Abstract
The problem investigated is of an elastic-perfectly plastic infinite plate containing two equal collinear and symmetrically situated straight cracks. The plate is subjected to loads at infinity inducing mode I type deformations at the rims of the cracks. Consequently, plastic zones are formed ahead of the tips of the cracks. The loads at infinity are increased to a limit such that the plastic zones formed at the neighbouring interior tips of the cracks get coalesced. The plastic zones developed at the tips of the cracks are closed by applying normal cohesive quadratically varying stress distribution over their rims. The opening of the cracks is consequently arrested. Complex variable technique is used in conjugation with Dugdale’s hypothesis to obtain analytical solutions. Closed form analytical expressions are derived for calculating plastic zone size and crack opening displacement. An illustrative numerical example is discussed to study the qualitative behaviour of the loads required to arrest the cracks from opening with respect to parameters viz. crack length, plastic zone length and inter-crack distance. Crack opening displacement at the tip of the crack is also studied against these parameters.
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Abbreviations
- a, b, c :
-
tips of the cracks
- E :
-
Young’s modulus
- K I :
-
stress intensity factor for mode I type deformations
- L j (j = 1, 2):
-
cracks
- P ij (i, j =x, y):
-
stress components
- P n(z),X(z):
-
complex functions
- u i (i =x, y):
-
displacement components
- z =x +iy :
-
complex variable
- Γ j (j = 1, 2, 3):
-
plastic zones
- μ :
-
shear modulus
- ν :
-
Poisson’s ratio
- σ ye :
-
yield point stress
- \(\sigma _\infty \) :
-
tension applied at infinite boundary
- φ(z),Ω(z),Φ(z):
-
complex potentials
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Bhargava, R.R., Agrawal, S.C. Two cracks with coalesced interior plastic zones — The generalised Dugdale model approach. Sadhana 22, 637–647 (1997). https://doi.org/10.1007/BF02802551
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DOI: https://doi.org/10.1007/BF02802551