Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T15:12:32.608Z Has data issue: false hasContentIssue false
  • English
  • Français

An Overall Approach for Microcrack and Inhomogeneity Toughening in Brittle Solids

Published online by Cambridge University Press:  05 May 2011

Huang Hsing Pan
Huang Hsing Pan*
Affiliation:
Department of Civil Engineering, National Kaohsiung Institute of Technology, Kaohsiung, Taiwan 807, R.O.C
*
*Associate Professor
Get access

Abstract

Based on the weight function theory and Hutchinson's technique, the analytic form of the toughness change near a crack-tip is derived. The inhomogeneity toughening is treated as an average quantity calculated from the mean-field approach. The solutions are suitable for the composite materials with moderate concentration as compared with Hutchinson's lowest order formula. The composite has the more toughened property if the matrix owns the higher value of the Poisson ratio. The composite with thin-disc inclusions obtains the highest toughening and that with spheres always provides the least effective one. For the microcrack toughening, the variations of the crack shape do not significantly affect the toughness change if the Budiansky and O'Connell crack density parameter is used. The explicit forms for three types of the void toughening and two types of the microcrack toughening are also shown.

Keywords

TougheningMicrocrackVoidInhomogeneity
Type
Articles
Information
Journal of Mechanics , Volume 15 , Issue 2 , June 1999 , pp. 57 - 68
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

l.Becher, P. F. and Tiegs, T. N., “Toughening Behavior Involving Multiple Mechanisms: Whisker Reinforcement and Zirconia Toughening,” J. American Ceramics Soc, Vol. 70, No. 9, pp. 651–654(1987).Google Scholar
2.Ruhle, M., Claussen, N. and Heuer, A. H., “Transformation and Microcrack Toughening as Complementary Processes in ZTA,” J. American Ceramics Soc, Vol. 69, No. 3, pp. 195–197 (1986).Google Scholar
3.Ruhle, M., Evans, A. G., McMeeking, R. M., Charalambides, P. G. and Hutchinson, J. W., “Microcrack Toughening in Alumina/Zirconia,” Acta Metallurgical Vol. 35, No. 11, pp. 2701–2710 (1987).Google Scholar
4.Charalambides, P. G. and McMeeking, R. M.,“Near-Tip Mechanics of Stress-Induced Microcracking in Brittle Materials,” J. American Ceramics Soc, Vol. 71, No. 6, pp. 465–472 (1988).Google Scholar
5.Dolgopolsky, A., Karbhari, V. and Kwak, S. S., “Microcrack Induced Toughening—An Interaction Model,” Acta Metallurgica, Vol. 37, No. 5, pp. 1349–1354 (1989).Google Scholar
6.Evans, A. G. and Faber, K. T., “Crack-Growth Resistance of Microcracking Brittle Materials,” J. American Ceramics Soc, Vol. 67, No. 4, pp. 255–260(1984).Google Scholar
7.Evans, A. G. and Fu, Y., “Some Effects of Microcracks on the Mechanical Properties of Brittle Solids—II. Microcrack Toughening,” Acta Metallurgical Vol. 33, pp. 1525–1531 (1985).Google Scholar
8.Fu, Y. and Evans, A. G., “Some Effects of Microcracks on the Mechanical Properties of Brittle Solids—I. Strain Relation,” Acta Metallurgica, Vol. 33, No. 8, pp. 1515–1523 (1985).Google Scholar
9.Hoagland, R. G. and Embury, J. D., “A Treatment of Inelastic Deformation Around a Crack Tip due to Microcracking,” J. American Ceramics Soc, Vol. 63, No. 7–8, pp. 404–410 (1980).Google Scholar
10.Rose, L. R. F., “Effective Fracture Toughness of Microcracked Materials,” J. American Ceramics Soc, Vol. 69, No. 3, pp. 212–214 (1986).Google Scholar
11.Charalambides, P. G. and McMeeking, R. M., “Finite Element Method Simulation of Crack Propagation in a Brittle Microcracking Solid,” Mech. Mater., Vol. 6, pp. 71–87 (1987).Google Scholar
12.Hutchinson, J. W., “Crack Tip Shielding by Micro-Cracking in Brittle Solids,” Acta Metallurgica, Vol.35, No. 7, pp. 1605–1619 (1987).Google Scholar
13.Curtin, W. A. and Futamura, K., “Microcrack Toughening?” Acta Metallurgica and Materials, Vol.38, No. 11, pp. 2051–2058 (1990).Google Scholar
14.Mura, T., Micromechanics of Defects in Solids, 2nd Edn, Martinus Nijhoff, Dordrecht (1987).Google Scholar
15.Mori, T. and Tanaka, K., “Average Stress in the Matrix and Average Elastic Energy of Materials with Misfitting Inclusions,” Acta Metallurgica, Vol. 21, pp. 571–574(1973).Google Scholar
16.Weng, G. J., “Some Elastic Properties of Reinforced Solids, with Special Reference to Isotropic Ones Containing Spherical Inclusion,” Int. J. Eng. Sci., Vol. 22, pp. 845–856(1984).Google Scholar
17.Pan, H. H. and Weng, G. J., “Elastic Moduli of Heterogeneous Solids with Ellipsoidal Inclusions and Elliptic Cracks,” Acta Mechanica, Vol. 110, pp. 73–94 (1995).Google Scholar
18.Bueckner, H. F., “A Novel Principle for the Computation of Stress Intensity Factors, Z. Angew. Math. Mech., Vol. 50, pp. 529–546 (1970).Google Scholar
19.Rice, J. R., “Some Remark on Elastic Crack-Tip Stress Fields,” Int. J. Solids Structures, Vol. 8, pp. 751–758(1972).Google Scholar
20.Rice, J. R., “Weight Function Theory for Three-Dimensional Elastic Crack Analysis,” Fracture Mech., ASTM STP 1020, pp. 29–57 (1989).Google Scholar
21.Eshelby, J. D., “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Relation Problem,” Proc. Roy. Soc London Ser., A 241, pp. 376–396(1957).Google Scholar
22.Tandon, G. P. and Weng, G. J., “The Effect of Aspect Ratio of Inclusions on the Elastic Properties of Unidirectionally Aligned Composites,” Polymer Comp., Vol. 5, pp. 327–333 (1984).Google Scholar
23.Tandon, G. P. and Weng, G. J., “Average Stress in the Matrix and Effective Moduli of Randomly Oriented Composites,” Comp. Sci. Tech., Vol. 27, pp. 111–132(1986).Google Scholar
24.McMeeking, R. M. and Evans, A. G., “Mechanics of Transformation-Toughening in Brittle Materials,” J. American Ceramics Soc, Vol. 65, No. 5, pp. 242–246(1982).Google Scholar
25.Paris, P. C., McMeeking, R. M. and Tada, H., “The Weight Function Method for Determining Stress Intensity Factors,” Cracks and Fracture, ASTM STP 601, pp. 471–489 (1976).Google Scholar
26.Rice, J. R., “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” J. Appl. Mech., pp. 379–386 (1968).Google Scholar
27.Ortiz, M., “A Continuous Theory of Crack Shielding in Ceramics,” J. Appl. Mech., Vol. 54, pp. 5448(1987).Google Scholar
28.Budiansky, B. and O'Connell, R. J., “Elastic Moduli of a Cracked Solids,” Int. J. Solids Structures, Vol. 12, pp. 81–97(1976).Google Scholar
29.Steif, P. S., “A Semi-Infinite Crack Partially Penetrating a Circular Inclusion,” J. Appl. Mech., Vol. 54, pp. 87–92(1987).Google Scholar