Fracture statistics

Baxevanakis, C. Jeulin, D., Valentin, D. (1993). Fracture statistics of single fiber composite specimen.Co/n/)os/7es Sci. Technol. 48, 47-56. 

R.H. Doremus, Fracture statistics A comparison of the normal, Weibull and type I extreme value distributions, J. Appl. Phys. 54, 193-201 (1983). 

In this paper the Weibull theory is applied to very small specimens. The analysis follows the ideas presented in [13]. The relationships between flaw population, size of the fracture initiating flaw and strength are discussed. It is shown that a limit for the applicability of the classical fracture statistics (i.e. Weibull statistics based on the weakest link hypothesis) exists for very small specimens (components). 

In the following, the relationship between fracture statistics and defect size distribution is discussed for the simple case of tensile tests (uniaxial and homogeneous stress state) on a homogeneous brittle material. The tests are performed on specimens of equal size. It is assumed that the volume of the specimens is V = V. The number of tested specimens (the sample size) isX. In each test the load is increased up to the moment of failure. The strength is the stress at the moment of failure. In each sample the strength values of the individual specimens are different, i.e. the strength is distributed. 

Bazant formulated a statistical theory of fracture for quasibrittle materials [5, 23, 24]. He assumed that there exist several hierarchical orders which each can be described by parallel and serial linking of so-called representative volume elements (RVEs). For large specimens (and low probability of failures) the fracture statistics is equal to the Weibull statistics, i.e. if the specimens size is larger than 500 to 1000 times of the size of one RVE. In the actual case this is similar to the diameter of the critical flaw. For smaller specimens the volume effect disappears and the fracture... 

A further and very important consequence of the Weibull distribution is the size effect, i.e. the mean strength decreases with increasing specimen size. This is the most important consequence of fracture statistics for designing with ceramics. 

R. Danzer, P. Supancic, J. Pascual, and T. Lube, Fracture Statistics of Ceramics - Weibull Statistics and Deviations from Weibull Statistics, Engineering Fracture Mechanics, 74, 2919-2932, (2007). 

C. Lu, R. Danzer, and F. D. Fischer, Fracture Statistics of Brittle Materials Weibull or Normal Distribution, Physical Review E, 65, 1 - 4, (2002). 

J. C. McNulty, F. W. Zok, Application of weakest-link fracture statistics to fiber-reinforced ceramic-matrix composites, 7. Am. Ceram. Soc. 80 1535-1543 (1997). 

Influence of Microstructure Flaw Populations on Fracture Statistics... 

In this chapter, a dose examination has been made of the phenomenon of fracture in ceramics. The macroscopic appearance of fracture and typical failure modes in ceramic materials has been analyzed, fracture mirrors and fracture origins have been identified, and the way in which fracture is intrinsically connected to the microstructure of a ceramic has been outlined. In particular, by detailing stress distributions it has been shown that fracture always starts at a single microstructural flaw, the stability of which can be described with simple linear elastic fracture mechanics. Notably, these features are responsible for the inherently statistical nature of failure in ceramic materials, an understanding of which can provide knowledge of the close corrdation between defect populations and fracture statistics, and of how to devdop materials parameters such as the characteristic strength. 

Danzer, R., Supancic, P., Pascual Herrero, J., and Lube, T. (2007) Fracture statistics of ceramics - Weibull statistics and deviations from Weibull statistics. Eng. Fract. Mech., 74 (18), 2919-2932. 

Pascual,)., Lube, T., and Danzer, R. (2008) Fracture statistics of ceramic laminates strengthened by compressive residual stresses. /. Eur. Ceram. Soc., 28 (8), 1551-1556. 

The design and application of reliable load-bearing structural components from ceramic materials requires a detailed understanding of the statistical nature of fracture in brittle materials. The overall objective of this program is to advance the current understanding of fracture statistics, especially in the following four areas ... 

S.B. Batdorf (1977), "Some Approximate Treatments of Fracture Statistics for Poly axial Tension," Inter. Jour, of Fracture, 13,1, 5-11. 

CARES. Ceramic Analysis and Reliability Evaluation of Structures. (Formerly known as scare - Structural Ceramic Analysis and Reliability Examination). A Fortran 77 computer program using Weibull and Batdorf fracture statistics to predict the fast-fracture reliability of isotropic ceramics. Carlton Shape. A tea-cup the top half of which is cylindrical, the bottom half being approximately hemispherical but terminating in a broad, shallow foot. For specification see B.S. 3542. 

S. B. Batdorf, Fracture statistics of brittle materials with intergranular cracks. Nuclear Engineering and Design, 35(3) 349-360, 1975. 

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