Plasticity and the crack opening displacement in shells

Ratwani, M.

doi:10.1007/bf00191103

Cited by 39 publications

(12 citation statements)

References 8 publications

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“…In add ition to linear elasticity, in the existing solutions [e.j., [1][2][3][4][5][6][7][8][9][10][11][12][13] it is as sumed that the shell is "infinitely" large, the curvatures are constant (i.e., the shell is a circular cylinder or a sphere), the crack is along a principal plane of curvature, and the material is isotropic and homogeneous. If these assumptions are disregarded, mathematically the problem does not seem to be tractable.…”

Section: -Imentioning

confidence: 99%

Crack problems in cylindrical and spherical shells

Erdogan

1977

Plates and Shells With Cracks

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Section: -Imentioning

confidence: 99%

Crack problems in cylindrical and spherical shells

Erdogan

1977

Plates and Shells With Cracks

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“…Using the results given in [11] and extrapolating them the crack opening area may be approximated by…”

Section: A Quasi Static Model For Gas-filled Cylindersmentioning

confidence: 99%

“…and by observin g that the differential equation (9) and the Models I to IV, i.e., (11), (12), (10) and (19) are of the form dt f(a,P)…”

Section: A Quasi Static Model For Gas-filled Cylindersmentioning

confidence: 99%

Crack Propagation and Arrest in Pressurized Containers

Delale

Owczarek

1977

Journal of Pressure Vessel Technology

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The problem of crack propagation and arrest in a finite volume cylindrical container filled with pressurized gas is considered. It is assumed that the cylinder contains a symmetrically located longitudinal part-through crack with a relatively small net ligament. The net ligament suddenly ruptures initiating the process of fracture propagation and depressurization in the cylinder. Thus the problem is a coupled gas dynamics and solid mechanics problem the exact formulation of which does not seem to be possible. It is formulated by making two major assumptions, namely that the shell problem is quasi-static and the gas dynamics problem is one-dimensional. The problem is reduced to a proper initial value problem by introducing a dynamic fracture criterion which relates the crack acceleration to the difference between a load factor and the corresponding strength parameter. The main results are demonstrated by considering two examples, an aluminum cylinder which may behave in a quasi-brittle manner, and a steel cylinder which undergoes ductile fracture. The results indicate that generally in gas-filled cylinders fracture arrest is not possible unless the material behaves in a ductile manner and the container is relatively long.

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“…It is natural to assume that one can use an analog of the 5k-model also for thin shells with cracks, when the membrane stresses are significantly larger than the bending stresses, in solving the corresponding problems. Under such assumptions the limit equilibrium state of shallow [10,11] and nonshallow [3,5] isotropic cylindrical shells with through and nonthrough longitudinal cracks has been studied. We give below a construction of a solution of the problem of limit equilibrium of a closed transversally isotropic cylindrical shell (with low shear stiffness) with a nonthrough surface crack.…”

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Limit equilibrium of a closed transversally isotropic cylindrical shell with a nonthrough longitudinal crack

Nikolishin¹

1997

J Math Sci

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In the context of an analog of the Leonov-Panasyuk-Dagdeil model we consider the problem of limit equilibrium of a nonshaltow transversally isotropic cylindrical shell weakened by a nonthrough surface longitudinal crack. Based on the equations that take account of the initial stresses, we reduce the problem to a system of two singular integral equations with unknown limits of integration. We carry out a numerical analysis of the dependence of the opening of the edges of the crack on the load and the geometric and physico-mechanical parameters of the shell.The enlargement of the doma.n of practical use of cr teria for the mechanics of fracture involves a need to study the stress-strain state near cracks in bodies with different configurations and loading conditions. At present the stress distribution has been well studied near through cracks in shell structural elements [2,7] made of isotropic materials. Significantly less study has been devoted to anisotropic materials, in particular to transversally isotropic shells with through cracks [6]. In the case of a shell with a nonthrough crack the problem becomes three-dimensional, and taking account of the plastic deformations that develop in the vicinity of the crack, that is, the study of a shell with a nonthrough crack in the elastoplastic formulation yields a very difficult problem. For that reason in the formulation of such problems it is worthwhile to pay attention to simplified models that are consistent with experimental data. Thus, in application to plates in a plane stressed state, whose fracture is preceded by the development of significant zones of plastic deformation, the 5k-model of Leonov-Panasyuk-Dagdeil [1, 9] is quite effective. It is natural to assume that one can use an analog of the 5k-model also for thin shells with cracks, when the membrane stresses are significantly larger than the bending stresses, in solving the corresponding problems. Under such assumptions the limit equilibrium state of shallow [10,11] and nonshallow [3,5] isotropic cylindrical shells with through and nonthrough longitudinal cracks has been studied. We give below a construction of a solution of the problem of limit equilibrium of a closed transversally isotropic cylindrical shell (with low shear stiffness) with a nonthrough surface crack.Suppose a closed transversally isotropic cylindrical shell whose middle surface is referred to the lines of curvature a, ~3 is weakened by a longitudinal nonthrough crack lal < a0, fl = 0 (h -2d) < 3' < h, and is subject to forces and moments that are symmetric with respect to the crack. Suppose that ao = lo/R, 2/0 and 2d are the length and depth of the crack, 2h and R are the thickness of the shell and the radius of its middle surface, and V is the coordinate normal to the middle surface. The behavior of the material, the load level, and the size of the crack are assumed to be such that plastic deformations develop as a narrow strip over the entire thickness of the shell in the vicinity of the crack. Here over the entire depth of the crack...

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Plasticity and the crack opening displacement in shells

Cited by 39 publications

References 8 publications

Crack problems in cylindrical and spherical shells

Crack problems in cylindrical and spherical shells

Crack Propagation and Arrest in Pressurized Containers

Limit equilibrium of a closed transversally isotropic cylindrical shell with a nonthrough longitudinal crack

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