Abstract
According to the elastic stress field solutions discussed in the previous chapter a stress singularity exists at the tip of an elastic crack. In practice, materials (especially metals) tend to exhibit a yield stress, above which they deform plastically. This means that there is always a region around the tip of a crack in a metal, where plastic deformation occurs, and hence a stress singularity cannot exist. The plastic region is known as the crack tip plastic zone. A rough estimate of the size of the plastic zone, whether in plane strain or plane stress, is simple to make. To start with, the considerations in this section are limited to plane stress.
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References
Irwin, G. R., Fracture, Handbuch der Physik VI, pp. 551–590, Flügge Ed., Springer (1958).
Irwin, G. R., Plastic zone near a crack and fracture toughness, Proc. 7th Sagamore Conf., p. IV-63 (1960).
Dugdale, D. S., Yielding of steel sheets containing slits, J. Mech. Phys. Sol., 8 (1960) pp. 100–108.
Burdekin, F. M. and Stone, D. E. W., The crack opening displacement approach to fracture mechanics in yielding materials, J. Strain Analysis, 1 (1966) pp. 145–153.
Barenblatt, G. I., The mathematical theory of equilibrium of cracks in brittle fracture, Advances in Appl. Mech., 7 (1962) pp. 55–129.
Bilby, B. A., Còttrell, A. H. and Swinden, K. H., The spread of plastic yield from a notch, Proc. Roy. Soc. A 272, (1963) pp. 304–310.
Bilby, B. A. and Swinden, K. H., Representation of plasticity at notches by linear dislocation arrays, Proc. Roy. Soc. A 285, (1965) pp. 22–30.
McClintock, F. A. and Irwin, G. R., Plasticity aspects of fracture mechanics, ASTM STP 381, (1965) pp. 84–113.
Duffy, A. R. et al., Fracture design practice for pressure piping, Fracture I, pp. 159–232. Liebowitz ed., Academic Press (1969).
Rooke, D. P., Elastic yield zone round a crack tip, Royal Aircr. Est., Farnborough, Tech. Note CPM 29 (1963).
Jacobs, J. A., Relaxation methods applied to the problem of plastic flow, Phil. Mag., F 41 (1950) pp. 349–358.
Stimpon, L. D. and Eaton, D. M., The extent of elastic-plastic yielding at the crack point of an externally notched plane stress tensile specimen, Aer. Res. Lab., Australia, Rept. ARL 24 (1961).
Hult, J. A. and McClintock, F. M., Elastic-plastic stress and strain distribution around sharp notches under repeated shear, IXth Int. Congr. Appl. Mech., 8 (1956) pp. 51–62.
McClintock, F. A., Ductile fracture instability in shear, J. Appl. Mech., 25 (1958) pp. 582–588.
McClintock, F. A., Discussion to fracture testing of high strength sheet materials, Mat. Res. and Standards, 1 (1961) pp. 277–279.
Tuba, I. S., A method of elastic-plastic plane stress and strain analysis, J. Strain Analysis, 1 (1966) pp. 115–122.
Rice, J. R. and Rosengren, G. F., Plane strain deformation near a crack tip in a power-law hardening material, J. Mech. Phys. Sol., 16 (1968) p. 1.
Bateman, D. A., Bradshaw, F. J. and Rooke, D. P., Some observations on surface deformation round cracks in stressed sheets, Roy. Aircr. Est. Farnborough TN-CPM 63 (1964).
Underwood, J. H. and Kendall, D. P., Measurement of plastic strain distributions in the region of a crack tip, Exp. Mechanics, (1969) pp. 296–304.
Hahn, G. T. and Rosenfield, A. R., Local yielding and extension of a crack under plane stress, Acta Met., 13 (1965) pp. 293–306.
Hahn, G. T., Hoagland, R. G. and Rosenfield, A. R., Local yielding attending fatigue crack growth, Met. Trans., 3 (1972) pp. 1189–1196.
Hahn, G. T. and Rosenfield, A. R., Plastic flow in the locale on notches and cracks in Fe-3Si steel under conditions approaching plane strain, Rept. to Ship structure Committee (1968).
Broek, D., A study on ductile fracture, Nat. Aerospace Inst. Amsterdam, Rept. TR 71021 (1971).
Dixon, J. R., Stress and strain distributions around cracks in sheet materials having various work hardening characteristics, Int. J. Fract. Mech., 1 (1965) pp. 224–243.
De Koning, A. U., Results of calculations with TRIM 6 and TRIAX 6 elastic-plastic elements, Nat. Aerospace Inst. Amsterdam, Rept. MP 73010 (1973).
Rice, J. R., The mechanics- of crack tip deformation and extension by fatigue, Brown University rept. NSF GK-286/3 (1966).
Swedlow, J. L., Williams, M. L. and Yang, W. H., Elastic-plastic stresses and strains in cracked plates, 1st ICF Conf., I, pp. 259–282 (1965).
Gerberich, W. W. and Swedlow, J. L., Plastic strains and energy density in cracked plates. Experiments, Exp. Mech., 4 (1964) pp. 335–344.
Gerberich, W. W. and Swedlow, J. L., Plastic strains and energy density in cracked plates. Theory, Exp. Mech., 4 (1964) pp. 345–351.
Oppel, G. U. and Hill, P. W., Strain measurements at the root of cracks and notches, Exp. Mechanics, 4 (1964) pp. 206–214.
Hahn, G. T. and Rosenfield, A. R., Experimental determination of plastic constraint ahead of a sharp crack under plane-strain conditions, ASM Trans., 59 (1966) pp. 909–919.
Allen, F. C., Effect of thickness on the fracture toughness of 7075 aluminium in the T6 and T73 conditions, ASTM STP 486, (1971) pp. 16–38.
Feddersen, C. E. et al., An experimental and theoretical investigation of plane stress fracture of 2024-T351 Al-alloy, Battelle Columbus rept. (1970).
Broek, D., The residual strength of light alloy sheets containing fatigue cracks, Aerospace Proeedings 1966, pp. 811–835, McMillan (1966).
Christensen, R. H. and Denke, P. H., Crack strength and crack propagation characteristics of high strength materials. ASD-TR-61-207 (1961).
Weiss, V. and Yukawa, S., Critical appraisal of fracture mechanics, ASTM STP 381, (1965) pp. 1–29.
Bluhm, J. I., A model for the effect of thickness on fracture toughness, ASTM Proc., 61 (1961) pp. 1324–1331.
Sih, G. C. and Hartranft, R. J., Variation of strain energy release rate with plate thickness, Int. J. Fracture, 9 (1973) pp. 75–82.
Anderson, W. E., Some designer oriented views on brittle fracture, Battelle Northwest rept. SA-2290 (1969).
Isherwood, D. P. and Williams, J. G., The effect of stress-strain properties on notched tensile fracture in plane stress, Eng. Fract. Mech., 2 (1970) pp. 19–35.
Broek, D. and Vlieger, H., The thickness effect in plane stress fracture toughness, Nat. Aerospace Inst. Amsterdam, Rept. TR 74032 (1974).
Broek, D., Fail safe design procedures, Agard Fracture Mechanics Survey, Chapter II (1974).
Irwin, G. R., Fracture mode transition of a crack traversing a plate, J. Basic Eng., 82 (1960) pp. 417–425.
Srawley, J. E. and Brown, W. F., Fracture toughness testing methods, ASTM STP, 381 (1965) pp. 133–196.
Broek, D., The effect of sheet thickness on fracture toughness, Nat. Aerospace Inst. Amsterdam. Rept. TR-M-2160 (1966).
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Broek, D. (1982). The crack tip plastic zone. In: Elementary engineering fracture mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4333-9_4
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DOI: https://doi.org/10.1007/978-94-009-4333-9_4
Publisher Name: Springer, Dordrecht
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