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At least 343 records · Page 19

Characterization of crack growth under combined loading

Room-temperature static and cyclic tests were made on 21 aluminum plates in the shape of a 91.4x91.4-cm Maltese cross with 45 deg flaws to develop crack growth and fracture toughness data under mixed-mode conditions. During cyclic testing, it was impossible to maintain a high proportion of shear-mode deformation on the crack tips. Cracks either branched or turned. Under static loading, cracks remained straight if shear stress intensity exceeded normal stress intensity. Mixed-mode crack growth rate data compared reasonably well with published single-mode data, and measured crack displacements agreed with the straight and branched crack analyses. Values of critical strain energy release rate at fracture for pure shear were approximately 50% higher than for pure normal opening, and there was a large reduction in normal stress intensity at fracture in the presence of high shear stress intensity. Net section stresses were well into the inelastic range when fracture occurred under high shear on the cracks.

Feldman, A.↗

Flight inspection data and crack initiation times

Lockheed C-130 service-flight inspection data is reduced by means of fracture mechanics and statistical analysis into a form from which the probability of time to crack initiation and the distribution of initial flaw sizes for various locations on the aircraft can be determined. Crack sizes are normalized by extrapolating a growing crack backwards from its first recorded size to .03 inches (crack initiation size) yielding the time to crack initiation. In a similar fashion, the crack is grown backwards to a time equal to zero to yield an initial flaw size. In order to perform the discussed computations, crack growth constants were computed for each individual location and were analyzed statistically. Statistical distributions were fitted to times to crack initiation and to initial flaw sizes in order to describe their expected behavior. Weibull and Johnson distributions have been found to fit the data reasonably well but for a better fit convolution integrals of Poisson load distributions and Weibull strength distributions are needed.

Johnson, W. S.↗

Stress intensity factors in bonded half planes containing inclined cracks and subjected to antiplane shear loading

The antiplane shear problem for two bonded dissimilar half planes containing a semi-infinite crack or two arbitrarily located collinear cracks was considered. For the semi-infinite crack the problem was solved for a concentrated wedge load and the stress intensity factor and the angular distribution of stresses were calculated. For finite cracks the problem was reduced to a pair of integral equations. Numerical results were obtained for cracks fully imbedded in a homogeneous medium, one crack tip touching the interface, and a crack crossing the interface for various crack angles.

Bassani, J. L.↗

Finite-element analysis of crack growth under monotonic and cyclic loading

An elastic-plastic (incremental) finite-element analysis, in conjunction with a crack-growth criterion, was used to study crack-growth behavior under monotonic and cyclic loading. The crack-growth criterion was based on crack-tip strain. Whenever the crack-tip strain equals or exceeds a critical strain value, the crack grows. The effects of element-mesh size, critical strain, strain hardening, and specimen type (tension or bending) on crack growth under monotonic loading were investigated. Crack growth under cyclic loading (constant amplitude and simple variable amplitude) were also studied. A combined hardening theory, which incorporates features of both isotropic and kinematic hardening under cyclic loading, was also developed for smooth yield surfaces and was used in the analysis.

Newman, J. C., Jr.↗

An elastic-plastic analysis of fatigue crack closure in modes I and II

In this paper, an efficient elastic-plastic finite element procedure to analyze crack-closure and, its effects on fatigue crack growth under general spectrum loading, is presented. A hybrid-displacement finite element procedure is used to properly treat the stress and strain singularities near the crack-tip; and crack-growth under cyclic loading is simulated by the translation of certain 'core' elements, near the crack-tip, in which proper stress and strain singularities were embedded. Both pure mode I and mode II types of cyclic loading are considered. In the mode I case, four types of cyclic loading, viz., constant amplitude block loading, high-to-low block loading, low-to-high block, and a single overload in an otherwise constant amplitude block loading are considered; whereas in mode II, only a constant amplitude block loading is considered. Detailed results are presented for the crack-closure and opening-stresses, crack-surface deformation profiles, etc., in each case. Certain observations, based on the present numerical results, concerning various factors that cause crack growth acceleration or retardation under general spectrum loading, are presented and discussed.

Nakagaki, M.↗

Stress intensity factors in bonded half planes containing inclined cracks and subjected to antiplane shear loading

The antiplane shear problem for two bonded dissimilar half planes containing a semi-infinite crack or two arbitrarily located collinear cracks is considered. For the semi-infinite crack the problem is solved for a concentrated wedge load and the stress intensity factor and the angular distribution of stresses are calculated. For finite cracks the problem is reduced to a pair of integral equations. Numerical results are obtained for cracks fully imbedded in a homogeneous medium, one crack tip touching the interface, and a crack crossing the interface for various crack angles.

Bassani, J. L.↗

Bonded orthotropic strips with cracks

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. It is assumed that the plane contains a series of collinear cracks perpendicular to the interfaces and is loaded in tension away from and perpendicular to the cracks. The problem of cracks fully imbedded into the homogeneous strips is considered. The singular behavior of the stresses for two special crack geometries is studied. The first is the case of a broken laminate in which the crack tips touch the interfaces. The second is the case of cracks crossing the interfaces. An interesting result found from the analysis of the latter is that for certain orthotropic material combinations the stress state at the point of intersection of a crack and an interface may be bounded whereas in isotropic materials at this point stresses are always singular. A number of numerical examples are worked out to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters. Some numerical results are given for the stress intensity factors in certain basic crack geometries and for typical material combinations.

Delale, F.↗

Stress intensity factors in a hollow cylinder containing a radial crack

An exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero and the normal traction is an arbitrary function of r. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk.

Delale, F.↗

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.↗

The effect of water vapor on fatigue crack Growth in 7475-t651 aluminum alloy plate

The effects of water vapor on fatigue crack growth in 7475-T651 aluminum alloy plate at frequencies of 1 Hz and 10 Hz were investigated. Twenty-five mm thick compact specimens were subjected to constant amplitude fatigue testing at a load ratio of 0.2. Fatigue crack growth rates were calculated from effective crack lengths determined using a compliance method. Tests were conducted in hard vacuum and at water vapor partial pressures ranging from 94 Pa to 3.8 kPa. Fatigue crack growth rates were frequency insensitive under all environment conditions tested. For constant stress intensity factor ranges crack growth rate transitions occurred at low and high water vapor pressures. Crack growth rates at intermediate pressures were relatively constant and showed reasonable agreement with published data for two Al-Cu-Mg alloys. The existence of two crack growth rate transitions suggests either a change in rate controlling kinetics or a change in corrosion fatigue mechanism as a function of water vapor pressure. Reduced residual deformation and transverse cracking specimens tested in water vapor versus vacuum may be evidence of embrittlement within the plastic zone due to environmental interaction.

Dicus, D. L.↗

Stress intensity factors in a hollow cylinder containing a radial crack

In this paper, an exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero, and the normal traction is an arbitrary function of radius. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk.

Delale, F.↗

Three-dimensional measurements of fatigue crack closure

Three dimensional fatigue crack opening profiles in transparent polymer test specimens were determined. The load required to separate crack faces was measured along the crack profile at various positions through the specimens thickness. Crack opening loads at the specimen surface (under plane stress conditions) were compared with measurements made under plane strain conditions the specimen interior. The fatigue crack opening load was correlated with fatigue crack retardation behavior caused by peak overloads, and the results discussed in terms of three dimensional aspects of the fatigue crack closure mechanism for fatigue crack retardation.

Grandt, A. F., Jr.↗

The crack-inclusion interaction problem

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Xue-Hui, L.↗

Effect of water vapor on fatigue crack growth in 7475-T651 aluminum alloy plate

The effects of water vapor on fatigue crack growth in 7475-T651 aluminum alloy plate at frequencies of 1 Hz and 10 Hz were investigated. Twenty-five mm thick compact specimens were subjected to constant amplitude fatigue testing at a load ratio of 0.2. Fatigue crack growth rates were calculated from effective crack lengths determined using a compliance method. Tests were conducted in hard vacuum and at water vapor partial pressures ranging from 94 Pa to 3.8 kPa. Fatigue crack growth rates were frequency insensitive under all environment conditions tested. For constant stress intensity factor ranges crack growth rate transitions occurred at low and high water vapor pressures. Crack growth rates at intermediate pressures were relatively constant and showed reasonable agreement with published data for two Al-Cu-Mg alloys. The existence of two crack growth rate transitions suggests either a change in rate controlling kinetics or a change in corrosion fatigue mechanism as a function of water vapor pressure. Reduced residual deformation and transverse cracking specimens tested in water vapor versus vacuum may be evidence of embrittlement within the plastic zone due to environmental interaction.

Dicus, D. L.↗

Analysis of Delamination Growth from Matrix Cracks in Laminates Subjected to Bending Loads

A major source of delamination damage in laminated composite materials is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies, and delaminations then grow from these cracks at the ply interfaces. The purpose of this study was to quantify the combined effects of bending and transverse shear loads on delamination initiation from matrix cracks. Graphite-epoxy laminates with 90 deg. plies on the outside were used to provide a two-dimensional simulation of the damage due to low-velocity impact. Three plate bending problems were considered: a 4-point bending, 3-point bending, and an end-clamped center-loaded plate. Under bending, a matrix crack will form on the tension side of the laminate, through the outer 90 deg. plies and parallel to the fibers. Delaminations will then grow in the interface between the cracked 90 deg. ply and the next adjacent ply. Laminate plate theory was used to derive simple equations relating the total strain energy release rate, G, associated with the delamination growth from a 90 deg. ply crack to the applied bending load and laminate stiffness properties. Three different lay-ups were tested and results compared. Test results verified that the delamination always formed at the interface between the cracked 90 deg. ply and the next adjacent ply. Calculated values for total G sub c from the analysis showed good agreement for all configurations. The analysis was able to predict the delamination onset load for the cases considered. The result indicated that the opening mode component (Mode I) for delamination growth from a matrix crack may be much larger than the component due to interlaminar shear (Mode II).

Murri, G. B.↗

Predicting crack growth direction in unidirectional composites

The purpose of this study is to gain a better understanding of the parameters affecting crack growth direction in unidirectional composite materials. To achieve this, the effect of anisotropy and biaxial, far field, loading on the direction of crack growth in unidirectional off-axis composite materials is investigated. Specific emphasis is placed on defining the crack-tip-stress field and finding a consistent criterion for predicting the direction of crack growth. An anisotropic crack-tip-stress analysis was implemented using three criteria (the normal stress ratio theory, the tensor polynomial failure criterion, and the strain energy density theory) to predict the direction of crack extension in unidirectional off-axis graphite-epoxy. The theoretically predicted crack extension directions were then compared with experimental results. It was determined that only the normal stress-ratio criterion correctly predicts the direction of crack extension.

Gregory, M. A.↗

The crack-inclusion interaction problem

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Liu, X.-H.↗

Dynamic delamination crack propagation in a graphite/epoxy laminate

The dynamic delamination crack propagation behavior during ballistic tests of (90/0)5s T-300/934 graphite/epoxy laminates with embedded interfacial cracks was investigated using high speed photography. The impact on the beam-like specimen was produced with a silicon rubber ball, and the crack propagation speeds and the threshold impact velocities required to initiate dynamic crack propagation were determined for several crack positions. The results suggest that the mode of crack propagation depends on the specimen geometry as well as the loading condition. A simplified finite element analysis of the experimental data obtained from one of the midplane-cracked specimens was used to estimate the critical strain energy release rate, which may determine the onset of unstable crack propagation.

Sun, C. T.↗