Statistical analysis of the Hertzian fracture of pyrex glass using the Weibull distribution function

Keshavan, M. K.; Sargent, G. A.; Conrad, H.

doi:10.1007/bf00552092

Cited by 32 publications

(17 citation statements)

References 11 publications

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“…It is interesting to note that the threshold stress also decreases with the increasing particle size. This is consistent with the experimental results of Keshavan et al [32]. Since the threshold stress is the breakage strength corresponding to a zero survival probability, it must also be size dependent as the characteristic stress is.…”

Section: Compression Responsessupporting

confidence: 86%

Size effect on the compression breakage strengths of glass particles

Huang

et al. 2014

Powder Technology

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Section: Compression Responsessupporting

confidence: 86%

Size effect on the compression breakage strengths of glass particles

Huang

et al. 2014

Powder Technology

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“…For glass fibers and cast glass the distribution can be adequately described using the Weibull statistic approach leading to a probabilistic strength for the glass used [1,2]. For the more common float glass this is more complicated.…”

Section: Introductionmentioning

confidence: 99%

The structural strength of glass: hidden damage

Veer

Rodichev

2011

Strength Mater

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We discuss "hidden damage" of glass by the rolling process, which results in heterogeneous distribution of microcracks on the edge surface of glass element, which are the fracture source deteriorating glass element strength. It is shown that removal of this damage on the edges of glass elements increases the engineering strength of float glass significantly. Using the "hidden damage" approach, we provide strength determination for the weakest specimens that is statistically relevant and is based on a reliable engineering parameter.Keywords: glass, rolling process, hidden damage, engineering parameter, microcracks. Introduction.Glass is commonly used in engineering, when a transparent, durable, and stiff material is needed. Although glass is not usually used for load-bearing applications, in most cases glass still carries a load. In an automobile, the front and rear windows are an integral part of the structure responsible for a significant part of the total stiffness and resisting the considerable forces generated by the air pressure at high-speed driving.However, the reliable value for the glass strength is an open issue: the tensile strength cannot easily be determined, since glass in direct tensile test will break at the grip. In certain cases, bending test results provide scattered values of the bending strength with a spread of 30 to 50% of the mean strength.For glass fibers and cast glass the distribution can be adequately described using the Weibull statistic approach leading to a probabilistic strength for the glass used [1,2]. For the more common float glass this is more complicated. Results of bending experiments by various authors suggest that the processing and specimen size influence the results and suggest systematic data deviation from the Weibull statistic distribution [3][4][5].A likely explanation for this is that the usual processing of float glass results in multiple types of defects which provides a multilinear Weibull plot [6,7].To investigate this systematically it was decided to look in more depth at the effect of processing on float glass strength. The initial step, which is described in this paper, deals with the effect of cutting and breaking quality on the strength of processed float glass.Float glass is produced as 6´3.21 m "jumbo" plates. These are cut into the required size and the cut edges are usually grinded and polished. The cutting is usually done by scratching the glass with a glazier's diamond or rolling it with a tungsten carbide roller producing a cut on the upper surface. This is schematically shown in Fig. 1. By bending the plate slightly, as is shown by the arrows, tension is generated at the cut resulting in an unstable crack-cut growing down on the figured straight arrow through the thickness separating the glass parts. Surface damages such as crumbled arrises and cross microcracks are forming on edges of both glass parts under the contact cutter action.The depth values of these specific cross microcracks are larger than those of the initial surface microcracks which ...

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“…The Weibull model was first applied by Waloddi Weibull (1887Weibull ( -1970 for testing the breaking strength of different materials [32]. Up to date, the Weibull model has been frequently applied in numerous applied fields for example, adhesive wear in metals Queeshi and Sheikh [24], coatings by Almeida [1], fracture strength of glass due to Keshevan et al [14], composite materials by Newell et al [20] and pitting corrosion in pipes by Sheikh et al [27]. Majeske [18], Attardi et al [2] and Bucar et al [7] used Weibull model for modeling automobile data.…”

Section: Introductionmentioning

confidence: 99%

Generalized Flexible Weibull Extension Distribution

Ahmad¹,

Iqbal²

2017

CCS Archive

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In this article, a four parameter generalization of the flexible Weibull extension distribution so-called generalized flexible Weibull extension distribution is studied. The proposed model belongs to T-X family of distributions proposed by Alzaatreh et al. [5]. The suggested model is much flexible and accommodates increasing, unimodal and modified unimodal failure rates. A comprehensive expression of the numerical properties and the estimates of the model parameters are obtained using maximum likelihood method. By appropriate choice of parameter values the new model reduces to four sub models. The proposed model is illustrated by means of three real data sets.

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Statistical analysis of the Hertzian fracture of pyrex glass using the Weibull distribution function

Cited by 32 publications

References 11 publications

Size effect on the compression breakage strengths of glass particles

Size effect on the compression breakage strengths of glass particles

The structural strength of glass: hidden damage

Generalized Flexible Weibull Extension Distribution

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