Engineering topics

Erdogan, F.

Publications and source records attributed to Erdogan, F..

At least 163 records · Page 9

NASA NTRS1973

The problem of edge cracks in an infinite strip

The elastostatic plane problem of an infinite strip containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of a singular integraL equation with the derivative of the crack surface displacement as the density function. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. The limiting case of the edge cracks is then considered in some detail. The fundamental function of the integral equation is obtained and a numerical technique for solving the singular integral equations with this particular type of fundamental function which is characteristic of the edge cracks is described. The stress intensity factor for the complete range of net ligament-to-width ratio is calculated. The results also include the solution of the edge crack problem in an elastic half plane.

Gupta, G. D.↗

NASA NTRS1973

A half plane and a strip with an arbitrarily located crack

A technique is presented for dealing with the problem of an elastic domain containing an arbitrarily oriented internal crack. The problem is formulated as a system of integral equations for a fictitious layer of body forces imbedded in the plane along a closed smooth curve encircling the original domain. The problems of a half plane with a crack in the neighborhood of its free boundary and of an infinite strip containing a symmetrically located internal crack with an arbitrary orientation are considered as examples. In each case the stress intensity factors are computed and are given as functions of the crack angle.

Erdogan, F.↗

NASA NTRS1973

The inclusion problem with a crack crossing the boundary

The problem of an elastic plane containing an elastic inclusion is considered. It is assumed that both the plane and the inclusion contain a radial crack and the two cracks are collinear. The problem is formulated in terms of a system of singular integral equations. In the interesting limiting cases in which the crack tips approach the interface from either one or both sides, the dominant parts of the kernels become generalized Cauchy kernels giving rise to stress singularities of other than minus 1/2 power. For these unusual cases of a crack terminating at or crossing the interface stress intensity factors are defined and some detailed results are given for various crack-inclusion geometries and material combinations.

Erdogan, F.↗

NASA NTRS1973

A cylindrical shell with an axial crack under skew-symmetric loading.

The skew-symmetric problem for a cylindrical shell containing an axial crack is considered. It is assumed that the material has a special orthotropy - namely, that the shear modulus may be evaluated from the measured Young's moduli and Poisson ratios and is not an independent material constant. The problem is solved within the confines of an eighth-order linearized shallow shell theory. As numerical examples, the torsion of an isotropic cylinder and that of a specially orthotropic cylinder (titanium) are considered. The membrane and bending components of the stress intensity factor are calculated and are given as functions of a dimensionless shell parameter. In the torsion problem for the axially cracked cylinder the bending effects appear to be much more significant than that found for the circumferentially cracked cylindrical shell. Also, as the shell parameter increases, unlike the results found in the pressurized shell, the bending stresses around crack ends do not change sign.

Yuceoglu, U.↗

NASA NTRS1973

Two bonded half planes with a crack going through the interface

The plane problem of two bonded elastic half planes containing a finite crack perpendicular to and going through the interface is considered. The problem is formulated as a system of singular integral equations with generalized Cauchy kernels. Even though the system has three irregular points, it is shown that the unknown functions are algebraically related at the irregular point on the interface and the integral equations can be solved by a method developed previously. The system of integral equations is shown to yield the same characteristic equation as that for two bonded quarter planes in the general case of the through crack, and the characteristic equation for a crack tip terminating at the interface in the special case. The numerical results given in the paper include the stress intensity factors at the crack tips, the normal and shear components of the stress intensity factors at the singular point on the interface, and the crack surface displacements.

Erdogan, F.↗

NASA NTRS1973

A note on the interference of two collinear cracks in a cylindrical shell

A stress analysis of a pressurized shallow cylindrical shell containing two collinear axial cracks of equal length was conducted. The mathematical relationships for conducting the stress analysis are developed. Graphs are presented to show the stress intensity factor ratio in the cylindrical shell and the bending components of the stress intensity factor ratio.

Erdogan, F.↗

NASA NTRS1973

Contact problem for an elastic reinforcement bonded to an elastic plate

The stiffening layer is treated as an elastic membrane and the base plate is assumed to be an elastic continuum. The bonding between the two materials is assumed to be either one of direct adhesion ro through a thin adhesive layer which is treated as a shear spring. The solution for the simple case in which both the stiffener and the base plate are treated as membranes is also given. The contact stress is obtained for a series of numerical examples. In the direct adhesion case the contact stress becomes infinite at the stiffener ends with a typical square root singularity for the continuum model, and behaving as a delta function for the membrane model. In the case of bonding through an adhesive layer the contact stress becomes finite and continuous along the entire contact area.

Erdogan, F.↗

NASA NTRS1973

On the effect of orthotropy in a cracked cylindrical shell

A pressurized cylindrical shell containing a longitudinal crack is considered. The shear modulus of the sheet may be evaluated from the measured Young's moduli and the Poisson's ratios rather than being an independent material constant. Two examples, one for a mildly orthotropic (titanium) and the other for a strongly orthotropic (graphite) material approximately satisfying the condition of special orthotropy are given. The results show that the stress intensity factors are rather strongly dependent on the degree of orthotropy.

Erdogan, F.↗

NASA NTRS1972

Plasticity and the crack opening displacement in shells.

The plastic deformations and the crack opening displacement, delta, in cylindrical shells with an axial or circumferential crack and spherical shells with a meridional crack are considered. It is assumed that outside the perturbation zone of the crack the shell is subjected to uniform membrane loads perpendicular to the crack. The plastic strip model is used to calculate the plastic zone size. The crack opening displacement is calculated as the crack surface displacement at the crack tips by using the conventional superposition technique. In cylindrical shells with an axial crack the crack surface displacement perpendicular to the shell surface (i.e., the bulging) is also evaluated. The results are applied to a set of existing experimental data on the fracture of cylindrical shells. The tentative conclusion is that in dealing with the fracture of thin-walled structures, among various fracture models delta = constant appears to be the most satisfactory criterion.

Erdogan, F.↗

NASA NTRS1972

Fracture problems in composite materials.

In this paper a series of fracture problems in composite materials are identified, their methods of solution are briefly discussed, and some sample results are presented. The main problem of interest is the determination of the stress state in the neighborhood of localized imperfections such as cracks and inclusions which may exist in the composite. Particular emphasis is placed on the evaluation of quantities such as the stress intensity factors, the power of the stress singularity, and the strain energy release rate, which may be used directly or indirectly in connection with an appropriate fracture criterion for the prediction of fracture initiation and propagation load levels.

Erdogan, F.↗

NASA NTRS1972

A sandwich plate with a part-through and a debonding crack.

The stress analysis of a metal base plate stiffened by a fiber-reinforced composite layer is considered. It is assumed that the two materials are bonded through an adhesive of constant thickness which is treated as a two-dimensional shear spring in the analysis. The metal plate is assumed to contain a through crack of finite length. The composite plate has no flaws. However, due to the high stress concentration around the crack and on the interface, a debonding crack is assumed to exist, encircling the crack in the base plate. The problem is reduced to a pair of integral equations of the second kind with Fredholm-type kernels. By solving these equations the stress intensity factor in the base plate, the boundary of the debonding crack, and the interface shear stresses acting on the adhesive are calculated.

Erdogan, F.↗

NASA NTRS1972

Stresses in bonded materials with a crack perpendicular to the interface.

The problem of two elastic bonded half planes containing a crack perpendicular to the interface is considered. First the solution for the semi-infinite crack under concentrated wedge loading is given. Then the problem of a finite crack fully imbedded in one of the half planes of terminating at the interface is considered. The Mellin transform in conjunction with the dislocations is used to formulate the problem and to derive the integral equation. The integral equation is solved; the stress intensity factors, the crack surface displacement, and the stresses around the crack tip terminating at the interface are obtained. Noting that the power of the singularity for the interface tip of the crack is not -1/2, a tentative fracture criterion dealing with the initiation of fracture propagation is proposed.

Cook, T. S.↗

NASA NTRS1972

Fracture problems in composite materials

A series of fracture problems in composite materials are identified, their methods of solution are briefly discussed, and some sample results are presented. The main problem of interest is the determination of the stress state in the neighborhood of localized imperfections such as cracks and inclusions which may exist in the composite. Particular emphasis is placed on the evaluation of quantities such as the stress intensity factors, the power of the stress singularity, and the strain energy release rate, which may be used directly or indirectly in connection with an appropriate fracture criterion for the prediction of fracture initiation and propagation load levels. The topics discussed include a crack in layered composites, a crack terminating at and going through a bi-material interface, a penny-shaped crack in a filament-reinforced elastic matrix, and inclusion problems in bonded materials.

Erdogan, F.↗

NASA NTRS1972

Stresses near a flat inclusion in bonded dissimilar materials.

The plane elastostatic problem for bonded materials containing a flat inclusion is considered. It is assumed that the inclusion is located parallel to or on the interface and may be rigid or elastic with negligible bending rigidity. The integral equations for various cases are derived and their solutions are described. The stress state around the singular points are investigated and a pair of stress intensity factors similar to that for crack problems are defined. A series of numerical examples for two bonded half planes and for a half plane is worked out. The stress intensity factors are presented as functions of the ratio of the distance from the interface to the length of the inclusion.

Erdogan, F.↗

NASA NTRS1972

A circumferential crack in a cylindrical shell under torsion.

The fully antisymmetric problem for a cylindrical shell with a circumferential crack is considered. The solution of the problem is reduced to that of a system of singular integral equations of the first kind. As an example the torsion of the cylinder is discussed and membrane and bending components of the stress intensity factor ratio are given.

Erdogan, F.↗

NASA NTRS1972

Penny-shaped interface crack between an elastic layer and a half space.

The axially symmetric elastostatic problem for a layer bonded to a half space with different material properties is considered. It is assumed that the bi-material interface contains a penny-shaped crack the surfaces of which are subjected to known tractions. The solution of the problem is reduced to that of a system of singular integral equations of the second kind. A numerical example for an aluminum-epoxy material combination is given. The stress intensity factors and the strain energy release rate are calculated and are given as functions of layer thickness-to-crack radius ratio.

Erdogan, F.↗

NASA NTRS1972

Fracture of cylindrical and spherical shells containing a crack.

Fatigue and fracture of cylindrical and spherical shells containing a through crack and subjected to internal pressure or torsion are considered. The stress intensity factor ratios giving the effect of curvature are obtained as functions of a dimensionless shell parameter. By using the conventional plastic strip model the plastic zone size around the crack tip and the crack opening displacement are calculated. The calculated COD values are shown to be in good agreement with the experimental results. The fracture criterion of critical COD is verified by using the results of the burst tests in titanium and aluminum alloy cryogenic pressure vessels. Modified fatigue crack propagation models taking into account the bending effect in shells are introduced and are applied to the analysis of experimental data obtained from flat plates, and cylindrical shells under axial tension, internal pressure, and torsion. Finally, the paper includes the effect of humidity on the crack growth rate and the effect of load biaxiality on the rupture strength.

Erdogan, F.↗

NASA NTRS1971

The problem of an elastic stiffener bonded to a half plane.

The contact problem of an elastic stiffener bonded to an elastic half plane with different mechanical properties is considered. The governing integral equation is reduced to an infinite system of linear algebraic equations. It is shown that, depending on the value of a parameter which is a function of the elastic constants and the thickness of the stiffener, the system is either regular or quasi-regular. A complete numerical example is given for which the strength of the stress singularity and the contact stresses are tabulated.

Erdogan, F.↗