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NASA NTRS1979

Interlaminar crack growth in fiber reinforced composites during fatigue

This paper presents an investigation of interlaminar crack growth behavior in fiber-reinforced composites subjected to fatigue loading. In the experimental phase of the study, interlaminar crack propagation rates and mechanisms were determined for the cases of various geometries, laminate parameters and cyclic stress levels. An advanced singular hybrid-stress finite element method was used in conjunction with the experimental results to examine the local crack-tip behavior and to characterize the crack propagation during fatigue. Results elucidate the basic nature of the cyclic delamination damage and relate the interlaminar crack growth rate to the range of mixed-mode crack-tip stress intensity factors. The study provides fundamental insight into the problem, reveals several important features of the interlaminar fatigue failure, and should be of practical importance in selection, testing and design of composite materials.

Wang, S. S.↗

NASA NTRS1978

Crack extension from flaws in a brittle material subjected to compression

The mechanisms by which cracks extend from flaws in brittle materials subjected to compressive loads are presented. Although it is recognized that most geological materials are neither dense nor single-phase, this experimental study and analysis are restricted to single-phase, dense materials in order to provide a model amenable to analysis and experimental confirmation. The flaws which occur in dense, single-phase materials are divided into three types, each type having different characteristics of crack extension. Experimental studies of crack extension from flaws introduced into blocks of polymethylmethacrylate plastic are described. The studies show that crack extension from three dimensional flaws is more complex than two-dimensional theories predict. The extension of secondary cracks may result in more damage than that which would be predicted by considering only the primary crack extension treated by current theories. The importance of the dynamic behavior of flaws which stick and then suddenly slip is shown.

Adams, M.↗

NASA NTRS1979

The problem of an inclined crack in an orthotropic strip

The elastostatic problem for an infinite orthotropic strip containing a crack is considered. It is assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack is located along an axis of orthotropy, hence at an arbitrary angle with respect to the sides of the strip. The general problem is formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes I and II stress-intensity factors are calculated for the strip having an internal or an edge crack with various lengths and angular orientations. In most calculations uniform tension or uniform bending away from the crack region is used as the external load. Limited results are also given for uniform normal or shear tractions on the crack surface.

Delale, F.↗

NASA NTRS1979

Mode I crack surface displacements for a round compact specimen subject to a couple and force

Mode I displacement coefficients along the crack surface are presented for a radially cracked round compact specimen, treated as a plane elastostatic problem, subjected to two types of loading; a uniform tensile stress and a nominal bending stress distribution across the net section. By superposition the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load location. Load line displacements are presented for A/D ratios ranging from 0.40 to 0.95, where A is the crack length measured from the crack mouth to the crack tip and D is the specimen diameter. Through a linear extrapolation procedure crack mouth displacements are also obtained. Experimental evidence shows that the results of this study are valid over the range of A/D ratios analyzed for a practical pin loaded round compact specimen.

Gross, B.↗

NASA NTRS1979

The fracture criteria for crack growth under biaxial loading

The paper examines the fracture criteria for crack growth under biaxial loading. A finite element theory was formulated for the problem of crack propagation to failure which is based on the incremental theory of plasticity and is mathematically equivalent to that of a nonlinear moving-mixed-boundary-value problem. It was found that during the crack growth the plastic energy of the specimen and the crack size are linearly related for center-cracked specimens of an aluminum alloy subjected to uniaxial and or biaxial loading when experimental data relating applied stress and crack size have been used as input.

Liebowitz, H.↗

NASA NTRS1980

Effect of propellant deformation on ignition and combustion processes in solid propellant cracks

A comprehensive theoretical model was formulated to study the development of convective burning in a solid propellant crack which continually deforms due to burning and pressure loading. In the theoretical model, the effect of interrelated structural deformation and combustion processes was taken into account by considering (1) transient, one dimensional mass, momentum, and energy conservation equations in the gas phase; (2) a transient, one dimensional heat conduction equation in the solid phase; and (3) quasi-static deformation of the two dimensional, linear viscoelastic propellant crack caused by pressure loading. Partial closures may generate substantial local pressure peaks along the crack, implying a strong coupling between chamber pressurization, crack combustion, and propellant deformation, especially when the cracks are narrow and the chamber pressurization rates high. The maximum pressure in the crack cavity is generally higher than that in the chamber. The initial flame-spreading process is not affected by propellant deformation.

Kumar, M.↗

NASA NTRS1981

The crack problem for a half plane stiffened by elastic cover plates

An elastic half plane containing a crack and stiffened by a cover plate is discussed. The asymptotic nature of the stress state in the half plane around an end point of the stiffener to determine the likely orientation of a possible fracture initiation and growth was studied. The problem is formulated for an arbitrary oriented radial crack in a system of singular integral equations. For an internal crack and for an edge crack, the problem is solved and the stress intensity factors at the crack tips and the interface stress are calculated. A cracked half plane with two symmetrically located cover plates is also considered. It is concluded that the case of two stiffeners appears to be more severe than that of a single stiffener.

Delale, F.↗

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 NTRS1981

Fatigue crack growth in 7475-T651 aluminum alloy plate in hard vacuum and water vapor

Compact specimens of 25 mm thick aluminum alloy plate were subjected to constant amplitude fatigue testing at a load ratio of 0.2. Crack growth rates were determined at frequencies of 1 Hz and 10 Hz in hard vacuum and laboratory air, and in mixtures of water vapor and nitrogen at water vapor partial pressures ranging from 94 Pa to 3.8 kPa. A significant effect of water vapor on fatigue crack growth rates was observed at the lowest water vapor pressure tested. Crack rates changed little for pressures up to 1.03 kPa, but abruptly accelerated at higher pressures. At low stress intensity factor ranges, cracking rates at the lowest and highest water vapor pressure tested were, respectively, two and five times higher than rates in vacuum. Although a frequency was observed in laboratory air, cracking rates in water vapor and vacuum are insensitive to a ten-fold change in frequency. Surfaces of specimens tested in water vapor and vacuum exhibited different amounts of residual deformation. Reduced deformation on the fracture surfaces of the specimens tested in water vapor suggests embrittlement of the plastic zone ahead of the crack tip as a result of environmental interaction.

Dicus, D. L.↗

NASA NTRS1981

Methods and models for predicting fatigue crack growth under random loading

Papers are presented in the volume summarizing the baseline data, methodology, procedures, and results of a round-robin analysis which was conducted to predict the fatigue crack growth in 2219-T851 aluminum center-cracked specimens subjected to flight loading in random cycle-by-cycle format. The objective of the analysis was to assess whether data from constant-amplitude fatigue crack growth tests on center-cracked specimens can be used to predict fatigue crack growth lives under random loading. The following approaches are discussed in detail: a root-mean-square approach, a crack-closure model, a multi-parameter yield zone model, and a load-interaction model.

Chang, J. B.↗

NASA NTRS1982

Moving singularity creep crack growth analysis with the /Delta T/c and C/asterisk/ integrals

The physical meaning of (Delta T)c and its applicability to creep crack growth are reviewed. Numerical evaluation of (Delta T)c and C(asterisk) is discussed with results being given for compact specimen and strip geometries. A moving crack-tip singularity, creep crack growth simulation procedure is described and demonstrated. The results of several crack growth simulation analyses indicate that creep crack growth in 304 stainless steel occurs under essentially steady-state conditions. Based on this result, a simple methodology for predicting creep crack growth behavior is summarized.

Stonesifer, R. B.↗

NASA NTRS1982

Finite element models for predicting crack growth characteristics in composite materials

Two dimensional and quasi-three dimensional, linear elastic finite element models for the prediction of crack growth characteristics, including crack growth direction, in laminated composite materials are presented. Mixed mode crack growth in isotropic materials, unidirectional and laminated composites is considered. The modified crack closure method is used to predict the applied load level for crack extension and two failure theories, modifications of the point stress and the Hashin failure criteria, are proposed to predict the direction of crack extension in composites. Comparisons are made with the Tsai-Wu failure criterion and the Sih strain energy density criterion as well as with experimental results. It is shown that the modified versions of point stress and Hashin criteria compare well with experiment.

Buczek, M. B.↗

NASA NTRS1982

A cylindrical shell with an arbitrarily oriented crack

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system of five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented.

Yahsi, O. S.↗

NASA NTRS1983

A note on the cracked plates reinforced by a line stiffener

The problem of a cracked plate reinforced by a line stiffener is reconsidered. The original solution of this problem was given in the literature. Also, a variation of the problem with debonding between the plate and the stiffener near the cracked region was reported in the literature. However, the special case of the problem in which the crack tip terminates at the stiffener does not appear to have been studied. In practice, the solution may be necessary in order to assess the crack arrest effectiveness of the stiffener. The problem of a stiffened plate with a crack is reformulated, the asymptotic stress state near the crack tip terminating at the stiffener is examined, and numerical results are given for various stiffness constants.

Yahsi, O. S.↗

NASA NTRS1983

Characteristics of thermally-induced transverse cracks in graphite epoxy composite laminates

The characteristics of thermally induced transverse cracks in T300/5208 graphite-epoxy cross-ply and quasi-isotropic laminates were investigated both experimentally and analytically. The formation of transverse cracks and the subsequent crack spacing present during cool down to -250 F (116K) and thermal cycling between 250 and -250 F (116 and 394K) was investigated. The state of stress in the vicinity of a transverse crack and the influence of transverse cracking on the laminate coefficient of thermal expansion (CTE) was predicted using a generalized plane strain finite element analysis and a modified shear lag analysis. A majority of the cross-ply laminates experienced transverse cracking during the initial cool down to -250 F whereas the quasi-isotropic laminates remained uncracked. The in situ transverse strength of the 90 degree layers was more than 1.9 times greater than the transverse strength of the unidirectional 90 degree material for all laminates investigated.

Adams, D. S.↗

NASA NTRS1983

A note on the cracked plates reinforced by a line stiffener

Yahsi, O. S.↗

NASA NTRS1983

A cylindrical shell with a stress-free end which contains an axial part-through or through crack

The interaction problem of a through or a part through crack with a stress free boundary in a semi-infinite cylindrical shell is considered. It is assumed that the crack lies in a meridional plane which is a plane of symmetry with respect to the external loads as well as the geometry. The circular boundary of the semi-infinite cylinder is assumed to be stress free. By using a transverse shear theory the problem is formulated in terms of a system of singular integral equations. The line spring model is used to treat the part through crack problem. In the case of a through crack the interaction between the perturbed stress fields due to the crack and the free boundary is quite strong and there is a considerable increase in the stress intensity factors caused by the interaction. On the other hand in the problem of a surface crack the interaction appears to be much weaker and consequently the magnification in the stress intensity factors is much less significant.

Erdogan, F.↗

NASA NTRS1983

A cylindrical shell with an arbitrarily oriented crack

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system to five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented. Previously annunced in STAR as N83-16783

Yahsi, O. S.↗