Weibull glasses

As ean be seen from the above equation, for brittle materials like glass and eeramies, we ean seale the strength for a proposed design from a test speeimen analysis. In a more useful form for the 2-parameter Weibull distribution, the probability of failure is a funetion of the applied stress, L. 

Gulino, R. and Phoenix, L. (1991). Weibull strength statistics for graphite fibers measured from the break progression in a model graphite/glass/cpoxy microcomposites. J. Mater. Sci. 26, 3107-3118. 

Figure 7.13 Failure probability of 1 m and 10m gage length optical glass fibers. The long lengths of optical glass fibers have multiple flaw populations, i.e. there is more than one source of flaws, thus they do not follow the simple Weibull distribution (after Maurer, 1985).

The telecommunication industry requires optical glass fibers with very high strength (>1 GPa) over very long lengths (>1 km). For example, the True Wave single mode fiber of Lucent Technologies is routinely subjected to a proof stress of 0.7 GPa (see below) while the Weibull modulus is claimed to be 147 (Kummer,... 

Figure 4. Weibull distributions for treated and untreated(a.r ) glasses.

Table 3. Weibull modulus of the strengthened glasses in different baths along with the as-received glass...

This has been demonstrated for a commercial glass ceramic [38], and for alumina [39]. It has been suggested that the microstructure and the defect populations themselves may vary throughout the volume of a component, causing variations in strength unpredictable by Weibull analysis [40,41]. An attempt to verify the minimal specimen size required for strength determination was carried out lately [42]. 

Pemot, F., Etienne, P., Boschet, F., Datas, L, "Weibull Parameters and the Tensile Strength of Porous Phosphate Glass-Ceramics.," Journal of the American Ceramic Society, vol. 82, no. 3, pp. 641-648,1999. 

Fij . 17. Weibull plots of optical glass fibers subjected to pulse-irradiation and continuous wave treatments. The use ol pulsed exeitner radiation lowered the liber t racture strength by as rniich as a factor of 4 compared to the liber that was subjected to a CW argon-ion laser. The lower fracture strength ol pulse-irradiated liber is a result of the formation of microcracks in the material (after Varelas el al.. 1997). 

Measured strengths of identically prepared glass fibers always show a distribution. Although without any fundamental basis, it is customary to plot the measured strength distribution on a Weibull plot where the ordinate is ln(ln [l/(l — F)] and the abscissa is In S. Here P S) is the cumulative probability of failure for strengths less than or equal to... 

Fig. 7. Weibull plot for the room temperature intrinsic strength of E-glass fibers (Gupta, 1994).

Surface Condition. As a result of wear-induced surface defects, glass and glass-ceramic articles have practical tensile strengths of 20-200 N/mm = 20-200 MPa, depending on the surface condition and the atmospheric-exposure condition. To characterize the strength, a Weibull distribution for the cumulative failure probability F is assumed ... 

In most instances, a group of ceramic or glass samples produced under nominally identical conditions will have worst flaws that vary in severity and location. As a consequence, strength values for those samples will vary, often over a rather wide range. The distribution of failure stresses is usually analyzed in terms of the extreme value statistics developed by Weibull. The most common functional form used in these statistical treatments is... 

---