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NASA NTRS2019

Estimation of Delamination Crack Depth Using Passive Thermography

Passive thermography is used to monitor small increases in temperature resulting from delamination damage formation in a composite hat-stiffened panel during quasi-static loading. The heating is composed of two heat generation components. The first component is an instantaneous response due to a strain release during quasi-static loading. The second component is mechanical heating, at the interface of failure, due to fracture damage. This second component produces a transient rise in temperature that is a function of the damage depth and thermal diffusivity. The first component defines the thermal start time for the transient response. A one-dimensional thermal model is used to determine the damage depth. The results are compared to ultrasonic and X-ray CT data. The advantages and limitations of the thermal technique for damage depth detection are discussed.

Zalameda, Joseph N.↗
NASA NTRS1984

Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.

Newman, J. C., Jr.↗
NASA NTRS1981

An empirical stress-intensity factor equation for the surface crack

This paper presents an empirical stress-intensity factor equation for a surface crack as a function of parametric angle, crack depth, crack length, plate thickness and plate width for tension and bending loads. The stress-intensity factors used to develop the equation were obtained from a previous three-dimensional, finite-element analysis of semielliptical surface cracks in finite elastic plates subjected to tension or bending loads. A wide range of configuration parameters was included in the equation. The ratios of crack length to plate thickness and the ratios of crack depth to crack length ranged from 0 to 1.0. The effects of plate width on stress-intensity variations along the crack front were also included. The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. The equation was also used to correlate surface-crack fracture data for a brittle epoxy material within + or - 10 percent for a wide range of crack shapes and crack sizes.

Newman, J. C., Jr.↗
NASA NTRS1972

Deformation mechanics of deep surface flaw cracks

A combined analytical and experimental program was conducted to determine the deformation characteristics of deep surface cracks in Mode I loading. An approximate plane finite element analysis was performed to make a parameter study on the influence of crack depth, crack geometry, and stress level on plastic zones, crack opening displacement, and back surface dimpling in Fe-3Si steel and 2219-T87 aluminum. Surface replication and profiling techniques were used to examine back surface dimple configurations in 2219-T87 aluminum. Interferometry and holography were used to evaluate the potential of various optical techniques to detect small surface dimples on large surface areas.

Francis, P. H.↗
NASA NTRS1981

Stress-intensity factor equations for cracks in three-dimensional finite bodies

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Newman, J. C., Jr.↗
NASA NTRS2015

Simulating the X-Ray Image Contrast to Set-Up Techniques with Desired Flaw Detectability

The paper provides simulation data of previous work by the author in developing a model for estimating detectability of crack-like flaws in radiography. The methodology is being developed to help in implementation of NASA Special x-ray radiography qualification, but is generically applicable to radiography. The paper describes a method for characterizing X-ray detector resolution for crack detection. Applicability of ASTM E 2737 resolution requirements to the model are also discussed. The paper describes a model for simulating the detector resolution. A computer calculator application, discussed here, also performs predicted contrast and signal-to-noise ratio calculations. Results of various simulation runs in calculating x-ray flaw size parameter and image contrast for varying input parameters such as crack depth, crack width, part thickness, x-ray angle, part-to-detector distance, part-to-source distance, source sizes, and detector sensitivity and resolution are given as 3D surfaces. These results demonstrate effect of the input parameters on the flaw size parameter and the simulated image contrast of the crack. These simulations demonstrate utility of the flaw size parameter model in setting up x-ray techniques that provide desired flaw detectability in radiography. The method is applicable to film radiography, computed radiography, and digital radiography.

Koshti, Ajay M.↗
NASA NTRS1985

Stress-intensity factors for circumferential surface cracks in pipes and rods under tension and bending loads

The purpose of this paper is to present stress-intensity factors for a wide range of nearly semi-elliptical surface cracks in pipes and rods. The configurations were subjected to either remote tension or bending loads. For pipes, the ratio of crack depth to crack length (a/c) ranged from 0.6 to 1; the ratio of crack depth to wall thickness (a/t) ranged from 0.2 to 0.8; and the ratio of internal radius to wall thickness (R/t) ranged from 1 to 10. For rods, the ratio of crack depth to crack length also ranged from 0.6 to 1; and the ratio of crack depth to rod diameter (a/D) ranged from 0.05 to 0.35. These particular crack configurations were chosen to cover the range of crack shapes (a/c) that have been observed in experiments conducted on pipes and rods under tension and bending fatigue loads. The stress-intensity factors were calculated by a three-dimensional finite-element method. The finite-element models employed singularity elements along the crack front and linear-strain elements elsewhere. The models had about 6500 degrees of freedom. The stress-intensity factors were evaluated using a nodal-force method.

Raju, I. S.↗
NASA NTRS1986

Stress-intensity factors for circumferential surface cracks in pipes and rods under tension and bending loads

The purpose of this paper is to present stress-intensity factors for a wide range of nearly semi-elliptical surface cracks in pipes and rods. The configurations were subjected to either remote tension or bending loads. For pipes, the ratio of crack depth to crack length (a/c) ranged from 0.6 to 1; the ratio of crack depth to wall thickness (a/t) ranged from 0.2 to 0.8; and the ratio of internal radius to wall thickness (R/t) ranged from 1 to 10. For rods, the ratio of crack depth to crack length also ranged from 0.6 to 1; and the ratio of crack depth to rod diameter (a/D) ranged from 0.05 to 0.35. These particular crack configurations were chosen to cover the range of crack shapes (a/c) that have been observed in experiments conducted on pipes and rods under tension and bending fatigue loads. The stress-intensity factors were calculated by a three-dimensional finite-element method. The finite-element models employed singularity elements along the crack front and linear-strain elements elsewhere. The models had about 6500 degrees of freedom. The stress-intensity factors were evaluated using a nodal-force method.

Raju, I. S.↗
NASA NTRS1988

Stress-intensity factors for small surface and corner cracks in plates

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

Raju, I. S.↗
NASA NTRS1989

Stress-intensity factors for small surface and corner cracks in plates

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

Raju, Ivatury S.↗
NASA NTRS1980

Stress-intensity factors for internal surface cracks in cylindrical pressure vessels

The paper presents stress-intensity factors for a wide range of semi-elliptical surface cracks on the inside of pressurized cylinders. The ratio of crack depth to crack length ranged from 0.2 to 1; the ratio of crack depth to wall thickness ranged from 0.2 to 0.8; and the ratio of wall thickness to vessel radius was 0.1 to to 0.25. The stress-intensity factors were calculated by a three-dimensional finite-element method using singularity elements along the crack front and linear-strain elements elsewhere. An equation for the stress-intensity factors was obtained which applies over a wide range of configuration parameters and was within about 5 percent of the present results. A comparison was also made between the results and other analyses of internal surface cracks in cylinders. The results from a boundary-integral equation method were in agreement and those from another finite-element method were in fair agreement (+ or - 8 percent) with the results.

Newman, J. C., Jr.↗
NASA NTRS1988

A re-evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method.

Tan, P. W.↗
NASA NTRS1979

Analysis of surface cracks in finite plates under tension or bending loads

Stress-intensity factors calculated with a three-dimensional, finite-element analysis for shallow and deep semielliptical surface cracks in finite elastic isotropic plates subjected to tension or bending loads are presented. A wide range of configuration parameters was investigated. The ratio of crack depth to plate thickness ranged from 0.2 to 0.8 and the ratio of crack depth to crack length ranged from 0.2 to 2.0. The effects of plate width on stress-intensity variations along the crack front was also investigated. A wide-range equation for stress-intensity factors along the crack front as a function of crack depth, crack length, plate thickness, and plate width was developed for tension and bending loads. The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. A modified form of the equation was also used to correlate surface-crack fracture data for a brittle epoxy material within + or - 10 percent for a wide range of crack shapes and crack sizes.

Newman, J. C., Jr.↗
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 NTRS1976

Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface

The stress intensity factors (SIFs) at the end points of flaws emanating from the corner formed by the intersection of a plate with a hole were determined using stress freezing photoelasticity and a numerical technique known as the Taylor series correction method to extract the SIF values from the photoelastic data. The geometries studied were crack depth to thickness ratios of about 0.2, 0.5, and 0.75; crack depth to crack length ratios of about 1.0 to 2.0; and crack length to hole radius ratios of about 0.5 to 2.0. The SIFs were determined at the intersection of the flaw border with the plate surface (KS) and with the edge of the hole (KH). It is shown that extension of a crack emanating from a corner of intersection of a hole with a plate under monotonically increasing load is not self-similar and that as the flaw depth increases, KH decreases and KS increases. Existing theories and design criteria significantly overestimate the SIF at both the hole and the surface except for shallow flaws at the hole and deep flaws at the surface.

Mcgowan, J. J.↗
NASA NTRS1974

Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface

A technique consisting of a marriage between stress freezing photoelasticity and a numerical method was used to obtain stress intensity factors for natural cracks emanating from the corner at which a hole intersects a plate surface. Geometrics studied were: crack depth to thickness ratios of approximately 0.2, 0.5, and 0.75; crack depth to crack length ratios of approximately 1.0 to 2.0. All final crack geometries were grown under monotonic loading and growth was not self similar with most of the growth occurring through the thickness under remote extension. Stress intensity plate surface K sub s factors were determined at the intersection of the flaw border with the plate surface K sub s and with the edge of the hole K sub h. Results showed that for the relatively shallow flaws K sub h approximately equal to 1.5 K sub s, for the moderately deep flaws K sub h approximately equal to K sub s, and for the deep flaws K sub h approximately equal to 0.5 K sub s, revealing a severe sensitivity of K to flaw geometry.

Mcgowan, J. J.↗
NASA NTRS1974

Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface

A technique consisting of freezing photo-elasticity and a numerical method was used to obtain stress intensity factors for natural cracks emanating from the corner at which a hole intersects a plate surface. Geometries studied were: (1) crack depth to thickness ratios of approximately 0.2, (2) 0.5 and 0.75; (3) crack depth to crack length ratios of approximately 1.0 to 2.0; and (4) crack length to hole radius ratios of about 0.5 to 2.0. All final crack geometries were grown under monotonic loading and growth was not self similar, with most of the growth occuring through the thickness under remote extension. Stress intensity factors were determined at the intersection of the flaw border.

Mcgowan, J. J.↗
NASA NTRS1976

Stress-intensity factors for a thick-walled cylinder containing an annular imbedded or external or internal surface crack

The elastostatic axisymmetric problem for a long thick-walled cylinder containing a ring-shaped internal or edge crack is considered. 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.↗