Non-linear fracture mechanics

Burns, S. J.; Pollet, J.-C.; Chow, C. L.

doi:10.1007/bf00034691

Cited by 23 publications

(2 citation statements)

References 11 publications

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“…Notice that (48,49) reduce to the classical Castigliano's theorem for a linear system, in which Ψ = −U where U is strain energy. As a result, as noted by Burns et al (1978)…”

Section: Appendixmentioning

confidence: 59%

Crack propagation at the interface between viscoelastic and elastic materials

Ciavarella¹,

McMeeking²

2020

Preprint

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Crack propagation in viscoelastic materials has been understood with the use of Barenblatt cohesive models by many authors since the 1970's. In polymers and metal creep, it is customary to assume that the relaxed modulus is zero, so that we have typically a crack speed which depends on some power of the stress intensity factor. Generally, when there is a finite relaxed modulus, it has been shown that the toughness increases between a value at very low speeds at a threshold toughness G 0 , to a very fast fracture value at G ∞ , and that the enhancement factor in infinite systems (where the classical singular fracture mechanics field dominates) simply corresponds to the ratio of instantaneous to relaxed elastic moduli.Here, we apply a cohesive model for the case of a bimaterial interface between an elastic and a viscoelastic material, assuming the crack remains at the interface, and neglect the details of bimaterial singularity. For the case of a Maxwell material at low speeds the crack propagates with a speed which depends only on viscosity, and the fourth power of the stress intensity factor, and not on the elastic moduli of either material. For the Schapery type of power law material with no relaxation modulus, there are more general results. For arbitrary viscoelastic materials with nonzero relaxed modulus, we show that the maximum toughness enhancement will be reduced with respect to that of a classical viscoelastic crack in homogeneous material.

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“…Notice that (48,49) reduce to the classical Castigliano's theorem for a linear system, in which Ψ = −U where U is strain energy. As a result, as noted by Burns et al (1978)…”

Section: Appendixmentioning

confidence: 59%

Crack propagation at the interface between viscoelastic and elastic materials

Ciavarella¹,

McMeeking²

2020

Preprint

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“…Critical points [34] and repulsive points [35] share some similar characteristics. However, they are very different as critical points have an intrinsic instability; the many points in chemical phase diagrams and the spinodal have wide influences.…”

Section: Discussionmentioning

confidence: 94%

77 new thermodynamic identities among crystalline elastic material properties leading to a shear modulus constitutive law in isotropic solids

Burns

2018

Journal of Applied Physics

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Thermodynamics of crystalline materials is analyzed using strain volumes, an incremental tensorial state variable which is the volume per unit mass multiplied by the incremental strain. It is shown that the derivatives of the strain volume variables with respect to the stresses reduces to conventional well known isothermal, elastic, crystallographic compliances and crystallographic thermal expansion coefficients. The formulism is extended to all third order derivatives which establish 77 new thermodynamic identities: 27 are thermal and 50 are among selected stress components of elastic compliances. The stress dependence of the heat capacity is typically coupled into the crystallographic thermal expansion coefficient's temperature dependence; the temperature dependence of the elastic compliances is related to the stress dependence of the thermal expansion coefficients; stress dependent relationships among elastic compliances are also found. The paper emphasizes internal self-consistency. General triclinic identity relations which are of academic interest are applied to specific higher symmetries including orthorhombic, tetragonal and cubic; identities in higher symmetry crystals are very useful. A new generalized, constitutive law is found and applied to isotropic polycrystalline materials; the concept is based on zero shear thermal expansion coefficients. The constitutive modulus relation describes thermal and pressure properties only through an isochoric modulus.

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Response: Discussion of ?J integral analysis of stable crack growth,? by S. J. Burns [1]

1980

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Burns [i] has asserted that, in general, the formulation of J that we proposed recently [2] only applies to a very restricted class of test specimens, mainly including constant J specimens. He suggests that in the general case J is a state function [3] of two variables among: displacement angle @ associated with the crack region, i.e., @ ~ @c, uncracked ligament length b and bending moment M for a bend bar of thickness B. In such a case, we agree with his formulation, part of which [3] anticipates our earlier work [2], and indeed we show that it also agrees with the recent work of Ernst et al. [4]. However, there are situations where the work of cracking leading to J is in fact reversible, but j need not be a function of any state variable or where J is some representation of irreversible processes and hence where his formulation need not apply.

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Non-linear fracture mechanics

Cited by 23 publications

References 11 publications

Crack propagation at the interface between viscoelastic and elastic materials

Crack propagation at the interface between viscoelastic and elastic materials

77 new thermodynamic identities among crystalline elastic material properties leading to a shear modulus constitutive law in isotropic solids

Response: Discussion of ?J integral analysis of stable crack growth,? by S. J. Burns [1]

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