Weibull strength

Mischke, C. R. 1992 Fitting Weibull Strength Data and Applying it to Stochastic Mechanical Design. Journal of Mechanical Design, 114, 35-41. 

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. 

G. D. Quinn, "Weibull Strength Scaling for Standardized Rectangular Flexure Specimens", Journal of the American Ceramic Society, vol. 86, pp. 508-510, 2003. 

WEIBULL STRENGTH DISTRIBUTION PLOTS FOR FIBER PROCESSED AT 1500 C... 

Quinn, C.D. (2003) Weibull strength scaling for standardized rectangular flexure specimens. J. Am. Ceram. Soc., 86 (3), 508-510. 

Steve D, Eric B, Jim K, Andy W, Curt J (2003) Weibull strength parameter requirements for Si3N4 Turbine rotor reliability. Paper presented at the environmental barrier coatings workshop, Gaylord Opryland Resort Convention Center, Nashville, TN, USA, 18-19 Nov 2003 http //www.oml.gOv/sci/de materials/documents/DuffyEBC2003 000.pdf. Accessed on 18 May 2010... 

The Swedish engineer, Weibull, invented the following way of handling the statistics of strength. Fie defined the survival probability PJ.Vg) as the fraction of identical samples, each of volume Vg, which survive loading to a tensile stress a. Fie then proposed that... 

Weibull - Fatigue enduranee strength of metals and strength of eeramie materials. 

It has been shown that the ultimate tensile strength, Su, for brittle materials depends upon the size of the speeimen and will deerease with inereasing dimensions, sinee the probability of having weak spots is inereased. This is termed the size effeet. This size effeet was investigated by Weibull (1951) who suggested a statistieal fune-tion, the Weibull distribution, deseribing the number and distribution of these flaws. The relationship below models the size effeet for deterministie values of Su (Timoshenko, 1966). 

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. 

A high shape faetor in the 2-parameter model suggests less strength variability. The Weibull model ean also be used to model duetile materials at low temperatures whieh exhibit brittle failure (Faires, 1965). (See Waterman and Ashby (1991) for a detailed diseussion on modelling brittle material strength.)... 

Figure 4.16 Short-term tensile strength Weibull parameters for an alloy steel at various temperatures (Upson eta/., 1967)...

In the problem here, the loading stress is a Normal distribution and the strength is a 3-parameter Weibull distribution. Beeause the Normal distribution s CDF is not in elosed form, the 3-parameter Weibull distribution ean be used as an approximating distribution when [3 = 3.44. The parameters for the 3-parameter Weibull distribution. 

Suppose again that both the stress and strength distributions of interest are of the Normal type, where the loading stress is given as L A (350,40) MPa and the strength distribution is S A (500, 50) MPa. The Normal distribution eannot be used with the integral transform method, but ean be approximated by the 3-parameter Weibull distribution where the CDF is in elosed form. It was determined above that the loading stress parameters for the 3-parameter Weibull distribution were ... 

Similarly, the strength parameters for the Weibull distribution ean be approximated by the same method to ... 

Whereas in the second approach of the size effects it is also assumed that fracture is controlled by defects, the strength is now considered a statistically distributed parameter rather than a physical property characterised by a single value. The statistical distribution of fibre strength is usually described by the Weibull model [22,23]. In this weakest-link model the strength distribution of a series arrangement of units of length L0 is given by... 

Fig. 2 Weibull plot of the filament strength for a test length of 10 cm of a PpPTA yarn yielding a Weibull modulus of 20.6. The average filament strength is 3.2 GPa... 

Weibull plots of various fibre properties, such as the filament count, modulus, elongation at break and the strength, can provide important information on the quality and performance of the manufacturing process. The results can be used to formulate a strategy for the improvement of the yarn properties. 

Goda, K., Park, J. M. and Netravali, A. N., A new theory to obtain weibull fibre strength parameters from a single-fibre composite test, J. Mater. Sci., 30, 2722 (1995). 

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