Fatigue crack propagation under non-proportional mixed mode loading

Under non-proportional mixed I+II loading, two kinds of stable crack propagation may be distinguished. An existing precrack will either kink, mode I controlled (tensile mode), or will propagate, coplanarly mode II controlled (shear mode). Shear mode growth will occur if the effective mode II range exceeds the material-specific threshold ΔK_{II th sm} and in addition to that, the ΔK_II-value on the starter crack is larger than the ΔK¹_I (Δϕ)-range on the infinitesimally short additional crack. Examination under the scanning electron microscope showed that flaws are not the reason for the mode II controlled crack propagation and support the criteria introduced. If the crack opening is large enough, the crack propagation rate is higher for shear-stress controlled crack growth than for normal-stress controlled crack extension, the deviation angle of which is well predictable via the MTS criterion due to Erdogan and Sih [On the crack extension in plates under plane loading and transverse shear. J Basic Engng 1963;85:519–25].     

Fatigue crack propagation under variable-amplitude loading

A finite-element analysis has been performed to investigate quantitatively the level at which fatigue crack surfaces come into contact during fatigue cycles. The results agreed well with experimental observations and suggest that quantitative design rules may be developed, based upon the crack-closure hypothesis.A summary of remarks made during a seminar held at the Institute for Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev, October 21, 1976.NASA-Langley Research Center, Hampton, Virginia 23665. Published in Problemy Prochnosti, No. 10, pp. 26–29, October, 1977.     

Fracture from a straight crack subjected to mixed mode loading

Fracture from a straight crack under mixed mode loading conditions and small scale of yielding is studied. It is assumed that crack growth occurs in either mode I or mode II. Comparison of theoretically obtained values of the mode I stress intensity factor at incipient kinking with experimental results indicates that mode I is preferred to mode II when the loading is such that the crack surfaces are traction-free, i.e. in the absence of a confining pressure. Mode II would be preferred only if the ratio K _{II c}/K _{I c} between the stress intensity factors is very low, between 0.38–0.81, depending on the load situation. Since there are reasons to believe that most materials are characterized by higher values of K _{II c}/K _{I c}, the conclusion is that mode II hardly occurs in the absence of a high confining pressure.

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Résumé On etudie la rupture entraînée par une fissure droite sujette à des sollicitations selon un mode mixte et comportant une plastification sur une petite échelle. On suppose que la croissance de la fissure se produit sous un mode I ou un mode II.En comparant les valeurs théoriques du facteur d'intensité de contraintes selon le mode I correspondant à l'évasement initial et les résultats expérimentaux, il s'indique que le mode I est privilégié par rapport au mode II lorsque la sollicitation est telle que les surfaces de la fissure sont libres de toutes contraintes, c'est-à-dire en l'absence de toute pression de confinement.Le mode II ne serait privilégié que si le rapport K _{II c}/K _{I c} des facteurs d'intensité de contraintes est très faible, à savoir entre 0,38 et 0,81, selon les conditions de sollicitation.Comme il y a de bonnes raisons de croire que la plupart des matériaux sont caractérisés par des rapports K _{II c}/K _{I c} plus élevés, on en conclut que, en l'absence de hautes pressions de confinement, le mode II a peu de chances de se manifester.

     

Can pure mode III fatigue loading contribute to crack propagation in metallic materials?

The possibility of pure mode III crack growth is analysed on the background of theoretical and experimental results obtained in the last 20 years. Unlike for modes I and II, there is no plausible micromechanistic model explaining a pure mode III crack growth in ductile metals. In order to realize 'plain' mode III fracture surface, we propose the propagation of a series of pure mode II cracks along the crack front. Fractographical observations on crack initiation and propagation in a low alloy steel under cyclic torsion support such a model. The authors have not seen any clear indication of a pure mode III crack growth micromechanism in metals until now.     

A penny-shaped crack in a functionally graded piezoelectric strip under thermal loading

The mixed-mode thermoelectromechanical fracture problem for a functionally graded piezoelectric material (FGPM) strip with a penny-shaped crack is considered. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under thermal loading. The crack faces are supposed to be insulated thermally and electrically. The thermal and electromechanical problems are reduced to singular integral equations and solved numerically. The stress and electric displacement intensity factors are presented for different crack size, crack position and material nonhomogeneity.     

Weld root crack propagation under mixed mode I and III cyclic loading

This study examined fatigue propagation behaviour and fatigue life of weld root cracks under mixed mode I and III loading. Fatigue tests were performed on butt-welded joints with a continuous lack-of-penetration (LOP) inclined at angles of 0°, 15°, 30° or 45° to the normal direction of the uniaxial cyclic load. Branch and/or co-planar crack propagation was observed, depending on the initial mode I stress intensity factor (SIF) range. Co-planar crack propagation predominated when the SIF range was large. The fatigue crack propagation mode affected fatigue life; the life of branch crack propagation was longer than that of co-planar crack propagation. Using an initial equivalent SIF range based on a maximum strain energy release rate criterion, the results obtained from the 0°, 15°, 30°, and 45° specimens indicated almost the same fatigue lives, despite the different inclination angles.     

On a possible model of crack propagation in a solid subjected to a cyclic loading

By the use of the Griffith model, the propagation of a crack in a solid subjected to a cyclic loading is studied. It is assumed that all the energy lost per cycle in the Bauschinger process is transferred to the crack to increase its size.The paper is divided in two parts, the first dealing with materials which do not undergo work-hardening and the second with materials subjected to said phenomenon during cyclic loading. Notwithstanding the crude approximation of this model, it is shown that the main features of fatigue phenomena are accounted for.

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Zusammenfassung DurchGebrauch des Griffithschen Models, wind die Fortpflanzung eines Risses in einem zyklischbeladenenfesten Körper studiert. Es wird angenommen, dass alle in einem Zyklus verlorene Energie während des Bauschingerverfahrens zum Riss übergehen wird, um dessen Grösse zu erweiters.Das Werk umfasst zwei Teile. Der erste Teil behandelt Stoffe, die der Bearbeitungsverhärtung nichtausgesetzt siud; and der zweite Tell Stoffe, die dem Verfahren während zyklischer Belastung uaterworfen werden. Trotz dergrossen Annäherung dieses Models, wird gezeigt, dass die Hauptzüge der Zermürphassomeneerklärt werden.

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Résumé L'étude de la propagation d' une fissure dans un solide soumis à des charges cycliques a été entreprise en partant du modèle de Griffith, et d' une hypothèse selon laquelle 1' énergie dissipée au cours de chaque cycle d'hystéresis sert intégralement à accroitre la dimension de la fissure.On considère séparément le cas des materiaux qui ne subissent pas un durcissement en cours de sollicitation cyclique, et le cas des materiaux qui sont sujets à un tel durcissement.Malgré la faiblesse des hypotheses de base, due à lent caractère de grossière approximation, les résultats de l'analyse concordent qualitativement avec les caractéristiques principales du phénomène de fatigue.

     

Fatigue crack propagation under loading with negative R-values

From a survey of the literature and experimental results obtained with two austenitic steels it is concluded that for fatigue crack propagation with negative R-values the often used relation ΔK_eff = K_max underestimates the crack growth rate. Relations between ΔK_eff and ΔK are presented.     

Fatigue crack initiation and propagation under cyclic contact loading

A computational model for contact fatigue damage analysis of gear teeth flanks is presented in this paper. The model considers the conditions required for the surface fatigue crack initiation and then allows for proper simulation of the fatigue crack propagation that leads to the appearance of small pits on the contact surface. The fatigue process leading to pitting is divided into crack initiation and a crack propagation period.The model for prediction of identification of critical material areas and the number of loading cycles, required for the initial fatigue crack to appear, is based on Coffin-Manson relations between deformations and loading cycles, and comprises characteristic material fatigue parameters. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed and results of cyclic loading conditions are obtained using the finite element method analysis.The short crack theory together with the finite element method is then used for simulation of the fatigue crack growth. The virtual crack extension (VCE) method, implemented in the finite element method, is used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The relationship between the stress intensity factor K and crack length a, which is needed for determination of the required number of loading cycles N_p for a crack propagation from the initial to the critical length, is shown.     

On the dynamic propagation of an anti-plane shear crack in a functionally graded piezoelectric strip

Summary. In this paper, a finite crack propagating at constant speed in a functionally graded piezoelectric material (FGPM) is studied. It is assumed that the electroelastic material properties of the FGPM vary continuously according to exponential gradients along the thickness of the strip, and that the strip is under anti-plane shear mechanical and in-plane electrical loads. The analysis is conducted on the electrically unified (natural) crack boundary condition, which is related to the ellipsoidal crack parameters. By using the Fourier transform, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, crack propagation speed, electric field, FGPM gradation, crack length, and electromechanical coupling coefficient. It reveals that there are considerable differences between traditional electric crack models and the present unified crack model.     

Fatigue crack growth in plate specimens under Mode III loading

Fatigue crack growth in plate specimens of aluminium and an aluminium alloy has been investigated under Mode III loading conditions. It has been found that only when a fully plastic situation exists, does crack extension proceed by a valid Mode III mechanism. When plasticity is restricted to planes of maximum shear there is a strong component of Mode I cracking which results in delamination in the direction of macroscopic growth. Under constant load amplitude cycling the crack growth curve exhibits three stages: a reduction in rate is followed by a period of steady growth prior to acceleration in the final stages. Such a profile is independent of material condition or failure mechanism. Cycling between fixed displacement limits leads to a reducing growth and crack arrest which occurs at a length proportional to the square of the displacement.     

Variations of stress intensity factor of a semi-elliptical surface crack subjected to mixed mode loading

Maximum stress intensity factors of a surface crack usually appear at the deepest point of the crack, or a certain point along crack front near the free surface depending on the aspect ratio of the crack. However, generally it has been difficult to obtain smooth distributions of stress intensity factors along the crack front accurately due to the effect of corner point singularity. It is known that the stress singularity at a corner point where the front of 3 D cracks intersect free surface is depend on Poisson's ratio and different from the one of ordinary crack. In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3-D semi-elliptical surface crack in a semi-infinite body under mixed mode loading. The body force method is used to formulate the problem as a system of singular integral equations with singularities of the form r ⁻³ using the stress field induced by a force doublet in a semi-infinite body as fundamental solution. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately. Distributions of stress intensity factors are indicated in tables and figures with varying the elliptical shape and Poisson's ratio.     

Transient response of a functionally graded piezoelectric strip with a penny-shaped crack under electric time-dependent loading

Summary The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a penny-shaped crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip vary continuously along the thickness direction of the strip, and that the strip is under time-dependent electric load. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the crack location and the material nonhomogeneity.     

Fatigue crack propagation under variable amplitude loading in PMMA and bone cement

Fatigue failure of PMMA bone cement is an important factor in the failure of cemented joint replacements. Although these devices experience widely varying loads within the body, there has been little or no study of the effects of variable amplitude loading (VAL) on fatigue damage development. Fatigue crack propagation tests were undertaken using CT specimens made from pure PMMA and Palacos R bone cement. In PMMA, constant amplitude loading tests were carried out at R- ratios ranging from 0.1 to 0.9, and VAL tests at R = 0.1 with 30% overloads every 100 cycles. Palacos R specimens were tested with and without overloads every 100 cycles and with a simplified load spectrum representing daily activities. The R- ratio had a pronounced effect on crack propagation in PMMA consistent with the effects of slow crack growth under constant load. Single overloads caused pronounced crack retardation, especially at low da/dN. In Palacos R, similar overloads had little effect, whilst individual overloads at low da/dN caused pronounced acceleration and spectrum loading retarded crack growth relative to Paris Law predictions. These results demonstrate that VAL can have dramatic effects on crack growth, which should be considered when testing bone cements.     

Singular stress and electric fields of a piezoelectric ceramic strip with a finite crack under longitudinal shear

Summary Following the theory of linear piezoelectricity, we consider the problem of determining the singular stress and electric fields in an orthotropic piezoelectric ceramic strip containing a Griffith crack under longitudinal shear. The crack is situated symmetrically and oriented in a direction parallel to the edges of the strip. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate for piezoelectric ceramics are obtained, and the results are graphed to display the influence of the electric field.