Fracture

Irwin, G. R.

doi:10.1007/978-3-642-45887-3_5

Cited by 466 publications

(229 citation statements)

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“…The measured half crack opening profiles (u) versus crack length behind the crack tip (X) are shown in Fig 2(a) and are used to calculate K I0,Ir by the following equation that describes the near-tip COD profile for a straight crack (Irwin, 1958;Lawn, 1993) [Irwin, 1958;Lawn, 1993], and the crack closure stress near the crack tip, the width and length of the cohesive zone and the corresponding crack tip toughness based on cohesive zone solutions developed for Dugdale-Muskhelishvili crack model by Goodier and Field [Dugdale, 1960;Goodier and Field, 1963;Hahn and Rosenfeld, 1965;Hahn, 1976 ( )…”

Section: Resultsmentioning

confidence: 99%

“…The crack opening up to 10µm behind the crack tip are not associated with observable ligament bridges and are used in the calculation. A key assumption in utilizing the Irwin's 'near-field' solutions is that the crack walls behind the tip remain free of traction (Irwin, 1958;Lawn, 1993). u versus X 1/2 was plotted ( Fig.…”

Section: Resultsmentioning

confidence: 99%

“…2(b) Similar to Eq. (1), the mode III crack tip toughness, K III0,Ir can be described by the following equation (Irwin, 1958;Lawn, 1993), with u z being the height difference of two crack walls (Fig. 1(e) (C) Cohesive zone: The u versus X plot ( Fig.…”

Section: Resultsmentioning

confidence: 99%

“…With this information Irwin's crack tip solution (Irwin, 1958;Lawn 1993) is applied to evaluate K I0 .…”

Section: Introductionmentioning

confidence: 99%

“…AFM is used as a high spatial resolution tool for COD measurement to calculate K I0 (Irwin, 1958;Lawn 1993). The information is also used to apply a cohesive zone models developed by Goodier and Field (Goodier and Field, 1963;Hahn, 1976;Hahn and Rosenfeld, 1965) for the Dugdale-Muskhelishvili crack model (Dugdale, 1960;Muskhelishvili, 1953) to compute the closure stresses at the crack tip, the cohesive zone width and length, as well as the corresponding crack tip toughness.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sub-10-micrometer toughening and crack tip toughness of dental enamel

Ang

Schulz

Fernandes

et al. 2011

Journal of the Mechanical Behavior of Biomedical Materials

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In previous studies, enamel showed indications to occlude small cracks in-vivo and exhibited R-curve behaviors for bigger cracks ex-vivo. This study quantifies the crack tip toughness (K I0, K III0 ), the crack closure stress and the cohesive zone size at the crack tip of enamel and investigates the toughening mechanisms near the crack tip down to the length scale of a single enamel crystallite. The crack-opening-displacement (COD) profile of cracks induced by Vickers indents on mature bovine enamel was studied using atomic force microscopy (AFM). The mode I crack tip toughness K I0 of cracks along enamel rod boundaries and across enamel rods exhibit similar range of values: K I0,Ir =0.5-1.6MPa.m 0.5 (based on Irwin's 'nearfield' solution) and K I0,cz =0.8-1.5MPa.m 0.5 (based on the cohesive zone solution of the Dugdale-Muskhelishvili (DM) crack model). The mode III crack tip toughness K III0,Ir was computed as 0.02-0.15MPa.m 0.5 . The crack-closure stress at the crack tip was computed as 163-770MPa with a cohesive zone length and width 1.6-10.1µm and 24-44nm utilizing the cohesive zone solution. Toughening elements were observed under AFM and SEM: crack bridging due to protein ligament and hydroxyapatite fibres (micro-and nanometer scale) as well as microcracks were identified.

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