PFS : Physical Aspects of Fracture Scaling
Technical Committee PFS
Fracture scaling, size effects on strength and fracture energy are timely topics that have been heatedly debated over the past decades. Historically the work of Leonardo DaVinci, Gallileo, and more recent the classical weakest link theory of Weibull (1939) are quite well known. The notion that the strength of a structure depends on its size was clearly shown in a series of flexural fracture experiments by Walsh (1973), who argued that beyond a certain size classical strength of materials theory looses its validity and fracture strength scales according to -1/2 on a log-log-scale in a strength-size diagram. The transition from a horizontal asymptote describing the strength of a structure independent of size towards this LEFM-dictated asymptote forms the basis of the model (Size Effect Law, in short SEL) developed by Bazant in 1984, which is explained from non-linear fracture mechanics, first proposed by Hillerborg and co-workers (1976). This latter theory is commonly used now and considered as an improvement of original linear fracture models. For describing fracture scaling in concrete correctly, one should apply non-linear fracture models that include a process zone where additional stress can be transferred over a smaller or larger area of the crack. Although the details of the fracture process are not considered in these global energetic models, they seem capable of capturing some essential features of fractureing of brittle-disordered materials like concrete and rock. The size effect model by Bazant has been further developed and ammended, a proces still continuing to date. The definition of the material parameters is of extreme importance since they decide whether the model can be used to predict scaling of fracture strength, rather than to fit experimental data obtained in the laboratory. The latter exercise is relatively simple, and it can be shown that in the regime where test-data are available (roughly range of 1:32 for uniaxial tension; up to 1:64 for simpler test situations), the fit of the model can be extremely good, with correlation coefficients as large as 0.99. Since 1994 a competing model was developed by Carpinteri and coworkers (this model is called the multi-fractal scaling model, in short MFSL). In this approach the fractality of the particle structure of concrete forms the basis for model development. The model predicts a large strength for very small sizes, which is in strong contrast to the SEL, which is based on a horizontal asymptote for small structure sizes. For large sizes the asymptotes differ as well, which has led to tremendous discussion over the past decade. The MFSL fits to experimental data with the same accuracy as mentioned for the SEL, i.e. for the range of available experimental data. Both SEL and MFSL lead to problems when predictions outside the range of experimental observations muct made, and as mentioned the two models make contradictory predictions at small and large scales. Scaling is predicted directly from the Hillerborg Fictitious Crack Model as well, but also from micromechanics, for example lattice models directly describe scaling of fracture strength by considering the microcrack processes in minute detail. The micromechanical considerations show that before the strength of a structure is reached, a considerable amount of stable microcracking may occur depending on the amount of aggregates included in the material (e.g. Prado & Van Mier (2003)). It is possible to construct a micro-structure that will show Weibull type behaviour, where fatal cracking will occur instantaneously. One can also design microstructures where a maximum amount of stable microcracking develops distributed throughout the structure, after which fatal fracture will occur. In the latter case, substantial hardening is observed, and scaling laws MUST be different from Weibull scaling. In newly developed modern (hybrid) fibre concretes an extended hardening behaviour can be achieved as well and understanding the role of hardening is considered an important aspect of any scaling theory. In the field of metal fracture there have been attempts to derive scaling laws for elasto-plastic fracture (Atkins (1999)), which might well apply to these new fibre concretes since fracture processes can be relatively well compared (Van Mier (2004)). The microfracturing taking place in the hardening regime leads to a final fracture surface, and its morphology or roughness can possibly be related to macroscopic fracture parameters such as fracture energy, fracture strength or fracture toughness (Morel et al. (2002)). This may lead the way to base scaling laws on the structure of the considered materials and fracture processes therein. It remains an issue whether it suffices to consider the final fracture surface roughness or morphology, or whether detailed information is needed on the fracture distribution at peak strength. Although SEL and MFSL fit very well to existing laboratory scale experiments under a variety of loadings, the global energetic approach used in the two models leads to the above mentioned material parameters based on global characteristics of the material such as tensile strength and fracture energy. In each of the models, a complication arrises in the sense that a material characteristic length must be provided, namely the length of the process zone cf in the SEL, and characteristic length lch in MFSL. These length scale parameters depend directly on the fracture process before fatal failure occurs, and are dependent on the composition of the considered material. The effectiviness of a scaling model depends on the quality of the model parameters. A correct parameter identification procedure must lie at the basis of an approach that could be included in model codes. In this committee, it will be tried to get a better grip on the definition of model parameters for fracture (scaling) models. Basically model parameters should at best have a physical meaning and it should be indicated how they are determined (derived or measured). References Atkins, A.G. (1999), Scaling Laws for Elastoplastic Fracture, Int.J.Fract., 95, 51-65. Bažant Z.P. (1984), Size Effect in Blunt Fracture: Concrete, Rock, Metal. J.Eng. Mech., 110, 518-535. Bažant, Z.P. et al. (2004), RILEM TC QFS: Quasi-brittle Fracture Scaling and Size Effect – Final Report”, Mater. Struct. (RILEM), 37(272), 547-568. Carpinteri, A. and Chiaia, B. (1995), Multifractal Nature of Concrete Fracture Surfaces and Size Effects on Nominal Fracture Energy, Mater. Struct. (RILEM), 28, 435-443. Carpinteri, A., Chiaia, B. and Cornetti, P. (2003), On the Mechanics of Quasi-Brittle Materials with a Fractal Microstructure, Eng.Fract.Mech., 70, 2321-2349. Morel, S., Bouchaud, E. and Valentin, G. (2002), Size Effect in Fracture: Roughening of Crack Surfaces and Asymptotic Analysis, Phys.Rev. B., 65, 104101/1-8. Prado, E.P. and Van Mier, J.G.M. (2003), Effect of Particle Structure on Mode I Fracture Process in Concrete, Eng. Fract. Mech., 70(14), 1793-1807. Van Mier, J.G.M. (2004), Reality Behind Fictitious Cracks?, In Proc. 5th Int. Conf. on ‘Fracture of Concrete and Concrete Structures’ (FraMCoS-V), (Li, V.C., Leung, C.K.Y., Willam, K.J. and Billington, S.L., eds.), Vail, Colorado, April 12-16, 2004, IA-FraMCoS, Evanston, IL, 11-30. Van Vliet M.R.A. and Van Mier, J.G.M. (1999), Effect of Strain Gradients on the Size Effect of Concrete in Uniaxial Tension, Int. J. Fract., 95, 195-219.
Terms of reference
The committee will start as a relatively small group of experts, who will form the international scientific committee of a workshop to be organised approximately one year after the formation of the committee. The workshop will be by invitation only, and a state-of-the-art report on fracture scaling will be written based on the workshop contributions. Central questions to be addressed are physical aspects of fracture scaling, including energetic, micro-mechanical and fractographic considerations. Most central is the definition of the model parameters and the way they should be determined/derived from possible simple laboratory experiments. The workshop will not only address concrete, but will cover geo-materials in the widest sense of the word (i.e. including rock, clay, sand, ice, etc), with diversions to wood, metal and polymers. The state-of-the-art report must be completed three years after committee start. Depending on the progress made during these first three years, it will be decided to either follow-up the work by addressing parameter identification procedures, or otherwise to close the committee and propose a new mandate for a follow-up committee.
The committee will run as a combined RILEM/ESIS committee. Within ESIS (European Structural Intergrity Society, formerly: European Group on Fracture), TC-9 addresses fracture of concrete. The committee is currently chaired by professor B.L. Karihaloo, but from 2007 professor J.G.M. van Mier will act as the new chair. It is proposed to set-up the new committee as a joint RILEM/ESIS committee, which makes sense in view of the past work in both organisations in the field of fracture of concrete. Past RILEM committees on fracture mechanics include 50-FMC, 89-FMT, 90-FMA, QFS, 184-SSC, and 187-SOC, i.e. since 1985 one or two committees have been dedicated to fracture within RILEM.187-SOC is the last active committee, where an editorial group is now finalizing the committee report. The ESIS involvement dates back to 1990.
The committee will organize a workshop; the proceedings will be prepared in the form of a state-of-the-art report on fracture scaling, with emphasis on parameter identification procedures. The work should eventually lead to a parameter identification procedure for fracture (scaling) models, which might be the basis for inclusion in model codes for use by practical engineers. The final goal is improvement of model codes.
Group of users
The state-of-the-art report will be useful for academics, testing laboratories, industrialists and pactitioners; the recommended parameter identification procedure will be useful for practitioners, at least when they are included in model codes.
Specific use of the results
The activities by RILEM EAC will to a major extend be of very specific nature, as exemplified in point 4 above. The activities will be of direct benefit for the single user, but also of more diffuse value for the RILEM community. It is not possible to evaluate the economic impact.