Technical Papers
Oct 16, 2013

Correlation between Cohesive Crack-Tip Local Fracture Energy and Peak Load in Mortar Beams

Publication: Journal of Materials in Civil Engineering
Volume 26, Issue 10

Abstract

Mortar, as concrete-like coarse-structured materials, has a fracture process zone ahead of crack tip after the crack initiation. The maximum fracture load must be related to the cohesive crack-tip local fracture energy due to the relatively limited crack growth in the critical state. The intention of this paper is to correlate the local fracture energy with the maximum loads in mortar specimens. An analytical approach is proposed on the correlation between the two parameters. Then a fracture test has been performed on three-point-bending notched mortar beams with a wide range of notch depths. Upon comparison of the predicted and experimentally measured peak loads, it is found that the crack-tip local fracture energy indeed varies with notch depth and beam height. Thus, the trilinear model for the local fracture energy distribution is confirmed in mortar specimens, indicating both the front and back free boundary effects. Based on the trilinear model, the size-independent fracture energy can be obtained if the notch depth and the ligament length are long enough. The proposed approach is analytical and convenient without the load-displacement curves in tests.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The authors gratefully acknowledge that the National Natural Science Foundation of China (Grant No. 50908136) have supported this work.

References

Abdalla, H. M., and Karihaloo, B. L. (2003). “Determination of size-independent specific fracture energy of concrete from three-point bend and wedge splitting tests.” Mag. Concr. Res., 55(2), 133–141.
Abdalla, H. M., and Karihaloo, B. L. (2004). “A method for constructing the bilinear tension softening diagram of concrete corresponding to its true fracture energy.” Mag. Concr. Res., 56(10), 597–604.
Bažant, Z. P. (1984). “Size effect in blunt fracture: Concrete, rock, metal.” J. Eng. Mech., 518–535.
Bažant, Z. P., and Kazemi, M. (1990). “Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete.” Int. J. Fract., 44(2), 111–131.
Carpinteri, A., and Chiaia, B. (1995). “Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy.” Mater. Struct., 28(8), 435–443.
Carpinteri, A., and Chiaia, B. (1996). “Size effects on concrete fracture energy: Dimensional transitions from order to disorder.” Mater. Struct., 29(5), 259–266.
Carpinteri, A., Chiaia, B., and Ferro, G. (1995). “Size effects of nominal tensile strength of concrete structures: Multifractality of materials ligaments and dimensional transition from order to disorder.” Mater. Struct., 28(6), 311–317.
Cifuentes, H., Alcalde, M., and Medina, F. (2013). “Measuring the size-independent fracture energy of concrete.” Strain, 49(1), 54–59.
Duan, K., Hu, X. Z., and Wittmann, F. H. (2003). “Boundary effect on concrete fracture and non-constant fracture energy distribution.” Eng. Fract. Mech., 70(16), 2257–2268.
Elices, M., Guinea, G. V., and Planas, J. (1992). “Measurement of the fracture energy using three-point bend tests: Part 3—Influence of cutting the P-δ tail.” Mater. Struct., 25(6), 327–334.
Foote, R. M. L., Mai, Y. W., and Cotterell, B. (1986). “Crack-growth resistance curves in strain-softening materials.” J. Mech. Phys. Solids., 34(6), 593–607.
General Administration of Quality Supervision, Inspection and Quarantine; and National Standardizing Committee. (2007). “Common portland cement.” Chinese Standard GB 175, Beijing, The People’s Republic of China.
Go, C. G., and Swartz, S. E. (1986). “Energy methods for fracture-toughness determination in concrete.” Exp. Mech., 26(3), 292–296.
Guinea, G. V., Planas, J., and Elices, M. (1992). “Measurement of the fracture energy using three-point bend tests: Part 1—Influence of experimental procedures.” Mater. Struct., 25(4), 212–218.
Hillerborg, A. (1983). “Analysis of one single crack.” Fracture mechanics of concrete, F. H. Wittmann, ed., Elsevier, Amsterdam, The Netherlands, 223–249.
Hillerborg, A., Modeer, M., and Petersson, P. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res., 6(6), 773–782.
Hu, X. Z. (1995). “Fracture process zone and strain softening in cementitious materials.”, ETH, Zürich Switzerland; Aedificatio, Freiburg, Germany.
Hu, X. Z. (2002). “An asymptotic approach to size effect on fracture toughness and fracture energy of composites.” Eng. Fract. Mech., 69(5), 555–564.
Hu, X. Z. (2011). “Size effect on tensile softening relation.” Mater. Struct., 44(1), 129–138.
Hu, X. Z., and Duan, K. (2004). “Influence of fracture process zone height on fracture energy of concrete.” Cem. Concr. Res., 34(8), 1321–1330.
Hu, X. Z., and Duan, K. (2007). “Size effect: Influence of proximity of fracture process zone to specimen boundary.” Eng. Fract. Mech., 74(7), 1093–1100.
Hu, X. Z., and Duan, K. (2008). “Size effect and quasi-brittle fracture: The role of FPZ.” Int. J. Fract., 154(1–2), 3–14.
Hu, X. Z., and Duan, K. (2010). “Mechanism behind the size effect phenomenon.” J. Eng. Mech., 60–68.
Hu, X. Z., Liang, L., and Yang, S. T. (2013). “Weibull-strength size effect and common problems with size effect models.” Proc., 7th Int. Conf. on Fracture Mechanics of Concrete and Concrete Structures, J. G. M. Van Mier, G. Ruiz, C. Andrade, R. C. Yu, and X. X. Zhang, eds., Toledo, Spain, 1–11.
Hu, X. Z., and Wittmann, F. H. (1990). “Experimental method to determine extension of fracture process zone.” J. Mater. Civ. Eng., 15–23.
Hu, X. Z., and Wittmann, F. H. (1992). “Fracture energy and fracture process zone.” Mater. Struct., 25(6), 319–326.
Hu, X. Z., and Wittmann, F. H. (2000). “Size effect on toughness induced by crack close to free surface.” Eng. Fract. Mech., 65(2), 209–221.
Liaw, B. M., Jeang, F. L., Du, J. J., Hawkins, N. M., and Kobayashi, A. S. (1990). “Improved nonlinear model for concrete fracture.” J. Eng. Mech., 429–445.
Ministry of Housing and Urban-Rural Construction. (2009). “Standard for test method of basic properties of construction mortar.” Chinese Standard JGJ/T 70, Beijing, The People’s Republic of China.
Muralidhara, S., Raghu Prasad, B. K., Karihaloo, B. L., and Singh, R. K. (2011). “Size-independent fracture energy in plain concrete beams using tri-linear model.” Constr. Build. Mater., 25(7), 3051–3058.
Petersson, P. E. (1981). “Crack growth and development of fracture zones in plain concrete and similar materials.”, Div. of Building Materials, LTH, Lund Univ., Sweden.
Planas, J., Elices, M., and Guinea, G. V. (1992). “Measurement of the fracture energy using three-point bend tests: Part 2—Influence of bulk energy dissipation.” Mater. Struct., 25(5), 305–312.
Reinhardt, H. W. (1985). “Crack softening zone in plain concrete under static loading.” Cem. Concr. Res., 15(1), 42–52.
RILEM. (1985). “Determination of the fracture energy of the mortar and concrete by means of three-point bend tests on notched beams.” 50-FCM Draft Recommendation, Mater. Struct., 18(106), 287–290.
Saliba, J., Loukili, A., Grondin, F., and Regoin, J.-P. (2012). “Experimental study of creep-damage coupling in concrete by acoustic emission technique.” Mater. Struct., 45(9), 1389–1401.
Su, R. K. L., Chen, H. H. N., and Kwan, A. K. H. (2012). “Incremental displacement collection method for the evaluation of tension softening curve of mortar.” Eng. Fract. Mech., 88, 49–62.
Tada, H., Paris, P. C., and Irwin, G. R. (1985). The stress analysis of cracks handbook, Paris Productions, St. Louis, MO.
Vydra, V., Trtík, K., and Vodák, F. (2012). “Size independent fracture energy of concrete.” Constr. Build. Mater., 26(1), 357–361.
Wu, Z. M., Yang, S. T., Hu, X. Z., and Zheng, J. J. (2006). “An analytical model to predict the effective fracture toughness of concrete for three-point bending notched beams.” Eng. Fract. Mech., 73(15), 2166–2191.
Xu, F., Wu, Z. M., Zheng, J. J., Zhao, Y. H., and Liu, K. (2011). “Crack extension resistance curve of concrete considering variation of FPZ length.” J. Mater. Civ. Eng., 703–710.
Yang, S. T., Hu, X. Z., and Wu, Z. M. (2011). “Influence of local fracture energy distribution on maximum fracture load of three-point-bending notched concrete beams.” Eng. Fract. Mech., 78(18), 3289–3299.
Zhao, Y. H., Xu, S. L., and Wu, Z. M. (2007). “Variation of fracture energy dissipation along evolving fracture process zones in concrete.” J. Mater. Civ. Eng., 625–633.

Information & Authors

Information

Published In

Go to Journal of Materials in Civil Engineering
Journal of Materials in Civil Engineering
Volume 26Issue 10October 2014

History

Received: Feb 18, 2013
Accepted: Oct 14, 2013
Published online: Oct 16, 2013
Published in print: Oct 1, 2014
Discussion open until: Oct 20, 2014

Permissions

Request permissions for this article.

Authors

Affiliations

Shutong Yang [email protected]
Associate Professor, Dept. of Civil Engineering, College of Engineering, Ocean Univ. of China, Qingdao 266100, P.R. China (corresponding author). E-mail: [email protected]
Winthrop Professor, School of Mechanical and Chemical Engineering, Univ. of Western Australia, Perth, WA 6009, Australia. E-mail: [email protected]
Master Student, Dept. of Civil Engineering, College of Engineering, Ocean Univ. of China, Qingdao 266100, P.R. China. E-mail: [email protected]
Master Student, Dept. of Civil Engineering, College of Engineering, Ocean Univ. of China, Qingdao 266100, P.R. China. E-mail: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share