Abstract
The increasing number of analytical and numerical solutions for the crack-tip stress-intensity factor has greatly widened the scope of application of linear elastic fracture-mechanics technology. Experimental verification of a particular solution by elastic stress analysis is often a necessary supplement to provide the criteria for proper application to actual design problems.
In this paper, it is shown that the photoelastic technique can be used to obtain rather good estimates of the stress-intensity factor for various specimen geometries and loading conditions. Treated are the following cases: wedge-opening load specimen, several notched rotating-disk configurations, and a notched pressure vessel. A sharp crack is simulated by a relatively narrow notch terminating in a root radius of 0.010 in or less. Stress distributions along the section of symmetry ahead of the notch tip are obtained using three-dimensional frozen-stress photoelasticity. The results are used to determine the stress-intensity factor, cK I , by three methods. Two of these are based on Irwin's expressions for the elastic stress field at the tip cf a crack, and the other is a result of Neuber's hyperbolic-notch analysis. Agreement, with available analytical solutions is good.
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Abbreviations
- a :
-
radius of hole, in
- b :
-
outside radius of disk, in
- B :
-
thickness of WOL specimen, in
- c :
-
distance from hole center to notch tip, in
- d :
-
minimum section ahead of notch tip, in
- D i :
-
inside diameter of notched pressure vessel, in
- h :
-
length of notch,h=c-a, in
- H :
-
half height of WOL specimen, in
- K I :
-
stress-intensity factor for Mode I type of displacement, psi-in. 1/2
- N :
-
rotational speed, rpm
- p :
-
pressure, psi
- P :
-
load, Ib
- R n :
-
notch-root radius, in
- t :
-
thickness of disk, in
- T :
-
wall thickness of pressure vessel, in
- x, y, z :
-
Cartesian-coordinate system
- r, θ, z :
-
cylindrical-coordinate system
- σ x , σ y , σ z :
-
stress components in Cartesian system
- σ r , σ θ , σ z :
-
stress components in cylindrical system
- σ n :
-
nominal stress, psi
- σ y max :
-
maximum stress at the notch tip, psi
- μ:
-
Poisson's ratio
- ρ:
-
mass density, 1b sec2/in.4
- ω:
-
rotational speed, radians/sec
References
Irwin G. R., Kies, J. A. andSmith, H. L., “Fracture Strengths Relative to Onset and Arrest of Crack Propagation,”Proc. ASTM,58,640–657 (1958).
Paris, P. C. and Sih, G., “Stress Analysis of Cracks, Fracture Toughness Testing and its Applications, ASTM Special Technical Publication No. 381.
Wells, A. A. andPost, D., “The Dynamic Stress Distribution Surrounding a Running Crack—A Photoelastic Analysis,”Proc. SESA,16 (1),69–92 (1958).
Irwin, G.R., Discussion of Ref. 3 above, Proc. SESA,16, (1),93–96 (1958).
Smith, D. G. and Smith, C. W., “Photoelastic Determination of Mixed Mode Stress Intensity Factors,” Presented at the Fourth National Symposium on Fracture Mechanics, Pittsburgh, Penna. (August 24–26, 1970).
Bradley, W. B. andKobayashi, A. S., “An Investigation of Propagating Cracks by Dynamic Photoelasticity,”Experimental Mechanics,10 (3),106–113 (March1970).
Bowie, O. L. andNeal, D. M., “The Effective Length of an Edge Slot in a Semi-Infinite Sheet Under Tension,”Int. Jnl. Fracture Mech.,3 (2),111–119 (June1967).
Neuber, H., “Theory of Notch Stresses,” Springer-Verlag, Berlin Translation by United States Atomic Energy Commission (1958).
Weiss, V. and Yukawa, S. “Critical Appraisal of Fracture Mechanics,” Fracture Toughness Testing and Its Applications, ASTM Special Technical Publication No. 381 (1965).
Peterson, R. E., “Stress Concentration Design Factors,”John Wiley and Sons, Inc., New York, Chapter 2 (1953).
Frocht, M. M., “Photoelasticity,”,1,John Wiley and Sons, Inc. (1941).
Manjoine, M. J., “Biaxial Brittle Fracture Tests”,Trans. ASME, Jnl. Basic Engr.,87,293–298 (June1965).
Brown, W. F. and Srawley, J. E., “Plane Strain Crack Toughness Testing of High Strength Metallic Materials,” Discussion by M.J. Manjoine, ASTM Special Technical Publication No. 410, 66–70 (1966).
Sankey, G. O., “Spin Fracture Tests of Nickel-Molybdenum-Vanadium Rotor Steels in the Brittle Fracture Range,”Proc. ASTM,60,721–732 (1960).
Winne, D. H. andWundt, B. M., “Application, of the Griffith-Irwin Theory of Crack Propagation to the Bursting Behavior of Disks, Including Analytical and Experimental Studies,”Trans. ASME,80,1643–1656 (Nov.1958).
Marloff, R. H., “A Photoelastic Verification of Energy Release Rates for Effectively Notched Rotating Disks,” M.S. Thesis, University of Pittsburgh (1964).
Ringler, T. N., “A Photoelastic Analysis of Singly Notched Spin Disk Specimens with Calculation of Stress Intensity Factors,” M.S. Thesis, University of Pittsburgh (1970).
Beuckner, H. F. and Giaever, I., “The Stress Concentration in a Notched Rotor Subjected to Centrifugal Forces,” Zeitschrift fur Angewante Mathematic und Mechanik, Band 46, Heft 5 (1966).
Bowie, O. L., “Analysis of an Infinite Plate Containing Radial Cracks Originating at the Boundary of an Internal Circular Hole,”Jnl. Math. & Physics,35,60–71 (April1956).
Gross, B. and Srawley, J. E., “Stress-Intensity Factors for Single-Edge-Notch Specimens in Bending or Combined Bending and Tension by Boundary Collocation of a Stress Function,” NASA Technical Note D-2603 (Jan. 1965).
Creager, M., “The Elastic Stress Field Near the Tip of a Blunt Crack,” M.S. Thesis, Lehigh University (1966).
Wahl, A. M., Leven, M. M. and Wilson, W. K., “Energy Release Rates for Biaxial Brittle Fracture Test Specimen,” Research Report WERL-8844-1 Westinghouse Research Laboratories (Aug. 1964).
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Marloff, R.H., Leven, M.M., Ringler, T.N. et al. Photoelastic determination of stress-intensity factors. Experimental Mechanics 11, 529–539 (1971). https://doi.org/10.1007/BF02329095
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DOI: https://doi.org/10.1007/BF02329095