R. L. Carlson

A model for fatigue crack closure

Abstract The phenomenon of fatigue crack closure has attracted continued interest over recent years. This paper concerns itself with one aspect of the phenomenon namely the effects of a single asperity on the crack face close to the crack tip and under dominantly plane strain Mode 1 loading conditions. The model as developed is two dimensional in character but the nature of the closure processes allows it to be applied to real materials. The model illustrates the influence of asperity height, the distance from the crack tip of the asperity and rigidty of the asperity on the crack closure stress intensity. Application of the model to the case of microstructural asperities in nickel alloys and to oxide asperities in steels has met with reasonable success.

Experimental studies of the buckling of complete spherical shells.

Complete spherical shells with radius-to-thickness ratios of from 1570 to 2120 were produced by electroforming. For specimens of good quality and for optimum testing conditions, buckling pressures up to 86 percent of the classical value were obtained.The effect of loading-system characteristics was examined by pressurizing spherical shells in rigid and soft systems and no difference in buckling pressure was observed. It was found that buckling behavior is strongly influenced by the nature and severity of flaws or imperfections; i.e., low buckling pressures can be correlated with the presence of severe flaws or nonuniformities.

The effects of overloads in fatigue crack growth

Abstract Several theories have been proposed to explain the transient fatigue crack growth decelerations and accelerations which follow overloads. The mechanisms that have been proposed to explain retardation after a tensile overload, for example, include residual stress, crack deflection, crack closure, strain hardening, and plastic blunting/resharpening. These mechanisms are reviewed in the light of recent experimental results, and implications with regard to their applicability are examined. It is suggested that no single mechanism can be expected to represent observed effects over the entire range of da/dN versus ΔK; eg, behaviour ranging from the near threshold region to the Paris region.

On the buckling of thin tensioned sheets with cracks and slots

The problem of local buckling in tensioned sheets with holes is discussed in relation to its effect on fracture and fatigue characteristics. The results of an experimental investigation designed to determine the tensile buckling stress are presented. The results indicate that for the range of the parameters investigated, the sheet thickness to hole length ratio and a nondimensional hole shape parameter are the dominant geometric variables. It is shown that the results obtained in the investigation described and the results obtained by other investigators can be described by a single formula. The physical significance of local buckling is discussed and particular emphasis is placed on the importance of accounting for buckling in residual strength analyses of thin cracked sheets. Recommendations are made for the standardization of the buckling stress determination in terms of its relationship to the effect of middle-surface stretching due to the bending. Finally, the influence of the buckling process on plane stress fracture toughness values, Kc, obtained from center cracked sheet specimens is discussed.

Effects of compressive load excursions on fatigue crack growth

Abstract The variable-amplitude loading encountered in service often includes compressive excursions. It has been a common practice to ignore these excursions for fatigue crack growth analyses. Recently, experimental data on both smooth bars and cracked specimens with intermittent negative R ratio loadings have indicated that the effects of compressive excursions are not negligible.

Experimental studies of the postbuckling behavior of complete spherical shells

In experiments performed on elastic, complete spherical shells of large radius-to-thickness ratio, pressure and volume-displacement instrumentation and photography were used to study postbuckling behavior. Photographs of a number of the distinct modes observed are presented.

A mixed mode fatigue crack closure model

Abstract Fatigue crack closure conditions leading to mixed mode crack-tip stress states are discussed. A closure model based on contact between impinging fracture surface asperities is introduced. Asperity angle, magnitude of mode II interference, friction between contacting surfaces and distance of the contact surfaces from the crack-tip are features included in the model. The magnitudes of mode I and mode II stress intensity factors due to closure contact are found to vary substantially with asperity angle. Also, because of a reversal of friction force direction during cycle loading, the stress intensity factors exhibit a complex behavior. During the closure phase of the loading cycle, the mode II contribution is found to be quite significant. For loading through an entire cycle, which includes both the closure and crack open phases, nonproportional stress states are developed. Also, it is concluded that the mixed mode states developed could provide the conditions required for crack branching.

An experimental study of the parametric excitation of a tensioned sheet with a cracklike opening

The problem of the parametric excitation of a thins tensioned sheet with a cracklike opening is discussed Data obtained from an experimental investigation are presented and they indicated that both principal and secondary regions of instability are developed. Plts of the stability boundaries are presented in terms of excitation frequency, mean tensile load and alternating load.The principal region is observed to be significantly larger than the secondary region and the amplitudes of the oscillations associated with the principal region are also much larger than those of the secondary region. Oscillation amplitudes of the order of twelve times the thickness are reported and amplitude vs. excitation-frequency data are shown to exhibit an overhang behavior in the direciton of increasing frequency. This indicates the presence of a nonlinear stiff effect which is attributed to middle-surface stretching due to bending.Although damping and membrane effects were found to prevent the development of unbounded oscillations, it is noted that the large deflections associated with the principal region of instability could be expected to have a deterious effect on both crack nucleation and crack propagation.

Near tip stress and strain fields for short elastic cracks

Recent experimental fatigue crack growth studies have concluded an apparent anomalous behavior of short cracks. To investigate the reasons for this unexpected behavior, the present paper focuses on identifying the crack length circumstances under which the requirements for a single parameter (K1 or ΔK1 if cyclic loading is considered) characterization are violated. Furthermore, an additional quantity, the T stress, as introduced by Rice, and the related biaxiality ratio B are calculated for several crack lengths and two configurations, the single-edge-cracked and the centrally-cracked specimen. It is postulated that a two-parameter characterization by K and T (or B) is needed for the adequate description of the stress and strain field around a short crack. To further verify the validity of this postulate, the influence of the third term of the Williams series on the stress, strain and displacement fields around the crack tip and in particular on the B parameter is also examined. It is found that the biaxiality ratio would be more negative if the third term effects are included in both geometries. The study is conducted using the finite element method with linearly elastic material and isoparametric elements and axial (mode I) loading. Moreover, it is clearly shown that it is not proper to postulate the crack size limits for ‘short crack’ behavior as a normalized ratio with the specimen width a/w; it should instead be stated as an absolute, or normalized with respect to a small characteristic dimension such as the grain size. Finally, implications regarding the prediction of cyclic (fatigue) growth of short cracks are discussed.

Buckling and vibration of a thin tensioned sheet with an elliptical hole

The out-of-plane deflection which can be developed in a thin tensioned sheet containing a central opening is discussed. It is noted that this behavior is of practical importance because it can alter the stress concentration and fatigue properties.The results of an experimental and analytical study of the buckling and vibration behavior of tensioned sheets with an elliptical opening are presented. Data from buckling and vibration experiments for several opening shapes ranging between a crack and a circle are presented. A generalized Galerkin method for solving the governing differential equations is used and the results obtained are presented in terms of buckling loads and natural frequencies.The experimental-buckling-stress estimates are correlated with the analytical results. The data from the vibration experiments indicate that the load-frequency behavior is dependent on the size of the test specimen and the opening shape. The analytical results display a load-frequency behavior which is experimentally observed for a narrow elliptical hole; i.e., for a small value of the ratio of minor axis to major axis. Some features of the analytical and experimental vibration results differ substantially, however. The analysis indicates that the frequency decreases to zero as the applied load approaches the buckling load. The experimental results do not exhibit this behavior. The sources of this difference in behavior are discussed.