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International Journal of Fracture

, Volume 13, Issue 5, pp 641–654 | Cite as

Crack propagation, resulting from a monotonic increasing applied stress, in a linear viscoelastic material

  • L. N. McCartney
Article

Abstract

A theory of crack propagation, resulting from the application of a monotonic increasing applied stress, in a linear viscoelastic material, is derived based upon an energy balance fracture criterion. It is shown that for a Maxwell solid the crack growth law can be derived either from a global energy balance taking full account of the energy dissipation resulting from viscoelastic flow, or from a local energy balance taking account of the dissipation in the failure zones. The local energy balance method allows the derivation of the crack growth law for more general linear viscoelastic solids. The theory predicts the well known Griffith condition for fracture when the material is simply linear elastic. For a crack having failure zones in a linear viscoelastic solid the growth law for a constant applied stress is where c(t) is the time dependent half-crack length, 641-1 is the yield or crazing stress in the failure zone, K(t) is the time dependent stress intensity factor, Γ is the fracture energy, ν is Poisson's ratio and J(t) is the uniaxial creep function of the viscoelastic material. This growth law is valid if either J(t)≡0 for all times t>0 (i.e. a Maxwell solid) or if 641-1 641-2 641-3

Keywords

Stress Intensity Factor Applied Stress Failure Zone Creep Function Viscoelastic Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Résumé

Une théorie de propagation d'une fissure résultant de l'application d'une contrainte monotonique croissante dans un matériau linéaire viscoélastique est dérivée sur la base d'un critère d'équilibre d'énergie de rupture. On montre que, pour un solide de Maxwell, la loi de croissance d'une fissure peut être déduite soit d'un équilibre global de l'énergie tenant complètement compte de la dissipation de l'énergie qui résulte de l'écoulement viscoélastique ou d'un équilibre local de l'énergie tenant compte de la dissipation de l'énergie dans les zônes de rupture. La méthode de l'équilibre d'énergie locale permet de dériver une loi de croissance de la fissure pour des solides viscoélastiques linéaires de caractère plus général. La théorie prédit la condition bien connue de Griffith pour la fracture dans le cas d'un matériau de linéarité élastique simple. Dans le cas d'une fissure qui présente des zônes de rupture dans un solide viscoélastique, la loi de croissance pour une contrainte appliquée est fournie. Dans cette loi, c(t) est la longueur de la demi-fissure dépendant du temps, 654-1 est la limite élastique dans la zône fissurée, K(t) est le facteur d'intensité de contrainte dépendant du temps, Г est l'énergie de rupture, ν est le module de Poisson et J(t) est la fonction uniaxiale de fluage dans le matériau viscoélastique. Cette loi de croissance est valable pour des conditions particulières de J(t).

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Copyright information

© Noordhoff International Publishing-Alphen aan den Rijn 1977

Authors and Affiliations

  • L. N. McCartney
    • 1
  1. 1.National Physical LaboratoryTeddingtonUK

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