Engineering topics

Erdogan, F.

Publications and source records attributed to Erdogan, F..

At least 19 records

NASA NTRS1991

The crack problem in bonded nonhomogeneous materials

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip termination at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

Erdogan, F.↗

NASA NTRS1991

The mode III crack problem in bonded materials with a nonhomogeneous interfacial zone

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.

Erdogan, F.↗

NASA NTRS1990

Crack problems involving nonhomogeneous interfacial regions in bonded materials

Consideration is given to two classes of fracture-related solid mechanics problems in which the model leads to some physically anomalous results. The first is the interface crack problem associated with the debonding process in which the corresponding elasticity solution predicts severe oscillations of stresses and the crack surface displacements vary near the crack tip. The second deals with crack intersecting the interface. The nature of the solutions around the crack tips arising from these problems is reviewed. The rationale for introducing a new interfacial zone model is discussed, its analytical consequences within the context of the two crack-problem classes are described, and some examples are presented.

Erdogan, F.↗

NASA NTRS1989

Surface crack problems in plates

The mode I crack problem in plates under membrane loading and bending is reconsidered. The purpose is to examine certain analytical features of the problem further and to provide some new results. The formulation and the results given by the classical and the Reissner plate theories for through and part-through cracks are compared. For surface cracks the three-dimensional finite element solution is used as the basis of comparison. The solution is obtained and results are given for the crack/contact problem in a plate with a through crack under pure bending and for the crack interaction problem. Also, a procedure is developed to treat the problem of subcritical crack growth and to trace the evolution of the propagating crack.

Joseph, P. F.↗

NASA NTRS1989

Cracking of coated materials under transient thermal stresses

The crack problem for a relatively thin layer bonded to a very thick substrate under thermal shock conditions is considered. The effect of surface cooling rate is studied by assuming the temperature boundary condition to be a ramp function. Among the crack geometries considered are the edge crack in the coating layer, the broken layer, the edge crack going through the interface, the undercoat crack in the substrate and the embedded crack crossing the interface. The primary calculated quantity is the stress intensity factor at various singular points and the main variables are the relative sizes and locations of cracks, the time, and the duration of the cooling ramp. The problem is solved and rather extensive results are given for two material pairs, namely a stainless steel layer welded on a ferritic medium and a ceramic coating on a steel substrate.

Rizk, A. A.↗

NASA NTRS1988

A surface crack in shells under mixed-mode loading conditions

The present consideration of a shallow shell's surface crack under general loading conditions notes that while the mode I state can be separated, modes II and III remain coupled. A line spring model is developed to formulate the part-through crack problem under mixed-mode conditions, and then to consider a shallow shell of arbitrary curvature having a part-through crack located on the outer or the inner surface of the shell; Reissner's transverse shear theory is used to formulate the problem under the assumption that the shell is subjected to all five moment and stress resultants.

Joseph, P. F.↗

NASA NTRS1988

Interface crack in a nonhomogeneous elastic medium

The linear elasticity problem for an interface crack between two bonded half planes is reconsidered. It is assumed that one of the half planes is homogeneous and the second is nonhomogeneous in such a way that the elastic properties are continuous throughout the plane and have discontinuous derivatives along the interface. The problem is formulated in terms of a system of integral equations and the asymptotic behavior of the stress state near the crack tip is determined. The results lead to the conclusion that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip. The problem is solved for various values of the nonhomogeneity parameter and for four different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated.

Delale, F.↗

NASA NTRS1988

Surface and through crack problems in orthotropic plates

The present treatment of the general mode I crack problem in bending- and membrane-loaded orthotropic plates proceeds by formulating the bending problem for a series of planar and through-cracks; by independently varying the six independent constants, the effect of material orthotropy on the stress intensity factor is determined. The surface-crack problem is then formulated by means of the line-spring model, using a transverse-shear theory of plate bending. Attention is given to composite laminates with through-cracks or semielliptic surface cracks. A significant effect is noted for material orthotropy.

Erdogan, F.↗

NASA NTRS1987

On the solution of integral equations with a generalized Cauchy kernel

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Kaya, A. C.↗

NASA NTRS1987

The surface crack problem in an orthotropic plate under bending and tension

The elasticity problem for an infinite orthotropic flat plate containing a series of through and part through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three-dimensional material orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants were used. The effects of material orthotropy on the stress intensity factors was determined, the interaction between two asymmetrically arranged collinear cracks was investigated, and extensive numerical results regarding the stress intensity factors are provided. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.

Wu, Bing-Hua↗

NASA NTRS1987

On the solution of integral equations with strongly singular kernels

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

Kaya, A. C.↗

NASA NTRS1986

The surface crack problem in an orthotropic plate under bending and tension

The elasticity problem for an infinite orthotropic flat plate containing a series of through and part-through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three dimensional materials orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants has been used. The main purpose of this study is to determine the effect of material orthotropy on the stress intensity factors, to investigate the interaction between two asymmetrically arranged collinear cracks, and to provide extensive numerical results regarding the stress intensity factors. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.

Wu, B. H.↗

NASA NTRS1986

The crack problem in a reinforced cylindrical shell

A partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z = 0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

Yahsi, O. S.↗

NASA NTRS1986

Line Spring Model and Its Applications to Part-Through Crack Problems in Plates and Shells

The line spring model is described and extended to cover the problem of interaction of multiple internal and surface cracks in plates and shells. The shape functions for various related crack geometries obtained from the plane strain solution and the results of some multiple crack problems are presented. The problems considered include coplanar surface cracks on the same or opposite sides of a plate, nonsymmetrically located coplanar internal elliptic cracks, and in a very limited way the surface and corner cracks in a plate of finite width and a surface crack in a cylindrical shell with fixed end.

Erdogan, F.↗

NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernal

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗

NASA NTRS1986

On the solution of integral equations with strongly singular kernels

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

Kaya, A. C.↗

NASA NTRS1986

The crack problem in a reinforced cylindrical shell

In this paper a partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z=0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

Yahsi, O. S.↗

NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernel

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗