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NASA NTRS1978

A thick-walled cylinder with an axisymmetric internal or edge crack

The paper considers the elastostatic axisymmetric problem for a long thick-walled cylinder containing a ring-shaped internal or edge crack. Using the standard transform technique the problem is formulated in terms of an integral equation which has a simple Cauchy kernel for the internal crack and a generalized Cauchy kernel for the edge crack as the dominant part. As examples the uniform axial load and the steady-state thermal stress problems have been solved and the related stress-intensity factors have been calculated. Among other findings the results show that in the cylinder under uniform axial stress containing an internal crack the stress-intensity factor at the inner tip is always greater than that at the outer tip for equal net ligament thicknesses and in the cylinder with an edge crack which is under a state of thermal stress the stress-intensity factor is a decreasing function of the crack depth, tending to zero as the crack depth approaches the wall thickness.

Erdol, R.↗

NASA NTRS1989

A probabilistic approach to crack instability

A probabilistic model of brittle fracture is examined with reference to two-dimensional problems. The model is illustrated by using experimental data obtained for 25 macroscopically identical specimens made of short-fiber-reinforced composites. It is shown that the model proposed here provides a predictive formalism for the probability distributions of critical crack depth, critical loads, and crack arrest depths. It also provides similarity criteria for small-scale testing.

Chudnovsky, A.↗

NASA NTRS1996

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semi-elliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT vs. SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application.

McClung, R. C.↗

NASA NTRS1996

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

McClung, R. C.↗

NASA NTRS1999

A Comparison of Single-Cycle Versus Multiple-Cycle Proof Testing Strategies

Single-cycle and multiple-cycle proof testing (SCPT and MCPT) strategies for reusable aerospace propulsion system components are critically evaluated and compared from a rigorous elastic-plastic fracture mechanics perspective. Earlier MCPT studies are briefly reviewed. New J-integral estimation methods for semielliptical surface cracks and cracks at notches are derived and validated. Engineering methods are developed to characterize crack growth rates during elastic-plastic fatigue crack growth (FCG) and the tear-fatigue interaction near instability. Surface crack growth experiments are conducted with Inconel 718 to characterize tearing resistance, FCG under small-scale yielding and elastic-plastic conditions, and crack growth during simulated MCPT. Fractography and acoustic emission studies provide additional insight. The relative merits of SCPT and MCPT are directly compared using a probabilistic analysis linked with an elastic-plastic crack growth computer code. The conditional probability of failure in service is computed for a population of components that have survived a previous proof test, based on an assumed distribution of initial crack depths. Parameter studies investigate the influence of proof factor, tearing resistance, crack shape, initial crack depth distribution, and notches on the MCPT versus SCPT comparison. The parameter studies provide a rational basis to formulate conclusions about the relative advantages and disadvantages of SCPT and MCPT. Practical engineering guidelines are proposed to help select the optimum proof test protocol in a given application.

McClung, R. C.↗

NASA NTRS1984

Edge crack growth of thermally aged graphite/polyimide composites

Laminates of Celion 6000/LARC-160 and Celion 6000/PMR-15 graphite/polyimide composite materials were aged in air at temperatures of 202, 232, 260 and 288 C for various times up to 15,000 hours. Three unidirectional specimen types were studied: short beam shear (SBS), flexure, and 153 mm square panels. The interior region of the square panels exhibited little or no property degradation, whereas both laminate materials degraded and cracked preferentially at the specimen edge perpendicular to the fibers. Using a dye penetrant, the specimens were X-rayed and the crack depth measured as a function of time and temperature. A time temperature superposition of the crack data was successfully performed using an Arrhenius form for the shift factor. A direct correlation was found for edge crack depth and SBS strength for the LARC-160 laminates but the correlation for PMR-15 laminates was more complex.

Nelson, J. B.↗

NASA NTRS1994

The Relationship Between Constraint and Ductile Fracture Initiation as Defined by Micromechanical Analyses

The use of small laboratory specimens to predict the integrity of large, complex structures relies on the validity of single parameter fracture mechanics. Unfortunately, the constraint loss associated with large scale yielding, whether in a laboratory specimen because of its small size or in a structure because it contains shallow flaws loaded in tension, can cause the breakdown of classical fracture mechanics and the loss of transferability of critical, global fracture parameters. Although the issue of constraint loss can be eliminated by testing actual structural configurations, such an approach can be prohibitively costly. Hence, a methodology that can correct global fracture parameters for constraint effects is desirable. This research uses micromechanical analyses to define the relationship between global, ductile fracture initiation parameters and constraint in two specimen geometries (SECT and SECB with varying a/w ratios) and one structural geometry (circumferentially cracked pipe). Two local fracture criteria corresponding to ductile fracture micromechanisms are evaluated: a constraint-modified, critical strain criterion for void coalescence proposed by Hancock and Cowling and a critical void ratio criterion for void growth based on the Rice and Tracey model. Crack initiation is assumed to occur when the critical value in each case is reached over some critical length. The primary material of interest is A516-70, a high-hardening pressure vessel steel sensitive to constraint; however, a low-hardening structural steel that is less sensitive to constraint is also being studied. Critical values of local fracture parameters are obtained by numerical analysis and experimental testing of circumferentially notched tensile specimens of varying constraint (e.g., notch radius). These parameters are then used in conjunction with large strain, large deformation, two- and three-dimensional finite element analyses of the geometries listed above to predict crack initiation loads and to calculate the associated (critical) global fracture parameters. The loads are verified experimentally, and microscopy is used to measure pre-crack length, crack tip opening displacement (CTOD), and the amount of stable crack growth. Results for A516-70 steel indicate that the constraint-modified, critical strain criterion with a critical length approximately equal to the grain size (0.0025 inch) provides accurate predictions of crack initiation. The critical void growth criterion is shown to considerably underpredict crack initiation loads with the same critical length. The relationship between the critical value of the J-integral for ductile crack initiation and crack depth for SECT and SECB specimens has been determined using the constraint-modified, critical strain criterion, demonstrating that this micromechanical model can be used to correct in-plane constraint effects due to crack depth and bending vs. tension loading. Finally, the relationship developed for the SECT specimens is used to predict the behavior of circumferentially cracked pipe specimens.

Panontin, Tina L.↗

NASA NTRS1992

Stress Intensity Factors for Part-Through Surface Cracks in Hollow Cylinders

Flaws resulting from improper welding and forging are usually modeled as cracks in flat plates, hollow cylinders or spheres. The stress intensity factor solutions for these crack cases are of great practical interest. This report describes some recent efforts at improving the stress intensity factor solutions for cracks in such geometries with emphasis on hollow cylinders. Specifically, two crack configurations for cylinders are documented. One is that of a surface crack in an axial plane and the other is a part-through thumb-nail crack in a circumferential plane. The case of a part-through surface crack in flat plates is used as a limiting case for very thin cylinders. A combination of the two cases for cylinders is used to derive a relation for the case of a surface crack in a sphere. Solutions were sought which cover the entire range of the geometrical parameters such as cylinder thickness, crack aspect ratio and crack depth. Both the internal and external position of the cracks are considered for cylinders and spheres. The finite element method was employed to obtain the basic solutions. Power-law form of loading was applied in the case of flat plates and axial cracks in cylinders and uniform tension and bending loads were applied in the case of circumferential (thumb-nail) cracks in cylinders. In the case of axial cracks, the results for tensile and bending loads were used as reference solutions in a weight function scheme so that the stress intensity factors could be computed for arbitrary stress gradients in the thickness direction. For circumferential cracks, since the crack front is not straight, the above technique could not be used. Hence for this case, only the tension and bending solutions are available at this time. The stress intensity factors from the finite element method were tabulated so that results for various geometric parameters such as crack depth-to-thickness ratio (a/t), crack aspect ratio (a/c) and internal radius-to-thickness ratio (R/t) or the crack length-to-width ratio (2c/W) could be obtained by interpolation and extrapolation. Such complete tables were then incorporated into the NASA/FLAGRO computer program which is widely used by the aerospace community for fracture mechanics analysis.

Mettu, Sambi R.↗

NASA NTRS2008

Fatigue Crack Growth Behavior Evaluation of Grainex Mar-M 247 for NASA's High Temperature, High Speed Turbine Seal Test Rig

The fatigue crack growth behavior of Grainex Mar-M 247 is evaluated for NASA s Turbine Seal Test Facility. The facility is used to test air-to-air seals primarily for use in advanced jet engine applications. Because of extreme seal test conditions of temperature, pressure, and surface speeds, surface cracks may develop over time in the disk bolt holes. An inspection interval is developed to preclude catastrophic disk failure by using experimental fatigue crack growth data. By combining current fatigue crack growth results with previous fatigue strain-life experimental work, an inspection interval is determined for the test disk. The fatigue crack growth life of the NASA disk bolt holes is found to be 367 cycles at a crack depth of 0.501 mm using a factor of 2 on life at maximum operating conditions. Combining this result with previous fatigue strain-life experimental work gives a total fatigue life of 1032 cycles at a crack depth of 0.501 mm. Eddy-current inspections are suggested starting at 665 cycles since eddy current detection thresholds are currently at 0.381 mm. Inspection intervals are recommended every 50 cycles when operated at maximum operating conditions.

Delgado, Irebert R.↗

NASA NTRS1987

Plates and shells containing a surface crack under general loading conditions

Various through and part-through crack problems in plates and shells are considered. The line-spring model of Rice and Levy is generalized to the skew-symmetric case to solve surface crack problems involving mixed-mode, coplanar crack growth. Compliance functions are introduced which are valid for crack depth to thickness ratios at least up to .95. This includes expressions for tension and bending as well as expressions for in-plane shear, out-of-plane shear, and twisting. Transverse shear deformation is taken into account in the plate and shell theories and this effect is shown to be important in comparing stress intensity factors obtained from the plate theory with three-dimensional solutions. Stress intensity factors for cylinders obtained by the line-spring model also compare well with three-dimensional solution. By using the line-spring approach, stress intensity factors can be obtained for the through crack and for part-through crack of any crack front shape, without recalculation integrals that take up the bulk of the computer time. Therefore, parameter studies involving crack length, crack depth, shell type, and shell curvature are made in some detail. The results will be useful in brittle fracture and in fatigue crack propagation studies. All problems considered are of the mixed boundary value type and are reducted to strongly singular integral equations which make use of the finite-part integrals of Hadamard. The equations are solved numerically in a manner that is very efficient.

Joseph, Paul F.↗

NASA NTRS1972

Experimental characterization of yield induced by surface flaws.

Recent experimental findings related to the surface deformation and plastic zones associated with a deep surface flaw in Mode I tension loading are surveyed. Results of front and back surface dimpling, as determined by replica profiling and interferometry, are presented. The stresses required to initiate back surface dimpling are inversely related both to the crack depth and to the crack length. The plastic zone at the crack tip is described using results obtained from Fe-3Si specimens which have been studied with the electrolytic etching technique. It is shown that the plastic zone may be identified with a state of plane strain around the entire crack perimeter, except for the very thin layer near the crack tips on the front surface, where the deformation state approximates plane stress.

Francis, P. H.↗

NASA NTRS1979

Advanced quantitative magnetic nondestructive evaluation methods - Theory and experiment

The paper reviews the scale of fatigue crack phenomena in relation to the size detection capabilities of nondestructive evaluation methods. An assessment of several features of fatigue in relation to the inspection of ball and roller bearings suggested the use of magnetic methods; magnetic domain phenomena including the interaction of domains and inclusions, and the influence of stress and magnetic field on domains are discussed. Experimental results indicate that simplified calculations can be used to predict many features of these results; the data predicted by analytic models which use finite element computer analysis predictions do not agree with respect to certain features. Experimental analyses obtained on rod-type fatigue specimens which show experimental magnetic measurements in relation to the crack opening displacement and volume and crack depth should provide methods for improved crack characterization in relation to fracture mechanics and life prediction.

Barton, J. R.↗

NASA NTRS1979

Inspecting cracks in foam insulation

Dye solution indicates extent of cracking by penetrating crack and showing original crack depth clearly. Solution comprised of methylene blue in denatured ethyl alcohol penetrates cracks completely and evaporates quickly and is suitable technique for usage in environmental or structural tests.

Cambell, L. W.↗

NASA NTRS1982

Analysis of a turbine rotor containing a transverse crack at Oak Creek Unit 17

Transient increases in one, two and three per revolution vibration characteristics of a low pressure steam turbine were observed during steam temperature reduction operations. Vibration and fracture mechanics analyses suggested the presence of a transverse shaft crack which was eventually identified by ultrasonic inspection and confirmed by destructive sectioning. Signature analyses of vibration data recorded over a two-year period prior to crack identification are correlated with fatigue crack growth, which occurred intermittently during transient temperature decreases. The apparent increased response of the rotor to vibration is due to asymmetric stiffness changes introduced by the growing transverse crack. The vibration response is predicted to increase with increasing crack depths in excess of 10% of the shaft diameter. Fracture mechanics analyses predict that fatigue crack growth occurred during periods of steam temperature decrease, when high surface tensile stresses are present. These same transient thermal stresses are shown to have retarded and prevented subsequent fatigue crack growth during steady operation.

Rogers, G. W.↗

NASA NTRS1974

Mixed mode stress intensity factors for semielliptical surface cracks

The three-dimensional equations of elasticity are solved for a flat elliptical crack which has nonuniform shear stresses applied to its surfaces. An alternating method is used to determine the mode two and mode three stress intensity factors for a semielliptical surface crack in the surface of a finite thickness solid. These stress intensity factors are presented as a function of position along the crack border for a number of crack shapes and crack depths. This same technique is followed to determine the mode one stress intensity factors for the semielliptical surface crack which has normal loading applied to its surface. Mode one stress intensity factors are presented and compared with the results obtained from previous work.

Smith, F. W.↗

NASA NTRS1981

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

Delale, F.↗

NASA NTRS2015

Grainex Mar-M 247 Turbine Disk Life Study for NASA's High Temperature High Speed Turbine Seal Test Facility

An experimental and analytical fatigue life study was performed on the Grainex Mar-M 247 disk used in NASA s Turbine Seal Test Facility. To preclude fatigue cracks from growing to critical size in the NASA disk bolt holes due to cyclic loading at severe test conditions, a retirement-for-cause methodology was adopted to detect and monitor cracks within the bolt holes using eddy-current inspection. For the NASA disk material that was tested, the fatigue strain-life to crack initiation at a total strain of 0.5 percent, a minimum to maximum strain ratio of 0, and a bolt hole temperature of 649 C was calculated to be 665 cycles using -99.95 percent prediction intervals. The fatigue crack propagation life was calculated to be 367 cycles after implementing a safety factor of 2 on life. Thus, the NASA disk bolt hole total life or retirement life was determined to be 1032 cycles at a crack depth of 0.501 mm. An initial NASA disk bolt hole inspection at 665 cycles is suggested with 50 cycle inspection intervals thereafter to monitor fatigue crack growth.

Delgado, Irebert R.↗

NASA NTRS2017

Some Observations on Damage Tolerance Analyses in Pressure Vessels

AIAA standards S080 and S081 are applicable for certification of metallic pressure vessels (PV) and composite overwrap pressure vessels (COPV), respectively. These standards require damage tolerance analyses with a minimum reliable detectible flaw/crack and demonstration of safe life four times the service life with these cracks at the worst-case location in the PVs and oriented perpendicular to the maximum principal tensile stress. The standards require consideration of semi-elliptical surface cracks in the range of aspect ratios (crack depth a to half of the surface length c, i.e., (a/c) of 0.2 to 1). NASA-STD-5009 provides the minimum reliably detectible standard crack sizes (90/95 probability of detection (POD) for several non-destructive evaluation (NDE) methods (eddy current (ET), penetrant (PT), radiography (RT) and ultrasonic (UT)) for the two limits of the aspect ratio range required by the AIAA standards. This paper tries to answer the questions: can the safe life analysis consider only the life for the crack sizes at the two required limits, or endpoints, of the (a/c) range for the NDE method used or does the analysis need to consider values within that range? What would be an appropriate method to interpolate 90/95 POD crack sizes at intermediate (a/c) values? Several procedures to develop combinations of a and c within the specified range are explored. A simple linear relationship between a and c is chosen to compare the effects of seven different approaches to determine combinations of aj and cj that are between the (a/c) endpoints. Two of the seven are selected for evaluation: Approach I, the simple linear relationship, and a more conservative option, Approach III. For each of these two Approaches, the lives are computed for initial semi-elliptic crack configurations in a plate subjected to remote tensile fatigue loading with an R-ratio of 0.1, for an assumed material evaluated using NASGRO (registered 4) version 8.1. These calculations demonstrate that for this loading, using Approach I and the initial detectable crack sizes at the (a/c) endpoints in 5009 specified for the ET and UT NDE methods, the smallest life is not at the two required limits of the (a/c) range, but rather is at an intermediate configuration in the range (a/c) of 0.4 to 0.6. Similar analyses using both Approach I and III with the initial detectable crack size at the (a/c) endpoints in 5009 for PT NDE showed the smallest life may be at an (a/c) endpoint or an intermediate (a/c), depending upon which Approach is used. As such, analyses that interrogate only the two (a/c) values of 0.2 and 1 may result in unconservative life predictions. The standard practice may need to be revised based on these results.

Raju, Ivatury S.↗