0
REVIEW ARTICLES

Stress singularities in classical elasticity–I: Removal, interpretation, and analysis

[+] Author and Article Information
GB Sinclair

Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803-6413

Appl. Mech. Rev 57(4), 251-298 (Oct 12, 2004) (48 pages) doi:10.1115/1.1762503 History: Online October 12, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.

References

Thomson (Lord Kelvin)  W (1848), Note on the integration of the equations of equilibrium of an elastic solid, Camb. Dublin Math. J. 3, 87–89.
Boussinesq  J (1878), Equilibrium of an elastic isotropic half-space supporting different loads in the absence of gravity, Acad. Sci., Paris, C. R. 86, 1260–1263 (in French).
Cerruti V (1882), Studies of the equilibrium of isotropic elastic bodies, Reale Academia dei Lincei, Serie3a,Memorie della Classe di Scienze Fisiche, Matematiche e Naturali13 , 81–122 (in Italian).
Mindlin  RD (1936), Force at a point in the interior of a semi-infinite solid, Physics (N.Y.) 7, 195–202.
Poulos HG, and Davis EH (1974), Elastic Solutions for Soil and Rock Mechanics, John Wiley and Sons, Inc, New York, NY.
Michell  JH (1900), Elementary distributions of plane stress, Proc. London Math. Soc. 32, 35–61.
Flamant  M (1892), On the distribution of stresses in a two-dimensional solid under transverse loading, Acad. Sci., Paris, C. R. 114, 1465–1468 (in French).
Boussinesq  J (1892), On the local disturbances which are produced under concentrated loads, uniformly distributed in the out-of-plane direction, and acting on the upper surface of a half-space, either horizontally or as a pair vertically, Acad. Sci., Paris, C. R. 114, 1510–1516 (in French).
Melan  E (1932), The state of stress due to a concentrated load applied within a half-plane, Z. Angew. Math. Mech. 12, 343–346 (in German).
Kurshin  LM (1959), Mixed plane boundary value problem of the theory of elasticity for a quadrant, J. Appl. Math. Mech. 23, 1403–1408.
Sternberg  E, and Eubanks  RA (1955), On the concept of concentrated loads and an extension of the uniqueness theorem in the linear theory of elasticity, J. Ration. Mech. Anal. 4, 135–168.
Love AEH (1944), A Treatise on the Mathematical Theory of Elasticity, 4th Edition, Dover Publ, New York NY.
Turteltaub  MJ, and Sternberg  E (1968), On concentrated loads and Green’s functions in elastostatics, Arch. Ration. Mech. Anal. 29, 193–240.
Chowdhury  KL (1983), Solution of the problem of a concentrated torque on a semi-space by similarity transformations, J. Elast. 13, 87–90.
Chen  T (1992), Some remarks on the solutions of a concentrated torque and double forces on an elastic half-space, ASME J. Appl. Mech. 59, 690–692.
Timoshenko SP, and Goodier JN (1970), Theory of Elasticity, 3rd Edition, McGraw-Hill Book Co, New York NY.
Kolossoff G (1910), On an application of the theory of complex variables to the two-dimensional problem of elasticity theory, Dissertation, St Petersburg, Russia.
Kolossoff  G (1914), On some properties of the plane problem of elasticity theory, Math. Phys. 62, 384–409 (in German).
Inglis  CE (1913), Stresses in a plate due to the presence of cracks and sharp corners, Inst. Nav. Archit. Mar. Eng., Trans. 55, 219–241.
Williams  ML (1952), Stress singularities resulting from various boundary conditions in angular corners of plates in extension, ASME J. Appl. Mech. 19, 526–528.
Williams  ML (1959), The stresses around a fault or crack in dissimilar media, Bull. Seismol. Soc. Am. 49, 199–204.
Sadowsky  MA (1928), Two-dimensional problems of elasticity theory, Z. Angew. Math. Mech. 8, 107–121 (in German).
Abramov  BM (1937), The problem of contact of an elastic infinite half-plane with an absolutely rigid rough foundation, C. R. (Dokl.) Acad. Sci. URSS 17, 173–178.
Zak  AR (1964), Stresses in the vicinity of boundary discontinuities in bodies of revolution, ASME J. Appl. Mech. 31, 150–152.
Dempsey  JP, and Sinclair  GB (1981), On the singular behavior at the vertex of a bi-material wedge, J. Elast. 11, 317–327.
Thomson W, and Tait PG (1867), A Treatise on Natural Philosophy, Cambridge Univ Press, Cambridge, UK (this book is also available in two parts as Principles of Mechanics and Dynamics, Dover Pub Inc, New York NY).
Brahtz  JHA (1933), Stress distribution in a reentrant corner, Trans. ASME Ser. E. 55, 31–37.
Knein  M (1926), On the theory of pressure testing, Z. Angew. Math. Mech. 6, 414–416 (in German).
Dempsey  JP, and Sinclair  GB (1979), On the stress singularities in the plane elasticity of the composite wedge, J. Elast. 9, 373–391.
Sneddon IN (1951), Fourier Transforms, McGraw-Hill Book Co, New York NY.
ABAQUS personnel (1997), ABAQUS Standard User’s Manual, Revision 5.7, Vol I, Hibbitt, Karlsson and Sorensen Inc, Pawtucket RI.
ANSYS personnel (1995), ANSYS User’s Manual, Revision 5.2, Vol I, ANSYS Inc, Canonsburg PA.
Sinclair  GB, and Epps  BE (2002), On the logarithmic stress singularities induced by the use of displacement shape functions in boundary conditions in submodelling, Commun. Numer. Methods Eng. 18, 121–130.
Frisch-Fay R (1962), Flexible Bars, Butterworth Inc, Washington DC.
Kondo  M, and Sinclair  GB (1985), A simple substructuring procedure for finite element analysis of stress concentrations, Commun. Numer. Methods Eng. 1, 215–218.
Cherepanov  GP (1967), Crack propagation in continuous media, J. Appl. Math. Mech. 31, 503–512.
Hutchinson  JW (1968), Singular behaviour at the end of a tensile crack in a hardening material, J. Mech. Phys. Solids 16, 13–31.
Rice  JR, and Rosengren  GF (1968), Plane strain deformation near a crack tip in a power-law hardening material, J. Mech. Phys. Solids 16, 1–12.
Ramberg W, and Osgood WR (1943), Description of stress-strain curves by three parameters, Tech Note 902, Natl Advisory Committee on Aeronautics, Washington DC.
Chao  YT, and Yang  S (1992), Singularities at the apex of a sharp V-notch in a linear strain hardening material, Int. J. Fract. 57, 47–60.
Rudge  MRH, and Tiernan  DM (1995), Interfacial stress singularities in a bimaterial wedge, Int. J. Fract. 74, 63–75.
Zhang  N, and Joseph  PF (1998), A nonlinear finite element eigenanalysis of singular plane stress fields in bimaterial wedges including complex eigenvalues, Int. J. Fract. 90, 175–207.
Wong  FS, and Shield  RT (1969), Large plane deformations of thin elastic sheets of neo-Hookean material, Z. Angew. Math. Phys. 20, 176–199.
Knowles  JK, and Sternberg  E (1973), An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack, J. Elast. 3, 67–107.
Knowles  JK, and Sternberg  E (1974), Finite-deformation analysis of the elastostatic field near the tip of a crack: Reconsideration and higher-order results, J. Elast. 4, 201–233.
Geubelle  PH, and Knauss  WG (1994), Finite strains at the tip of a crack in a sheet of hyperelastic material: I. Homogeneous case, J. Elast. 35, 61–98.
Geubelle  PH, and Knauss  WG (1994), Finite strains at the tip of a crack in a sheet of hyperelastic material: II. Special bimaterial cases, and III. General bimaterial case, J. Elast. 35, 99–174.
Knowles  JK, and Sternberg  E (1975), On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elasticity, Int. J. Solids Struct. 11, 1173–1201.
Ru  CQ (1997), Finite deformations at the vertex of a bi-material wedge, Int. J. Fract. 84, 325–350.
Duva  JM (1990), The singularity strength at the apex of a wedge undergoing finite deformation, ASME J. Appl. Mech. 57, 577–580.
Griffith  AA (1920), The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. London, Ser. A A221, 163–198.
Mansfield EH (1967), On the stresses near a crack in an elastic sheet, Tech Report 67030, Royal Aircraft Est, Cranfield UK.
Truesdell  C (1952), The mechanical foundations of elasticity and fluid dynamics, J. Ration. Mech. Anal. 1, 125–300; (1953), 2, 593–616.
Zheltov  YuP, and Khristianovitch  SA (1955), On the mechanism of hydraulic fracture of an oil bearing stratum, Izvestiya Akademiia Nauk SSSR, Otd. Tekhn. Nauk 5, 3–41 (in Russian).
Tada H, Paris PC, and Irwin GR (1985), The Stress Analysis of Cracks Handbook, 2nd Edition, Paris Productions Inc, St Louis MO.
Barenblatt  GL (1959), On the equilibrium of cracks due to brittle fracture, Dokl. Akad. Nauk SSSR 127, 47–50 (in Russian).
Barenblatt  GI (1962), The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech. 7, 55–129.
Willis  JR (1967), A comparison of the fracture criteria of Griffith and Barenblatt, J. Mech. Phys. Solids 15, 151–162.
Goodier JN (1968), Mathematical theory of equilibrium cracks, Fracture, An Advanced Treatise H Liebowitz (ed), Vol II, Academic Press, New York NY, 1–66.
Peierls  R (1940), The size of a dislocation, Proc. Phys. Soc. London 52, 34–37.
Hirth JP, and Lothe L (1968), Theory of Dislocations, McGraw-Hill Book Co, New York NY.
Cherepanov GP (1979), Mechanics of Brittle Fracture, McGraw-Hill Book Co, New York NY.
Lennard-Jones  JE (1931), Cohesion, Proc. Phys. Soc. London 43, 461–482.
Israelachvili JN (1992), Intermolecular and Surface Forces, 2nd Edition, Academic Press, San Diego CA.
Lamé MG (1852), Lectures on the Mathematical Theory of the Elasticity of Solid Bodies, Bachelier Pub, Paris, France (in French).
Sinclair  GB, and Meda  G (2001), On some anomalies in Lamé’s solutions for elastic solids with holes, ASME J. Appl. Mech. 68, 132–134.
Sinclair  GB (1996), On the influence of cohesive stress-separation laws on elastic stress singularities, J. Elast. 44, 203–221.
Sinclair GB (1999), A bibliography on the use of cohesive laws in solid mechanics, Report SM 99-8, Dept of Mech Eng, Carnegie Mellon Univ, Pittsburgh PA.
Cribb  JL, and Tomkins  B (1967), On the nature of the stress at the tip of a perfectly brittle crack, J. Mech. Phys. Solids 15, 135–140.
Needleman A (1994), Computational modeling of material failure, Proc of 12th US Nat Congress of Appl Mech, Seattle WA, S34–S42.
Sinclair GB, Meda G, and Smallwood BS (1995), On the physical stress field for the Griffith crack, Proc of 15th Canadian Congress of Appl Mech, Victoria, British Columbia, 1 , 210–211.
Sinclair GB (2000), Ridding elastic configurations of stress singularities, Proc of 20th Southeastern Conf of Theoretical and Appl Mech, Callaway Gardens, GA, pp SM93.1–8.
Johnson KL (1985), Contact Mechanics, Cambridge Univ Press, Cambridge, UK.
Hertz  H (1882), On the contact of elastic solids, J. Reine Angew. Math. 92, 156–171 (in German: for an account in English, see Johnson [73], Ch 4).
Steuermann  E (1939), To Hertz’s theory of local deformations in compressed elastic bodies, C. R. (Dokl.) Acad. Sci. URSS 25, 359–361.
Persson A (1964), On the stress distribution of cylindrical elastic bodies in contact, Dissertation, Chalmers Univ of Technology, Göteborg, Sweden.
Gladwell GML (1980), Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff Int Pub, Alphen aan den Rijn, The Netherlands.
Mossakovskii  VI (1954), The fundamental mixed problem of the theory of elasticity for a half-space with a circular line separating the boundary conditions, Prikl. Mat. Mekh. 18, 187–196 (in Russian).
Goodman  LE (1962), Contact stress analysis of normally loaded rough spheres, ASME J. Appl. Mech. 29, 515–522.
Mossakovskii  VI (1963), Compression of elastic bodies under conditions of adhesion (axisymmetric case), J. Appl. Math. Mech. 27, 630–643.
Spence  DA (1968), Self similar solutions to adhesive contact problems with incremental loading, Proc. R. Soc. London, Ser. A A305, 55–80.
Spence  DA (1975), The Hertz contact problem with finite friction, J. Elast. 5, 297–319.
Dundurs  J, and Comninou  M (1979), Some consequences of the inequality conditions in contact and crack problems, J. Elast. 9, 71–82.
Irwin  GR (1957), Analysis of stresses and strains near the end of a crack traversing a plate, ASME J. Appl. Mech. 24, 361–364.
Keating  RF, and Sinclair  GB (1995), On the fundamental energy argument of elastic fracture mechanics, Int. J. Fract. 74, 43–61.
Eshelby  JD (1951), The force on an elastic singularity, Philos. Trans. R. Soc. London, Ser. A A244, 87–112.
Sanders  JL (1960), On the Griffith-Irwin fracture theory, ASME J. Appl. Mech. 27, 352–353.
Rice  JR (1968), A path independent integral and the approximate analysis of strain concentration by notches and cracks, ASME J. Appl. Mech. 35, 379–386.
Irwin GR (1948), Fracture dynamics, Fracturing of Metals, Am Soc for Metals, Cleveland OH, 147–166.
Orowan  E (1949), Fracture and strength of solids, Reports on Progress in Physics 12, 185–232.
England  AH (1965), A crack between dissimilar media, ASME J. Appl. Mech. 32, 400–402.
Comninou  M (1977), The interface crack, ASME J. Appl. Mech. 44, 631–636.
Sinclair  GB (1980), On the stress singularity at an interface crack, Int. J. Fract. 16, 111–119.
Atkinson  C (1977), On stress singularities and interfaces in linear elastic fracture mechanics, Int. J. Fract. 13, 807–820.
He  M-Y, and Hutchinson  JW (1989), Kinking of a crack out of an interface, ASME J. Appl. Mech. 56, 270–278.
Suo  Z, and Hutchinson  JW (1989), Sandwich test specimens for measuring interface crack toughness, Mater. Sci. Eng., A A107, 135–143.
Malyshev  BM, and Salganik  RL (1965), The strength of adhesive joints using the theory of cracks, Int. J. Fract. Mech. 1, 114–128.
Comninou  M (1990), An overview of interface cracks, Eng. Fract. Mech. 37, 197–208.
Knowles  JK, and Pucik  TA (1973), Uniqueness for plane crack problems in linear elastostatics, J. Elast. 39, 223–236.
Irwin GR (1960), Fracture mechanics, Structural Mechanics, Proc of 1st Symp on Naval Structural Mechanics JN Goodier and NJ Hoff (eds), Pergamon Press, Oxford, UK, 557–591.
Rice JR (1968), Mathematical analysis in the mechanics of fracture, Fracture, An Advanced Treatise H Liebowitz (ed), Vol II, Academic Press, New York, NY 191–311.
Erdogan  F, and Sih  GC (1963), On the crack extension in plates under plane loading and transverse shear, ASME J. Basic Eng. 85, 519–527.
Rice  JR (1988), Elastic fracture mechanics concepts for interfacial cracks, ASME J. Appl. Mech. 55, 98–103.
Hutchinson  JW, and Suo  Z (1991), Mixed mode cracking in layered materials, Adv. Appl. Mech. 29, 63–191.
Rooke DP, and Cartwright DJ (1976), Compendium of Stress Intensity Factors, Hillingdon Press, Uxbridge, Middlesex, UK.
Sih GC (1973), Handbook of Stress Intensity Factors, Vol 1, Inst of Fracture and Solid Mechanics, Lehigh Univ, Bethlehem PA.
Murakami Y, Aoki S, Hasebe N, Itoh Y, Miyata H, Miyazaki N, Terada H, Tohgo K, Toya M, and Yuuki R (1987), Stress Intensity Factors Handbook, Vol 1, Pergamon Press, Oxford, UK.
Murakami Y, Aoki S, Hasebe N, Itoh Y, Miyata H, Miyazaki N, Terada H, Tohgo K, Toya M, and Yuuki R (1990), Stress Intensity Factors Handbook, Vol 2, Revised Edition, Pergamon Press, Oxford, UK.
Murakami Y, Hanson MT, Hasebe N, Itoh Y, Kishimoto K, Miyata H, Miyazaki N, Terada H, Tohgo K, and Yuuki R (1992), Stress Intensity Factors Handbook, Vol 3, Pergamon Press, Oxford, UK.
Srawley JE, and Brown Jr, WF (1965), Fracture toughness testing methods, Fracture Toughness Testing and Its Applications, STP No 381, Am Soc for Testing and Materials, Philadelphia, PA 133–196.
ASTM (1998), Standard test method for plane-strain fracture toughness of metallic materials, E399-90 (reapproved 1997), 1998 Annual Book of ASTM Standards, Vol 3.01, Am Soc for Testing and Materials, Philadelphia PA, 413–443.
Heyer RH, and McCabe DE (1970) Evaluation of a method of test for plane strain fracture toughness using a bend specimen, Review of Developments in Plane Strain Fracture Toughness Testing, STP No 463, Am Soc for Testing and Materials, Philadelphia PA, 22–41.
McCabe  DE (1972), Evaluation of the compact tension specimen for determining plane strain fracture toughness of high strength materials, J. Mater. 7, 449–454.
Underwood  JH, and Kendall  DP (1978), Cooperative plane strain fracture toughness tests with C-shaped specimens, J. Test. Eval. 6, 296–300.
Hudson  CM, and Seward  SK (1978), A compendium of sources of fracture toughness and fatigue-crack growth data for metallic alloys, Int. J. Fract. 14, R151–R184.
Hudson  CM, and Seward  SK (1982), A compendium of sources of fracture toughness and fatigue-crack growth data for metallic alloys—Part II, Int. J. Fract. 20, R59–R117.
Hudson  CM, and Seward  SK (1989), A compendium of sources of fracture toughness and fatigue-crack growth data for metallic alloys—Part III, Int. J. Fract. 39, R43–R63.
Hoysan  SF, and Sinclair  GB (1993), On the variability of fracture toughness, Int. J. Fract. 60, R43–R49.
Sinclair  GB, and Chambers  AE (1987), Strength size effects and fracture mechanics: What does the physical evidence say? Eng. Fract. Mech. 26, 279–310.
Sinclair  GB, and Pieri  RV (1990), On obtaining fatigue crack growth parameters from the literature, Int. J. Fatigue 12, 57–62.
Chamis CC (1969), Failure criteria for filamentary composites, NASA Tech Note D-5367, NASA, Washington DC.
Valliappan S, Kjellberg S, and Svensson NL (1980), Finite element analysis of total hip prosthesis, Proc of Int Conf on Finite Elements in Biomechanics, Tucson AZ, Vol 2, 527–548.
Belie  RG, and Reddy  JN (1980), Direct prediction of fracture for two-dimensional plane stress structures, Comput. Struct. 11, 49–53.
Kim  YJ, and Hsu  TR (1982), A numerical analysis on stable crack growth under increasing load, Int. J. Fract. 20, 17–32.
Chen  C-N (1993), Nonlinear fracture assessment by using the finite element method, Eng. Fract. Mech. 46, 57–77.
Wells AA (1961), Unstable crack propagation in metals—Cleavage and fast fracture, Proc of the Crack Propagation Symp, Cranfield, UK, Vol 1, 210–230.
Andersson  H (1973), A finite-element representation of stable crack-growth, J. Mech. Phys. Solids 21, 337–356.
British Standards Inst (1979), Methods for crack opening displacement (COD) testing, BS 5762, British Standards Inst, London, UK.
ASTM (1998), Standard test method for crack-tip opening displacement (CTOD) fracture toughness measurement, E1290-93, 1998 Annual Book of ASTM Standards, Vol. 3.01, Am Soc for Testing and Materials, Philadelphia, PA, 814–823.
Cottrell AH (1961), Theoretical aspects of radiation damage and brittle fracture in steels, Steels for Reactor Pressure Circuits, Special Report No 69, Iron and Steel Inst, London, UK, 281–296.
Burdekin  FM (1981), Assessment of defects: The C.O.D. approach, Philos. Trans. R. Soc. London, Ser. A A299, 155–167.
Sinclair  GB (1985), Some inherently unreliable practices in present day fracture mechanics, Int. J. Fract. 28, 3–16.
Williams ML (1951), Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending, Proc of 1st US Natl Congress of Appl Mech, Illinois Inst of Tech, Chicago IL, 325–329.
Kitover  KA (1952), On the use of special systems of biharmonic functions for the solution of some problems in the theory of elasticity, Prikl. Mat. Mekh. 16, 739–748 (in Russian).
Huth  JH (1953), The complex-variable approach to stress singularities, ASME J. Appl. Mech. 20, 561–562.
Williams  ML (1956), The complex-variable approach to stress singularities—II, ASME J. Appl. Mech. 23, 477–478.
Bogy  DB (1968), Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading, ASME J. Appl. Mech. 35, 460–466.
Tranter  CJ (1948), The use of the Mellin transform in finding the stress distribution in an infinite wedge, Q. J. Mech. Appl. Math. 1, 125–130.
Coker EG, and Filon LNG (1931), A Treatise on Photo-Elasticity, Cambridge Univ Press, UK.
Williams  ML (1957), On the stress distribution at the base of a stationary crack, ASME J. Appl. Mech. 24, 109–114.
Bogy  DB (1970), On the problem of edge-bonded elastic quarter-planes loaded at the boundary, Int. J. Solids Struct. 6, 1287–1313.
Bogy  DB, and Wang  KC (1971), Stress singularities at interface corners in bonded dissimilar isotropic elastic materials, Int. J. Solids Struct. 7, 993–1005.
Dempsey  JP (1981), The wedge subjected to tractions: A paradox resolved, J. Elast. 11, 1–10.
Ting  TCT (1984), The wedge subjected to tractions: A paradox re-examined, J. Elast. 14, 235–247.
Ting  TCT (1996), Paradoxes puzzles, and dilemmas in mechanics, Chinese J. Mech. 12, 25–32.
Sinclair  GB (1980), On the singular eigenfunctions for plane harmonic problems in composite regions, ASME J. Appl. Mech. 47, 87–92.
Ting  TCT (1985), Asymptotic solution near the apex of an elastic wedge with curved boundaries, Q. Appl. Math. 42, 467–476.
Atkinson  C (1979), Stress singularities and fracture mechanics, Appl. Mech. Rev. 32, 123–135.
Hwang  KC, Yu  SW, and Yang  W (1990), Theoretical study of crack-tip singularity fields in China, Appl. Mech. Rev. 43, 19–33.
Murakami Y (1992), Stress singularity for notch at bimaterial interface, Stress Intensity Factors Handbook, Vol 3, Murakami et al. Pergamon Press, Oxford, UK, Ch 18, 963–1062.
Sinclair GB (1998), FEA of singular elasticity problems, Proc of 8th Int ANSYS Conf, Pittsburgh, PA, Vol 1, 225–236.
Westergaard  HM (1939), Bearing pressures and cracks, ASME J. Appl. Mech. 6, A-49–A-53.
Gallagher RH (1978), A review of finite element techniques in fracture mechanics, Proc of 1st Int Conf on Numerical Methods in Fracture Mechanics, AR Luxmoore and DRJ Owen (eds), Univ of Wales, Swansea UK, 1–25.
Luxmoore AR, and Owen DRJ (eds) (1978), Proceedings of the First International Conference on Numerical Methods in Fracture Mechanics, Univ of Wales, Swansea, UK.
Luxmoore AR, and Owen DRJ (eds) (1980), Proceedings of the Second International Conference on Numerical Methods in Fracture Mechanics, Univ of Wales, Swansea, UK.
Luxmoore AR, and Owen DRJ (eds) (1984), Proceedings of the Third International Conference on Numerical Methods in Fracture Mechanics, Univ of Wales, Swansea, UK.
Luxmoore AR, Owen DRJ, Rajapakse YPS, and Kanninen MF (eds) (1987), Proceedings of the Fourth International Conference on Numerical Methods in Fracture Mechanics, Southwest Research Institute, San Antonio, TX.
Luxmoore AR, and Owen DRJ (eds) (1990), Proceedings of the Fifth International Conference on Numerical Methods in Fracture Mechanics, FhG Inst für Werkstoffmechnik, Freiburg, Germany.
Henshell  RD, and Shaw  KG (1975), Crack tip finite elements are unnecessary, Int. J. Numer. Methods Eng. 9, 495–507.
Barsoum  RS (1976), On the use of isoparametric finite elements in linear fracture mechanics, Int. J. Numer. Methods Eng. 10, 25–37.
Wait  R (1978), Finite element methods for elliptic problems with singularities, Comput. Methods Appl. Mech. Eng. 13, 141–150.
Lim  IL, Johnston  IW, and Choi  SK (1993), Application of singular quadratic distorted isoparametric elements in linear fracture mechanics, Int. J. Numer. Methods Eng. 36, 2473–2499.
Meda G, and Sinclair GB (1994), On the use of the H-integral to extract stress intensity factors, Proc of 6th Int ANSYS Conf, Pittsburgh PA, Vol 2, 6.39–6.60.
Irwin GR (1958), Fracture, Handbuch der Physik, Springer-Verlag Ltd, Berlin, Germany, Vol VI, 551–590.
Cooper  DB, Meda  G, and Sinclair  GB (1995), A comparison of crack-flank displacement fitting for estimating K with a path independent integral, Int. J. Fract. 70, 237–251.
Chan  SK, Tuba  IS, and Wilson  WK (1970), On the finite element method in linear fracture mechanics, Eng. Fract. Mech. 2, 1–17.
Parks  DM (1974), A stiffness derivative finite element technique for determination of crack tip stress intensity factors, Int. J. Fract. 10, 487–502.
Rybicki  EF, and Kanninen  MF (1977), A finite element calculation of stress intensity factors by a modified crack closure integral, Eng. Fract. Mech. 9, 931–938.
Stern M (1973), A boundary integral representation for stress intensity factors, Proc of 10th Anniversary Meeting of the Soc of Engineering Science, Raleigh, NC, 125–132.
Stern  M, Becker  EB, and Dunham  RS (1976), A contour integral computation of mixed-mode stress intensity factors, Int. J. Fract. 12, 359–368.
Stern  M, and Soni  ML (1976), On the computation of stress intensities at fixed-free corners, Int. J. Solids Struct. 12, 331–337.
Hong  C-C, and Stern  M (1978), The computation of stress intensity factors in dissimilar materials, J. Elast. 8, 21–34.
Carpenter  WC (1984), Calculation of fracture mechanics parameters for a general corner, Int. J. Fract. 24, 45–58.
Sinclair  GB, Okajima  M, and Griffin  JH (1984), Path independent integrals for computing stress intensity factors at sharp notches in elastic plates, Int. J. Numer. Methods Eng. 20, 999–1008(see also (1985), Int. J. Fract. 27, R81–R85).
Okajima M, and Sinclair GB (1986), The C-integral: A path independent integral for computing singularity participation at a butt joint, Proc of Int Conf on Computational Mech, Tokyo, Japan, Vol 1, V11–V16.
Carpenter  WC, and Byers  C (1987), A path independent integral for computing stress intensities for V-notched cracks in a bi-material, Int. J. Fract. 35, 245–268.
Banks-Sills  L (1997), A conservative integral for determining stress intensity factors of a bimaterial strip, Int. J. Fract. 86, 385–398.
Banks-Sills  L, and Sherman  D (1986), Comparison of methods for calculating stress intensity factors with quarter-point elements, Int. J. Fract. 32, 127–140.
Pang  HLJ (1993), Linear elastic fracture mechanics benchmarks: 2D finite element test cases, Eng. Fract. Mech. 44, 741–751.
Pang HLJ, and Leggat RH (1990), 2D test cases in linear elastic fracture mechanics, Report R0020, National Agency for Finite Element Methods and Standards, Glasgow, UK.
Banks-Sills  L (1991), Application of the finite element method to linear elastic fracture mechanics, Appl. Mech. Rev. 44, 447–461.
Meda  G, Messner  TW, Sinclair  GB, and Solecki  JS (1996), Path-independent H integrals for three-dimensional fracture mechanics, Int. J. Fract. 94, 217–234.

Figures

Grahic Jump Location
Some limiting configurations for doublet states: a) concentrated moment, b) force doublet without a moment, c) center of compression
Grahic Jump Location
Some singular configurations: a) three-point-bend test piece of fracture mechanics, b) section through a tire on a relatively rigid pavement, c) section through a piston with a ring pressed into a cylinder wall, d) section of a shaft with a stress-free keyway under torsion and lateral loading, e) adhesive butt joint under tension, f ) rough heavy block sticking to an elastic base, g) steel chisel just starting to indent a wooden slab, h) displacement shape functions as submodel boundary conditions
Grahic Jump Location
Tensile crack in a hardening material
Grahic Jump Location
Genesic Griffith crack configuration
Grahic Jump Location
Pressurized crack configuration
Grahic Jump Location
Barenblatt’s crack tip
Grahic Jump Location
Schematic of cohesive stress-separation law
Grahic Jump Location
Sketches of atomic or molecular “springs” at a sharp crack-tip for various boundary conditions: a) classical stress-free conditions, b) Barenblatt’s cohesive stress conditions, c) consistent cohesive stress conditions, d) alternate cohesive stress conditions
Grahic Jump Location
Crack flank configurations when introducing cohesive stresses: a) mathematically sharp crack, b) stress-free crack, c) intervening crack
Grahic Jump Location
Contact configurations: a) unloaded roller bearing, b) loaded roller bearing, c) journal bearing under load, d) piston ring pressing against a cylinder wall (deformation not indicated)
Grahic Jump Location
Local contact configuration at C in Fig. 10b: coordinates and consequences of singularities
Grahic Jump Location
Tensile stress ahead of a crack and displacements accompanying a small extension under symmetric (Mode I) loading
Grahic Jump Location
Modes of deformation at a crack tip: a) Mode I, b) Mode II, c) Mode III
Grahic Jump Location
An interface crack configuration
Grahic Jump Location
Crack-tip models for the interface crack: a) contact zone model, b) crack opening angle model, c) intervening layer model with constant moduli, d) intervening layer model with continuously varying moduli
Grahic Jump Location
Tensile stress ahead of a reentrant corner and displacements accompanying a small extension under symmetric loading
Grahic Jump Location
K-controlled annulus at a crack tip
Grahic Jump Location
Size dependence of fracture toughness
Grahic Jump Location
Finite element grids for reentrant corner under tension: a) initial grid with 48 elements, b) first refinement with 192 elements
Grahic Jump Location
Local arrangement of quarter-point elements at a crack tip (following ANSYS recommendations)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In