Theoretical and Experimental Load‐CMOD Curves Through Softening to Failure
Publication: Journal of Engineering Mechanics
Volume 116, Issue 6
Abstract
A model for process‐zone growth and crack propagation is discussed and the model predictions are compared to experimental results. Critical crack tip opening displacement is used as a traction‐free crack extension criterion. It is assumed, as a first approximation, that has two critical values, initial and secondary. Based on the parameter analysis, comparison to experimental results, and findings of other researchers, it is concluded that changes during crack propagation and depends on specimen size and crack length. Model predictions are compared successfully to experimental results obtained on concrete beams in a broad range of sizes and initial crack lengths from initial loading through nonlinear prepeak and postpeak softening response to failure.
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References
1.
Barenblatt, G. I. (1962). “The mathematical theory of equilibrium cracks in brittle fracture.” Advances in Applied Mechanics, 7, H. L. Dryden et al., eds., Academic Press, New York, N.Y., 55–129.
2.
Bassani, J. L., Brown, N., and Lu, X. (1988). “J‐integral correlation of the initiation of slow crack growth in linear polyethylene.” Int. J. Fracture, 38, Sep., 43–59.
3.
Bažant, Z. P., and Cedolin, L. (1979). “Blunt crack band propagation in finite element analysis.” J. Engrg. Mech. Div., ASCE, 105, Apr., 297–315.
4.
Bažant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” Matls. and Structs., 16, May–June, 155–177.
5.
Bueckner, H. F. (1970). “A novel principle for the computation of stress intensity factors.” Zeitschrift fur angewandte Mathematik und Mechanik, 50(9), 529–545.
6.
Carpinteri, A. (1984). “Interpretation of the Griffith instability as a bifurcation of the global equilibrium.” Application of Fracture Mechanics to Cementitious Composites, S. P. Shah, ed., Martinus Nijhof Publishers, Dordrecht, The Netherlands, 287–316.
7.
Cedolin, L., Dei Poli, S., and Iori, I. (1987). “Tensile behavior of concrete.” J. Engrg. Mech., ASCE, 113, Mar., 431–449.
8.
Cho, K. Z., et al. (1984). “Fracture process zone of concrete cracks.” J. Engrg. Mech., ASCE, 110, Aug., 1174–1184.
9.
Clarin, P. G. (1987). “Fracture analysis of center cracked infinite plates of linearly softening materials.” Engrg. Fracture Mech., 27(2), 231–245.
10.
Dugdale, D. S. (1960). “Yielding of steel sheets containing slits.” J. Mech. and Physics of Solids, 8, May, 100–104.
11.
Gopalaratnam, V. S., and Shah, S. P. (1985). “Softening response of plain concrete in direct tension.” ACI J., 82, May–June, 310–323.
12.
Gopalaratnam, V. S., and Shah, S. P. (1987). “Tensile failure of steel fiber‐reinforced mortar.” J. Engrg. Mech., ASCE, 113, May, 635–652.
13.
Hillerborg, A., Modeer, M., and Petersson, P.‐E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cement and Concr. Res., 6(6), 773–782.
14.
Hollman, K., and Backlund, J. (1988). “Notch sensitivity of linearly softening materials exhibiting tensile fracture.” Engrg. Fracture Mech., 31(4), 577–590.
15.
Hollmann, K., and Hahn, H. T. (1989). “Plane‐strain fracture toughness of epoxics at different loading rates.” Polymer Engrg. and Sci., 29(4), 523–530.
16.
Hoover, W. R., and Allred, R. E. (1974). “The J‐integral as a failure criterion for a borsic‐Al composite.” Failure Modes in Composites II, J. N. Fleck and R. L. Mehan, eds., 160–187.
17.
Ingraffea, A. R., and Gerstle, W. H. (1985). “Non‐linear fracture models for discrete crack propagation.” Application of fracture mechanics to cementitious composites, S. P. Shah, ed., Martinus Nijhof Publishers, Dordrecht, The Netherlands, 247–285.
18.
Jenq, Y. S., and Shah, S. P. (1985). “Nonlinear fracture parameters for cement based composites: Theory and experiments.” Application of fracture mechanics to cementitious composites, S. P. Shah, ed., Martinus Nijhof Publishers, Dordrecht, The Netherlands, 319–359.
19.
Joyce, J. A. (1983). “Instability testing of compact and pipe specimens utilizing a test system made compliant by computer control.” Elastic‐Plastic Fracture: Second Symp. II: Fracture Resistance Curves and Engrg. Applications, ASTM STP 803, Philadelphia, Pa., 439–463.
20.
Li, V. C., and Liang, E. (1986). “Fracture process in concrete and fiber reinforced cementitious composites.” J. Engrg. Mech., ASCE, 112, June, 566–586.
21.
Neimitz, A., and Aifantis, E. C. (1987). “On the size and shape of the process zone.” Engrg. Fracture Mech., 26(4), 491–503.
22.
Ojdrovic, R. P. (1988). “Process zone growth and crack propagation in softening materials.” Thesis presented to Duke University, at Durham, N.C., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
23.
Ojdrovic, R. P., and Petroski, H. J. (1990a). “Process zone analysis of the single‐edge notched specimen: Part I. Process zone size and crack profile.” Int. J. Frac., in press.
24.
Ojdrovic, R. P., and Petroski, H. J. (1990b). “Process zone analysis of the single‐edge notched specimen: Part II. Process zone growth and crack propagation.” Int. J. Frac., in press.
25.
Perdikaris, P. C., Calomino, A., and Chudnovsky, A. (1986). “Effect of fatigue on fracture toughness of concrete.” J. Engrg. Mech., ASCE, 112, Aug., 776–791.
26.
Petroski, H. J., and Achenbach, J. D. (1978). “Computation of the weight function from a stress intensity factor.” Engrg. Fracture Mech., 10(2), 257–266.
27.
Petroski, H. J. (1979). “Dugdale plastic zone size for edge cracks.” Int. J. Fracture, 15, June, 217–230.
28.
Read, H. E., and Hegemier, G. A. (1984). “Strain softening of rock, soil and concrete—A review article.” Mech. Matls., 3(4), 271–294.
29.
Reinhardt, H. W. (1985). “Plain concrete modeled as an elastic strain‐softening material at fracture.” Engrg. Fracture Mech., 22(5), 787–796.
30.
Rice, J. R. (1966). “Plastic yielding at crack tip.” Proceedings of the 1st Conference on Fracture, T. Yokobari, et al., eds., Japanese Soc. for Strength and Fracture of Matls., Tokyo, Japan, 283–308.
31.
Rice, J. R. (1972). “Some remarks on elastic stress fields.” Int. J. Solids and Structs., 8, June, 751–758.
32.
Sandler, I. S. (1984). “Strain softening for static and dynamic problems.” Constitutive Equations: Macro and computational aspects, K. J. Willam, ed., ASME, New York, N.Y., 217–231.
33.
Schreyer, H. L., and Chen, Z. (1986). “One‐dimensional softening with localization.” J. Appl. Mech., 53(12), 791–797.
34.
Smith, E. (1974). “The structure in the vicinity of a crack tip: A general theory based on the cohesive zone mode.” Engrg. Fracture Mech., 6(2), 213–222.
35.
Smith, E. (1986). “The condition for unstable crack growth in a solid subject to displacement control loadings.” Int. J. Pressure Vessels and Piping, 23(4), 251–257.
36.
Ungsuwarungsri, T., and Knauss, W. K. (1988a). “A nonlinear analysis of an equilibrium craze: Part I—Problem formulation and solution.” J. Appl. Mech., 55, Mar., 44–51.
37.
Ungsuwarungsri, T., and Knauss, W. K. (1988b). “A nonlinear analysis of an equilibrium craze: Part II—Simulation of craze and crack growth.” J. Appl. Mech., 55, Mar., 52–58.
38.
Wecharatana, M., and Shah, S. P. (1983). “Predictions of nonlinear fracture process zone in concrete.” J. Engrg. Mech., ASCE, 109, Oct., 1231–1246.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 116 • Issue 6 • June 1990
Pages: 1317 - 1331
Copyright
Copyright © 1990 ASCE.
History
Published online: Jun 1, 1990
Published in print: Jun 1990
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