No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Abstract
A slice synthesis methodology is developed and used to construct a modified strip-yield model for the semielliptical surface flaw, enabling prediction of plasticity-induced closure along the crack front and subsequent fatigue crack growth. A mathematical description of the model is presented. Slice synthesis methodologies have previously been limited to stress intensity factor and elastic crack displacement computation. Predictions of flaw shape evolution under cyclic loading are compared with experimental data for aluminium alloy specimens under uniform constant amplitude loading with R = 0.1, 0.3 and 0.6. Model predictions are shown to correlate well with experimental data. An empirical correlation of relative crack opening stress with applied R ratio from the literature is shown to underestimate the level of closure at the deepest point of penetration when compared with the model predictions.
... The original SY model was conceived for a centrecrack tension specimen. Using formulations based on the weight function method, Wang and Blom 7 and Daniewicz et al. [30][31][32] generalized the Newman model 6 to allow treatment of arbitrary 2D or 3D geometries with through cracks 30 or part-through cracks (e.g. surface crack). ...
... surface crack). 31,32 In the latter case, a slice synthesis methodology, first proposed by Fujimoto 33 for the SIF calculation, was utilized. As detailed by Daniewicz and Aveline, 32 the behaviour of a surface flaw is synthesized using two groups of throughcrack slices by cutting a 3D body into vertical and horizontal flat slices, Fig. 6, with keeping the crack surface continuous. ...
... Principle of the slice synthesis model.31 ...
Deterministic models developed to predict fatigue crack growth in metallic materials are considered with special emphasis on approaches suitable for variable amplitude load histories. Part I gave a concise review of available models and their assessment based on reported in the literature comparisons between predicted and observed results. It was concluded that the so-called strip yield model based on the plasticity-induced crack closure mechanism is a most versatile predictive tool convenient to use in the case of mode I crack growth under arbitrary variable amplitude loading. Part II of the paper is focused on the strip yield model and its predictive capabilities. Implementations of this type prediction approach reported in the literature are reviewed. It is shown that decisions regarding the constraint factor conception, a choice of the crack driving force parameter, the crack growth rate description and various numerical details can have a profound effect on the model results and the prediction quality.
... It has been used by other researches for various purposes, e.g. SIFs determination of curved cracks in gears [46], strip-yield analysis of part-through cracks [47][48][49], and computation of SIFs for surface cracks in residual stress fields [50], etc. Recently, closed form 2D weight functions of two unequal-length hole-edge cracks were derived by the present authors [51]. ...
... An general polynomial function proposed by Zhao et al. [33,34], given in Eq. (9), is adopted here to represent the spring stress S(x, y). It is an approximate engineering representation without loss of generality, and has been successfully used in references [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. It should be noted that several theoretical aspects of the SSWFM, including the adopted assumptions, have been discussed and evaluated in detail by Zhao et al. [33,34] for three 3D crack configurations (embedded elliptical crack, semi-elliptical surface crack, quarter-elliptical corner crack); the appropriateness of the COD-compatibility and assumptions have been established in Ref. [35]. ...
Stress intensity factors (SIFs) of two eccentric and asymmetric surface cracks and surface-corner cracks at a hole are rare in the literature, since the problem is too complicated to be tackled by analytical methods and too costly by numerical approaches. A 3D slice synthesis weight function method (SSWFM) is developed to compute their 3D SIFs. The results agree well with those from finite element method (FEM). The SSWFM is about 450 times faster in calculation of the SIFs than FEM/Franc3D, and is very useful for 3D fatigue crack growth analyses of complicated surface and corner cracks at a hole.
... The application of slice synthesis methodology is extending to perform the numerical calculation of a crack opening profile and plastic zone length for a semi-elliptical surface cracks in an elastic-perfectly plastic body under monotonic loading [7] [8]. However, these approaches are limited to a part-through semielliptical crack in semi-infinite body. ...
... The expression of S´x yµ is the same of P´x yµ for applied force. S´x yµ had not be applied in the previous researches [7] [8] related SSM in elastic-plastic condition. From preliminary investigations by authors, it is conducted that introducing of the additional spring force S´x yµ for cohesive force seems to be unavoidable if the SSM in elastic-perfect plastic body is applied to finite geometry cracked body. ...
Applicability evaluation of the developed weight function based strip yield model for an embedded crack by applying the slice synthesis methodology in elastic-perfect plastic bodies under monotonic uniform loading is performed. Although the weight function based strip yield model for a part-through semi-elliptical surface crack in an elastic-perfect plastic bodies under monotonic uniform loading was proposed by Daniewicz and Aveline (2000), applicable geometries of cracked bodies is limited. Their proposed strip yield model treats only a semi-elliptical surface crack in semi-infinite bodies. Besides, quantitative investigations of the applicability seem to be insufficient. The authors proposed the improved strip yield model with slice synthesis methodology for an embedded crack, which enables to treat the finite boundary problems. By applying proposed model, the back surface effect of the crack opening behaviour and the plastic zone growth can be considered. The validity of improved strip yield model for embedded cracks is confirmed by comparing crack opening profiles under some crack geometries with elastic-plastic finite element analyses.
The stress intensity factor (SIF) is the foundation of fracture mechanics analysis. Accurate determination of SIFs is at the very heart of damage tolerance design and fatigue crack growth life prediction. The weight function method (WFM) is a powerful method for SIF‐determination involving complex load conditions. This article presents a review of the historical development over the past five decades and the current state‐of‐the‐art in three‐dimensional (3D) WFMs. The discussions are focused on the slice synthesis weight function method (SSWFM) and the point weight function method (PWFM). The powerfulness of the 3D WFMs is shown by a variety of examples with complex part‐through crack configurations under uni‐ and bi‐variant loadings. Solution accuracy is verified by comparisons of SIFs with various numerical methods. Use of the substitute geometry concept to expand the capability of 3D WFMs for solving real‐world engineering 3D crack problems is demonstrated. Some remaining challenges are briefly discussed.
Three-dimensional (3D) crack problems are much more complicated and analytically intractable than 2D cases because the stress intensity factor (SIF) is a function of position along the crack front, the crack size and also several other geometric variables. The weight function methods (WFMs) provide efficient and reliable means for analysis of 3D crack problems, especially when multi-geometry parameters and complex load conditions are considered. In this chapter, several 3D WFMs are described. The slice synthesis weight function method (SSWFM) based on the combination of the slice-synthesis technique and the 2D analytical WFM is presented, and verified with various practical cases. Accurate SIFs for surface/corner cracks subjected to power stresses in various configurations are determined and tabulated. Various point load weight function methods (PWFMs) for 3D cracks in bi-variant stress fields are discussed. Simple engineering approaches for 3D SIFs at the deepest and surface points are briefly introduced.
Applicability of slice synthesis methodology with weight function to calculate stress intensity factor and crack opening displacement in elastic condition for three dimensional cracks is investigated. Although slice synthesis methodology has already proposed, quantitative investigations of the applicability seem to be insufficient.The authors make it clear the applicable limits to the embedded elliptical cracks by comparing conventional formula based on finite element analyses. It is confirmed that the ratio of crack depth to plate thickness or back surface affects the accuracy of elastic crack opening displacement and stress intensity factor by applying slice synthesis methodology.Besides, the authors suggest modified SSM which enables to evaluate the effect of back surface. And it is concluded that modified SSM enables to give stress intensity factor and crack opening displacement of embedded cracks in elastic condition with high accuracy.
Applicability evaluation of the developed weighth function based strip yield model for an embedded crack by applying the slice synthesis methodology ln elastic-perfect plastic bodies under monotonic uniform loading is performed.Although the weight function based strip yield model for a part-through semi-elliptical surface crack was proposed by Daniewicz and Aveline (2000), applicabl egeometries of cracked bodies is limited. Their proposed strip yield model treats only a semi-elliptical surface crack in semi-infinite bodies. Besides, quantitative investigations of the applicability seem to be insufficient.The authors proposed the improved strip yield model with slice synthesis methodology for an embedded crack, which enables to treat the finite boundary proplems. By applying proposed model, the back surface effect of the crack opening behavior and the plastic zone growth can be considered.The validity of improved strip yield model for embedded cracks is confirmed by comparing crack opening profiles under some crack geometries with elastic-plastic finite element analyses.
Fatigue crack growth behavior of a rolled AZ31 magnesium plate is investigated and modelled in this study. Fatigue crack growth tests were performed on compact tension specimens at load ratios of R=0.1 and R=0.7 to provide data for a strip-yield based fatigue crack growth model. Minimal differences in crack closure were observed between the two load ratios. Threshold values for the stress intensity factor range were found to be often less than those reported in previous literature. The reason for lower threshold values could be related to the nontraditional compression pre-cracking method used in this study, which was employed in an attempt to produce a more accurate measurement of the fatigue crack threshold. In addition to the long crack, fatigue crack growth testing using compact tension specimens, load controlled fatigue tests were conducted on flat, reduced gage specimens at load ratios of R=0.1 and R=−1.0 to study the microstructurally small crack growth behavior and to extend the model capability to predict the microstructurally small crack growth behavior. The reduced gage specimens were found to spend the majority of their life in the crack growth stage. Cracks primarily grew in a planar fashion other than where multiple cracks coalesced. The microstructurally small crack growth data from these experiments were also compared with predictions from the fatigue crack growth model. Crack growth modeling revealed that traditional calculations using plasticity-induced crack closure concepts and an effective stress intensity factor range were not able to predict the microstructurally small crack growth behavior of these specimens. In contrast, computing crack growth rate from crack tip opening displacement was shown to give satisfactory results. Crack opening stresses for the fully reversed tests revealed that the compressive loading largely nullified the effect of the plastic wake on fatigue crack growth.
Das Fließstreifenmodell ist ein verbreitetes Hilfsmittel zur Berechnung der zyklischen Rissspitzenöffnungsverschiebung und des Ermüdungsrisswachstums von Strukturen unter isothermer zyklischer Belastung. Im Zuge einer Modellerweiterung kommt das rheologische Masing‐Modell zum Einsatz, das aus parallel geschalteten Reihenschaltungen von Feder und Reibelement besteht. Indem den Reibelementen unterschiedliche Fließspannungen zugeordnet werden, kann mit dem Masing‐Modell die zyklische Spannungs‐Dehnungs‐Kurve des Werkstoffs beschrieben werden. Anstelle einer konstanten Fließspannung werden diese verschiedenen Fließspannungen zufällig den einzelnen Elementen, in die die Riss‐Ligament‐Linie im Fließstreifenmodell unterteilt ist, zugewiesen. Neben einer besseren Modellierung des mechanischen Materialverhaltens ist auf diese Weise die Berücksichtigung mikrostruktureller Aspekte des Ermüdungsrisswachstums möglich, wenn auf die Werte der Fließspannungen im Bereich des frühen mikrostrukturellen Risswachstums Einfluss genommen wird. Zur Untersuchung thermomechanischer Ermüdung werden die Fließspannungen in Abhängigkeit von der Temperatur formuliert.
This chapter focuses on the effects of the compressive residual stresses generated due to laser shock processing (LSP) on the stress intensity factor (SIF) of a through-the-thickness radial crack at the edge of the circular hole, the effects of laser shock peening on the fatigue crack initiation and propagation of 7050-T7451 aluminum alloy, and a new kind of statistical data model which described the fatigue cracking growth with limited data and the effects of the reliability and the confidence level to the fracture growth. Many materials have displayed pronounced improvements in fatigue life after LSP. It has shown that LSP treatment improves the materials mechanical properties, fatigue resistance, foreign object damage (FOD), and fatigue life.
The limit of applicability of the former published method for an embedded cack in a finite body is investigated by comparing with the conventional stress intensity factor formula. The error of estimated stress intensity factors by published slice synthesis methodology increases for a decreasing distance of the crack tip from the back surface of the body. The reason is considered that the former published slice synthesis methodology conform the crack opening behavior of an embedded crack obtained analytical solution in an infinite cracked body to the ones obtained by the slice synthesis methodology. The improved slice synthesis methodology to increase accuracy of stress intensity factor solutions in a finite body is proposed by incorporating a correction coefficient into the formulation. The validity of improved slice synthesis methodology is confirmed by comparing the stress intensity factor solutions with ones by finite element analyses.
The strip-yield model is a common tool to calculate the cyclic crack tip opening displacement and the fatigue crack growth life of structures in case of isothermal fatigue loading. The incorporation of a temperature-dependent yield stress already enables its application in thermal fatigue analyses. A further extension of the strip-yield model is presented here together with simulation results: The rheological Masing model consisting of spring-slider elements connected in parallel is used to describe the material's stress-strain curve. It results in different yield stresses belonging to the numerous sliding frictional elements. These different yield stresses are randomly arranged along the crack ligament line instead of the usually applied constant yield stress. They depend on temperature as the procedure should still be used at non-isothermal loading. Besides an improved modelling of the mechanical material behavior the consideration of microstructural aspects of fatigue crack growth becomes possible by influencing the values of the yield stresses near the crack initiation site.
This research investigated how a semi-elliptical surface crack grows in a 2024-T4 aluminium alloy under constant-amplitude loading. For the investigation, Sih's energy approach for predicting through-thickness crack growth was generalized to predict surface crack growth. The generalized Sih's energy approach accurately predicted experimental results and the prediction of the Paris equation in the depth direction. Additionally, the generalized approach accurately predicted fatigue life of the surface crack. Finally, a model was established to predict crack shape development by using the measured surface length.
The 2D weight function was integrated with slice synthesis model in order to probe into the influence of compressive stress by high strain rate laser shock processing on stress intensity factor of 3D non-through hole-edge crack. The influence of compressive stress by laser shock of high strain rate on stress intensity factor was deduced by means of slice synthesis model from the calculation of 3D crack tip stress intensity factor. It is applicable to obtain the stress intensity factor at each point at the surface crack front. According to the computational solution, the stress intensity factor subjecting to the modification of impact zone was smaller than that without modification when the inhibiting effect was imposed by the laser shock plastic zone on the crack development. The experiment aims to probe into the influence of high power, short pulse laser shock on the stress intensity factor of crack tip in metal plastic deformation zone by focusing on the inhibiting effect of residual stress produced on the crack development in the plastic zone.
Newman's crack opening stress equation [Newman JC. Jr. A crack opening stress equation for fatigue crack growth. Int. J. Fract. 1984;24:R131-R135.] was extended to predict the crack opening stress of part-through cracks within a finite body. The extended equation was obtained by replacing the normalized maximum applied stress S(max)/σ0 as the normalized stress intensity factor (SIF) K(max)/K0, where K(max) is the SIF including the geometry correction factor F, and K0 is the stress intensity factor for flow stress. In order to verify the crack opening stress obtained from the extended equation, the modified strip-yield model using a slice synthesis technique [Daniewicz SR. A modified strip-yield model for prediction of plasticity-induced closure in surface flaws. Fatigue Fract. Engng. Mater. Struct. 1998;21:885-901.] was utilized and the approximate weight function was modified to consider the effect of the restraint due to the uncracked area. For a corner crack or surface crack within a finite body, the crack opening stresses obtained from this model were correlated well with the results of the extended equation. Additionally, the crack shape evolutions of surface crack subjected to uniaxial constant amplitude loading or four-point bending loading were predicted by the extended crack opening stress equation and compared with experimental data for aluminium alloy specimens with R = 0.1. The predictions were in good agreements with experimental data.
A slice synthesis methodology is developed and used to construct a weight function based strip-yield model for a semi-elliptical part-through surface flaw in an elastic–perfectly plastic body under monotonic loading. The model enables rapid approximate computation of the crack surface displacements and the crack front plastic zone size in the crack plane. A detailed mathematical description of the model is presented. Crack surface displacements from the model are shown to compare well with results from detailed three-dimensional elastic–plastic finite element analyses. From the finite element analyses, the crack plane plastic zone is shown to give an unrealistic perspective of overall crack front plasticity.
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.
Description
Covers fatigue crack closure from materials characterization to practical application in industry. Peer reviewed papers provide information and experiences on new crack-closure measurement techniques, advanced crack-closure analysis methods, and practical applications of the crack-closure concept to predict crack-propagation lives of aerospace and automotive components under complex load histories.
Description
Covers fatigue crack closure from materials characterization to practical application in industry. Peer reviewed papers provide information and experiences on new crack-closure measurement techniques, advanced crack-closure analysis methods, and practical applications of the crack-closure concept to predict crack-propagation lives of aerospace and automotive components under complex load histories.
Description
Covers fatigue crack closure from materials characterization to practical application in industry. Peer reviewed papers provide information and experiences on new crack-closure measurement techniques, advanced crack-closure analysis methods, and practical applications of the crack-closure concept to predict crack-propagation lives of aerospace and automotive components under complex load histories.
Description
Subjects covered fall into several categories: theoretical, numerical, and experimental aspects of the mechanics of fracture; high-cycle fatigue; material influences on fracture; and elasto-plastic fracture mechanics.
Description
Helps those responsible for predicting structural integrity understand the most common type of crack growth in structural components. 22 papers divided into sections on Models and Experiments, and Fatigue Crack Growth.
Description
The Fourteenth National Symposium on Fracture Mechanics was held in Los Angeles, Calif., 30 June-2 July 1981. ASTM Committee E24 on Fracture Testing sponsored the symposium. J. C. Lewis, of the TRW Space and Technology Group, and George Sines, of the University of California at Los Angeles, served as symposium chairmen and edited this publication.
Description
The symposium on Cyclic Stress-Strain and Plastic Deformation Aspects of Fatigue Crack Growth was presented at a meeting held in St. Louis, Mo., 2—8 May 1976. The symposium was sponsored by the American Society for Testing and Materials through its Committee E09 on Fatigue. L. F. Impellizzeri, McDonnell Aircraft Company, presided as symposium chairman.
Studies have shown that fatigue growth of semielliptic surface flaws in plates is not adequately predicted solely by stress intensity factor analysis. The variation in stress field triaxiality along the flaw border must be an important factor contributing to differences between predicted and observed fatigue crack growth behavior. An analysis is formulated to examine surface flaw fatigue growth accounting for constraint variation using the concept of crack closure. The extent of crack closure is quantified for plane stress versus plane strain conditions. Changes in the geometric parameters describing flaw size and shape are studied. Applications of the analysis are compared with experiments.
Description
This book describes the procedures used by various analysis groups to predict fatigue-crack growth under random loading. This aspect is important in the design, analysis, and test evaluation of a structure.
Contains the following main sections: 1. Introductory theory of elasticity; 2. Energy considerations; 3. Stresses and displacements in cracked bodies; 4. Determination of stress intensity factors; 5. Mixed-mode fracture mechanics; 6. Crack tip plasticity and associated effects; 7. Fatigue crack growth; 8. The fracture mechanics design process. (A.D.)
A usual unloading elastic compliance method for determiing the crack opening point is based on a unloading curve whose uppermost part looks like a straight line. By this method there is the possibility of obtaining a wrong conclusion, since the crack closure behavior is always accompanied with plastic deformation. In this paper the tension-compression fatigue tests were carried out (stress ratio were taken as 0 and minus 1), and the opening and closure point is successfully measured by the S shaped unloading curve. The crack closure point measured from the S shaped unloading curve does not coincide with the opening point.
A theoretical study is made of the implications of a Dugdale-Barenblatt model for fatigue crack growth under steady cyclic loading. Residual plastic stretches and the effects of crack closure on crack opening and closing loads are calculated by complex function methods for a range of loading ratios. An assessment is made of the influx cyclic strain hardening and softening.
In this paper an analytical crack closure model is developed, based on the Dugdale model, but modified to take into account the plastically deformed material left in the wake of an advancing crack. For specified maximum and minimum stress values expressed as fractions of the yield stress, the model predicts a crack opening stress from which an effective stress intensity factor may then be computed. Using this factor, the constant amplitude fatigue crack growth rate data for several stress ratios for each of three different aluminium alloys are shown to reduce to a single curve. From these data and the model, growth rates may be predicted without further tests for all steady-state cyclic conditions.
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.
This paper reviews the capabilities of a plasticity-induced crack-closure model and life-prediction code, FASTRAN, to predict fatigue lives of metallic materials using small-crack theory. Crack-tip constraint factors, to account for three-dimensional state-of-stress effects, were selected to correlate large-crack growth rate data as a function of the effective-stress-intensity factor range (ÎK{sub eff}) under constant-amplitude loading. Some modifications to the ÎK{sub eff}-rate relations were needed in the near-threshold regime to fit small-crack growth rate behavior and endurance limits. The model was then used to calculate small- and large-crack growth rates, and to predict total fatigue lives, for notched specimens made of several aluminum alloys and a titanium alloy under constant-amplitude and spectrum loading. Fatigue lives were calculated using the crack-growth relations and microstructural features like those that initiated cracks for the aluminum alloys. An equivalent-initial-flaw-size concept was used to bound the fatigue lives for the titanium alloy. Results from the tests and analyses agreed well.
Using a modified strip-yield model, plane stress constant-amplitude fatigue crack growth simulations under conditions of small-scale yielding were performed for the edge-cracked strip in tension, the edge-cracked strip in bending, and the compact tension specimen with load ratios R = 0.5, 0.0, −1.0and−2.0. From these simulations, fatigue crack opening loads were predicted as a function of crack length. Geometry, loading type and crack length were observed to affect crack opening loads. The geometry-loading dependence was particularly evident for extended fatigue crack growth. Geometry-loading dependence was observed to increase for R < 0. Reductions in the crack opening loads following extended crack growth were also observed. These reductions were demonstrated to occur in the absence of large-scale plasticity in the remaining ligament. A normalized maximum applied stress intensity factor Kmax/σo√W, where σo and W represent the flow stress and specimen width respectively, was demonstrated to represent an approximate measure of small-scale yielding crack closure response similitude under plane stress conditions with R ⩾ 0. When crack opening loads were correlated in terms of this parameter, little geometry-loading dependence was observed.
A two-dimensional, weight-function-based, non-linear elastic-plastic analytical model has been developed for considering fatigue crack propagation in a pre-existing residual stress field. This model is restricted to two-dimensional cracked bodies with through-thickness cracks under mode I loading. Geometries consisting of a crack emanating from a free surface may be considered, including the propagation of fatigue cracks from stress concentrations such as holes or notches. Using predictions of crack opening stress, the effective stress intensity factor range at the fatigue crack tip under a given cyclic loading is computed. A fatigue crack growth rate correlation employing the effective stress intensity range is required for subsequent prediction of crack growth. For demonstration purposes, the analytical model is used to predict fatigue crack propagation in an edge-cracked panel exhibiting prescribed hypothetical residual stress fields, and comparisons are made with an elastic superposition methodology. The use of superposition is demonstrated to be conservative in comparison with the analytical model for a particular residual stress field exhibiting compressive stress at the surface (point of fatigue crack initiation). In contrast, for a similar residual stress distribution with tensile stress at the surface, elastic superposition is shown to be nonconservative.
To understand the behavior of corner cracks involving displacement-controlled loading, the mode-I stress intensity factors and crack face displacements are determined for a quarter-elliptical corner crack undergoing uniform end displacement. A 3-D weight function method is used for the analysis. Various crack aspect ratios and crack-length-to-plate-height ratios are considered. The results show that the stress intensity factor and the crack opening profile for the uniform displacement-controlled loading can be significantly different from those for the uniform-stress controlled loading.
The weight function method developed in part I is used to determine stress intensity factors for half-elliptical surface cracks at a hole in finite thickness plates under polynomial crack face loading. Superpositions of these results allow determination of stress intensity factors for this crack configuration under general stress distributions. The approach is demonstrated by obtaining stress intensity factors for a variety of load cases including biaxial tension (compression), wedge loading in the hole and simulated pin loading. Both single and double crack configurations are considered and their difference in stress intensity factors is investigated. These results are compared, where possible, with other solutions available in the literature. Very good agreement is obtained.
Weight functions have been widely used to compute stress intensity factors and crack surface displacements in cracked bodies under arbitrary applied stress fields. For many geometries and applied stress fields of interest, these computations require the application of numerical integration or quadrature.Weight functions exhibit a crack tip singularity. This singularity, if ignored, can lead to inaccurate or inefficient stress intensity factor and crack surface displacement computations. The numerical integration of weight functions using Qauss-Chebyshev quadrature is demonstrated. This type of quadrature is ideally suited for weight function integration as it allows removal of the integrable crack tip singularity, enabling accurate and efficient computation of stress intensity factors and crack surface displacements.Stress intensity factors and crack surface displacements for the edge cracked half-plane under uniform tension have been computed applying both Gauss-Chebyshev and Gauss-Legendre quadrature. Gauss-Chebyshev quadrature is shown to be superior in terms of both accuracy and computational efficiency.
Results of an investigation are presented, which indicate that a fatigue crack, propagating under zero-to-tension loading may be partially or completely closed at zero load. An analysis of the stress distribution acting on the fracture surfaces shows that the local compressive stress maxima may exceed the yield stress of the material. Fractographic evidence is presented to show that crack closure may influence the shape of the striation pattern on the fracture surfaces.RésuméOn présente les résultats d'une recherche indiquant qu'une fissure due à la fatigue, se propageant sous une charge allant de zéro à la tension qui peut être partiellement ou complètement refermée à la charge zéro. Une analyse de la distribution de la tension agissant sur les surfaces de fracture, montre que les maxima de la force locale de compression, peuvent dépasser la tension limite du matériau. La preuve fractographique est présentée dans le but de montrer que la fermeture de la fissure peut influencer la forme du modèle de striation sur les surfaces de fracture.ZusammenfassungEs werden die Ergebnisse einer Untersuchung dargelegt, die daraufhindeuten, dass ein unter Ursprungsbelastung wachsender Ermündungsbruch im unbelasteten Zustand teilweise oder ganz gescholssen sein kann. Eine Analyse der auf der Bruchfläche vorhandenen Spannungsverteilung zeigt, dass die örtlichen Druckspannungshöchstwerte die Fliessgrenze des Werkstoffes übertreffen können. Es wird fraktographisches Beweismaterial geliefert um zu zeigen, dass ein Schliessen des Risses die Form des Markierungsmusters auf den Bruchflächen beeinflussen kann.
Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.
Abstract— The fatigue crack closure response was investigated for a surface crack in BS4360 50B structural steel, subjected to (1) constant amplitude loading and (2) constant amplitude loading interrupted by a single peak overload. A variety of compliance techniques was employed to determine closure behaviour. The crack mouth gauge measured the bulk, plane strain closure load, while the near tip strain gauge indicated the surface, plane stress closure response. For constant amplitude loading it was found that the surface regions of a surface crack are closed for a greater portion of the load cycle than the maximum depth point. A single peak overload caused different closure and growth rate transients at the surface of the thumbnail crack and at the maximum depth point. For growth rates above 10-6 mm/cycle, such behaviour agrees with the response of a through crack when subjected to constant amplitude loading, and a single peak overload.
A strip crack closure model, based on the Dugdale-Barenblatt model but modified to leave plastically deformed material in the wake of the crack tip, was investigated for various aspects of fatigue crack growth behaviour. A constraint factor was introduced into the model to account for the 3D effect at the crack tip to extend the applicable range of the original Dugdale-Barenblatt model to the plane strain condition. Comparisons with experimental data show that the constraint factor in the strip model results in a fairly good prediction for the fatigue crack closure under the plane strain condition. A variable constraint factor makes it possible for the model to account for the gradual change of stress state from plane strain to plane stress when the crack grows large. The change of stress state occurs typically for the fatigue crack in plates where the stress state at the crack tip is mainly determined by the relative ratio for the crack tip plastic zone size and the plate thickness. The change of stress state has a significant influence on fatigue crack growth behaviour. Weight functions were combined in the modified Dugdale model because crack surface displacement solutions can be derived and the stress intensity factors for complex stress fields can be obtained from corresponding weight functions. It has been shown that a great many problems can be solved when approximate weight function techniques are used. Comparisons were made between predictions from the model and experimental data available in the literature. There was very good agreement for the fatigue crack growth under constant amplitude loading with different stress ratios (R-ratios), for the load interaction effects in both plane stress and plane strain conditions, for the fatigue crack growth in plates under spectrum loading, for the fatigue crack growth in residual stress fields, and for the small crack growth behaviour.
The growth behaviour of semi-elliptical and semicircular cracks subjected to crack extensions due to tensile constant amplitude loading (R = 0.1) was investigated using a three-dimensional elastic-plastic finite-element analysis of fatigue crack growth and closure. Based on this analysis, for both semicircular and semi-elliptical meshes, the crack first closed on the exterior (free) surface (θ = 0°) and then closed towards the interior region upon further unloading of the cyclic loading. The closure and opening behaviour of crack surfaces for both semicircular and semi-elliptical geometries are investigated. An experimental investigation of semi-elliptical flaws under fin spectrum loading was conducted to simulate realistic growth rate behaviour for the semi-elliptical geometry.
A finite difference procedure for the computation of stress and deformation in a three-dimensional elastic-plastic solid is presented. This iterative technique, based on Newton's method for determining the roots of a system of polynomials, is applicable to both linear and nonlinear problems. The procedure requires a minimum of computer storage capability and moderate computer running time. Three sample stress-concentration problems are treated. The first problem is the analysis of a plate in plane strain with a slit at its center, the second is the analysis of a thick plate with a rectangular slit through its thickness, and the last is the analysis of a thick plate containing a semi-elliptical slit which extends only halfway through the thickness. The loading condition in all sample problems is uniaxial tension normal to the slit.
A weight function technique for analyses of three dimensional crack problems has been developed based on the general expressions of weight functions for two dimensional crack problems and the slice synthesis technique. The weight function method is then used to determine stress intensity factors for an embedded elliptical crack in a finite plate under symmetric loadings. The results, where possible, are compared with other solutions available in the literature. The versatility, efficiency and accuracy of this method are demonstrated.
Yielding at the end of a slit in a sheet is investigated, and a relation is obtained between extent of plastic yielding and external load applied. To verify this relation, panels containing internal and edge slits were loaded in tension and lengths of plastic zones were measured.
The present paper is concerned with the development and application of an analytical model of cyclic crack growth that includes the effects of crack closure. The model was based on a concept like the Dugdale model, but was modified to leave plastically deformed material in the wake of the advancing crack tip. The model was used to correlate crack growth rates under constant-amplitude loading and to predict crack growth under aircraft spectrum loading on 2219-T851 aluminum alloy plate material. The predicted crack growth lives agreed well with experimental data. The ratio of predicted-to-experimental lives ranged from 0.66 to 1.48.
Description
The Symposium on Damage Tolerance in Aircraft Structures was conducted in two sessions at the Seventy-third Annual Meeting of the American Society for Testing and Materials, held in Toronto, Ontario, Canada, 21-26 June 1970. The symposium was sponsored by ASTM Committee E09 on Fatigue. M. S. Rosenfeld, of the Naval Air Development Center, served as symposium chairman, with P. C. Paris, Del Research Corp., Hellertown, Pa., and R. J. Hebert, Canadair, Ltd., Montreal, Ontario, presiding as chairmen of the first and second sessions, respectively.
Fatigue crack growth patterns and lives for surface cracks, surface cracks at holes, and corner cracks at holes in three dimensional bodies were predicted using linear-elastic fracture mechanics concepts that were modified to account for crack-closure behavior. The predictions were made by using stress intensity factor equations for these crack configurations and the fatigue crack-growth (delta K against rate) relationship for the material of interest. The crack configurations were subjected to constant-amplitude fatigue loading under either remote tension or bending loads. The predicted crack growth patterns and crack growth lives for aluminum alloys agreed well with test data from the literature.
A surface crack review: elastic and elastic-plastic behavior Surface Crack Growth: Models, Experiments and Structures
- Dm Parks
D. M. Parks (1990) A surface crack review: elastic and elastic–plastic behavior. In: Surface Crack Growth: Models, Experiments and Structures, AST M ST P 1060, pp. 9–33.
Analytical and experimental study of crack closure behavior based on an S-shaped unloading curve
- DChen
- HNisitani
Conception and development of improved analytical prediction models for fatigue induced tooth breakage due to cyclic bending in spur gear teeth
- Sr Daniewicz
Leak prediction by use of a generalized Dugdale model for semi-elliptical surface flaws in plates under tension loading
- C Mattheck
Weight function method for three dimensional crack problems-II
- Zhao
Weight Functions and Stress Intensity Factor Solutions, Pergamon Press, Oxford
- XRWu
- AJCarlsson
The Stress Analysis of Cracks Handbook, Paris Production & Del Research, St
- HTada
- PCParis
- GRIrwin
Weight Functions and Stress Intensity Factor Solutions
- A J Xr Wu
- Carlsson
Görner1984Leak prediction by use of a generalized Dugdale model for semi-elliptical surface flaws in plates under tension loadingProc
- Cmattheckf