Showing papers on "Crack closure published in 1984"

Subcritical crack growth in geological materials

Abstract: A review is presented of the experimental data on subcritical crack growth in geological materials. The main parameters describing subcritical crack growth are the critical stress intensity factor Kc, the subcritical crack growth limit Ko, and the stress intensity factor-crack velocity (K-v) relationship between Ko and Kc. The K-v data are presented in terms of an equation in which the crack velocity depends on stress intensity factor raised to a power n because this is common practice in experimental studies. These data are presented as tables and in synoptic diagrams. For silicates the value of n increases as the environment becomes depleted in hyroxyl species and with increase in the microstructural complexity of the solid. Values of n as low as 9.5 have been found for tensile cracking of quartz in basic environments and as high as 170 for tensile cracking of basalt in moist air. Insufficient experimental data are available to predict subcritical crack growth behavior at depth in the earth's crust without major extrapolations of the data base. Schematic outlines are presented, therefore, of the probable influence on subcritical crack growth of some key parameters in the crustal environment. These include stress intensity factor, temperature, pressure, activity of corrosive environmental agent, microstructure, and residual strains. In addition, a discussion is presented of the likely magnitude of the subcritical crack growth limit. For stress corrosion tensile crack growth of quartz a limit of approximately 0.2 of the critical stress intensity factor is inferred from theoretical calculations. Further problems discussed with regard to the extrapolation of experimental data to crustal conditions include the choice of a suitable equation to describe crack growth and the magnitude of parameters in these equations. A brief discussion of the double torsion testing method is presented in order to aid the interpretation of experimental results because it is almost the sole method used to study subcritical cracking in rocks.

A crack opening stress equation for fatigue crack growth

Abstract: A general crack opening stress equation is presented which may be used to correlate crack growth rate data for various materials and thicknesses, under constant amplitude loading, once the proper constraint factor has been determined. The constraint factor, alpha, is a constraint on tensile yielding; the material yields when the stress is equal to the product of alpha and sigma. Delta-K (LEFM) is plotted against rate for 2024-T3 aluminum alloy specimens 2.3 mm thick at various stress ratios. Delta-K sub eff was plotted against rate for the same data with alpha = 1.8; the rates correlate well within a factor of two.

An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching

Abstract: This is the third in a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite-100 such that crack growth in an unbounded plate is simulated. In the first paper crack initiation resulting from stress wave loading to the crack tip as well as crack arrest were reported. It was found that for increasing rates of loading in the microsecond range the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.

Measurement of adherence of residually stressed thin films by indentation. I. Mechanics of interface delamination

Abstract: A fracture analysis of indentation‐induced delamination of thin films is presented. The analysis is based on a model system in which the section of film above the delaminating crack is treated as a rigidly clamped disc, and the crack extension force is derived from changes in strain energy of the system as the crack extends. Residual deposition stresses influence the cracking response by inducing buckling of the film above the crack and by providing an additional crack driving force once buckling occurs. A relation for the equilibrium crack length is derived in terms of the indenter load and geometry, the film thickness and mechanical properties, the residual stress level, and the fracture toughness of the interface. The analysis provides a basis for using controlled indentation cracking as a quantitative measure of interface toughness and for evaluating contact‐induced damage in thin films.

An experimental investigation into dynamic fracture: I. Crack initiation and arrest

Abstract: Problems of dynamic crack propagation are examined experimentally in a series of four papers. In this paper, the first of this series, crack initiation and arrest are investigated in thin sheets of Homalite-100. It is found that as the rate of loading increases to as high as 105 MPa/sec, the stress intensity factor required to initiate crack growth increases markedly. Crack arrest resulting from a simulated pressurized semi-infinite crack in an unbounded medium was found to occur abruptly. There was no continuous deceleration and the crack always stopped at a constant value of the stress intensity factor, which value was lower than the stress intensity factor required for quasi-static crack growth initiation. The second paper in this series deals with the occurrence of micro cracks at the front of the running main crack which control the rate of crack growth. The micro cracks are recorded by real time photography. By the same means it is shown that these micro cracks grow and turn away smoothly from the direction of the main crack in the process of branching. The third contribution establishes the hitherto unreported occurrence that cracks can propagate rapidly with constant velocity even though the stress intensity factor varies considerably during this propagation. This velocity is determined by the initial stress wave loading on the crack tip, and is changed, within limits, only by stress pulses of sufficient magnitude and brevity of rise time. The final paper in the series deals with the effect of stress waves on the behavior of running cracks, in particular with the influence of stress waves on the branching phenomenon. Also, crack curving under transient stress waves is examined. These results are believed to apply to materials other than Homalite 100 and the reasons for this belief are discussed in this first contribution.

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

Abstract: 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.

An experimental investigation into dynamic fracture: II. Microstructural aspects

Abstract: This is the second of a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite 100 simulating crack growth in an unbounded plate. In the first paper crack initiation resulting from stress wave loading to the crack tip and crack arrest were investigated. It was found that for increasing rates of loading in the micro second range, the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity below that value which causes initiation under quasi-static loading.

Crack propagation in a glass particle-filled epoxy resin

Abstract: The investigation outlined in the preceding paper has been extended to cover the effect of particle/matrix adhesion upon crack propagation in an epoxy resin reinforced with spherical glass particles. The behaviour has again been interpreted in terms of crack pinning and blunting. It has again been shown that in the absence of blunting a critical crack opening displacement criterion can be applied. The strength of the particle/matrix interface is found to affect both the crack propagation behaviour and the appearance of the fracture surface. It is also found to have a profound effect upon the fracture strength of the composites. The best overall mechanical properties are obtained for composites containing particles treated with coupling agent.

Crack Shear in Concrete: Crack Band Microflane Model

Abstract: The crack band model is applied to the problem of crack shear in concrete. The constitutive law for concrete within the crack band is provided by the microplane model, in which the microstrains on weak planes of various orientations (the microplanes) are assumed to conform to the same macroscopic strain tensor, and the microstresses from all the microplanes are superimposed. Due to the neglect of shear stiffness on individual microplanes, the material behavior is completely characterized by the relation between the normal stress and strain for each microplane. To simulate crack shear, the law for unloading contribution on the microplanes after previous tensile strain‐softening is important, since the shear stresses resisting crack shear, as well as the normal confining stresses and crack dilatancy, result from compression along lines inclined with regard to the crack plane. A satisfactory agreement with the existing results from shearing tests of cracked concrete blocks (i.e., aggregate interlock tests) i...

An experimental investigation into dynamic fracture: IV. On the interaction of stress waves with propagating cracks

Abstract: This is the last in a series of four papers dealing with experimental observations of dynamic crack propagation in thin, large sheets of a Homalite 100 plastic material which allow simulation of crack growth in unbounded plates. In the first paper crack initiation resulting from stress wave loading was examined as well as crack arrest. It was found that for increasing rates of loading in the microsecond range the stress intensity factor required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.

Fatigue crack growth threshold concepts

Abstract: This symposium was organized specifically to concentrate on the concepts underlying the fatigue crack growth threshold. Research has led to an improved understanding of the many mechanisms influencing the near-threshold behavior of fatigue crack growth in engineering materials. These proceedings deal with many aspects of near-threshold fatigue crack growth including the roles of composition, microstructure, environment, temperature, crack closure, crack size, and variable amplitude loading. The current level of knowledge of fatigue thresholds is accurately reflected by the contents of the manuscripts.

Mechanisms of Slow Fatigue Crack Growth in High Strength Aluminum Alloys: Role of Microstructure and Environment

Abstract: The role of microstructure and environment in influencing ultra-low fatigue crack propagation rates has been investigated in 7075 aluminum alloy heat-treated to underaged, peak-aged, and overaged conditions and tested over a range of load ratios. Threshold stress intensity range, ΔK0, values were found to decrease monotonically with increasing load ratio for all three heat treatments fatigue tested in 95 pct relative humidity air, with ΔK 0 decreasing at all load ratios with increased extent of aging. Comparison of the near-threshold fatigue behavior obtained in humid air with the data forvacuo, however, showed that the presence of moisture leads to a larger reduction in ΔK0 for the underaged microstructure than the overaged condition, at all load ratios. An examination of the nature of crack morphology and scanning Auger/SIMS analyses of near-threshold fracture surfaces revealed that although the crack path in the underaged structure was highly serrated and nonlinear, crack face oxidation products were much thicker in the overaged condition. The apparent differences in slow fatigue crack growth resistance of the three aging conditions are ascribed to a complex interaction among three mechanisms: the embrittling effect of moisture resulting in conventional corrosion fatigue processes, the role of microstructure and slip mode in inducing crack deflection, and crack closure arising from a combination of environmental and microstructural contributions.

Influence of texture on fatigue properties of Ti-6Al-4V

Abstract: Tensile properties, high cycle fatigue strength, and fatigue crack propagation behavior were evaluated on highly textured Ti-6Al-4V material to investigate the influence of a preferred crystallographic orientation on mechanical properties. Thermomechanical treatments were used to develop three different textures: a basal, basal/transverse, and transverse type, all of which exhibited the same homogeneously equiaxed microstructure. The Young’s modulus was found to vary between 107 and 126 GNm-2, and yield strength changed from 1055 to 1170 MNm-2. Ductility was only slightly affected by texture. High cycle fatigue and fatigue crack growth measurements were performed in vacuum, laboratory air, and a 3.5 pct NaCl solution. It is shown that laboratory air can be regarded as a quite corrosive environment. In vacuum the highest fatigue strength values were measured whenever loads were perpendicular to basal planes. However, these conditions had the highest susceptibilities to air and 3.5 pct NaCl solution environments. Nearly no influence of texture on fatigue crack propagation was found in vacuum, but in a corrosive environment crack growth parallel to (0002)-planes was much faster than perpendicular to these planes. To explain the corrosive effect on the fatigue properties of the textured material hydrogen is thought to play a key role.

The effect of microstructure and environment on fatigue crack closure of 7475 aluminum alloy

Abstract: The effects of slip character and grain size on the intrinsic material and extrinsic closure contributions to fatigue crack growth resistance have been studied for a 7475 aluminum alloy. The alloy was tested in the underaged and overaged conditions with grain sizes of 18 μm and 80 μm. The fracture surface exhibited increased irregularity and planar facet formation with increased grain size, underaging, and tests in vacuum. These changes were accompanied by an increased resistance to fatigue crack growth. In air the 18 μm grain size overaged material exhibited relatively poor resistance to fatigue crack growth compared with other microstructural variants, and this was associated with a lower stress intensity for closure. All materials exhibited a marked improvement in fatigue crack growth resistance when tested in vacuum, with the most significant difference being ˜1000× at a ΔK of 10 MPa m1/2 for the 80 μm grain size underaged alloy. This improvement could not be accounted for by either an increase in closure or increased crack deflection and is most likely due to increased slip reversibility in the vacuum environment. The intrinsic resistance of the alloy to fatigue crack growth was microstructurally dependent in vacuum, with large grains and planar slip providing the better fatigue performance.

Measurements of adherence of residually stressed thin films by indentation. II. Experiments with ZnO/Si

Abstract: Indentation‐induced delamination between thin films of ZnO and Si substrates is examined. Delamination occurs by the growth of lateral cracks, either along the interface or within the film adjacent to the interface. The crack path is determined by the indenter load and the film thickness, as well as by residual stresses formed during deposition. A change in crack path from the interface to the film, accompanied by an increase in crack radius, is observed and is interpreted as a buckling‐induced stress intensification. The interface fracture toughness is estimated from the relative crack lengths in the buckled and unbuckled films.

Formation and growth of extensional fracture sets

Abstract: Naturally occurring extension fractures, including some joints and veins, form sets consisting of numerous subparallel fractures, each with well-defined ends. In order to correctly interpret these fractures in the field, it is necessary to determine which factors control the geometries of fracture sets. This requires consideration of the conditions leading to both the initiation and the cessation of fracture propagation. A fracture begins to propagate when the crack extension force reaches a critical value, which is a property of the rock and of environmental conditions. After propagation initiates, the crack extension force varies owing to: (1) increase in crack length, (2) change in remote strain, (3) elastic interaction with nearby cracks, (4) change in internal fluid pressure, and (5) stress relaxation due to growth of cracks in the surrounding rock. Each fracture continues to propagate as long as its crack extension force exceeds the critical value and terminates when this condition is no longer met. Neglecting fluid effects, the final geometry of the fracture set is a function of the remote strain history and the initial crack geometry, which can be characterized by the initial crack density. For low initial densities, large increases in crack length occur with little or no increase in remote strain. However, for large initial densities, crack lengths increase only if the applied strain increases. This analysis is used to estimate the variation in remote strain during formation of a fracture set in granitic rock from observations of the final fracture geometry.

Short crack behaviour in nodular cast iron

Abstract: Fatigue crack growth rates have been determined on standard specimens containing long cracks (∼5–10mm) and on specimens containing two-dimensional short cracks (∼0.10–0.50mm). Large differences have been observed indicating that at a given stress intensity factor short cracks propagate much faster than long cracks. Mouth opening displacement measurements for both specimen geometries have shown that the crack closure effect is largely responsible for the observed effect. These results are used to rationalize the behaviour of short cracks initiated from natural sites which were either graphite nodules or microshrinkage pores. The three-dimensional aspect of these natural small cracks is analysed and discussed in detail.

Tension and bending of finite thickness plates with a semi-elliptical surface crack

Abstract: This paper deals with the tension and bending of finite thickness plates with a semi-elliptical surface crack. The analysis is performed by means of a modified body force method, in which the accuracy and the validity are greatly improved by using reasonable patterns of the body force densities and the resultant force boundary conditions. Numerical calculations are done for various combinations of the shape and the size of the crack, and practically exact values of the stress intensity factors are determined by extrapolating the numerical results for several mesh patterns. Empirical formulae in polynomial forms are also presented for convenience of practical use.

Rate-dependent extensional deformation resulting from crack growth in rock

Abstract: Quasi-static propagation and dilation of macroscopic mode I cracks is considered as a source of inelastic strain in crustal rocks undergoing extensional deformations. The approach here is to first characterize the propagation of a single dilating crack and then to consider how a large two-dimensional array of similar, parallel cracks accomodates an applied deformation. The driving force for propagation of each crack, Gi, is found as a function of the applied strain and the instantaneous crack lengths ci. The rate of crack propagation is taken to be a function of the instantaneous crack extension force ċi = ċ (Gi). A specific propagation rate extension force relation is developed that both fits the available experimental data and has vanishing propagation rate at a finite value of G. From these results a specific internal state variable constitutive law is derived relating uniaxial stress to the instantaneous uniaxial strain and crack density. For strains less than those necessary to cause crack propagation, the rock is predicted to behave like a linear elastic solid. Following the onset of propagation, the average stress may continue to increase if the strain rate accommodated by crack growth is slow in comparison to the applied strain rate. For constant strain rate boundary conditions the solutions exhibit strain softening, leading to peak stress and then a stress decrease. The peak stress increases nearly logarithmically with increasing applied strain rate. The response to unloading depends strongly on whether or not cracks heal. Unloading that follows sealing of the cracks with mineral precipitates causes the rock to undergo a permanent nonrecoverable strain.

Problems of mixed mode crack propagation

Abstract: 1. The strain energy density criterion.- 1.1. Introductory remarks.- 1.2. The strain energy density concept.- 1.3. Basic hypotheses of the theory.- 1.4. Fracture trajectories.- References.- 2. The general two-dimensional crack problem.- 2.1. Introduction.- 2.2. Strain energy density theory for the two-dimensional crack problem.- 2.3. The infinite plate with an inclined crack under uniform uniaxial stress.- 2.4. Finite width effects on the crack extension angle.- 2.5. The cracked plate subjected to a concentrated force or moment.- References.- 3. Branched cracks.- 3.1. Introduction.- 3.2. The symmetrically branched crack.- 3.3. The asymmetrically branched crack.- 3.4. The bent crack.- 3.5. Crack branches emanating from an elliptical crack.- References.- 4. Interacting cracks.- 4.1. Introduction.- 4.2. Two equal skew-parallel cracks.- 4.3. Two equal symmetrically inclined cracks.- 4.4. Two equal inclined cracks.- 4.5. X-formed arrays of cracks.- References.- Chapters 5. Arc-shaped cracks.- 5.1. Introduction.- 5.2. The circular crack under uniform stress.- 5.3. A periodic array of circular cracks.- 5.4. A star-shaped array of circular cracks.- References.- 6. Cracks emanating from holes and rigid inclusions.- 6.1. Introduction.- 6.2. Two equal cracks emanating from a circular hole.- 6.3. An array of surface cracks emanating from a circular hole.- 6.4. Fracture of a plate with a rigid inclusion having cuspidal points.- 6.5. Fracture of a plate with a rigid fiber inclusion.- References.- 7. Composite materials.- 7.1. Introduction.- 7.2. A bimaterial plate with a crack arbitrarily oriented to the interface.- 7.3. A three-layered composite with cracks.- 7.4. A bimaterial plate with a circular crack.- 7.5. A bimaterial plate with a crack along the interface.- 7.6. Interaction between a crack and a circular inclusion.- References.- 8. Plates and shells.- 8.1. Introduction.- 8.2. A cracked bent plate with an inclined crack.- 8.3. A cracked cylindrical shell with semispherical heads.- References.- 9. Three-dimensional crack problems.- 9.1. Introduction.- 9.2. The elliptical crack.- References.- Author index.

Dugdale plastic zone size and CTOD equations for the compact specimen

Abstract: With the aim of applying the Dugdale model to the compact specimen, the equations for stress intensity factor and crack surface displacement are obtained for a pair of pin loads and a uniform stress acting on a segment of the crack surface. The plastic zone size is calculated from the 'finiteness' condition of Dugdale, and the results agree well with collocation results from Terada (1983). The load that causes incipient yielding at the compression point of the compact specimen is calculated from a finite element strip yield analysis for an elastic-perfectly plastic material. The crack tip opening displacement for the compact specimen is calculated by adding the displacement at the tip of the physical crack length due to the pin load and due to the uniform stress. The results are within 1.5 percent of current collocation results.

Short crack fatigue behaviour in a medium carbon steel

Abstract: The initiation stage and short crack behaviour in torsional fatigue of a 0.4% C steel was investigated by a replication technique. The fatigue cracks initiated and propagated in the ferrite phase which is located at the prior austenite grain boundaries in the form of long allotriomorphs. At this stage of crack development it is proposed that crack growth rate depends on the extent and intensity of plasticity at the tip of the crack. Crack growth per cycle is correspondingly proportional to the strength of the slip band. The ferrite-pearlite boundaries are strong barriers to crack propagation, which is manifested by a deceleration of growth and possible arrest. On raising the stress level the previously non-propagating cracks may continue to grow by branching or joining with other cracks in the ferrite phase. This process is repeated until the stress fields of one or more dominant cracks attain a critical value to sustain continued growth that leads to failure.

Creation of Stable Cracks in Hardmetals Using ‘Bridge’ Indentation

Abstract: Bridge indentation involves the initiation of a precrack at thq centre of the top surface of the sample by meajns of diamond indentation (i.e. a Palmqvist crack). Growth of this crack is then induced by pressing either side of it with rectangular punches having their edges parallel with the crack direction. With I increasing load, the crack grows outwards and downwards, and eventually forms a straight-through crack. The present authors have made a study of the effect of experimental variables such as punch spacing, punch contact area, and diamond indentation load on the crack growth. Specimens of a WC–6Co alloy cracked in this way were subsequently used for K 1C measurement. An important result was that the cracks grew to a stable depth, the value of which could be determined by suitable choice of indentation parameters. Numerical analysis using a boundary element method (BEM) was used to explore the stress situation in bridge indentation and provided a qualitative prediction of the experimental r...

The influence of crack tip plasticity in the growth of small fatigue cracks

Abstract: In order to rationalize observed differences in the growth behavior of large and small cracks, local crack tip opening micromechanics have been characterized for both crack size regimes in a high strength aluminum alloy. It is found that crack tip opening displacement, crack tip opening load, and crack opening mode all differ widely for large and small cracks at equivalent cyclic stress intensities (ΔK). High crack tip opening displacements and relatively low, approximately constant, crack opening loads for microcracks account both for their rapid rate of growth relative to large cracks and the absence of a microcrack threshold stress intensity. Crack tip plastic zone sizes also were measured, and it was found that the ratio of plastic zone size to crack length for small cracks is ∼ 1.0, while for large cracks the same ratio is ≪ 1. Simple empirical corrections to ΔK are found inadequate to correlate the growth of large and small cracks. It is concluded that for small cracks, linear elastic fracture mechanics similitude does not apply, and that an alternative crack driving force must be formulated.

Fatigue crack propagation in dual-phase steels: Effects of ferritic-martensitic microstructures on crack path morphology

Abstract: microstructures with maximum resistance to fatigue crack extension while maintaining high strength levels. A wide range of crack growth rates has been examined, from ~10-8 to 10-3 mm per cycle, in a series of duplex microstructures of comparable yield strength and prior austenite grain size where intercritical heat treatments were used to vary the proportion, morphology, and distribution of the ferrite and martensite phases. Results of fatigue crack propagation tests, conducted on “long cracks” in room temperature moist air environments, revealed a very large influence of microstructure over the entire spectrum of growth rates at low load ratios. Similar trends were observed at high load ratio, although the extent of the microstructural effects on crack growth behavior was significantly less marked. Specifically, microstructures containing fine globular or coarse martensite in a coarse-grained ferritic matrix demonstrated exceptionally high resistance to crack growth without loss in strength properties. To our knowledge, these microstructures yielded the highest ambient temperature fatigue threshold stress intensity range ΔK0 values reported to date, and certainly the highest combination of strength and ΔK0 for steels (i.e., ΔK0 values above 19 MPa√m with yield strengths in excess of 600 MPa). Such unusually high crack growth resistance is attributed primarily to a tortuous morphology of crack path which results in a reduction in the crack driving force from crack deflection and roughness-induced crack closure mechanisms. Quantitative metallography and experimental crack closure measurements, applied to currently available analytical models for the deflection and closure processes, are presented to substantiate such interpretations.

An elastic-plastic finite element analysis of crack initiation, stable crack growth, and instability

Abstract: Studies have been conducted to develop efficient techniques to simulate crack extension and to examine various local and global fracture criteria. Of the considered criteria, the crack-tip-opening angle (CTOA) or displacement (CTOD) at a specified distance from the crack tip was shown to be most suited for modeling stable crack growth and instability during the fracture process. The results obtained in a number of studies show the necessity for studying different crack configurations when assessing the validity of any fracture criteria. One of the objectives of the present investigation is related to a critical evaluation of the CTOD growth criterion using an elastic-plastic finite element analysis under monotonic loading to failure. The analysis was found to predict three stages of crack growth behavior under monotonic loading to failure. Calculated CTOD values agreed well with experimental values for crack growth initiation.