Simulation of ductile crack growth in thin panels using the crack tip opening angle

The aim of this work is the assessment of the efficiency of the crack tip opening angle (CTOA) with respect to the transferability from one geometry to another, in particular the transferability obtained from Kahn tear tests to M(T) panels. The load-displacement behaviour recorded during a Kahn tear test was reproduced by means of finite element analysis using a variable CTOA as a function of crack length. The CTOA extracted from Kahn tests has then been used to simulate the R-curve of M(T) panels with different widths. Experiments and simulations were run first on a 6013-T6 aluminium alloy and then also on butt, friction stir welded butt joints of the same material.     

Fatigue crack growth in thin steel sheets

Surface fatigue crack growth is considered for thin steel sheets composed of two steels widely used in cryogenic engineering: 12Kh18N10T and 07Kh13N4AG20. Specimens with thicknesses of 4, 8, and 12 mm have been tested at 293 and 77 K (in liquid nitrogen). There is a boundary between the zones affected by the rear and front edges of the specimen in the plane of semielliptical crack growth, which affects the stress and strain patterns near the crack front. The boundary between the zones is approximated by a second-order curve. The thickness and the temperature affect the slope of the curve. The kinetic features are seen at points in the crack front at such boundaries.Translated from Problemy Prochnosti, No. 2, pp. 27–34, February, 1992.     

Determining the magnitude of crack tip opening in elastoplastic bodies

An analytic method has been developed for approximately determining the opening of a separation crack in three-dimensional bodies when the self-similitude conditions are not satisfied. This method is based on the assumption that the relation between the magnitudes of the crack openings obtained for a plane stressed state and for a plane strain is invariant with respect to the magnitude of the plastic zone at its tip. Thus the problem has been reduced to finding the opening within the framework of the _K-model, for whose determination an effective approach has also been proposed. Old and new problems were solved by this method, in particular the problems of stretching of a cylinder with a circular or annular crack, and also of a plate with a semielliptic surface crack.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 6, pp. 53–61, November–December, 1990.     

Large crack tip deformations and plastic crack advance during fatigue

Finite-deformation elastoplastic analysis of a crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip deformations is presented. Cyclic crack tip opening displacements agreed with predictions of simpler models, where available. Crack closure was not detected. Plastic crack advance was evidenced. Its rate per cycle reproduced common trends of the fatigue cracking dependence on loading range and overload.     

Methods for crack opening load and crack tip shielding determination: a review

In this paper a review of the literature on crack closure/opening load and crack tip shielding effects determination methods is presented. Commonly used ‘subjective’ (visual) and ‘non‐subjective’ approaches have been included. Procedures associated with the determination of an effective crack driving force for both Elber type and that of partial (or incremental) crack closure models have been covered. Comparison among different methods of analyses based on compliance and fatigue crack growth rate measurements is discussed together with their implications and difficulties in fatigue crack growth correlations.     

Comparison of methods for crack tip opening displacement toughness determination

The crack tip opening displacement (CTOD) initiation toughness has been obtained by different methods in Cr and Cr-Mo steels at 30, 200 and 400 C. The crack tip stretching and grain deformation has been investigated by scanning electron microscope and optical microscopic studies and by microhardness measurements. The resistance curve approach is used employing the average and the maximum crack growth and the initiation toughness determined are with respect to 0.2 mm crack growth ( ^0.2), the stretched zone width (SZW) and also using a blunting line approach. In addition, an initiation toughness using stretched zone depth (SZD) measurement is also obtained. The various initiation toughness values have been compared and an attempt has been made to identify the realistic plane strain CTOD toughness amongst the different values. The-CTOD relationship has also been investigated.     

The effect of shallow cracks on crack tip opening displacement

Further results given in the present paper confirm that shallow cracks have larger crack tip opening displacements at initiation than deep cracks. This difference in behaviour is shown to be principally caused by the different hydrostatic stresses existing at the tips of shallow and deep cracks. A new method based on lateral crack growth across the thickness is used in this work to measure crack tip opening displacements in specimens containing machined slots rather than fatigue pre-cracks. Justification and advantages of this method are discussed and compared to the conventional technique.     

The stereophotogrammetric determination of the critical crack tip opening displacement

The methods to determine the critical crack tip opening displacement (COD_i) are discussed. Stretched zone regions are analyzed using the method of stereophotogrammetry with the scanning electron microscope. The COD_i is determined on eight sections near the centre of the specimen. The scatter of the individual COD_i-values is surprisingly small.     

On the use of special crack tip elements in cracked elastic sheets

This paper presents a finite element method for determining the stress intensity factor in a cracked elastic sheet. Special cracked elements are placed around each crack tip; in each special element the stresses and displacements are derived from the exact stress function while the continuity of the displacements at the nodes is satisfied in a least square sense. A general procedure for evaluating the stiffness matrix of a cracked isotropic, or orthotropic, element is presented, and the numerical results obtained are compared with exact analytical results.

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Résumé Le mémoire présente une méthode par éléments finis pour déterminer le facteur d'intensité de contrainte dans un feuillard élastique fissuré. Des éléments spéciaux, présentant des fissures, sont disposés autour de chaque extrémité de fissures. Dans chacun de ces éléments spéciaux, les contraintes et les déplacements sont déduits de la fonction exacte d'une contrainte tandis que la continuité des déplacements aux noeuds satisfait à une règle des moindres carrés. Une procédure générale pour l'évaluation de la matrice de rigidité d'un élément fissuré à caractère isotrope ou orthotrope est présentée, et les résultats numériques obtenus sont comparés avec les résultats analytiques exacts.

     

Large strain field near an interface crack tip

In this paper the elastostatic field near the tip of an interface crack between two materials is analyzed with the fully nonlinear theory. By dividing the crack tip field into narrowing sectors and an expanding sector, the asymptotic equations for the crack tip field are derived and solved. The singular characters of stress and strain near the crack tip are revealed. The crack opening shape is discussed for various cases. It is shown that when large deformation is taken into account the oscillatory singularity does not occur.     

An assessment of various crack tip displacement based elastic-plastic fracture parameters to characterise ductile crack growth resistance

There is continuing interest in defining a fracture parameter which is capable of characterising the ductile crack growth resistance of a material under conditions of large scale plasticity. The aim of this study is to assess the capability of a number of elastic-plastic fracture parameters for the case of a C-Mn steel. The fracture parameters considered are: the crack opening displacement at the original crack tip (CTOD); the crack opening angle at the growing crack tip (CTOA); and the crack opening displacement at the growing crack tip (_a). The parameters were assessed by determining experimentally whether they were affected by changes in test specimen size and geometry in cases where there was no change in the crack tip constraint. Changes in the latter were assessed from changes in the CTOD at crack initiation (CTOD_i). Only _a was capable of characterising the crack growth resistance, as unlike both CTOD_i and _a, dCTOD/da and CTOA were dependent on specimen geometry.

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Résumé L'intérêt persiste à définir un paramètre de rupture capable de caractériser la résistance d'un matériau à la propagation ductile d'une fissure, dans des conditions de plastification à grande échelle. L'étude a pour objet d'établir la pertinence d'un certain nombre de paramètres élasto-plastiques relatifs à la rupture d'un acier CMn. On considère en particulier le déplacement d'ouverture de l'extrémité de la fissure initiale (CTOB), l'angle d'ouverture en cours de croissance de la fissure à son extrémité (CTOA) et le déplacement d'ouverture en cours de croissance de l'extrémité de la fissure (_a).L'analyse à porté sur la réaction expérimentale de ces paramètres à des changements de taille ou de géométrie d'éprouvettes, dans des cas où il ne se produisait pas de modifications des contraintes d'environnement à l'extrémité de la fissure. Lorsque celles-ci survenaient, le CTOD correspondant à l'amorçage (CTOD_i) y était sensible.II est apparu que seul _a pouvait caractériser la résistance à la croissance d'une fissure, dans la mesure où, á l'inverse du CTOD_i et du _a, le CTOA et la variation du CTOD en fonction de la longueur de la fissure sont dépendants de la géométrie de l'éprouvette.

     

An assessment of the crack tip opening displacement criterion for predicting creep crack growth

From a set of finite element (FE) simulations of creep crack growth in compact tension specimens, the critical value of the crack tip opening displacement, CTOD, for creep crack growth has been generated for a Ni-base superalloy (Waspaloy) at 700°C. It was found that the critical value is independent of the initial crack length, amount of previous creep crack growth and the load level. Hence, the CTOD seems likely to be a viable criterion for use in creep crack growth rate analysis. Good agreement was also obtained between the experimental test results and FE predictions of the creep crack growth with time and between the crack growth rate, da/dt, versus the C ^* parameter based on load-line displacement rate.     

The crack tip opening angle (CTOA) of the plane stress moving crack

Recently, Crack Tip Opening Angle (CTOA) was proposed by C.F. Shih et al. to describe the instability criterion of ductile crack propagation during plane strain (flat crack) conditions, and was derived by J. R. Rice analytically by means of the slip line field theory and the incremental theory of plasticity. CTOA appears to be applicable in (some or most) cases, but does not accurately describe the plane stress growing crack (slant crack).Unstable ductile crack propagation of the plane stress crack is widely studied for the safe design of highly pressurized gas pipelines. The impact absorption energy of the Charpy test is well correlated to the fracture arresting properties of the structures, but the mechanics of the fracture are not yet well established.In this paper, CTOA of the plane stress growing crack is derived from the plane stress plasticity of perfectly plastic materials by Sokolovsky's approach. Our proposed modification of CTOA expressed as follows: $\text{CTOA}\text{= (α/δ}{}_0\text{)(}\text{d}\text{J/}\text{d}\text{l) + β(δ}{}_0\text{/E)}\text{ln}\text{(eR/r)}$ where $\text{β = 1.40}$ under the plane stress conditions.CTOA in the Dugdale model is also defined and compared with the results of laboratory test. The results show that $\text{α = 0.5}$, and $\text{β = 1.27}$ for plane stress crack growth. These analyses give similar results to those obtained by Rice et al. for CTOA under plane strain conditions, that is, $\text{α = 0.65}$ from the experimental results and $\text{β = 5.08}$ from the slip line theory.The CTOA obtained for plane stress ductile crack growth is applied to the wide plate tensile crack growth test. The results of the present analysis coincide well with those of the plane stress finite element method (FEM) computed by T. Kanazawa et al. The phenomena of plane stress ductile crack propagation are also explained by the CTOA criterion under plane stress conditions.     

An elastic-plastic finite element analysis of crack tip fields under biaxial loading conditions

A square plate containing a central crack and subjected to biaxial stresses has been studied by a finite element analysis. An elastic analysis shows that the crack opening displacement and stress of separation ahead of the crack tip are not affected by the mode of biaxial loading and therefore the stress intensity factor adequately describes the crack tip states in an elastic continuum.

An elastic-plastic analysis involving more than localized yielding at the crack tip provides different solutions of crack tip stress fields and crack face displacements for the different modes of biaxial loading.

The equi-biaxial loading mode causes the greatest separation stress but the smallest plastic shear ear and crack displacement. The shear loading system induces the maximum size of shear ear and crack displacement but the smallest value of crack tip separation stress.

     

Determination of the asymptotic crack tip fields for a crack perpendicular to an interface between elastic-plastic materials

Summary The singular behavior near a crack tip at the interface between two power-law hardening materials with the crack perpendicular to the interface is studied for both Mode I and Mode II loading under either plane strain or plane stress conditions. The mathematical model developed can be expressed as a fourth order ordinary differential equation with homogeneous boundary condition. A shooting method is applied to obtain the eigenvalues and to solve the differential equation with homogeneous boundary conditions. When both materials have the same hardening exponent,N, another material parameter, , representing the relative resistance of two materials to plastic deformation, is introduced to reflect the joint effect of the two materials on the singularity. Results indicate that if both materials have the sameN, the singularity at the crack tip is reduced as increases; however, when becomes large there appears to be little change in the singularity for a fixedN. When the hardening exponents are not the same, the mathematical model assumes stress continuity across the interface. The results show that the order of the singularity depends largely on the softer material, with the largest stresses in the harder material.