Showing papers on "Fracture mechanics published in 1979"
TL;DR: In this paper, an explanation for non propagating fatigue cracks is presented based on the criterion that once the value of a particular strain intensity factor reduces to the threshold value for the material the crack should stop.
865 citations
TL;DR: In this article, the authors presented the stress-intensity factors for shallow and deep semi-elliptical surface cracks in plates subjected to tension and verified the accuracy of the three-dimensional finite-element models employed.
591 citations
TL;DR: In this article, the average growth rate for very short cracks considerably exceed those given by conventional stress intensity-crack growth laws fitted to long crack data, by introducing an effective crack length U into the solutions for intensity factors and the J integral method of analysis, and therefore the value of k can be obtained once the threshold stress intensity factor and the fatigue limit are known.
Abstract: Previous studies have shown that both threshold stress intensity factors and fatigue crack growth rates are dependent on crack size The average growth rates for very short cracks considerably exceed those given by conventional stress intensity-crack growth laws fitted to long crack data Elastic and elastic plastic fracture mechanics solutions are modified to predict this behavior of short cracks by introducing an effective crack length U into the solutions for intensity factors and the J integral method of analysis The threshold stress at a very short crack length approaches the fatigue limit of the material, and therefore the value of k can be obtained once the threshold stress intensity factor and the fatigue limit are known The accuracy of the term k in predicting crack growth rates for short cracks is found to be independent of the applied strain level It varies linearly with the grain size of material and can be considered at surface as a measure of the reduced flow resistance of surface grains due to their lack of constraint
573 citations
TL;DR: In this article, a statistical investigation of the fatigue crack propagation process was conducted and the results showed that the distribution of N as a function of crack length was best represented by the three-parameter log-normal distribution.
Abstract: : A statistical investigation of the fatigue crack propagation process was conducted. Sixty-eight replicate constant amplitude crack propagation tests were conducted on 2024-T3 aluminum alloy. The following distributions were considered: two-parameter normal distribution, three-parameter log-normal distribution, three-parameter Weibull distribution, two-parameter gamma distribution, three-parameter gamma distribution, the generalized three- parameter gamma distribution, and the generalized four-parameter gamma distribution. From the experimental data, the distribution of N as a function of crack length was best represented by the three-parameter log-normal distribution. Six growth rate calculation methods were investigated and the method which introduced the least amount of error into the growth rate data was found to be a modified secant method. Based on the distribution of da/dN, which varied moderately as a function of crack length, replicate a vs. N data were predicted. This predicted data reproduced the mean behavior but not the variant behavior of the actual a vs. N data.
511 citations
TL;DR: In this paper, a study of residual stress effects in the mechanics of median fracture in sharp indenter contact is made, and the authors show that the residual component of the indentation field may actually cause the median crack to continue in downward extension as the indenter is withdrawn, a response which is especially amenable to experimental investigation.
Abstract: A study is made of residual stress effects in the mechanics of median fracture in sharp indenter contact. Starting with a simplistic treatment of the elastic-plastic indentation field, the problem is conveniently resolved into two separable parts, involving reversible (elastic) and irreversible (residual) components. The assumption of geometrical similarity in the residual field about the deformation zone, later backed up by stress birefringence measurements, leads to a stress intensity factor for median crack propagation containing the elastic and residual parts as the sum of two terms. The resulting formulation for equilibrium fracture shows some differences in the crack response during the loading and unloading half-cycles. By imposing certain stress states on the specimen surface during indentation the residual component of the field may actually cause the median crack to continue in downward extension as the indenter is withdrawn, a response which is especially amenable to experimental investigation. Direct observations of median crack evolution in soda-lime glass confirm this and other essential predictions of the fracture mechanics theory. The contribution of the residual component to the crack growth is found to be by no means secondary in importance to that of the elastic component.
414 citations
TL;DR: In this article, the authors derived the variational principle governing the displacement distribution on a unit sphere about point 0 of the crack front edge at the surface of an elastic body, using spherical coordinates r, θ, φ and assuming all three displacements to be of the form r λ p p F ( θ, λ ) where p = distance from the singularity line (crack front edge or notch edge) and p = given constant.
373 citations
TL;DR: In this paper, a class of steady state shear crack propagation problems is analyzed, based on both a direct stress analysis approach and an energy integral approach which obviates the need for a complete stress analysis in some cases.
Abstract: A recent trend in seismology has been to model the earthquake source as a dynamically extending shear crack, and several basic concepts which seem to be important in this modeling process are examined. First, the universal spatial dependence of the plane elastodynamic stress and velocity fields near a sharp propagating crack tip is demonstrated for both subsonic and transsonic crack speeds, and the corresponding energy release rates are considered. Next, a class of steady state shear crack propagation problems is analyzed, based on both a direct stress analysis approach and an energy integral approach which obviates the need for a complete stress analysis in some cases. Several distinct stress differences which correspond to some of the common definitions of stress drop are involved in the analysis of these simple problems. Finally, some analytical considerations are presented which are relevant to rupture velocity determination for transient shear crack growth according to various fracture criteria, such as the critical stress intensity factor criterion, the critical energy release rate criterion, and the critical stress level criterion. Possible effects of spatially nonuniform stress drop and frictional resistance on rupture propagation are also discussed.
294 citations
TL;DR: In this paper, a new non-dimensional material parameter, T, the "tearing modulus," is defined and instability relationships are developed for various configurations, including some common test piece configurations, the surface flaw, and microflaws.
Abstract: This paper presents a new approach to the subject of crack instability based on the J-integral R-curve approach to characterizing a material's resistance to fracture. The results are presented in the chronological order of their development (including Appendices I and II). First, a new nondimensional material parameter, T, the "tearing modulus," is defined. For fully plastic (nonhardening) conditions, instability relationships are developed for various configurations, including some common test piece configurations, the surface flaw, and microflaws. Appendix I generalizes these results for the fully plastic case and Appendix II treats confined yielding cases. The results are presented for plane-strain crack-tip and slip field conditions, but may be modified for plane-stress slip fields in most cases by merely adjusting constants. Moreover, an accounted-for compliance of loading system is included in the analysis. Finally, Appendix III is a compilation of tearing modulus, T, properties of materials from the literature for convenience in comparing the other results with experience.
293 citations
TL;DR: In this article, a scan electron microscope was used to study the growth and development of cracks in Barre granite under load, and the tensile character of stress-induced cracks and other observatios by Tapponnier and Brace were confirmed.
286 citations
TL;DR: In this paper, a very detailed finite-strain/finite-element analysis of deeply cracked bend specimens was performed using nonhardening and power-law-hardening constitutive laws.
Abstract: Very detailed finite-strain/finite-element analyses of deeply cracked plane-strain center-notch panel and single-edge crack bend specimens were generated using nonhardening and power-law-hardening constitutive laws. The deformation was followed from small-scale yielding into the fully plastic range. The objective was to provide insight as to the minimum specimen size limitations, relative to the characteristic crack-tip opening dimension J/σ o , necessary to assure a J-based dominance of the crack-tip region. The criterion used to judge the degree of dominance was the extent of agreement of the present stress and deformation fields at the blunted crack tips with those calculated by McMeeking for small-scale yielding. For deeply cracked bend specimens, we find very close agreement of the near-tip fields with those of small-scale yielding up to J values of σ o L/25, where L represents the remaining uncracked ligament (and in the deeply cracked case, the only pertinent specimen dimension). This value is consistent with previously proposed J testing size limitations. However, we find that quite detectable deviation from the small-scale yielding fields occurs in both hardening and nonhardening center-crack specimens at considerably smaller J values relative to ligament dimension. This suggests that minimum specimen size requirements necessary to ensure a J-based characterization of the crack tip region may well be more stringent for center-crack or other low plastic constraint configurations than in bend-type specimens. A perhaps overly conservative value of 200 is proposed as the minimum ligament-to-J/σ o ratio which ensures a sensible J-based characterization of the crack-tip region in center-crack specimens of materials exhibiting moderate to low strain hardening.
01 Dec 1979
TL;DR: In this article, a three-dimensional finite-element analysis for shallow and deep semielliptical surface cracks in finite elastic isotropic plates subjected to tension or bending loads is presented.
Abstract: Stress-intensity factors calculated with a three-dimensional, finite-element analysis for shallow and deep semielliptical surface cracks in finite elastic isotropic plates subjected to tension or bending loads are presented. A wide range of configuration parameters was investigated. The ratio of crack depth to plate thickness ranged from 0.2 to 0.8 and the ratio of crack depth to crack length ranged from 0.2 to 2.0. The effects of plate width on stress-intensity variations along the crack front was also investigated. A wide-range equation for stress-intensity factors along the crack front as a function of crack depth, crack length, plate thickness, and plate width was developed for tension and bending loads. The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. A modified form of the equation was also used to correlate surface-crack fracture data for a brittle epoxy material within + or - 10 percent for a wide range of crack shapes and crack sizes.
TL;DR: In this article, the theoretical basis for use of the J-integral in crack growth analysis is discussed and conditions forJ-controlled growth are obtained for several deeply cracked specimen configurations.
Abstract: The theoretical basis for use of the J-integral in crack growth analysis is discussed and conditions forJ-controlled growth are obtained. Calculations related to the stability of crack growth are carried out for several deeply cracked specimen configurations. Relatively simple formulas are obtained which, in certain cases, permit an assessment of stability using data from a single load-displacement record. Numerical results for a bend specimen and for a center-cracked specimen illustrate the influence of strain-hardening and system compliance on stability.
TL;DR: In this article, a statistical fracture model was proposed to estimate the cleavage fracture toughness of a steel containing spheroidal carbide particles from a knowledge of the carbide particle radius distribution.
Abstract: The cleavage fracture of quenched and tempered steels at a sharp crack is seen to involve a statistical competition between different sized crack nuclei in the rapidly changing stress gradient ahead of the crack tip. A procedure is proposed, based on this statistical fracture model, whereby it is possible to estimate the cleavage fracture toughness of a steel containing spheroidal carbide particles from a knowledge of the carbide particle radius distribution. Predictions so made are seen to be in good agreement with experimentally determined fracture toughness values over a range of different temperatures and microstructures.
TL;DR: In this article, critical fracture stress and stress modified fracture strain models are utilized to describe the variation of lower and upper shelf fracture toughness with temperature and strain rate for two alloy steels used in the manufacture of nuclear pressure vessels.
Abstract: Critical fracture stress and stress modified fracture strain models are utilized to describe the variation of lower and upper shelf fracture toughness with temperature and strain rate for two alloy steels used in the manufacture of nuclear pressure vessels, namely SA533B-1 (HSST Plate 02) and SA302B (Surveillance correlation heat). Both steels have been well characterized with regard to static and dynamic fracture toughness over a wide range of temperatures (−190 to 200°C), although validJIc measurements at upper shelf temperatures are still somewhat scarce. The present work utilizes simple models for the relevant fracture micromechanisms and local failure criteria to predict these variations in toughness from uniaxial tensile properties. Procedures are discussed for modelling the influence of neutron fluence on toughness in irradiated steel, and predictions are derived for the effect of increasing fluence on the variation of lower shelf fracture toughness with temperature in SA533B-1.
TL;DR: In this article, the instantaneous stress-intensity factor was derived from the velocity of propagation of the crack. Butler et al. employed high-speed photographic systems with photoelastic methods to obtain a sequence of isochromatic-fringe patterns representing the state of stress associated with the propagating crack.
Abstract: Dynamic characterization of brittle fracture is possible by relating the instantaneous stress-intensity factorK(t) to the velocity of propagation of the crack. High-speed photographic systems are employed with photoelastic methods to obtain a sequence of isochromatic-fringe patterns representing the state of stress associated with the propagating crack. Methods for determiningK(t) from these isochromatic patterns are reviewed.
TL;DR: In this article, Eshelby's transformed-inclusion analysis has been used to model the transformation toughening: a transformation zone is calculated from an energy balance approach, the size of this zone determining the mechanical energy dissipated during crack propagation.
TL;DR: In this paper, the authors show that the crack initiation is characterizable by the critical value of J or 6, and stable crack growth is characterisable in terms of the J or δ resistance curves.
Abstract: Experimental results are presented which suggest that parameters based on the J-integral and the crack opening tip displacement δ are viable characterizations of crack initiation and stable crack growth. Observations based on some theoretical studies and finite-element investigations of the extending crack revealed that J and δ when appropriately employed do indeed characterize the near-field deformation. In particular, the analytical and experimental studies show that crack initiation is characterizable by the critical value of J or 6, and stable crack growth is characterizable in terms of the J or δ resistance curves. The crack opening angle, d6/da, appears to be relatively constant over a significant range of crack growth. Thus, appropriate measures of the material toughness associated with initiation are J I c and δ I c , and measures of material toughness associated with stable crack growth are given by the dimensionless parameters T J [= (E/σ o 2 )(dJ/da)] and T δ [= (E/σ o )(dδ/da)]. The two-parameter characterization of fracture behavior by J I c and T J or δ I c and T δ is analogous to the characterization of deformation behavior by the yield stress and strain hardening exponent.
TL;DR: In this paper, load relaxation and cross-head displacement rate-change experiments have been used to establish log10 stress intensity factor (K) versus log10 crack velocity (v) diagrams for double torsion specimens, of synthetic quartz cracked on thea plane in liquid water and moist air.
Abstract: Load relaxation and cross-head displacement rate-change experiments have been used to establish log10 stress intensity factor (K) versus log10 crack velocity (v) diagrams for double torsion specimens, of synthetic quartz cracked on thea plane in liquid water and moist air. For crack propagation normal toz and normal tor at 20°C,K
Ic (the critical stress intensity factor) was found to be 0.852±0.045 MN·m−3/2 and 1.002±0.048 MN·m−3/2, respectively. Subcritical crack growth at velocities from 10−3 m·s−1 to 10−9 m·s−1 at temperatures from 20°C to 80°C is believed to be facilitated by chemical reaction between the siloxane bonds of the quartz and the water or water vapour of the environment (stress corrosion). The slopes, of isotherms in theK-v diagrams are dependent upon crystallographic orientation. The isotherms have a slope of 12±0.6 for cracking normal tor and 19.9±1.7 for cracking normal toz. The activation enthalpy for crack propagation in the former orientation in liquid water at temperatures from 20°C to 80°C is 52.5±3.8 kJ·mole−1. A discussion is presented of the characteristics of theK-v diagrams for quartz.
TL;DR: In this paper, the authors present a review of the mechanisms of environmental failure and consider techniques for estimating and increasing the service-lifetimes of bonded components, with particular emphasis on the contribution from the application of continuum fracture mechanics concepts to the study of environmental attack on structural adhesive joints.
Abstract: A serious limitation frequently encountered in the use of structural adhesives is the deleterious effect moisture has upon the strength of a bonded component, especially when the component is also subjected to conditions of relatively high stress and temperature. It is generally recognised that while the locus of failure of well prepared joints is invariably by cohesive fracture in the adhesive layer, after environmental attack it is via failure in the interfacial regions. This interfacial locus of failure focuses attention on interfacial fracture mechanical considerations. This paper reviews mechanisms of environmental failure and considers techniques for estimating and increasing the service-lifetimes of bonded components. Particular emphasis is given to the contribution from the application of continuum fracture mechanics concepts to the study of environmental attack on structural adhesive joints.
TL;DR: In this article, a Vickers pyramid indenter under various loads at one scratching velocity is observed, and it is observed that the nature of the cracking is very similar to that occurring about a quasi-static pointed indenter.
Abstract: Observations of the microcracking about scratches in a number of brittle solids including sapphire and a variety of glasses are presented. The scratching was carried out primarily with a Vickers pyramid indenter under various loads at one scratching velocity. It is observed that the nature of the cracking is very similar to that occurring about a quasi-static pointed indenter. Directly beneath the indenter a well-defined median crack is formed, behind the indenter small partial Hertzian cracks develop within the track, and subsurface lateral cracking initiates from the region of the plastically deformed zone. With a Vickers pyramid the cracking phenomena may be conveniently divided into three regions with increasing load. At low loads ( P P P > 5N) the plastically deformed track appears to shatter and the extent of lateral and median cracking is less than that occurring for the higher loads in the intermediate region. The present observations and those of others in the literature have been interpreted in terms of an approximate indentation fracture mechanics analysis, and there is reasonable agreement between theory and experiment. The paper concludes with a discussion of the implications of this work to abrasive wear rate and to the residual strength of scratched bodies.
TL;DR: In this article, the process of cleavage crack initiation and the character of the effective grain size which controls the fracture toughness of pearlitic eutectoid steel has been investigated using smooth tensile and precracked Charpy impact specimens.
Abstract: The process of cleavage crack initiation and the character of the effective grain size which controls the fracture toughness of pearlitic eutectoid steel has been investigated using smooth tensile and precracked Charpy impact specimens. The results demonstrated that initial cracking in both specimens was largely the result of shear cracking of pearlite;i.e., localized slip bands in ferrite promoted cracking of the cementite plates, which was then followed by tearing of the adjacent ferrite laths. Such behavior initially results in a fibrous crack. In the tensile specimen, the initiation site was identified as a fibrous region which grew under the applied stress, eventually initiating an unstable cleavage crack. In precracked impact specimens, this critical crack size was much smaller due to the high state of stress near the precrack tip. Fracture mechanics analysis showed that the first one or two dimples formed by the shear cracking process can initiate a cleavage crack. Using thin foil transmission electron microscopy, a cleavage facet was found to be an orientation unit where the ferrites (and the cementites) of contiguous colonies share a common orientation. The size of this orientation unit, which is equal to the cleavage facet size, is controlled by the prior austenite grain size. The influence of austenite grain size on toughness is thus explained by the fact that the austenite grain structure can control the resultant orientation of ferrite and cementite in pearlitic structures.
TL;DR: In this article, a modified model for crack-particle interactions in brittle composites is proposed to account for penetrable obstacles, obstacle shape and secondary crack interactions, which is applied to a glass-unbonded nickel sphere composite system.
Abstract: Previous models for crack-particle interactions in brittle composites are modified to account for penetrable obstacles, obstacle shape and secondary crack interactions. The modified model is applied to a glass-unbonded nickel sphere composite system, the experimental aspects of which were summarized in Part 1. Increases in fracture energy are explained in terms of local crack blunting. It is shown that these results fall, as expected, between those for an entirely sharp crack front and an entirely blunt one.
TL;DR: In this article, the authors considered the fatigue lives of notched members are divided into crack initiation and propagation phases, and the extent of this field may be estimated from fracture mechanics analysis, with its size being of the order of one tenth of the notch radius.
Abstract: Fatigue lives of notched members are considered to be divided into crack initiation and propagation phases. Apparent size effects caused by crack propagation through the strain gradient of the notch are accounted for if initiation is defined as a crack size within the local notch field. The extent of this field may be estimated from fracture mechanics analysis, with its size being of the order of one tenth of the notch radius. Plasticity effects must be properly handled in predicting crack initiation, but linear elastic analysis is generally satisfactory for handling the propagation phase.
TL;DR: In this article, impact methods are used to create controlled dynamic fracture in Arkansas novaculite and laser interferometry is used to determine the time resolved stress during fracture Experimental fracture stresses and fracture energies are determined under varying dynamic tensile loading conditions.
TL;DR: In this article, the velocity of hydride induced subcritical crack growth in Zr-2.5 pct Nb has been determined using the potential drop method for measuring crack extension.
Abstract: The velocity of hydride induced subcritical crack growth in Zr-2.5 pct Nb has been determined using the potential drop method for measuring crack extension. A revised picture of the two-stage, crack velocity-stress intensity relationship has been obtained with a threshold stress intensity of 6 MPa·m1/2, independent of temperature. A consistent temperature dependence of the crack velocity has been determined for hydrided material but the velocity measurements in as-received material are unexpectedly high. A previous theoretical model has been improved. The improved model has provided a useful basis for explaining some of the present data which could not be rationalized in terms of the previous model. Criteria for the stepwise crack propagation behavior are discussed.
01 Jan 1979