Is Weibull distribution the most appropriate statistical strength distribution for brittle materials

Strength reliability, one of the critical factors restricting wider use of brittle materials in various structural applications, is commonly characterized by Weibull strength distribution function. In the present work, the detailed statistical analysis of the strength data is carried out using a larger class of probability models including Weibull, normal, log-normal, gamma and generalized exponential distributions. Our analysis is validated using the strength data, measured with a number of structural ceramic materials and a glass material. An important implication of the present study is that the gamma or log-normal distribution function, in contrast to Weibull distribution, may describe more appropriately, in certain cases, the experimentally measured strength data.

[1]  Zdeněk P. Bažant,et al.  Probability distribution of energetic-statistical size effect in quasibrittle fracture , 2004 .

[2]  B. Lawn.  Fracture of Brittle Solids by Brian Lawn , 1993 .

[3]  J. Vleugels,et al.  Toughness tailoring of yttria-doped zirconia ceramics , 2004 .

[4]  Bikramjit Basu,et al.  Toughening of yttria-stabilised tetragonal zirconia ceramics , 2005 .

[5]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[6]  R. Davidge,et al.  Mechanical Behaviour of Ceramics , 1979 .

[7]  Roger Morrell,et al.  Design Data for Engineering Ceramics: A Review of the Flexure Test , 1991 .

[8]  J. E. Ritter,et al.  Mechanical Behavior of Ceramics , 1991 .

[9]  Yet-Ming Chiang,et al.  Physical ceramics : principles for ceramic science and engineering / Yet-Ming Chiang, Dunbar P. Birnie, W. David Kingery , 1996 .

[10]  David R. Cox,et al.  Further Results on Tests of Separate Families of Hypotheses , 1962 .

[11]  A. A. Griffith.  The Phenomena of Rupture and Flow in Solids , 1921 .

[12]  Yongdong Xu,et al.  Optimization of sample number for Weibull function of brittle materials strength , 2001 .

[13]  Franz Dieter Fischer,et al.  Fracture statistics of brittle materials: Weibull or normal distribution. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  J. Vleugels,et al.  Statistical extreme value modeling of particle size distributions: experimental grain size distribution type estimation and parameterization of sintered zirconia , 2000 .

[15]  D. Kundu,et al.  Discriminating between the log-normal and generalized exponential distributions , 2005 .

[16]  Debasis Kundu,et al.  Discriminating between the Weibull and log‐normal distributions , 2004 .

[17]  Robert Danzer,et al.  Monte Carlo Simulations of Strength Distributions of Brittle Materials – Type of Distribution, Specimen and Sample Size , 2001, International Journal of Materials Research.

[18]  M. Matthewson,et al.  Mechanical properties of ceramics , 1996 .

[19]  Bikramjit Basu,et al.  Microstructure–toughness–wear relationship of tetragonal zirconia ceramics , 2004 .

[20]  I. Olkin,et al.  Can data recognize its parent distribution , 1999 .

[21]  J. Vleugels,et al.  Processing and mechanical properties of ZrO2-TiB2 composites , 2005 .

[22]  F. Lange,et al.  Powder Processing Science and Technology for Increased Reliability , 1989 .