Showing papers on "Crack closure published in 1974"
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01 Jan 1974TL;DR: In this paper, the authors proposed a method to detect cracks in a crack-penetrization model, based on the Griffith criterion, which is used to detect the presence of a crack at a crack tip.
Abstract: I Principles.- 1 Summary of basic problems and concepts.- 1.1 Introduction.- 1.2 A crack in a structure.- 1.3 The stress at a crack tip.- 1.4 The Griffith criterion.- 1.5 The crack opening displacement criterion.- 1.6 Crack propagation.- 1.7 Closure.- 2 Mechanisms of fracture and crack growth.- 2.1 Introduction.- 2.2 Cleavage fracture.- 2.3 Ductile fracture.- 2.4 Fatigue cracking.- 2.5 Environment assisted cracking.- 2.6 Service failure analysis.- 3 The elastic crack-tip stress field.- 3.1 The Airy stress function.- 3.2 Complex stress functions.- 3.3 Solution to crack problems.- 3.4 The effect of finite size.- 3.5 Special cases.- 3.6 Elliptical cracks.- 3.7 Some useful expressions.- 4 The crack tip plastic zone.- 4.1 The Irwin plastic zone correction.- 4.2 The Dugdale approach.- 4.3 The shape of the plastic zone.- 4.4 Plane stress versus plane strain.- 4.5 Plastic constraint factor.- 4.6 The thickness effect.- 5 The energy principle.- 5.1 The energy release rate.- 5.2 The criterion for crack growth.- 5.3 The crack resistance (R curve).- 5.4 Compliance.- 5.5 The J integral.- 5.6 Tearing modulus.- 5.7 Stability.- 6 Dynamics and crack arrest.- 6.1 Crack speed and kinetic energy.- 6.2 The dynamic stress intensity and elastic energy release rate.- 6.3 Crack branching.- 6.4 The principles of crack arrest.- 6.5 Crack arrest in practice.- 6.6 Dynamic fracture toughness.- 7 Plane strain fracture toughness.- 7.1 The standard test.- 7.2 Size requirements.- 7.3 Non-linearity.- 7.4 Applicability.- 8 Plane stress and transitional behaviour.- 8.1 Introduction.- 8.2 An engineering concept of plane stress.- 8.3 The R curve concept.- 8.4 The thickness effect.- 8.5 Plane stress testing.- 8.6 Closure.- 9 Elastic-plastic fracture.- 9.1 Fracture beyond general yield.- 9.2 The crack tip opening displacement.- 9.3 The possible use of the CTOD criterion.- 9.4 Experimental determination of CTOd.- 9.5 Parameters affecting the critical CTOD.- 9.6 Limitations, fracture at general yield.- 9.7 Use of the J integral.- 9.8 Limitations of the J integral.- 9.9 Measurement of JIc and JR.- 9.10 Closure.- 10 Fatigue crack propagation.- 10.1 Introduction.- 10.2 Crack growth and the stress intensity factor.- 10.3 Factors affecting crack propagation.- 10.4 Variable amplitude service loading.- 10.5 Retardation models.- 10.6 Similitude.- 10.7 Small cracks.- 10.8 Closure.- 11 Fracture resistance of materials.- 11.1 Fracture criteria.- 11.2 Fatigue cracking criteria.- 11.3 The effect of alloying and second phase particles.- 11.4 Effect of processing, anisotropy.- 11.5 Effect of temperature.- 11.6 Closure.- II Applications.- 12 Fail-safety and damage tolerance.- 12.1 Introduction.- 12.2 Means to provide fail-safety.- 12.3 Required information for fracture mechanics approach.- 12.4 Closure.- 13 Determination of stress intensity factors.- 13.1 Introduction.- 13.2 Analytical and numerical methods.- 13.3 Finite element methods.- 13.4 Experimental methods.- 14 Practical problems.- 14.1 Introduction.- 14.2 Through cracks emanating from holes.- 14.3 Corner cracks at holes.- 14.4 Cracks approaching holes.- 14.5 Combined loading.- 14.6 Fatigue crack growth under mixed mode loading.- 14.7 Biaxial loading.- 14.8 Fracture toughness of weldments.- 14.9 Service failure analysis.- 15 Fracture of structures.- 15.1 Introduction.- 15.2 Pressure vessels and pipelines.- 15.3 "Leak-bcfore-break" criterion.- 15.4 Material selection.- 15.5 The use of the J integral for structural analysis.- 15.6 Collapse analysis.- 15.7 Accuracy of fracture calculations.- 16 Stiffened sheet structures.- 16.1 Introduction.- 16.2 Analysis.- 16.3 Fatigue crack propagation.- 16.4 Residual strength.- 16.5 The R curve and the residual strength of stiffened panels.- 16.6 Other analysis methods.- 16.7 Crack arrest.- 16.8 Closure.- 17 Prediction of fatigue crack growth.- 17.1 Introduction.- 17.2 The load spectrum.- 17.3 Approximation of the stress spectrum.- 17.4 Generation of a stress history.- 17.5 Crack growth integration.- 17.6 Accuracy of predictions.- 17.7 Safety factors.- Author index.
2,539 citations
TL;DR: In this paper, the authors investigated the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position, and showed that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor.
Abstract: This paper deals with the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position. In a situation, when both of the stress-intensity factors,k
1,k
2 are present along the crack front, the crack may spread in any direction in a plane normal to the crack edge depending on the loading conditions. Preliminary results indicate that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor,S
cr. The basic assumption is that crack initiation occurs when the interior minimum ofS reaches a critical value designatedS
cr. The strain-energy-density factorS represents the strength of the elastic energy field in the vicinity of the crack tip which is singular of the order of 1/r where the radial distancer is measured from the crack front. In the special case of Mode I crack extensionS
cr is related tok
1c alone asS
cr = (κ − 1)k
1
2
/8μ. In general,S takes the quadratic forma
1 1
k
1 + 2a
1 2
k
1
k
2 +a
2 2
k
2 whose critical value is assumed to be a material constant. The analytical predictions are in good agreement with experimental data on the problem of an inclined crack in plexiglass and aluminum alloy specimens. The result of this investigation provides a convenient procedure for determining the critical crack size that a structure will tolerate under mixed mode conditions for a given applied stress.
2,066 citations
TL;DR: In this article, a finite element technique for determination of elastic crack tip stress intensity factors is presented, based on the energy release rate, and the solution for only a single crack length is required, where the crack is 'advanced' by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second analysis.
Abstract: A finite element technique for determination of elastic crack tip stress intensity factors is presented. The method, based on the energy release rate, requires no special crack tip elements. Further, the solution for only a single crack length is required, and the crack is 'advanced' by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second analysis. The promising straightforward extension of the method to general three-dimensional crack configurations is presented and contrasted with the practical impossibility of conventional energy methods.
736 citations
01 Jan 1974
TL;DR: In this article, the energy release rate for a crack subjected simultaneously to mode I and mode II conditions is computed by path independent integrals, using the elastic solution of a deflected crack, having a main branch and a propagation branch.
Abstract: : The energy release rate for a crack subjected simultaneously to mode I and mode II conditions is computed. The energy was computed by path-independent integrals, using the elastic solution of a deflected crack, having a main branch and a propagation branch. The elasticity solution was obtained from the functional integral equations by the process of iterations. This process leads to a point-wise exact solution in the limit as the propagation branch goes to zero. Using the Griffith-Irwin criterion, incipient paths of propagation of such a crack were obtained from the maximum value of the energy release rate. An experiment, which gives a pure mode II condition at the tip of the crack, was devised. The results were in excellent agreement with the theory. The energy release rate, in parametric form, can be used for any crack subjected to mode I and mode II loading conditions. (Author, modified-PL)
735 citations
TL;DR: In this article, the non-singular stress term for crack tip deformations and fracturing is examined and its effect on crack tip parameters, such as the opening displacement and J-integral, is less pronounced than the effect on the yield zone size.
Abstract: Recent finite-element results by S G Larsson and A J Carlsson suggest a limited range of validity to the 'small scale yielding approximation,' whereby small crack tip plastic zones are correlated in terms of the elastic stress intensity factor It is shown with the help of a model for plane strain yielding that their results may be explained by considering the non-singular stress, acting parallel to the crack at its tip, which accompanies the inverse square-root elastic singularity Further implications of the non-singular stress term for crack tip deformations and fracturing are examined It is suggested that its effect on crack tip parameters, such as the opening displacement and J-integral, is less pronounced than its effect on the yield zone size
587 citations
TL;DR: In this paper, the authors applied cyclic stresses with stress ratio R = 0.65 to sheet specimens of aluminium which have an initial crack inclined to the tensile axis at angles of 30°, 45°, 72° or 90°.
421 citations
TL;DR: In this article, the failure of materials due to slow crack growth, under dynamic loading conditions, is analyzed in terms of crack velocity, stress intensity relationships, and it is shown that this type of analysis can fully describe the failure characteristics for both constant strain-rate and constant stress-rate loading.
Abstract: The failure of materials due to slow crack growth, under dynamic loading conditions, is analyzed in terms of crack velocity, stress intensity relationships. It is shown that this type of analysis can fully describe the failure characteristics for both constant strain-rate and constant stress-rate loading. The analysis is used to predict the variations of strength and subcritical crack growth with strain-rate and stress-rate. Application of the analysis to several ceramic systems give data which are entirely consistent with available experimental data.
333 citations
TL;DR: In this article, a simple analytical model is developed to accompany experimental work on rapid crack propagation and arrest in the DCB test specimen, and it is demonstrated that kinetic energy makes an important contribution to maintaining unstable crack propagation.
Abstract: A simple analytical model is developed to accompany experimental work on rapid crack propagation and arrest in the DCB test specimen. The present work extends the beam-on-elastic foundation model used previously by taking account of shear deformation and of both translational and rotary inertia. Crack speeds predicted with the model are found to be in good agreement with the constant-speed behavior observed experimentally. It is demonstrated that kinetic energy makes an important contribution to maintaining unstable crack propagation and to crack arrest.
250 citations
01 Jan 1974
TL;DR: In this paper, a small-scale yielding analysis of an elastic-plastic body with a line crack under plane-strain conditions subject to combinations of Mode I and II loadings is examined.
Abstract: The small-scale yielding analysis of an elastic-plastic body with a line crack under plane-strain conditions subject to combinations of Mode I and II loadings is examined. The analysis of the near-tip field follows the works of Hutchinson and Rice and Rosengren. Dominant singularity solutions governing the asymptotic behavior of the stresses and strains at the crack tip are obtained for the complete range of loadings between Mode I and II. The results of an accurate finite element technique, which imbeds the dominant singularity solutions, directly relates the near-tip behavior to the elastic stress intensity factors K(I) and K(II). Implications of this study to mixed mode fracture mechanics is also discussed, particularly with respect to the direction of crack initiation and the relation of fracture toughness under mixed modes to that in Mode I. Details of the mixed mode plastic zone sizes and shapes are also given.
247 citations
01 Jan 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this paper, an analysis is presented which enables crack propagation rates under cyclic loading condiditions to be predicted from static slow crack growth parameters, and a comparison of the predicted times to failure under static and cyclic conditions with available measured failure times, for several ceramic materials at ambient temperatures, suggests that there is no significant enhancement of the slow-crack growth rate due to cycling.
Abstract: An analysis is presented which enables crack propagation rates under cyclic loading condiditions to be predicted from static slow crack growth parameters. A comparison of the predicted times to failure under cyclic conditions with available measured failure times, for several ceramic materials at ambient temperatures, suggests that there is no significant enhancement of the slow crack growth rate due to cycling. This is verified in a series of measurements of slow crack growth rates under static and cyclic conditions.
213 citations
TL;DR: In this paper, the fracture toughness of PMMA has been determined in the temperature range −190 to + 80° C and over the crack speed range of 10−2 to 102 mm sec−1.
Abstract: Experiments are described in which the fracture toughness,K
c, of PMMA has been determined in the temperature range −190 to + 80° C and over the crack speed range of 10−2 to 102 mm sec−1. Single edge notch tension was used for instability measurements but the other data were obtained using the double torsion method. In the range −80 to + 80°C the variations inK
c may be described in terms of modulus changes and a constant crack opening displacement criterion. Crack instabilities are correlated with isothermal-adiabatic transitions at the crack tip. Below −80° C there is an inverted rate dependence associated with thermal effects during post-instability crack propagation.
TL;DR: In this article, a technique for studying high temperature crack propagation in ceramic materials is developed, which is used to obtain relationships between the crack propagation rate and the stress intensity factor for hot-pressed silicon nitride up to 1400° C.
Abstract: A technique for studying high temperature crack propagation in ceramic materials is developed. The technique is used to obtain relationships between the crack propagation rate and the stress intensity factor for hot-pressed silicon nitride up to 1400° C. The data are then used to develop proof test diagrams which give values for the safe working stress levels for this material after proof testing (or any other flaw detection procedure).
TL;DR: In this paper, a Ti-6Al-4V titanium alloy was used to study the effect of crack closure on crack growth and showed that crack closure is not the sole cause for delay.
TL;DR: In this paper, a critical combination of hydrogen concentration and stress will develop at the edge of the plastic enclave, and this will produce an incremental crack growing from the edge to the crack tip.
TL;DR: In this article, the high-temperature strength of commercial hot-pressed Si3N4 was obtained for two materials with different impurity contents, weak and strong material directions, air and Ar ambients, and different stressing rates.
Abstract: The high-temperature strength of commercial hot-pressed Si3N4 was obtained for (1) two materials with different impurity contents, (2) the weak and strong material directions, (3) air and Ar ambients, and (4) different stressing rates. Strength degradation occurred at a lower temperature for the less pure material; both material directions exhibit the same rate of strength degradation. The testing ambient did not affect strength. The strength at temperatures ∼1200°C depended strongly on stressing rate. The presence of rough, crack-shaped topographical features on the fracture surface and the observation of large cracks that formed during stressing are reported as evidence for subcritical crack growth at high temperatures. It is hypothesized that accelerated creep caused by grain-boundary sliding at preexisting crack fronts is the mechanism responsible for the observed subcritical crack growth.
TL;DR: By means of the theory of nonlocal elasticity, the stress concentration at the tip of a crack subjected to a uniform tension perpendicular to the line of crack at infinity was determined in this paper.
TL;DR: In this article, it was shown that crack closure occurs only when the stress intensity conditions were reduced to below the minimum stress intensity level (KM I N) for the previous fatigue cycles.
TL;DR: In this paper, the application of acoustic emission to the detection of fatigue-crack propagation in 7075-T6 aluminum and 4140 steel is investigated, and the relationship between crack-growth rate, cyclic stress-intensity factor, load-cycling rate and observed acoustic-emission behavior is presented.
Abstract: The application of acoustic emission to the detection of fatigue-crack propagation in 7075-T6 aluminum and 4140 steel is investigated. The relationship between crack-growth rate, cyclic stress-intensity factor, load-cycling rate and observed acoustic-emission behavior is presented. Crack-growth rates of less than 10−6 in./ cycle could be detected, and acoustic-emission counts per cycle were shown to be closely related to the energy released by crack extension per cycle. A quantitative relationship for the threshold conditions for detection of fatigue-crack growth is presented which agrees with experimental test results. The results also showed that fatigue-crack growth occurs in an accelerating and decelerating manner, even though the stress-intensity range remains uniform, and that the count rate posses through a peak that is believed to be associated with a plane strain-plane stress transition. The effects of instrumentation sensitivity and frequency bandpass are also investigated. The results obtained indicate that acoustic-emission techniques should be suitable for in-service monitoring of a variety of cyclically loaded structures, even in the presence of high background noises.
TL;DR: In this article, the low growth rate and threshold properties of two pearlitic steels have been evaluated and an increasing effect of load ratio was observed as the threshold was approached, such that control of crack growth passed from ΔK to Kmax.
TL;DR: In this article, the authors considered the plane strain problem of a half-plane crack in an unbounded elastic solid, and the faces of the crack were subjected to suddenly applied, equal but opposite concentrated normal forces which tend to separate the crack faces.
TL;DR: In this article, the temperature distribution around the crack tip has been calculated and the temperatures are dependent on the radius of the heat source and the crack velocity, and the very high temperatures computed lead to the supposition that the observed light emission during fast fracture is of thermal origin.
Abstract: T he high energy concentration at the tip of a running crack leads to irreversible deformations, and a great amount of the deformation energy is set free as heat. Assuming that this moving heat source is of circular shape, the temperature distribution around the crack tip has been calculated. The temperatures are dependent on the radius of the heat source and the crack velocity. Some examples for the material glass are given. The very high temperatures computed lead to the supposition that the observed light emission during fast fracture is of thermal origin.
TL;DR: In this paper, a two-stage model for structure sensitive crack growth is proposed, where the transition from structure sensitive to structure insensitive can be correlated with the attainment of a critical value of the reverse plastic zone size equal to the α grain size of the microstructure in question.
TL;DR: In this article, a criterion for predicting the growth of three-dimensional cracks is developed on the basis of the strain energy density concept which has been used successfully for treating two-dimensional crack problems.
TL;DR: In this article, the authors used a simple and well reproducible crack geometries in copper single-crystals: the crack surfaces are macroscopically plane and the crack front can be forced by appropriate external force distributions into any preselected direction.
TL;DR: In this paper, the analysis of stress intensity factors of a semi-infinite body with an elliptical or semi-elliptical crack subject to tension is presented, where the authors focus on the stress intensity factor of the body with respect to tension.
Abstract: This paper is concerned with the analysis of stress intensity factors of a semi-infinite body with an elliptical or a semi-elliptical crack subject to tension.
TL;DR: In this article, a previously published model of fatigue crack propagation is refined and the resulting slip geometry at the crack tip is calculated, where the slip on both sides of the crack is assumed to occur on slip bands instead of the discrete slip planes used in the old model.
TL;DR: The cyclic stress-strain behavior of a wide variety of rigid polymers has been studied as mentioned in this paper, and three classes of fatigue response can be defined, each class displaying a characteristic evolutionary pattern in the stressstrain relation as deformation proceeds from the initial fatigue cycle to fatigue-crack propagation.
Abstract: The cyclic stress-strain behaviour of a wide variety of rigid polymers has been studied Three classes of fatigue response can be defined, each class displaying a characteristic evolutionary pattern in the stress-strain relation as deformation proceeds from the initial fatigue cycle to fatigue-crack propagation Ductile polymers undergo a marked decrease in deformation resistance prior to crack formation; the detailed mechanism by which this “softening” develops can be related to the material microstructure and thermomechanical history Amorphous polymers with a moderate degree of ductility soften slightly; in these materials crazing plays a dominant role in both the cyclic stress-strain response and the structural fatigue resistance Brittle and nearly-brittle polymers are essentially stable in cyclic deformation; the fatigue resistance of these materials is very sensitive to strain amplitude in cyclic deformation
01 Aug 1974
TL;DR: In this paper, the stage fatigue crack propagation in Ti-6A1-4V has been studied as a function of various fracture mechanics parameters, including the stress intensity range (ΔK) and both positive and negative ratios of the minimum to maximum stress (R).
Abstract: Stage fatigue crack propagation in Ti-6A1-4V has been studied as a function of various fracture mechanics parameters, including the stress intensity range (ΔK) and both positive and negative ratios of the minimum to maximum stress (R). It was found that the fracture surface appearance undergoes a transition from cyclic cleavage to striations at a ΔKeff of approximately 13 MNm-3/2 (11.8 ksi√in.). It was also observed that the measured striation spacings are generally within a factor of two of the optically measured crack growth rates. Both of these results can be particularly useful for determining unknown component cyclic loadings during failure analysis. The criterion for the cyclic cleavage to striation transition is considered to be a change from primarily single to multiple slip within the individual grains at the crack tip. This occurs when the cyclic plastic zone size becomes approximately equal to the α grain size.
01 Mar 1974-Metallurgical and Materials Transactions B-process Metallurgy and Materials Processing Science
TL;DR: In this article, the authors measured the rate of fatigue crack propagation for Ti-6Al-6V-2Sn and Ti- 6 A1-4V in aqueous environments.
Abstract: The rate of fatigue crack propagation for Ti-6Al-6V-2Sn and Ti-6 A1-4V in aqueous environments has been measured as a function of solution chemistry, frequency, and stress wave form. Depending on the specific encironment, three types of fatigue crack growth rate behavior have been observed as a function of frequency. Crack growth rates increase with decreasing frequency in distilled water, while addition of Na2SO4 produces frequency-independent behavior. In solutions containing chloride or bromide ions, a reversal in frequency-dependence takes place at ΔKscc. Below this transition ΔK level, crack growth rates decrease with decreasing frequency due to passive film formation at the crack tip. Above ΔKscc corrosion fatigue crack growth is due to SCC under cyclic loading. The ΔK transition in fatigue is lower than the static stress corrosion threshold because of repeated rupture of the passive film at the crack tip, approaching KIsco only for very slow cycling frequencies.