The Hertzian stress field and formation of cone cracks—II. Determination of fracture toughness

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

doi:10.1016/0956-7151(92)90329-d

Cited by 53 publications

(19 citation statements)

References 6 publications

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“…The main features seen at indentations m a d e at low loading rates (5 and 10 N s -t ) and at the impact sites are in g o o d agreement with previous work [- 2,4,7,8,12,[14][15][16][17][18]. Also, the true contact areas measured on coated glass slabs are in excellent agreement with the contact sizes predicted by Hertz theory…”

Section: Discussionsupporting

confidence: 87%

“…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%

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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: Discussionsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

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

1993

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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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“…Using published material data for Glassy Carbon [30], Zirconia 2 , fine grained Al 2 O 3 [24] and Mullite 2 , Table 2 shows the predicted crack lengths for two assumed indentation depths. Even though we cannot 2 Zirconia and Mullite data are estimated based a range of sources and in-kind experience.…”

Section: Reverse Analysis To Determine the Fracture Toughnessmentioning

confidence: 99%

“…Besides bulk materials, cone cracks developed beneath a spherical indenter in multi-layered structures are characterized by Evans and co-workers [21,22]. A method to determine the fracture toughness of a material based the length of the induced cone cracks from a spherical indentation tests was suggested in [23,24]. In addition, the formation of Hertzian cone cracks was simulated in [25,26].…”

Section: Introductionmentioning

confidence: 99%