Showing papers on "Crack closure published in 1983"

Overall moduli of solids with microcracks: Load-induced anisotropy

Abstract: For a linearly elastic brittle solid containing microcracks that may be closed or may undergo frictional sliding, a general method is developed for estimating the overall instantaneous moduli which depend on the loading conditions. When the cracks are all open and when they are randomly distributed, then the overall response is isotropic. The moduli for this case have been obtained by B udiansky and O'C onnell (1976). On the other hand, when some cracks close, and when some closed cracks undergo frictional sliding, then the overall response becomes anisotropic and dependent on the loading conditions, as well as on the loading path. The self-consistent method is used to estimate the overall moduli. The effects of crack closure and loadinduced anisotropy are included. Several illustrative examples are worked out, showing the important influence of the load path on the overall response when crack closure and frictional sliding are involved.

Crack deflection: Implications for the growth of long and short fatigue cracks

Abstract: The influences of crack deflection on the growth rates ofnominally Mode I fatigue cracks are examined. Previous theoretical analyses of stress intensity solutions for kinked elastic cracks are reviewed. Simple elastic deflection models are developed to estimate the growth rates of nonlinear fatigue cracks subjected to various degrees of deflection, by incorporating changes in the effective driving force and in the apparent propagation rates. Experimental data are presented for intermediate-quenched and step-quenched conditions of Fe/2Si/0.1C ferrite-martensite dual phase steel, where variations in crack morphology alone influence considerably the fatigue crack propagation rates and threshold stress intensity range values. Such results are found to be in good quantitative agreement with the deflection model predictions of propagation rates for nonlinear cracks. Experimental information on crack deflection, induced by variable amplitude loading, is also provided for 2020-T651 aluminum alloy. It is demonstrated with the aid of elastic analyses and experiments that crack deflection models offer a physically-appealing rationale for the apparently slower growth rates of long fatigue cracks subjected to constant and variable amplitude loading and for the apparent deceleration and/or arrest of short cracks. The changes in the propagation rates of deflected fatigue cracks are discussed in terms of thelocal mode of crack advance, microstructure, effective driving force, growth mechanisms, mean stress, slip characteristics, and crack closure.

The dynamic behaviour of slender structures with cross-sectional cracks

Abstract: A dynamic model for beams with cross-sectional cracks is discussed. It is shown that a crack can be represented by a consistent, static flexibility matrix. Two different methods for the determination of the flexibility matrix are discussed. If the static stress intensity factors are known, the flexibility matrix can be determined from an integration of these stress intensity factors. Alternatively, static finite element calculations can be used for the determination of the flexibility matrix. Both methods are demonstrated in the present paper. The mathematical model was applied to an edge-cracked cantilevered beam and the eigenfrequencies were determined for different crack lengths and crack positions. These results were compared to experimentally obtained eigenfrequencies. In the experiments, the cracks were modelled by sawing cuts. The theoretical results were, for all crack lengths, in excellent agreement with the experimental data. The dynamic stress intensity factor for a longitudinally vibrating, centrally cracked bar was determined as well. The results compared very well with dynamic finite element calculations. The crack closure effect was experimentally investigated for an edge-cracked beam with a fatigue crack. It was found that the eigenfrequencies decreased, as functions of crack length, at a much slower rate than in the case of an open crack.

Propagation and non-propagation of short fatigue cracks at a sharp notch

Abstract: — Sharply notched specimens of a structural low-carbon steel were fatigued under several ratios of the maximum to minimum loads. The growth behavior of a short fatigue crack near the notch tip was analyzed based on crack closure measurements. A fatigue crack first decelerates with increasing crack length, and then accelerates or becomes non-propagating depending on the applied stress. A similar deceleration is seen when the rate is correlated to the stress intensity range. The effective stress intensity range is a unique parameter in correlating the growth rate of a short crack for all the stress levels examined, and the relation is identical to that obtained for a long crack. By considering the increase in crack closure with crack length, a quantitative method is proposed for predicting the non-propagating crack length and the fatigue limit of notched specimens as a function of the applied stress and the notch geometry.

Increase of crack resistance during slow crack growth in Al2O3 bend specimens

Abstract: Fracture experiments under conditions of slow crack growth were performed with prenotched three-point bend specimens of polycrystalline alumina. The influence of notch depth, specimen geometry, mean grain size and deformation velocity on the crackresistance force (R) was investigated. Within one specimen R increases with crack propagation up to a factor of 4 (R-curve) accompanied by small changes (slight decrease) in crack velocity. No unique R-curve exists for these ceramics. Both the shape and the position of the R-curve are influenced by deformation velocity and notch depth. The latter effect means that for a certain crack length, R is larger in a specimen with the shorter notch (memory effect). The results are discussed in terms of energy dissipation by microcracks. The significance of both single R value and R-curve for fracture characterization of polycrystalline alumina is questioned.

Molecular dynamics simulation of crack tip processes in alpha‐iron and copper

Abstract: The intrinsic crack tip processes of either propagation by cleavage or blunting by the nucleation of dislocations from the nonlinearly stressed region at the crack tip have been simulated by a molecular dynamics approach in alpha‐iron and in copper, utilizing the Johnson and Morse potentials, respectively, and a new fixed stress boundary condition at the border between the inner discrete region and the outer anisotropic linear continuum. The simulations showed that alpha‐iron is inherently brittle, and fails by cleavage along a cube plane when the stress intensity factor reaches the critical Griffith value. No dislocations are nucleated in iron and even the development of restricted crack tip twinning in special orientations does not alter this intrinsic brittleness. In copper crack tip blunting at a level somewhat less than the Griffith stress intensity factor always prevented brittle crack growth by cleavage. Thus, copper is inherently ductile. Because it permitted the unhindered development of substantial nonlinear crack tip displacements, and did not prevent dislocations from penetrating through the border between the inner nonlinear material and the outer linear continuum, the new stress boundary condition was found to be far superior to the fixed or flexible boundary conditions used at this border by previous investigators. This is reflected in the observed critical stress intensity factors for brittle cleavage that were found to be nearly equal to the expected Griffith value for the stress boundary condition while the displacement boundary conditions gave results nearly three times higher.

Roughness-Induced Crack Closure: An Explanation for Microstructurally Sensitive Fatigue Crack Growth

Abstract: The concept of roughness-induced crack closure is utilized to explain the role of prior austenite grain size and pearlite interlamellar spacing on near-threshold fatigue crack propagation in fully pearlitic eutectoid steel tested at low and high stress ratio in lab air and purified helium. It is shown that at low load ratios, near-threshold growth rates are significantly reduced for coarse-grained microstructures, compared to fine-grained at constant yield strength, due to roughness-induced crack closure. Using roughness-profile microscopy, it was found that fracture surface roughness near threshold scaled with grain size and inversely with yield strength, macroscopic roughnesses at threshold being considerably larger than the conventionally calculated cyclic crack tip opening displacement. Auger analysis of near-threshold corrosion products showed it to be iron oxide; the oxide thickness was seen to be decreased by increased stress ratio. The significance of this model to near-threshold fatigue crack growth behavior, in terms of load ratio, microstructure, and environment is discussed.

Analysis of one single crack

Abstract: In concrete most cracks start from an uncracked surface and grow through a large portion of the depth of the specimen. Both formation and growth are influenced by stresses from imposed deformations, shrinkage, temperature etc. Thus fracture mechanics, when applied to concrete, should be able to analyse the following: 1. The formation of a crack in a specimen which is not notched or precracked. 2. The growth of a crack to a size of the same order as that of the specimen. 3. The influence of imposed deformations on crack formation and crack growth.(30 refs)

The Nature of Machining Damage in Brittle Materials

Abstract: The micromechanics of failure emanating from machining-induced cracks in brittle materials is investigated. In situ monitoring of crack response during breaking tests (with use of acoustic wave scattering), strength measurements and post-failure fractography all indicate that the crack response is dominated by residual stresses. Two components of residual stress have been identified: a crack-wedging force due to the plastic zone beneath the strength-controlling machining groove, and a compressive surface layer due to adjacent grooves. The wedging force dominates and causes stable equilibrium crack extension during a breaking test. The implications of the results for non-destructive evaluation of surface damage by acoustic wave scattering is discussed.

A microcrack model for the deformation and failure of brittle rock

Abstract: A continuum model derived from the mechanics of tensile microcracks is presented which describes the deformation of brittle rock. The model employs the assumption that stress and time-dependent microcrack growth is responsible for the inelastic deformation. Microcrack growth is assumed to occur by two mechanisms: stress-induced crack growth (time independent) and stress corrosion (stress and time dependent). From the analysis of individual cracks a criterion for the initiation of damage (crack growth) is derived. This results in the specification of initial and subsequent damage surfaces in stress space which are similar to yield surfaces in the theory of plasticity. When the stress state is below the damage surface, no stress-induced crack growth can take place. For stress states on the damage surface, crack growth accompanies any increase in loading, thus expanding the damage surface. By generalizing the results obtained from the analysis of single cracks, a continuum description of the behavior of an ensemble of cracks in an otherwise elastic body is derived. The resulting constitutive equation is essentially elastic but accounts for material behavior due to microcrack growth through the inclusion of an internal state variable which is a measure of the crack state. The form of the evolutionary equation for the crack state parameter is determined from the fracture mechanics analysis of single cracks and experimental results on time-dependent crack growth in rock. Model simulations of quasi-static uniaxial and triaxial compression tests are presented, and the results are compared to the results of a similar laboratory test on Westerly granite.

A nonlinear fracture mechanics approach to the growth of small cracks

Abstract: An analytical model of crack closure is used to study the crack growth and closure behavior of small cracks in plates and at notches. The calculated crack opening stresses for small and large cracks, together with elastic and elastic plastic fracture mechanics analyses, are used to correlate crack growth rate data. At equivalent elastic stress intensity factor levels, calculations predict that small cracks in plates and at notches should grow faster than large cracks because the applied stress needed to open a small crack is less than that needed to open a large crack. These predictions agree with observed trends in test data. The calculations from the model also imply that many of the stress intensity factor thresholds that are developed in tests with large cracks and with load reduction schemes do not apply to the growth of small cracks. The current calculations are based upon continuum mechanics principles and, thus, some crack size and grain structure exist where the underlying fracture mechanics assumptions become invalid because of material inhomogeneity (grains, inclusions, etc.). Admittedly, much more effort is needed to develop the mechanics of a noncontinuum. Nevertheless, these results indicate the importance of crack closure in predicting the growth of small cracks from large crack data.

Kinetics of shear-activated indentation crack initiation in soda-lime glass

Abstract: The initiation of radial cracks in Vickers indentation of soda-lime glass is found to be strongly rate dependent. For long contact durations the radial cracks pop in during the indentation event, at a reproducible stage of the unloading half-cycle; for short contacts the pop-in occurs after the event, with considerable scatter in delay time. The phenomenon is interpreted in terms of an incubation time to develop a critical nucleus for the ensuing fracture. Increasing either the water content of the environment or the peak contact load diminishes the incubation time. Scanning electron microscopy of the indentation patterns indicates that the sources of the crack nuclei are constrained shear faults within the deformation zone. A qualitative model is developed in terms of a two-step process, precursor faulting followed by crack growth to pop-in instability. Moisture may influence both these steps, in the first by interfacial decohesion and in the second by slow crack growth. No definitive conclusion is reached as to which of the steps is ratecontrolling, although it appears that it is the shear across the fault and not the tension across the crack which is vital in driving the initiation. The implications of these results in connection with the basic mechanical properties of brittle solids, particularly strength, are considered.

Interaction of a dislocation with a crack

Abstract: A solution is given of the field equations of nonlocal elasticity for a line crack interacting with a screw dislocation in an elastic plane under antiplane shear loading. Displacement and stress fields are determined throughout the core region and beyond. In the case when the dislocation is absent, the circumferential stress is shown to vanish at the crack tip, increasing to a maximum along the crack line afterwards decreasing to its classical value at large distances from the crack tip. This is in contradiction with the classical elasticity solutions which predicts stress singularity at the crack tip and it is in accordance with the physical condition that the crack tip surface must be free of surface tractions. The presence of the dislocation alters the stress distribution considerably when it is close to the crack tip. The stress distributions in the core region are displayed. A fracture criterion based on the maximum stress is established and used to determine the theoretical strengths of pure crystals that contain a line crack. Results are in good agreement with those based on the atomic theories and experiments.

Mode III and Mode I fatigue crack propagation behaviour under torsional loading

Abstract: Fatigue crack growth rates have been measured under cyclic torsional loading (R = −1, 1 Hz loading frequency) in AISI 4340 steel tempered at 650° C, with circumferentiallynotched specimens (12.7 mm specimen diameter). The Mode III fatigue crack growth curve for macroscopically flat fracture surface — being obtained by an extrapolation procedure which eliminates the “Mode III crack closure” influence — has higher crack growth rates and shows a greater slope than Mode I results in the stress intensity range of ΔKIIIeff = 18 to 50 MPa m1/2. In the range of ΔKIIIeff < 18 MPa m1/2, the fracture surface has “factory roof” morphology (Mode I). The difference between fatigue crack growth behaviour in Mode III and Mode I as well as mechanisms that can lead to a fracture mode change are discussed. A comparison of the Mode III crack closure influence for specimen diameters of 12.7 mm (this study) and of 24.5 mm (an earlier study) shows that this influence is not only dependent on the depth of the crack and applied torque but also on the specimen diameter. The extrapolated crack growth rates show good agreement with measurements for various specimen diameters.

A Griffith crack shielded by a dislocation pile-up

Abstract: The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.