Abstract
The current work is directed to the measurement and prediction of the fracture process zone (FPZ) with the compliance method. The method is renovated with a multi-cutting technique. A new compliance curve C p is established while FPZ in a damaged specimen is removed stepwise by saw-cutting. The length of FPZ can be well determined from C p in comparison with the compliance calibration curve. Results of two different mortars evidence that the multi-cutting method is applicable to cementitious materials.
A general theory is presented in conjunction with the multi-cutting experiment. The bridging stress transferred within FPZ is evaluated from C p by the theory. It is proven with a numerical simulation that the strain-softening relation derived from C p predicts well the global load and displacement relationship. The extension of FPZ at various stages of fracture can also be predicted with the theory if parameters of the strain-softening are available. Both experimental and analytical results affirm the intrinsic connection among FPZ, fracture toughness and fracture energy.
Similar content being viewed by others
References
A. Hillerborg, M. Modeer and P.E. Petersson, Cement and Concrete Research 6 (6) (1976) 773–782.
A. Hillerborg, in Fracture Mechanics of Concrete, F.H. Wittmann (ed.), Elsevier, Amsterdam (1983) 223–249.
Z.P. Bazant and L. Cedolin, Journal of the Engineering Mechanics Division, ASCE 105 (1979) 297–315.
Z.P. Bazant and B.H. Oh, Materials and Structures, RILEM 16 (1983) 155–177.
X.Z. Hu and F.H. Wittmann, Journal of Materials in Civil Engineering (1990).
X.Z. Hu and F.H. Wittmann, in Fracture of Concrete and Rock, S.P. Shah, S.P. Swartz and B. Barr (eds.), Elsevier, England (1989) 307–316.
X.Z. Hu and F.H. Wittmann, ‘An Analytical Method to Determine the Bridging Stress Transferred within the Fracture Process Zone: I, General Theory’, submitted to Cement and Concrete Research (1990).
X.Z. Hu and F.H. Wittmann, ‘An Analytical Method to Determine the Bridging Stress Transferred within the Fracture Process Zone: II, Application to Mortar’, submitted to Cement and Concrete Research (1990).
P. Nallathambi and B.L. Karihaloo, in Fracture Toughness and Fracture Energy of Concrete, F.H. Wittmann (ed.), Elsevier, Amsterdam (1986) 271–280.
A.S. Kobayashi, N.M. Hawkins, D.B. Barker and B.M. Liaw, in Applications of Fracture Mechanics to Cementitious Composities, S.P. Shah (ed.), Martinus Nijhoff Publishers, Dordrecht (1985) 25–50.
R. Knehans and R. Steinbrech, Journal of Materials Science, Letters 1 (1982) 327–329.
M. Sakai, J. Yoshimura, Y. Goto and M. Inagaki. Journal of American Ceramic Society 71 (8) (1988) 609–616.
X.Z. Hu and F.H. Wittmann, ‘Fracture Energy and Fracture Process Zone’, to be published (1990).
E. Bruhwiler and F.H. Wittmann, Engineering Fracture Mechanics, to be published.
X.Z. Hu, Fracture Process Zone and Strain-Softening in Cementitious Materials, Postdoctoral Research Report, Institute for Building Materials, Swiss Federal Institute of Technology, Zurich (1989).
RILEM Draft Recommendation, Materials and Structures 106 (1985) 285–290.
X.Z. Hu, B. Cotterell and Y.W. Mai, Proceedings of the Royal Society (London), A 401 (1985) 251–265.
X.Z. Hu, Statistical Fracture of Brittle Materials, Ph.D thesis, Department of Mechanical Engineering, Sydney University, Sydney (1988).
M.E. Raiss, J.W. Dougill and J.B. Newman, in Fracture of Concrete and Rock, S.P. Shah, S.E. Swartz and B. Barr, (eds.), Elsevier, Amsterdam (1989) 243–253.
T. Hashida, in International Workshop on Fracture Toughness and Fracture Energy-Test Methods for Concrete and Rock, Sendai, Japan (1988) 37–47.
R.M.L. Foote, Y.W. Mai and B. Cotterell, Journal of Mechanics and Physics of Solids 34 (6) (1986) 593–607.
A.M. Alvaredo, X.Z. Hu and F.H. Wittmann, in Fracture of Concrete and Rock, S.P. Shah, S.E. Swartz and B. Barr (eds.), Elsevier, Amsterdam (1989) 51–60.
Ph. Regnault and E. Bruhwiler, Engineering Fracture Mechanics, to be published.
D.D. Higgins and J.E. Bailey, Journal of Materials Science 11 (1976) 1995–2003.
B. Cotterell and Y.W. Mai, Journal of Material Science 22 (1987) 2734–2738.
S.L. Xu and G.F. Zhao, International Workshop on Fracture Toughness and Fracture Energy-Test Methods for Concrete and Rock, Sendai, Japan (1988) 157–163.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wittmann, F.H., Hu, X. Fracture process zone in cementitious materials. Int J Fract 51, 3–18 (1991). https://doi.org/10.1007/BF00020849
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00020849