A unified brittle fracture criterion for structures with sharp V-notches under mixed mode loading

Abstract

A unified brittle fracture criterion for cracks and V-notches under mixed mode loading is proposed by extending the maximum circumferential stress criterion and Novozhilov's criterion. The mixed mode fracture toughness and crack orientation of PMMA plates with a sharp V-notch are predicted by the proposed criterion. Tests were also carried out in order to investigate the mixed mode fracture of the PMMA plates. The fracture criterion is validated by comparison to experimental results.

A superposition approach to the stress fields for various blunt V‐notches

“…The analytical expression of a sharp V‐notch has already been treated by many researchers. Using the hypothesis of elastic behaviour for a material, the stress fields around the notch tip have been given in terms of polar coordinates ( r , θ) for its origin at the tip of a V‐notch by a linear combination of Mode I (opening mode) component and Mode II (sliding mode) component 4,5 where, and here, and show the singularity degrees of the stress fields for Mode I and Mode II , respectively. The boundary conditions for both the notch surfaces with arbitrary wedge angles = and γ 2 are traction free.…”

“…In Williams’ eigenfunction expansion series, 1 it is well known that the eigenvalues of Mode I can be obtained from λ I sin(2γ) + sin(2 γλ I ) = 0 and those of Mode II can be calculated from − λ II sin(2γ) + cos(2 γλ II ) = 0. In , the first eigenvalues of and with respect to opening mode and sliding mode have a singular term of r λ−1 when r → 0. The Mode I SIF K I associated with and the Mode II SIF K II related to are given by the following equation 4,5 …”

“…The stress intensity factors (SIFs) related only to the first terms in the Williams’ solution were investigated by Gross and Mendelson 2 using a boundary collocation method and by Lin and Tong 3 using special hybrid elements. Authors 4,5 also obtained the SIFs under mixed‐mode loading using the reciprocal work contour integral method by Carpenter 6,7 and Stern et al 8 . All of these works are focused on the methods for determining the SIFs of sharp V‐notches.…”

“…The key solution is the principle of superposition for linear elastic materials. Moreover, this work utilizes the very simple expressions in equation development of the stress field for a blunt notch by using the conventional stress fields for the sharp V‐notch generalized by early studies 4–5 . Consequently, based on the superposition method and the conventional stress fields for a sharp V‐notch, a stress field useful for any shape of notch and crack is proposed.…”

“…Moreover, this work utilizes the very simple expressions in equation development of the stress field for a blunt notch by using the conventional stress fields for the sharp V-notch generalized by early studies. [4][5] Consequently, based on the superposition method and the conventional stress fields for a sharp V-notch, a stress field useful for any shape of notch and crack is proposed. The traction-free boundary conditions for the various V-notch shapes can be satisfied by transformation of the stress fields for the sharp V-notch in curvilinear coordinate systems.…”