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NASA NTRS1996

Gear crack propagation investigations

Analytical and experimental studies were performed to investigate the effect of gear rim thickness on crack propagation life. The FRANC (FRacture ANalysis Code) computer program was used to simulate crack propagation. The FRANC program used principles of linear elastic fracture mechanics, finite element modeling, and a unique re-meshing scheme to determine crack tip stress distributions, estimate stress intensity factors, and model crack propagation. Various fatigue crack growth models were used to estimate crack propagation life based on the calculated stress intensity factors. Experimental tests were performed in a gear fatigue rig to validate predicted crack propagation results. Test gears were installed with special crack propagation gages in the tooth fillet region to measure bending fatigue crack growth. Good correlation between predicted and measured crack growth was achieved when the fatigue crack closure concept was introduced into the analysis. As the gear rim thickness decreased, the compressive cyclic stress in the gear tooth fillet region increased. This retarded crack growth and increased the number of crack propagation cycles to failure.

Lewicki, David G.↗

NASA NTRS1972

Plane elastostatic analysis of V-notched plates.

Solutions are given for several plane elastostatic problems of plates having a V-notch on one edge, and subjected to a variety of boundary conditions. The effect of the magnitude of the V-notch angle and specimen geometry on stress intensity factors KI and KII are obtained for unloaded notch surfaces. There is less than one per cent difference in opening model stress intensity factor in going from a zero degree notch angle to a 30 degree notch angle. Notch opening displacements at the plate edge were measured experimentally, and the results obtained were in excellent agreement with the computed results.

Gross, B.↗

NASA NTRS1992

Advances in fatigue life prediction methodology for metallic materials

The capabilities of a plasticity-induced crack-closure model to predict small- and large-crack growth rates, and in some cases total fatigue life, for four aluminum alloys and three titanium alloys under constant-amplitude, variable-amplitude, and spectrum loading are described. Equations to calculate a cyclic-plastic-zone corrected effective stress-intensity factor range from a cyclic J-integral and crack-closure analysis of large cracks were reviewed. The effective stress-intensity factor range against crack growth rate relations were used in the closure model to predict small- and large-crack growth under variable-amplitude and spectrum loading. Using the closure model and microstructural features, a total fatigue life prediction method is demonstrated for three aluminum alloys under various load histories.

Newman, J. C., Jr.↗

NASA NTRS1987

NASCRAC - A computer code for fracture mechanics analysis of crack growth

NASCRAC - a computer code for fracture mechanics analysis of crack growth - is described in this paper. The need for such a code is increasing as requirements grow for high reliability and low weight in aerospace components. The code is comprehensive and versatile, as well as user friendly. The major purpose of the code is calculation of fatigue, corrosion fatigue, or stress corrosion crack growth, and a variety of crack growth relations can be selected by the user. Additionally, crack retardation models are included. A very wide variety of stress intensity factor solutions are contained in the code, and extensive use is made of influence functions. This allows complex stress gradients in three-dimensional crack problems to be treated easily and economically. In cases where previous stress intensity factor solutions are not adequate, new influence functions can be calculated by the code. Additional features include incorporation of J-integral solutions from the literature and a capability for estimating elastic-plastic stress redistribution from the results of a corresponding elastic analysis. An example problem is presented which shows typical outputs from the code.

Harris, D. O.↗

NASA NTRS1993

Analytical stress intensity solution for the Stable Poisson Loaded specimen

An analytical calibration of the Stable Poisson Loaded (SPL) specimen is presented. The specimen configuration is similar to the ASTM E-561 compact-tension specimen with displacement controlled wedge loading used for R-curve determination. The crack mouth opening displacements (CMODs) are produced by the diametral expansion of an axially compressed cylindrical pin located in the wake of a machined notch. Due to the unusual loading configuration, a three-dimensional finite element analysis was performed with gap elements simulating the contact between the pin and specimen. In this report, stress intensity factors, CMODs, and crack displacement profiles, are reported for different crack lengths and different contacting conditions. It was concluded that the computed stress intensity factor decreases sharply with increasing crack length thus making the SPL specimen configuration attractive for fracture testing of brittle, high modulus materials.

Ghosn, Louis J.↗

NASA NTRS1984

On the use of marker loads and replicas for measuring growth rates for small cracks

The initiation and growth of small cracks (5-500 microns m) from edge notches in 2024-T3 aluminum alloy sheets were studied under constant amplitude loading. Two methods were used to measure crack shape and size. In the first method, striation marker bands were periodically formed along the crack front by interrupting the constant amplitude loading by either an elevated R-ratio load sequence, or by an overload sequence. In the second method, the surface crack length was monitored by taking surface replicas at regular intervals. The marker band techniques did not provide reliable crack length and crack shape information for cracks smaller than 2 mm. The replica technique provided accurate information for surface crack length at all crack lengths, and fracture tests on specimens with small cracks provided crack-shape information. Crack growth rates were plotted against the stress intensity factor ranges. The results exhibited the small crack effect, in that the small cracks grew faster than large cracks at the same stress-intensity factor range. A crack closure model was also used to analyze the growth of small cracks from small (inclusion) defects at the notch surface.

Swain, M. H.↗

NASA NTRS1992

Numerical calibration of the stable poisson loaded specimen

An analytical calibration of the Stable Poisson Loaded (SPL) specimen is presented. The specimen configuration is similar to the ASTM E-561 compact-tension specimen with displacement controlled wedge loading used for R-Curve determination. The crack mouth opening displacements (CMOD's) are produced by the diametral expansion of an axially compressed cylindrical pin located in the wake of a machined notch. Due to the unusual loading configuration, a three-dimensional finite element analysis was performed with gap elements simulating the contact between the pin and specimen. In this report, stress intensity factors, CMOD's, and crack displacement profiles are reported for different crack lengths and different contacting conditions. It was concluded that the computed stress intensity factor decreases sharply with increasing crack length, thus making the SPL specimen configuration attractive for fracture testing of brittle, high modulus materials.

Ghosn, Louis J.↗

NASA NTRS1973

Fracture analysis of surface- and through-cracked sheets and plates.

The Neuber stress-concentration relation for notches in an elastic-plastic material subjected to shear loading was generalized for a crack in a finite plate subjected to tensile loading. An equation was derived which related the linear elastic stress-intensity factor, the applied stress, and two material parameters. The equation was then used as a two-parameter fracture criterion for surface- and through-cracked specimens. Fracture data from the literature on surface- and through-cracked sheet and plate specimens of steel, titanium alloy, titanium weldment, and aluminum alloy tested at room and cryogenic temperature were analyzed according to the proposed equation. For surface cracks, wide ranges of crack-depth to crack-length ratio and crack-depth to specimen-thickness ratio were considered. For through cracks, wide ranges of crack length and specimen width were also considered.-

Newman, J. C., Jr.↗

NASA NTRS1974

Plane-stress fracture of compact and notch-bend specimens

Thin-gaged or high toughness materials containing cracks usually fail in a ductile manner with nominal failure stresses approaching the ultimate strength of the material. For such materials, a two-parameter fracture criterion was developed. An equation which related the linear elastic stress-intensity factor, elastic nominal stress, and two material parameters was previously derived and has been used as a fracture criterion for surface- and through-cracked specimens under tensile loading. This two-parameter fracture criterion was rederived in a more general form and was extended to compact and notch-bend fracture specimens. A close correlation was found between experimental and predicted failure stresses.

Newman, J. C., Jr.↗

NASA NTRS1977

Three-dimensional elastic stress and displacement analysis of finite geometry solids containing cracks

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement fields in finite geometry bars containing central, surface, and double-edge cracks under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Normal stresses and the stress intensity factor variation along the crack periphery are calculated using the obtained displacement field. The reported results demonstrate the usefulness of this method in calculating stress intensity factors for commonly encountered crack geometries in finite solids.

Kring, J.↗

NASA NTRS1976

Plane-stress fracture of compact and notch-bend specimens

Thin-gaged or high toughness materials containing cracks usually fail in a ductile manner with nominal failure stresses approaching the ultimate strength of the material. For such materials, a two-parameter fracture criterion was developed. An equation which related the linear elastic stress-intensity factor, elastic nominal stress, and two material parameters has previously been derived and has been used as a fracture criterion for surface- and through-cracked specimens under tensile loading. In the present paper the two-parameter fracture criterion was rederived in a more general form and was extended to compact and notch-bend fracture specimens. A close correlation was found between experimental and calculated failure stresses.

Newman, J. C., Jr.↗

NASA NTRS1977

Three-dimensional elastic stress and displacement analysis of finite geometry solids containing cracks

Kring, J.↗

NASA NTRS1979

The effect of transverse shear in a cracked plate under skew-symmetric loading

The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson's ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.

Delale, F.↗

NASA NTRS1985

A clamped rectangular plate containing a crack

The general problem of a rectangular plate clamped along two parallel sides and containing a crack parallel to the clamps is considered. The problem is formulated in terms of a system of singular integral equations and the asymptotic behavior of the stress state near the corners is investigated. Numerical examples are considered for a clamped plate without a crack and with a centrally located crack, and the stress intensity factors and the stresses along the clamps are calculated.

Tang, R.↗

NASA NTRS1985

A clamped rectangular plate containing a crack

Tang, R.↗

NASA NTRS1986

Effect of loading rate on dynamic fracture of reaction bonded silicon nitride

Wedge-loaded, modified tapered double cantilever beam (WL-MTDCB) specimens under impact loading were used to determine the room temperature dynamic fracture response of reaction bonded silicon nitride (RBSN). The crack extension history, with the exception of the terminal phase, was similar to that obtained under static loading. Like its static counterpart, a distinct crack acceleration phase, which was not observed in dynamic fracture of steel and brittle polymers, was noted. Unlike its static counterpart, the crack continued to propagate at nearly its terminal velocity under a low dynamic stress intensity factor during the terminal phase of crack propagation. These and previously obtained results for glass and RBSN show that dynamic crack arrest under a positive dynamic stress intensity factor is unlikely in static and impact loaded structural ceramics.

Liaw, B. M.↗

NASA NTRS1986

Numerical solution of random singular integral equation appearing in crack problems

The solution of several elasticity problems, and particularly crack problems, can be reduced to the solution of one-dimensional singular integral equations with a Cauchy-type kernel or to a system of uncoupled singular integral equations. Here a method for the numerical solution of random singular integral equations of Cauchy type is presented. The solution technique involves a Chebyshev series approximation, the coefficients of which are the solutions of a system of random linear equations. This method is applied to the problem of periodic array of straight cracks inside an infinite isotropic elastic medium and subjected to a nonuniform pressure distribution along the crack edges. The statistical properties of the random solution are evaluated numerically, and the random solution is used to determine the values of the stress-intensity factors at the crack tips. The error, expressed as the difference between the mean of the random solution and the deterministic solution, is established. Values of stress-intensity factors at the crack tip for different random input functions are presented.

Sambandham, M.↗

NASA NTRS1988

Predicting the growth of small and large cracks using a crack-closure model

An evaluation is conducted of the ability of a crack-closure model to predict the fatigue life of notched specimens under spectrum loading, for the cases of crack initiation and growth along the bore of a semicircular notch and the growth of large cracks in 2024-T3 Al alloy sheets under constant-amplitude loading. These cases are used to establish an initial defect size and relationship between the stress-intensity factor range and crack-growth rate. Experimental and calculation results for small-crack growth rates are in good agreement and exhibited a stress level effect at equal values of stress-intensity factor range.

Newman, J. C., Jr.↗