Skip to main content
SpringerLink
Log in

Influence of precatastrophic extension and other effects on local stresses in cracked plates under bending fields

Results of photoelastic experiments indicate that the Sih-Hartranft theory will reliably estimate local stresses near the tensile side of the plate even in the presence of crack closure on the compression side and precatastrophic extension on the tensile side

  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Using the technique of stress freezing and slicing, a set of photoelastic experiments was conducted on plates, each containing a single through internal crack in a remote cylindrical bending field, where each crack suffered precatastrophic extension on the tensile side of the plate as well as closure on the compression side. Resulting stresses were compared with the Sih-Hartranft theory. Results indicate substantial stress relaxation near the tensile side of the plate due to precatastrophic extension. It is concluded that: (1) the Sih-Hartranft theory may be used to estimate local elastic stresses on the tensile side of the plate even when closure and precatastrophic extension occur; (2) complex coupling of closure and precatastrophic extension effects preclude the use of simple correction factors for existing mathematical models except for relatively small precatastrophic extension.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

σ x , σ y , σ xy :

components of stress

σ o :

remote bending stress

r, R 1,R 2,θ,θ 1,θ 2 :

polar coordinates (see Fig. 1)

a * :

half crack length

Φ(1)* :

solution to Fredholm integral equation

ν:

Poisson's ratio

M o :

remote bending moment

h :

plate thickness

n :

constant

τ m :

maximum in-plane shearing stress

τ mo :

remote maximum in-plane shearing stress

λ:

\(\lambda = h/a\sqrt {10} \)

\(g\left( {\frac{{2a}}{h},\frac{{\delta a}}{a}} \right);l\left( {\frac{{\delta a}}{a}} \right);f\left( {\frac{{2a}}{h}} \right)\) :

correction factors which modify mathematical model to include precatastrophic extension, closure, and other effects

0(1):

order one

* a′, ϕ′(1):

primes refer to final crack length after precatastrophic extension

References

  1. Irwin, G. R., “Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate,”Trans. ASME, Jnl. Appl. Mech.,79,361–364 (Sept.1957).

    Google Scholar 

  2. Williams, M. L., “The Bending Stress Distribution at the Base of a Stationary Crack,” Jnl. Appl. Mech.,28,(March 1961), Trans. ASME,82,Series E, 78–82 (1961).

  3. Sih, G. C. Paris, P. C. andErdogan, F., “Crack-Tip, Stress-Intensity Factors for Plane Extension and Plate Bending Problems,”Jnl. Appl. Mech.,29,306–310 (June1962).

    Google Scholar 

  4. Muskhelishvili, N. I., Some Basic Problems of Mathematical Theory of Elasticity, (1933), english translation, P. Noordhoff and Company, New York, (1953).

    Google Scholar 

  5. Knowles, J. K. and Wang, N. M., “On the Bending of an Elastic Plate Containing a Crack,” Jnl. of Math. and Phys., 223–236 (Dec. 1961).

  6. Reissner, E., “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates,”Jnl. Appl. Mech.,12,A-69 (1945).

    Google Scholar 

  7. Williams, M. L., “Invited Discussion of ‘An Experimental Investigation of the Crack Tip Stress Intensity Factors in Plates under Cylindrical Bending’ by F. Erdogan, O. Tuncel and P. C. Paris,” GALCIT SM 62-91, Calif. Inst. of Tech. (March 1962).

  8. Hartranft, R. J. andSih, G. C., “Effect of Plate Thickness on the Bending Stress Distribution around Through Cracks,”Jnl. of Math. and Phys.,47 (3),276–291 (Sept.1968).

    Google Scholar 

  9. Wang, N. M., “Effects of Plate Thickness on the Bending of an Elastic Plate Containing a Crack, Jnl. of Math. and Phys.,27 (4),371–390 (1968).

    Google Scholar 

  10. Sih, G. C., “Bending of a Cracked Plate with Arbitrary Stress Distribution Across the Thickness,” Tech. Report No. 6, Lehigh Univ., April (1969). See also Intnat'l. Jnl. Fracture Mechanics,7 (1) (March 1971).

  11. Erdogan, F., Ozcan, T. and Paris, P. C., “An Experimental Investigation of the Crack Tip Stress Intensity Factors in Plates Under Cylindrical Bending,” Trans. ASME, Jnl. of Basic Engrg., 542–546 (Dec. 1962).

  12. Swedlow, J. L. and Liu, H. W., “Experimental Investigation of Extension-Bending Interaction of Centrally Cracked Plates,” GALCIT SM 62-5, Calif. Inst. of Tech. (April 1962).

  13. Wynn, R. H. and Smith, C. W., “An Experimental Investigation of Fracture Criteria for Combined Extension and Bending,” Jnl. of Basic Engrg. Trans. ASME, Series D,91 (4) (Dec. 1969).

  14. Smith, D. G. andSmith, C. W., “A Photoelastic Evaluation of the Influence of Closure and Other Effects upon the Local Bending Stresses in Cracked Plates,”Internatl. Jnl. Fracture Mech.,5 (3),305–318 (Sept.1970).

    Google Scholar 

  15. Post, D., “Photoelastic Stress Analysis for an Edge Crack in a Tensile Field,”Proc. SESA, XII (1),99–116 (1954).

    Google Scholar 

  16. Wells, A. A. andPost, D., “The Dynamic Stress Distribution Surrounding a Running Crack—A Photoelastic Analysis,”Proc. SESA, XXVI, (1),69–92 (1958).

    Google Scholar 

  17. Beebe, W. M., “An Experimental Investigation of Dynamic Crack Propagation in Plastics and Metals,” Doctoral Dissertation, Calif. Inst. of Tech., Dept. Engrg. Mech. (1966).

  18. Lange, F. F., “Interaction Between Overlapping Parallel Cracks: A Photvelastic Study,”Internatl. Jnl. of Fracture Mech.,4 (3),287–294 (September1968).

    Google Scholar 

  19. Stock, T. A. C., “Stress Field Intensity Factors for Propagating Brittle Cracks,”Internatl. Jnl. of Fracture Mech.,3 (2),121–129 (June1967).

    Google Scholar 

  20. Fessler, H., andMansell, D. O., “Photoelastic Study of Stresses Near Cracks in Thick Plates,”Jnl. of Mech. Engrg. Sci.,4 (3),213–225 (Sept1962).

    Google Scholar 

  21. Pih, H., “Three-dimensional Photoelastic Investigations of Circular Cylinders with Spherical Cavities in Axial Loading,”Experimental Mechanics,5 (3),90–96 (March1965).

    Google Scholar 

  22. Pih, H. andVanderveldt, H., “Stresses in Spheres with Concentric Spherical Cavities under Diametral Compression by Three-dimensional Photoelasticity,”Experimental Mechanics,6 (5),244–250 (May1966).

    Google Scholar 

  23. Brinson, H. F., “Mechanical and Optical Viscoelastic Characterization of Hysol 4290,”Experimental Mechanics,8 (12),561–566 (Dec.1968).

    Google Scholar 

  24. Fichter, W. B., “Stresses at the Tip of a Longitudinal Crack in a Plate Strip,” NASA TR R-265 (Aug. 1962).

  25. Smith, D. G. and Smith, C. W., “Photoelastic Determination of Mixed Mode Stress Intensity Factors,” in press, Engrg. Fracture Jnl.

Download references

Author information

Authors and Affiliations

  1. Tennessee Technological University, 38501, Cookeville, Tenn.

    D. G. Smith (Assistant Professor of Engineering Science)

  2. Virginia Polytechnic Institute and State University, USA

    C. W. Smith (Professor of Engineering Mechanics)

Authors
  1. D. G. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. W. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

was formerly Assistant Professor of Engineering Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smith, D.G., Smith, C.W. Influence of precatastrophic extension and other effects on local stresses in cracked plates under bending fields. Experimental Mechanics 11, 394–401 (1971). https://doi.org/10.1007/BF02327643

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02327643

Keywords

Search

Navigation