Abstract
The stress and strain distributions around cracks in sheet materials having various work-hardening characieristics are obtained for uniaxial loading. The strains in the plastic region at the crack tip tend to vary inversely as the distance from the crack. Expressions are derived for the energy absorbed in plastic deformation during both static and cyclic loadings.
Résumé
On a déterminé les répartitions des tensions et des déformations au voisinage de fissures dans des tôles a caractéristiques diverses d'écrouissage, pour le cas de traction uniaxiale. Les déformations dans la région plastique a la pointe de la fissure varient approximativement en raison inverse de la distance de la fissure. On a dérivé des expressions pour l'énergie dissipée en déformation plastique pour les sollicitations tant statiques que cycliques.
Zusammenfassung
Es werden bei einachsiger Zugbeanspruchung die Spannungs — und Verformungsverteilungen bei Anrissen in Blechen aus Werkstoffen mi.t verschiedenen V erfestigungseigenschaften festgestellt. Die Verformungen im plastischen Gebiet an der Anrisspitze verändern sich etwa umgekehrt mit deco Abstand vom Anriss. Es werden Ausdrücke abgeleitet fur die durch plastische Verformung bei statischer bzw. schwellender Beanspruchung aufgenommene Arbeit.
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Abbreviations
- 2b:
-
Sheet width
- E:
-
Modulus of elasticity
- Es,E′ s :
-
Secant moduli
- G:
-
Elastic shear modulus
- k:
-
Yield stress in shear
- L:
-
Applied stress across uncracked section
- l:
-
Half-crack length, crack length = 21
- r:
-
Polar co-ordinate
- rp :
-
Distance of elastic-plastic boundary from crack tip on loading
- rpr :
-
Distance of reversed plastic boundary from crack tip on unloading
- s:
-
Length of plastic region ahead of crack tip = (rpr)θ=0
- s′:
-
Lenght of reversed plastic region ahead of crack tip = (rpr)θ=0
- T:
-
Maximum applied stress across uncracked section
- t:
-
Thickness of sheet
- U:
-
Tensile strength
- Vp :
-
Total energy absorbed in plastic deformation per cycle, during cyclic loading
- vp :
-
Plastic energy density per cycle, during cyclic loading
- W:
-
Total energy of deformation during static loading
- w:
-
Strain energy density during static loading
- x, y:
-
Cartesian co-ordinates
- Y:
-
Yield stress in tension
- Z:
-
Parameter associated with yield in compression
- γ:
-
Maximum shear strain = ε1 − ε2
- γLP :
-
Shear strain at limit of proportionality
- γxy :
-
Shear strain
- γ0.1 :
-
Shear strain at 0.1 per cent proof stress
- Δ:
-
Denotes an increment during unloading
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Dixon, J.R. Stress and strain distributions around cracks in sheet materials having various work-hardening characteristics. Int J Fract 1, 224–244 (1965). https://doi.org/10.1007/BF00186858
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DOI: https://doi.org/10.1007/BF00186858