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

Abstract

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.

Résumé

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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Abbreviations

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

Γ:

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 (∞)

σ:

stress applied to the outer boundary surface

µ:

elastic shear modulus

ν:

Poisson's ratio

γ:

surface energy density per unit area

κ:

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

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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). https://doi.org/10.1007/BF01130613

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Keywords

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