Issue 30

L. Guerra Rosa et alii, Frattura ed Integrità Strutturale, 30 (2014) 438-445; DOI: 10.3221/IGF-ESIS.30.53 440 (1) where σ is the applied stress; P s is the corresponding probability of survival; σ 0 is the characteristic strength at which 63.2% of the test specimen will break; and m is the Weibull modulus, which is a measure of the amount of scatter in the distribution (the shape parameter); small values of m imply wide variations in strength, whereas large values imply more consistent strength values. Theoretical models were developed by Rosa et al [13-16] for estimating the fracture strength of brittle materials (such as ceramics and glasses, etc) under different typical loading conditions. The probability of survival P s for glasses in a stressed volume V can be calculated as [12]: (2) The application of Eq. (2) to uni-axial tension testing stress,  t , yields: (3) The above Eq. (3) can be expressed in the following linear equation, which facilitates to fit the Weibull parameters from test results: (4) Similarly, the application of Eq. (2) for 4-point bending testing stress,  4p , yields: (5) The above Eq. (5) can be expressed in the following linear equation, which facilitates to fit the Weibull parameters from test results: (6) In the same way, the application of Eq. (2) for 3-point bending testing stress,  3p , yields: (7) The above Eq. (7) can be expressed in the following linear equation, which facilitates to fit the Weibull parameters from experimental data: (8) The Weibull effective volume or surface can be used to scale ceramic and glass strengths from one component size to another, or from one loading state to another. Larger specimens or components are weaker, because of the bigger probability of containing larger and more critical flaws. The Weibull weakest-link model leads to a strength dependency on component size [12]:                 m s P 0 exp                    V m s dV P 0 exp                   m t s V P 0 exp     0 ln ln ln 1 ln ln                 t s mV P                       2 0 4 1 4 2 exp m mV P m p s       p m s m m mV P 4 0 2 ln 1 4 2 ln 1 ln ln                                          2 0 3 1 2 exp m V P m p s     p m s m m V P 3 0 2 ln 1 2 ln 1 ln ln                     