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Influence of load biaxiality on the fracture load of center cracked sheets


Analysis of the problem of a plane infinite elastic body with a centrally located crack subject to uniform biaxial load along the remote outer boundaries, indicates that loads applied parallel to the crack influence the value of the critical (fracture) tensile load applied perpendicular to it, with the Poisson ratio of the material determining the characteristics of this influence. Experimental information from specially designed biaxial test programs, obtained by the authors and also from the published data of other investigators, shows that, while tensile loads parallel to the crack raise the critical value of perpendicular load for an aluminum alloy, they have a reverse effect on the critical load for plexiglass (polymethylmethacrylate or PMMA), in qualitative agreement with the predictions of the analysis.


On analyse le problème d'un corps élastique plan infini comportant une fissure centrale soumise à une contrainte biaxiale le long de ses bords éloignés. L'analyse montre que les charges appliquées parallèlement à la fissure influencent la valeur de la contrainte critique de rupture en traction appliquée perpendiculairement à elle, les caractéristiques de cette influence étant régies par le rapport de Poisson du matériau. Des informations expérimentales venant de programme d'essais en condition biaxiale spécialement conçu et recueillies par les auteurs et par la littérature publiée par d'autres chercheurs montrent que tandis que les contraintes de traction parallèles à la fissure accroissent la valeur critique de la charge perpendiculaire dans le cas d'un alliage aluminium, elles ont un effet inverse sur la charge critique dans le cas du plexiglas (polyméthyleméthacrylate ou PMMA), ceci étant en accord qualitatif avec les prédictions de l'analyse.

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2α :

crack length

(x, y), (r, θ), (α, β):

rectangular, polar, elliptic coordinates, respectively

z :

x +iy, complex variable

t jk ,e jk :

components of the stress and strain tensors, respectively

T k ,u k ,b k :

components of the surface traction, displacement and body force vectors, respectively

t xx ,t xy ,t yy :

rectangular stress components

t αα ,t αβ ,t ββ :

elliptic stress components

u x ,u y ;u α ,u β :

rectangular and elliptic displacement components, respectively

U :

elastic strain energy per unit thickness

W :

work of forces applied to the body per unit thickness

P, V :

potential energies per unit thickness


surface energy per unit thickness

R :

bound region of thex-y plane

C 1,C 2 :

closed boundary curves ofR

Φ, Ω, ϕ, ω:

sectionally holomorphic functions of the complex variablez

E :

Young's modulus

k :

applied load biaxiality ratio,t xx (∞)/t yy (∞)


stress applied to the outer boundary surface


elastic shear modulus


Poisson's ratio


surface energy density per unit area


(3-ν)/(1+ν) for plane stress, (3-4ν) for plane strain


  1. [1]

    D.L. Jones and J. Eftis, Fracture and Fatigue Characterization of Aircraft Structural Materials Under Biaxial Loading. Interim Scientific Report. AFOSR, Washington, D.C. (1977).

  2. [2]

    W.T. Evans and A.R. Luxmore,Journal of Strain Analysis 11 (1977) 177–185.

  3. [3]

    J.J. Kibler and R. Roberts,Journal of Engineering for Industry (1970) 727–734.

  4. [4]

    D.L. Jones and J. Eftis, Fracture and Fatigue Characterization of Aircraft Structural Materials Under Biaxial Loading. Final Scientific Report. AFOSR, Washington, D.C. (1980).

  5. [5]

    C.D. Hopper and K.J. Miller,Journal of Strain Analysis 12 (1977) 23–28.

  6. [6]

    P.S. Leevers, L.E. Culver and J.C. Radon,Engineering Fracture Mechanics 11 (1979) 487–498.

  7. [7]

    S.Y. Zamrik and M.A. Shabara, The Application of Fracture Mechanics Analysts to Crack Growth in a Biaxial Stress Field. 4th Inter-American Conference on Materials Technology. Caracas (1975) 442–447.

  8. [8]

    S. Wästberg, Fatigue Crack Propagation in the Base Material, Weldment and the Heat Affected Zone of Two Ship Hull Plate Steels. Pub. No. 203, The Royal Institute of Technology, Stockholm (1977).

  9. [9]

    J. Eftis, N. Subramonian and H. Liebowitz,Engineering Fracture Mechanics 9 (1977) 189–210.

  10. [10]

    J. Eftis, N. Subramonian and H. Liebowitz,Engineering Fracture Mechanics 10 (1978) 753–764.

  11. [11]

    J. Eftis and N. Subramonian,Engineering Fracture Mechanics 10 (1978) 43–67.

  12. [12]

    A.A. Griffith,Philisophical Transactions, Royal Society London 221 (1921) 163–198.

  13. [13]

    K.Z. Wolf,Zeitschrift für Angewandte Mathematik und Mechanik 3, 2 (1923) 107–112.

  14. [14]

    J.L. Swedlow,International Journal of Fracture Mechanics 1 (1965) 210–216.

  15. [15]

    J.P. Berry, inFracture Processes in Polymeric Solids (Ed. B. Rosen) Wiley, New York (1964) 157–194.

  16. [16]

    A.J.M. Spencer,International Journal of Engineering Science 3 (1965) 441–449.

  17. [17]

    M.K. Kassir and G.C. Sih,International Journal of Engineering Science 5 (1967) 899–917.

  18. [18]

    G.C. Sih and H. Liebowitz,International Journal of Engineering Science 3 (1967) 1–22.

  19. [19]

    A.A. Griffith,Proceedings 1st International Congress of Applied Mechanics, Delft (1924) 55–63.

  20. [20]

    P.S. Leevers, J.C. Radon and L.E. Culver,Polymer 17, 7 (1976) 627–632.

  21. [21]

    J.C. Radon and P.S. Leevers, inFracture 1977, Vol. 3, ICF 4 Waterloo (1977) 1113–1118.

  22. [22]

    N.I. Muskhelishvili,Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1963).

  23. [23]

    I.S. Sokolnikoff,Mathematical Theory of Elasticity, McGraw-Hill, New York (1956).

  24. [24]

    L.L. Pennisi,Elements of Complex Variables, Holt, Rinehart and Winston, New York (1963).

  25. [25]

    D.V. Widder,Advanced Calculus, Prentice-Hall, Englewood Cliff, New Jersey (1961).

  26. [26]

    R.G. Bartle,The Elements of Real Analysis, J. Wiley, New York (1964).

  27. [27]

    G.R. Irwin,Transactions ASME, Journal of Applied Mechanics 79 (1957) 361–364.

  28. [28]

    C.E. Inglis,Transactions Institute of Naval Architects (London) 60 (1913) 219–230.

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Eftis, J., Jones, D.L. Influence of load biaxiality on the fracture load of center cracked sheets. Int J Fract 20, 267–289 (1982).

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  • Aluminum Alloy
  • PMMA
  • Polymethylmethacrylate
  • Critical Load
  • Outer Boundary