Open cracks at or near free edges

Nowell, D.; Hills, D.A.

doi:10.1243/03093247v223177

Cited by 110 publications

(71 citation statements)

References 13 publications

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“…This implies that the previous calculations may have overestimated the stress intensity factors, particularly for large flaws close to the contact area where the crack tip is far from the surface and hence experiences a complex state of stress. The method of distributed dislocations used by Nowell and Hills [23] for solving the mode I stress intensity factors relies on the availability of a closed-form solution for the stress field induced by a dislocation 1 near to a free surface. They considered that a short plane crack of depth c, normal to the free surface, is placed close to the contact area.…”

Section: Stress Intensity Factor K Imentioning

confidence: 99%

“…Nowell and Hills [23] employed the distributed dislocations method to develop a reliable, efficient and accurate method for solving the stress intensity factors for a short surface breaking crack (i.e., those whose depth is less than a/10) lying perpendicular to the free surface in steep gradients. This approach differs from previous work [24][25][26][27][28][29] where it was assumed that the crack path initially followed along the trajectory of the minimum principal stress, σ 3 .…”

Section: Stress Intensity Factor K Imentioning

confidence: 99%

“…These may be cancelled by the application of equal and opposite tractions along the crack faces, which may be generated by installing a distribution of dislocations. The state of stress induced by one of these dislocations is known and the expressions are given by Nowell [23]. Thus, the method consists of solving an integral equation in the dislocation density formed, which assumes that a line of the crack remains traction-free [23].…”

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confidence: 99%

“…The state of stress induced by one of these dislocations is known and the expressions are given by Nowell [23]. Thus, the method consists of solving an integral equation in the dislocation density formed, which assumes that a line of the crack remains traction-free [23]. The integral equation cannot be inverted directly, but powerful numerical quadratures are available which is helpful to solve this problem.…”

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Surface mechanical analyses by Hertzian indentation

Franco

Roberts

2004

Cerâmica

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of grain-boundary glassy phase [14][15][16][17]. The use of conventional fracture toughness evaluations to predict resistance to wear, erosion, and machining may lead to incorrect choices of materials for such applications.Fracture toughness may be determined from Hertzian tests by measuring the minimum load, P min , necessary to propagate cracks in a set of tests [18] on abraded samples (i.e., ones with a high surface flaw density). The test method uses flaws a few microns deep, and so gives results relevant to wear and erosion properties.Here we present surface flaw sizes of polished polycrystalline alumina specimens, with G=1.2, 3.8 and 14.1 µm, determined using the Hertzian indentation method [6][7][8]18], and fracture toughness values determined by the Hertzian method. These fracture toughness values are compared to those derived from Vickers indentation tests. The results are also compared to the rates of wet erosive wear for the same materials. AbstractHertzian indentation technique was used to measure surface flaw sizes on polished dense polycrystalline alumina specimens with grain sizes G = 1.2, 3.8 and 14.1 µm. Two surfaces finishes were studied: well-polished (Syton) and coarse-polished (45 µm diamond paste). Flaw sizes depended on the surface finish and increased with increasing grain size. Fracture toughness (K Ic ) for each material (relating to the propagation of flaws of a few µm depth) was determined from the minimum fracture load in a series of Hertzian tests. K Ic values were 3.58, 3.45 and 2.96 MPam 1/2 for G=1.2, 3.8 and 14.1 µm, respectively. Fracture toughness values were also determined by Vickers indentation over a range of loads; the K Ic values determined from the Hertzian tests were consistent with the trends in K Ic with crack size from the Vickers indentation tests. Keywords: surface, Hertzian indentation, flaw size, alumina. Resumo A técnica de indentação Hertziana foi usada para medir o tamanho das trincas nas superfícies de amostras densas de alumina Theoretical background -Hertzian indentationThe Hertzian indentation test is an alternative to the familiar Vickers indentation test for evaluation of the fracture properties of brittle materials. A great advantage of the Hertzian indentation test is that the deformation in the substrate produced by the indenter is wholly elastic until fracture occurs. This means that the complications associated with the residual stresses in Vickers indentation test do not exist. The stress field is independent of the plasticity properties of the substrate and varies continuously and smoothly near to the contact area. The contact stress field is not substantially affected by minor defects in the indenter geometry. The stress state induced can be found rigorously and exactly [19].On the other hand the Hertzian indentation test has some drawbacks. The stress fields have steep gradients in depth, thus it is difficult to accurately estimate the stress intensity factors for cracks driven by Herztian loads. The principal data needed are the loads at whic...

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Section: Stress Intensity Factor K Imentioning

confidence: 99%

Section: Stress Intensity Factor K Imentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Surface mechanical analyses by Hertzian indentation

Franco

Roberts

2004

Cerâmica

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“…1. The functions G yi j may be obtained from reference [9]. Rather than installing discrete dislocations, a continuous distribution of the Burgers vector density, B y , is employed along the line of the crack, so that the stress due to this distribution, together with the farfield stress, s 0 , is given by…”

Section: Example Problem: Edge Crackmentioning

confidence: 99%

The effect of a crack-tip radius on the validity of the singular solution

Dini

Hills

2004

Proceedings of the Institution of Mechanical Engineers, Part C:

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The influence of the finite crack-root radius on the local stress field at the root of a crack is found explicitly. This is then applied as an inner asymptotic solution, embedded with the conventional crack-tip singular solution, to quantify the possible influence of local rounding on the ability of the singular solution to capture the characteristics of the crack-tip process zone. The scaling factor employed is the conventional crack-tip stress intensity, and the example of a simple edge crack in a tension field is used to illustrate the method.

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Kinked Cracks: Finding Stress Intensity Factors

Hills

Nowell

1990

Applied Stress Analysis

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Open cracks at or near free edges

Cited by 110 publications

References 13 publications

Surface mechanical analyses by Hertzian indentation

Surface mechanical analyses by Hertzian indentation

The effect of a crack-tip radius on the validity of the singular solution

Kinked Cracks: Finding Stress Intensity Factors

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