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A numerical procedure for the approximate WF solution of mode I SIFs in 3D geometries under arbitrary load

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Abstract

A numerical procedure was developed for the approximate weigth function (AWF) evaluation of reliable stress intensity factor (SIF) for part-through Mode I cracks for general load. Different from other WF procedures which require closed form reference SIFs, this procedure requires only limited number of discrete SIF solutions directly obtained from other numerical methods as reference SIFs to compute continuous SIFs as function of both the crack size and the location along the crack front. As an implement to the general numerical methods in the Damage and Safe Life analysis, this procedure substantially increases the value of numerical SIF results. The present procedure is relative simple, with most of basic relations being analytically soved, and therefore efficient in use. Several examples were presented to demonstrate the accuracy of this procedure.

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References

  • AnderssonB.; BabuskaI.; vonPetersdorffT.; FalkU. 1992: Reliable stress and fracture mechanics analysis of complex aircraft components using a h-p version of FEM. FFA TN 1992-17, The Aeronautical Research Inst. of Sweden, Stockholm

    Google Scholar 

  • BuecknerH. G. 1970: A novel principle for the computation of stress intensity factors. ZAMM 50(9): 529–546

    Google Scholar 

  • FettT. 1989: An approximative crack opening displacement field for embedded cracks. Engng. Frac. Mech. 32(5): 731–737

    Google Scholar 

  • FettT.; MattheckC.; MunzD. 1987: On the calculation of crack opening displacement from the stress intensity factor, Engng. Frac. Mech. 27(6): 697–751

    Google Scholar 

  • GrandtA. F.Jr. 1981: Crack face pressure loading of semielliptical cracks located along the bore of a hole. Engng. Frac. Mech. 14: 843–852

    Google Scholar 

  • GrandtA. F.Jr.; KullgrenT. E. 1981: Stress intensity factors for corner cracked holes under general loading conditions. Trans. of the ASME, J. of Engng. Mater. and Tech. 103: 171–176

    Google Scholar 

  • HeliotJ.; LabbensR. C.; Pellissier-TanonA. 1979: Semi-elliptical cracks in a cylinder subjected to stress gradients. ASTM STP 677, (Edited by C. W. Smith) 341–364

    Google Scholar 

  • IsidaM.; NoguchiH. 1984: Tension of a plate containing an embedded elliptical crack. Engng Fracture Mech. 20: 387–408

    Google Scholar 

  • KullgrenT. E.; SmithF. W.; GanongG. P. 1978: Quarter-elliptical cracks emanating from holes in plates ASME J. of Engng. Mater. and Tech. 100: 144–149

    Google Scholar 

  • LeslieBanks-Sills 1991: Application of the finite element method to linear elastic fracture mechanics. Appl. Mech. Rev. 44(10): 447–461

    Google Scholar 

  • McGowan J. J., ed. 1980: A critical evaluation of numerical solutions to the ‘Benchmark’ surface flaw problem. Exper. Mech. 20(8): 253–264

    Google Scholar 

  • Murakami, T. et al. 1987: Stress intensity factors handbook. Pergamon Press

  • NewmannJ. C.Jr.; RajuI. S. 1981: An empirical stress intensity factor equation for the surface crack. Engng. Frac. Mech. 15(1–2): 185–192

    Google Scholar 

  • Newmann, J. C., Jr.; Raju, I. S. 1983: Stress-intensity factor equations for cracks in three-dimensional finite bodies. Fracture Mechanics: Fourteenth Symposium-V.I: Theory and Analysis. ASTM STP 791, J. C. Lewis and G. Sines, Eds., I-238–I-265

  • Newmann, J. C., Jr.; Raju, I. S. 1984: Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads. NASA Technical Memorandum 85793

  • Newmann, J. C., Jr.; Raju, I. S. 1979: Analysis of surface cracks in finite plates under tension or bending loads.NASA TP-1578

  • NewmannJ. C.Jr.; RajuI. S. 1981: Stress intensity factor equations for cracks in three-dimentional finite bodies. NASA Technical Memorandam 83200, 1–49

    Google Scholar 

  • NishiokaT.; AtluriS. N. 1983: Analytical solution for embedded elliptical cracks and finite element-alternating method for elliptical surface cracks, subjected to arbitrary loadings. Engng. Fracture Mech. 17: 247–268

    Google Scholar 

  • NishiokaT.; AtluriS. N. 1990: The first-order variation of the displacement field due to geometrical changes in an elliptical crack. J. of applied Mechanics, ASME 57(3): 639–646

    Google Scholar 

  • ParisP. C.; SihG. C. 1965: Stress analysis of cracks. ASTM STP 381: 32.

    Google Scholar 

  • PerezR.; TritschD. E.; GrandtA. F.Jr. 1986: Interpolative estimates of stress intensity factors for fatigue crack growth predictions. Eng. Frac. Mech. 24(4): 629–633

    Google Scholar 

  • PetroskiH. J.; AchenbachJ. D. 1978: Calculation of approximate weight function from a stress intensity factor. Eng. Frac. Mech. 10: 257–266

    Google Scholar 

  • RajuI. S.; NewmannJ. C.Jr. 1979: Stress-intensity factors for a wide range of semi-elliptical cracks in finite-thickness plates. Engng. Frac. Mech. 11: 817–829

    Google Scholar 

  • Raju, I. S.; Newman, J. C., Jr.; Atluri, S. N. 1992: Crack mouth displacements for semielliptical surface cracks subjected to remote tension and bending loads. in Fracture Mechanics: Twenty-Second Symposium (Vol. II), ASTM STP 1131: 19–28

  • RiceJ. R. 1972: Some remarks on elastic crack tip stress fields. Int. J. Solids Structure 8: 751–758

    Google Scholar 

  • RiceR. R.; LevyN. 1972: The part-through surface crack in an elastic plate. J. App. Mech. 39: 185–194

    Google Scholar 

  • SchijveJ. 1983: Interpolation between calculated stress-intensity factors for semi and quater elliptical cracks. Report LR-368, Delft University of Technology, The Netherlands (January)

    Google Scholar 

  • ShahR. C. 1976: Stress intensity factors for through and part-through cracks originating at fastener holes. in Mechanics of Crack Growth, ASTM STP 590: 429–459

    Google Scholar 

  • SmithF. W.; EmeryA. F.; KobayashiA. S. 1967: Stress intensity factors for semi-circular cracks, Part 2-Semi-infinite solid. J. Appl. Mech. 34, Trans, ASME 89: 953–959

    Google Scholar 

  • TimoshenkoS.; GoodierJ. N. 1951. Theory of Elasticity. 2nd Ends. P. 80, McGraw-Hill, New York

    Google Scholar 

  • TraceyK. M. 1973: 3D elastic singularity element of evaluation of K along an arbitrary crack front. Int. J. Fracture 9: 340–343

    Google Scholar 

  • VainshtokV. A.; VarfolomeyevI. V. 1988: A complete system of equations of the weight function method for three-dimensional crack problems. Int. J. of Fracture 38: R71–74

    Google Scholar 

  • VainshtokV. A.; VarfolomeyevI. V. 1990: Stress intensity factor analysis for part-elliptical cracks in structures. Int. J. of Fracture 46: 1–24

    Google Scholar 

  • WangG. S. 1992a: Weight function estimation of SIFs for Mode I part-elliptical crack under arbitrary load. Engng. Fracture Mech. 41(5): 659–684

    Google Scholar 

  • WangG. S. 1992b: SIFs of part-through moe I cracks for uniform crack surface pressure. Engng. Frac. Mech., 43: 353–378

    Google Scholar 

  • WangG. S. 1992c: A solution for SIFs of part-elliptical cracks based on approximate crack surface displacement and energy method. Int. J. of Fracture 58: 157–176

    Google Scholar 

  • WangG. S. 1993a: A generalised solution for the crack surface displacement of mode I two-dimensional part-elliptical crack. Int. J. Fracture, 59: 161–187

    Google Scholar 

  • WangG. S. 1993b: Some corrections and supplements to ‘A generalised solution for the crack surface displacement of the mode I two dimension part elliptical crack’. Int. J. of Fracture 62(3): R39-R48

    Google Scholar 

  • WangG. S. 1993c: A generalised WF solution for mode I 2D part-elliptical cracks. Engng. Frac. Mech. 45(2): 177–208

    Google Scholar 

  • ZouYong, 1990: The normal displacement of a crack surface with arbitrary shape, Eng. Frac. Mech. 37(3): 631–640

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Aeronautical and Astronautical Structures, the Royal Institute of Sweden, P. O. Box 11021, S-161 11, Bromma, Sweden

    G. S. Wang

  2. the Structures Division, The Aeronautical Research Institute of Sweden, P. O. Box 11021, S-161 11, Bromma, Sweden

    G. S. Wang

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  1. G. S. Wang
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Communicated by S. N. Atluri, 23 August 1994

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Wang, G.S. A numerical procedure for the approximate WF solution of mode I SIFs in 3D geometries under arbitrary load. Computational Mechanics 15, 426–442 (1995). https://doi.org/10.1007/BF00350356

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