Limit equilibrium of an orthotropic plate weakened by a periodic row of collinear cracks

Bogdanova, O. S.

doi:10.1007/s10778-008-0104-4

Int Appl Mech

2008

DOI: 10.1007/s10778-008-0104-4

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Limit equilibrium of an orthotropic plate weakened by a periodic row of collinear cracks

O. S. Bogdanova

Abstract: A modified d c -model is used to study the limiting state of an orthotropic plate weakened by a periodic row of collinear cracks and satisfying a general failure criterion. The failure mechanism of the plate is analyzed. A study is made of the effects of the degree of orthotropy, the biaxiality of external loading, and the geometrical parameters on the fracture process zones at the crack tips and the limiting state of the plate. The safe loading of an orthotropic viscoelastic plate with a periodic row of colli… Show more

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Cited by 4 publications

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“…The design of a compound plate weakened by a periodic set of cracks was considered in [4]. Orthotropic plates weakened by a periodic number of collinear cracks were addressed in [7]. The exact solution (as a function of four constants of integration) for and an equation for the critical compressive load of a column with an arbitrary number and arrangement of cracks were obtained in [8].…”

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Deformation of an elastic plate with an edge notch under the action of a plane shock wave: experimental research

2009

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The dynamics of a thin elastic plate with an edge notch under the action of a weak shock wave in air is experimentally studied. It is shown that the notch has a significant effect on the deformation process Keywords: thin elastic plate, edge notch, weak shock wave, deformation process Introduction. Special-purpose or process-induced inhomogeneities such as inserts, cover plates, notches, cracks, and holes in structural members (plates or shells) have a strong effect on their behavior under various loads. Such inhomogeneities influence the stress-strain state, critical load, and ultimate strength. Let us mention some recent publications addressing problems for bodies with various stress concentrators under static and dynamic loads.For example, plates under uniaxial or biaxial tension and shear were considered in the paper [2], which established how the thickness of the plate near holes should vary to decrease the stress concentration. The influence of a notch on the frequency characteristics of a plate was examined in [10]. A number of qualitative mechanical effects in a thin open spherical shell with an oblong elliptic hole were revealed in [11]. The change in the energy of an elastic plate after making a circular hole in it was studied in [12]. The stress-strain state at the boundary of a circular hole and at the interface between a plate and an eccentric circular cover plate was analyzed in [3]. The influence of rectangular plates reinforcing a cylindrical shell on the critical load, frequency, and vibration mode was experimentally examined in [13]. The design of a compound plate weakened by a periodic set of cracks was considered in [4]. Orthotropic plates weakened by a periodic number of collinear cracks were addressed in [7]. The exact solution (as a function of four constants of integration) for and an equation for the critical compressive load of a column with an arbitrary number and arrangement of cracks were obtained in [8]. The flexibility matrix with a crack and stiffness coefficients for a rotor were found in [9]. The deformation of elastic plates with a central notch parallel to two clamped edges under the action of a shock wave was experimentally studied in [6].The present paper outlines a procedure and results of experimental study of the influence of an edge notch on the nonstationary behavior of a thin elastic plate clamped at two opposite edges and subjected to the action of a normally incident staircase shock wave.1. Method of Analysis. The shock wave was generated in a diaphragm-type shock pipe. The experimental procedure from [6] was mainly used. A tested rectangular plate is made of SF-1-150 fiberglass plastic (GOST 10316-78) with density r = 1.7 g/cm 3 and elastic modulus E = 2.6×10 10 Pa and had a thickness of 2.5 mm, width a = 140 mm, and length l = 210 mm. The 140´250 mm plate was rigidly fixed on the short sides between two steel frames 18 mm thick each. The inside dimensions of the frames coincided with the effective cross-section of the diaphragm-type shock tube; the outside dimension...

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Deformation of an elastic plate with an edge notch under the action of a plane shock wave: experimental research

2009

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“…An extensive review of relevant studies can be found in [3]. The limit state of an orthotropic plate with periodic cracks is analyzed in [12,13]. The stress-strain state of spherical shells with an eccentric circular hole and prestressed shells was studied in [14,18].…”

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Limit equilibrium of a transversely isotropic spherical shell with two surface cracks

2009

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An analog of the d c -model is used to reduce the limit-equilibrium problem for a transversely isotropic spherical shell with surface cracks to a system of integral equations. An algorithm for numerical solution of this system is proposed Keywords: transversely isotropic spherical shell, surface crack, plastic strains, integral equations, crack opening displacement Introduction. When loaded, a solid with cracks undergoes plastic deformation at their tips. Since the classical solution of elastoplastic problems for cracked bodies involves severe difficulties (because two systems of equations, one in the elastic domain and the other in the plastic domain have to be solved simultaneously, with the boundary between these domain being unknown), simplified models that agree with experimental data take on special significance. For example, the d c -model [7,15] and its analogs [4,17] can effectively be applied to thin plates and shells whose fracture is preceded by the development of large plastic zones. This was demonstrated experimentally in [11] for plates and in [2, 10] for large-scale specimens such as welded joints of structural steels with low and medium strength. The satisfactory agreement of theoretical and experimental data was also observed when the shape of plastic zones in specimens differed from that in the d c -model. An analog of this model was used to study the stress state and limit equilibrium of cylindrical [16] and isotropic spherical shells with part-through cracks [4,5]. An extensive review of relevant studies can be found in [3]. The limit state of an orthotropic plate with periodic cracks is analyzed in [12,13]. The stress-strain state of spherical shells with an eccentric circular hole and prestressed shells was studied in [14,18]. The stress intensity factor for an orthotropic cylindrical shell of medium thickness with an internal surface crack was determined in [9].The present paper uses an analog of the d c -model and the refined Timoshenko-type theory of shells [3] to analyze the limit equilibrium of a transversely isotropic elastoplastic spherical shell weakened by two surface cracks.1. Let us consider a shell with two identical surface cracks arranged along a straight (in plan) line. The length and depth of the cracks are denoted by 2 0 l and 2d, the distance between their centers by 2l d . We choose a coordinate system XOY so that the OX-axis is aligned with the crack line and the origin is at the middle of the segment 2l d . The stress-strain state of the shell is symmetric about the lines X = 0and Y = 0. The external loads, crack length, and the behavior of the material are supposed to be such that the plastic zones originating at the crack front would develop as narrow strips on the crack continuation all the way throughout the thickness of the shell. Denote the length of the plastic zones near the internal (neighboring) tips by l p and near the external tips by l p . In accordance with [4], assuming that tensile stresses act near the crack tips, we model the plastic zones by the disco...

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Mechanics of the Delayed Fracture of Viscoelastic Bodies with Cracks: Theory and Experiment (Review)

Kaminsky

2014

Int Appl Mech

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Limit equilibrium of an orthotropic plate weakened by a periodic row of collinear cracks

Cited by 4 publications

References 12 publications

Deformation of an elastic plate with an edge notch under the action of a plane shock wave: experimental research

Deformation of an elastic plate with an edge notch under the action of a plane shock wave: experimental research

Limit equilibrium of a transversely isotropic spherical shell with two surface cracks

Mechanics of the Delayed Fracture of Viscoelastic Bodies with Cracks: Theory and Experiment (Review)

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