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NASA NTRS1972

Elastostatic stress analysis of orthotropic rectangular center-cracked plates

A mapping-collocation method was developed for the elastostatic stress analysis of finite, anisotropic plates with centrally located traction-free cracks. The method essentially consists of mapping the crack into the unit circle and satisfying the crack boundary conditions exactly with the help of Muskhelishvili's function extension concept. The conditions on the outer boundary are satisfied approximately by applying the method of least-squares boundary collocation. A parametric study of finite-plate stress intensity factors, employing this mapping-collocation method, is presented. It shows the effects of varying material properties, orientation angle, and crack-length-to-plate-width and plate-height-to-plate-width ratios for rectangular orthotropic plates under constant tensile and shear loads.

Gyekenyesi, G. S.↗

NASA NTRS1973

Three-dimensional elastic stress and displacement analysis of tensile fracture specimens containing cracks

A seminumerical method is presented for three-dimensional elastic analysis of finite geometry solids with traction-free cracks. Stress and displacement distributions are calculated for two rectangular bars which are loaded by a uniform surface stress distribution. The first bar contains a through-thickness central crack while the second bar has double-edge cracks. Stress intensity factors K sub I for both configurations are presented.

Gyekenyesi, J. P.↗

NASA NTRS1973

The problem of a finite strip compressed between two rough rigid stamps

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress intensity factor is presented graphically.

Gupta, G. D.↗

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

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

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 NTRS1973

Bonded half planes containing an arbitrarily oriented crack

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.

Erdogan, F.↗

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

A study of fatigue and fracture in 7075-T6 aluminum alloy in vacuum and air environments

Axial load fatigue life, fatigue-crack propagation, and fracture toughness experiments were conducted on sheet specimens made of 7075-T6 aluminum alloy. These experiments were conducted at pressures ranging from atmospheric to 5 x 10 to the minus 8th torr. Analysis of the results from the fatigue life experiments indicated that for a given stress level, lower air pressures produced longer fatigue lives. At a pressure of 5 x 10 to the minus 8th torr fatigue lives were 15 or more times as long as at atmospheric pressure. Analysis of the results from the fatigue crack propagation experiments indicated that for small stress intensity factor ranges the fatigue crack propagation rates were up to twice as high at atmospheric pressure as in vacuum. The fracture toughness of 7075-T6 was unaffected by the vacuum environment. Fractographic examination showed that specimens tested in both vacuum and air developed fatigue striations. Considerably more striations developed on specimens tested at atmospheric pressure, however.

Hudson, C. M.↗

NASA NTRS1973

A microscopic study of crack initiation mechanisms in 7075 aluminum alloy sheets.

A study of the opening mode of crack initiation in 7075-T6 aluminum alloy sheets has been conducted with the aid of a scanning electron microscope. Observations were made from several orientations, including the top view of the specimen which showed the notch profile and the edge view of the specimen which showed the entire notch front along the specimen thickness. It was found that the edge view exhibited the first signs of permanent deformation at about 55% of the breaking strength. These changes took the form of deformation bands which were aligned in the direction of the tensile axis and apparently defined limiting regions of homogeneous slip. It is felt that the appearance of microcracks at loads approaching the breaking strength was of fundamental importance in the formation of the final fracture surface. Many of these microcraks were initiated at intermetallic particles and other metallurgically weak regions on the notch surface. It was also possible to correlate the strain in the notch with the stress intensity factor for the various loads. Very large plastic strains were observed on the notch tip as compared to published values of elongation at fracture for unnotched specimens.

Jones, D. L.↗

NASA NTRS1973

An integral equation approach to the semi-infinite strip problem.

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. The integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. The stress singularity at the strip corner is obtained from the singular integral equation, which is then solved numerically. Stresses along the rigid end are determined, and the effect of the material properties on the stress-intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

Gupta, G. D.↗

NASA NTRS1973

The elliptical crack subjected to nonuniform shear loading.

The equations of elasticity are solved for the problem of a flat elliptical crack which has nonuniform shear stresses applied to its surfaces. The shear stresses are prescribed independently in two directions on the crack surface and are expressed in the form of a third-degree polynomial. Mode-two and mode-three stress-intensity factors are presented in analytical and graphical form as functions of position along the crack border.

Smith, F. W.↗

NASA NTRS1973

A layered composite with a broken laminate.

The problem of a laminate composite in presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. Integral transform technique is used to formulate the problem in terms of a singular integral equation from which the power of stress singularity around the crack tip terminating at the interface is obtained. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.

Gupta, G. D.↗

NASA NTRS1971

The influence of temperature on fatigue-crack growth in a mill-annealed Ti-6Al-4V alloy

To understand the influence of temperature on the rate of fatigue crack growth in high strength metal alloys, constant load amplitude fatigue crack growth experiments were carried out using a 1/4 inch thick (6.35 mm) mill-annealed Ti-6Al-4V alloy plate as a model material. The rates of fatigue crack growth were determined as a function of temperature, ranging from room temperature to about 290 C and as a function of the crack tip, stress intensity factor K, in dehumidified high purity argon environment. The dependence of the rate of fatigue crack growth on K appears to be separable into two regions. The transition correlates with changes in both the microscopic and macroscopic appearances of the fracture surfaces, and suggests a change in the mechanism and the influence of microstructure on fatigue crack growth.

Wei, R. P.↗

NASA NTRS1973

Transverse cracks in a strip with reinforced surfaces

The symmetrical problem of two transverse cracks in an elastic strip with reinforced surfaces is formulated in terms of a singular integral equation. The special cases of one central crack or two edge cracks are discussed. Numerical methods for solving the problems with internal cracks are outlined and stress intensity factors are presented for various geometrics and degrees of surface reinforcement.

Krenk, S.↗

NASA NTRS1974

Effects of proof loads and combined mode loadings on fracture and flaw growth characteristics of aerospace alloys

This experimental program was undertaken to determine the effects of (1) combined tensile and bending loadings, (2) combined tensile and shear loadings, and (3) proof overloads on fracture and flaw growth characteristics of aerospace alloys. Tests were performed on four alloys: 2219-T87 aluminum, 5Al-2.5Sn (ELl) titanium, 6Al-4V beta STA titanium and high strength 4340 steel. Tests were conducted in room air, gaseous nitrogen at -200F (144K), liquid nitrogen and liquid hydrogen. Flat center cracked and surface flawed specimens, cracked tube specimens, circumferentially notched round bar and surface flawed cylindrical specimens were tested. The three-dimensional photoelastic technique of stress freezing and slicing was used to determine stress intensity factors for surface flawed cylindrical specimens subjected to tension or torsion. Results showed that proof load/temperature histories used in the tests have a small beneficial effect or no effect on subsequent fracture strength and flaw growth rates.

Shah, R. C.↗

NASA NTRS1973

The partially closed Griffith crack

A solution is presented for a Griffith crack subjected to an arbitrary polynomial loading function which causes one end of the crack to remain closed. Closed form expressions are presented for the crack opening length and for the stress and displacements in the plane of the crack. The special case of pure bending is presented as an example and for this case the stress intensity factor is computed.

Thresher, R. W.↗

NASA NTRS1973

Computational fracture mechanics

Numerical procedures for accurate determination of elastic stress intensity factors for the general two-dimensional crack problem are reviewed. The elastic perfectly plastic state of crack tip deformation is studied by a finite element procedure. Elastic-plastic fields in the immediate vicinity of a crack tip are determined numerically by finite element procedures based on asymptotic studies of crack tip singularities in plastic materials. The small-scale yielding problem is modeled, and expressions for crack tip opening displacement, shear singularity amplitude, and plastic zone extent are derived. A finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained. The three-dimensional aspects of flawed structures and numerical methods of treating them are studied. Ductile fracture mechanisms, in particular crack tip fracture on the microscale, are discussed.

Rice, J. R.↗