The Hertzian stress field and formation of cone cracks—I. Theoretical approach

Zeng, Kaiyang; Breder, Kristin; Rowcliffe, D. J.

doi:10.1016/0956-7151(92)90328-c

Cited by 69 publications

(41 citation statements)

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“…The different indentation techniques that can be used have been described by Rowcliffe [!1] (indentor shapes, load ranges, stress fields). If the indentations with a spherical indentor are kept within the limits required by Hertz theory, some material parameters can be determined, for example fracture toughness [1,12] and elastic modulus [13].…”

Section: Introductionmentioning

confidence: 99%

“…Since then this problem has been extensively studied [1][2][3][4][5][6] both theoretically and experimentally and attempts have been made to extend the original theory to dynamic loading. Expressions for the maximum dynamic load delivered to a target have been derived, assuming that all the kinetic energy of the impacting sphere is transformed into strain energy in the target [7,8].…”

Section: Introductionmentioning

confidence: 99%

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Loading rate effects during indentation and impact on glass with small spheres

1993

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In order to study the relationship between static and dynamic behaviour of soda-lime glass, both quasi-static and dynamic experiments have been conducted. The difference in material behaviour when using the two test methods suggests a loading-rate dependence in the fracture of glass. To investigate this further, quasi-static tests using different loading rates were made. This investigation showed a clear difference in material behaviour when the loading rate was increased from ~< 10 Ns -1 to ~> 100 Ns -1 . The results also suggest that Hertzian theory can be used to calculate contact zone sizes even when simple cracking occurs in quasi-static and dynamic cases. The Hertzian description breaks down once crushing occurs.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Loading rate effects during indentation and impact on glass with small spheres

1993

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“…One of the most interesting features of cone cracking is that it seems to be very sensitive to Poisson's ratio. [63]. For vitreous carbon (ν ∼ 0.27-0.29) the angle the cone (ball indentation test) makes with the surface is 22.5 • on average [64].…”

Section: (D) the Effect Of High Pressurementioning

confidence: 99%

Driving force for indentation cracking in glass: composition, pressure and temperature dependence

Rouxel

2015

Phil. Trans. R. Soc. A.

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The occurrence of damage at the surface of glass parts caused by sharp contact loading is a major issue for glass makers, suppliers and end-users. Yet, it is still a poorly understood problem from the viewpoints both of glass science and solid mechanics. Different microcracking patterns are observed at indentation sites depending on the glass composition and indentation cracks may form during both the loading and the unloading stages. Besides, we do not know much about the fracture toughness of glass and its composition dependence, so that setting a criterion for crack initiation and predicting the extent of the damage yet remain out of reach. In this study, by comparison of the behaviour of glasses from very different chemical systems and by identifying experimentally the individual contributions of the different rheological processes leading to the formation of the imprint-namely elasticity, densification and shear flow-we obtain a fairly straightforward prediction of the type and extent of the microcracks which will most likely form, depending on the physical properties of the glass. Finally, some guidelines to reduce the driving force for microcracking are proposed in the light of the effects of composition, temperature and pressure, and the areas for further research are briefly discussed.

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“…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 . However, it is likely that small surface cracks (produced by polishing and grinding) lie perpendicular to the free surface, and only when they start to grow will they follow the minimum principal stress trajectory, σ 3 , (this path is normal to the maximum principal stress, σ 1 ).…”

Section: Stress Intensity Factor K Imentioning

confidence: 52%

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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The Hertzian stress field and formation of cone cracks—I. Theoretical approach

Cited by 69 publications

References 7 publications

Loading rate effects during indentation and impact on glass with small spheres

Loading rate effects during indentation and impact on glass with small spheres

Driving force for indentation cracking in glass: composition, pressure and temperature dependence

Surface mechanical analyses by Hertzian indentation

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