In the chevron notched specimens (eg, chevron bend [CB], short rod [SR], cracked chevron notched Brazilian disc [CCNBD], and cracked chevron notched semicircular bend [CCNSCB]), a macroscopic crack can be initiated at the tip of the chevron notched ligament under a load lower than the critical/maximum load of the test, and the critical crack associated with the K Ic calculation can thus be generated during the loading process.…”

Notch ductile failure with significant strain‐hardening: The modified equivalent material concept

“…In perfectly brittle materials, since the plastic zone does not form around the notch border during loading, the notched component withstands elastically against the applied load up to final fracture . Under such conditions, almost all of the strain energy is absorbed for initiating the crack (s) from the notch border, and just a negligible amount of energy is absorbed during crack propagation, leading to a rapid or sudden crack growth.…”

“…In perfectly brittle materials, since the plastic zone does not form around the notch border during loading, the notched component withstands elastically against the applied load up to final fracture. [2][3][4][5][6][7][8][9][10] Under such conditions, almost all of the strain energy is absorbed for initiating the crack (s) from the notch border, and just a negligible amount of energy is absorbed during crack propagation, leading to a rapid or sudden crack growth. In quasi-brittle materials, a small nonlinear portion is usually seen in the stress-strain curve, and, hence, just a small plastic zone forms around the notch border at the onset of crack initiation from the notch border.…”

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 …”