The distribution of strain within crack tip plastic zones

Strains ahead of cracks both growing due to cyclic loading and loaded only in tension, as experimentally determined using the stereoimaging technique, have been used to derive equations for the strain distribution. Both logarithmic and power function relations were fitted to the strains and the logarithmic function was found to be the best fit to most data. Materials examined were 7075 and 7091 aluminum alloys, Ti-6Al-4V titanium alloy and austenitic 304 stainless steel.     

Fatigue crack tip plastic zones in low carbon steel

Microscopic plastic zone parameters at the tips of fatigue cracks in low carbon steel, as derived by the X-ray microbeam technique, have been correlated with measurement of some of the same parameters by the electron channeling contrast technique. Good correlation has been obtained for the parameters common to both techniques. The results for low carbon steel are found to correlate well with fatigue crack plasticity in other metals.

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Résumé On met en corrélation les paramètres de la microdéformation plastique à l'extrémité des fissures de fatigue dans l'acier doux, tels qu'ils se déduisent d'une technique de microbombardement par des rayons X, et la mesure de certains de ces paramètres par une technique d'émission électronique à contraste renforcé.Une bonne corrélation a été obtenue pour les paramètres qui sont communs aux deux techniques et les résultats pour l'acier doux sont en corrélation satisfaisante avec les caractéristiques de plasticité des fissures de fatigue dans d'autres métaux.

     

The configuration of moving crack tip zones

The dynamic elasticity solution of a steady state crack is used for determination of the geometrical characteristics and of the displacement rates within the discrete crack zones which are formed as a result of the selective propagation of cleavage microcracks ahead of the tip of a running brittle crack in a mild steel plate. The zone length and the stress distribution in the zone are found to be strongly dependent on the assumed form of the stress-displacement relation for the progressively fracturing metal. On the other hand, the crack opening displacement rate is much less sensitive to the assumed form. The magnitudes of the nominal plastic strain rates, found by an approximate procedure, are of the order of 10⁵ to 10⁶ sec^?1. A comparison with the results of dynamic tension tests on similar steels indicates that the flow stress at these strain rates would exceed the twinning stress, and therefore, it is suggested in agreement with experimental observations, that twinning is the principal deformation mode in the crack zone. Accordingly, the crack tip boundary conditions considered in the solution of crack propagation problems can be assumed as independent of crack velocity. Also, their possible dependence on temperature would not be related to the deformation mode in the crack zone.     

The effect of tip plastic energy on mixed-mode crack initiation

An approach to the fracture initiation prediction of a ductile crack with mixed-mode loading (mode I and II) conditions is presented. The tip plastic energy around the crack tip is applied for evaluating the crack initiation load and the plastic zone shape. It is proposed that a mixed-mode crack will initiate as the tip plastic energy reaches a critical value. Numerical results for various loading conditions are illustrated. These results indicate that the predicted crack initiation loads correlate well with the experimental data available. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Tensile crack tip fields in elastic-ideally plastic crystals

Crack tip stress and deformation fields are analyzed for tensile-loaded ideally plastic crystals. The specific cases of (0 1 0) cracks growing in the [1 0 1] direction, and (1 0 1) cracks in the [0, 1, 0] direction, are considered for both fcc and bcc crystals which flow according to the critical resolved shear stress criterion. Stationary and quasistatically growing crack fields are considered. The analysis is asymptotic in character; complete elastic-plastic solutions have not been determined. The near-tip stress state is shown to be locally constant within angular sectors that are stressed to yield levels at a stationary crack tip, and to change discontinuously from sector to sector. Near tip deformations are not uniquely determined but fields involving shear displacement discontinuities at sector boundaries are required by the derived stress state. For the growing crack both stress and displacement must be fully continuous near the tip. An asymptotic solution is given that involves angular sectors at the tip that elastically unload from, and then reload to, a plastic state. The associated near-tip velocity field then has discontinuities of slip type at borders of the elastic sectors. The rays, emanating from the crack tip, on which discontinuities occur in the two types of solutions are found to lie either parallel or perpendicular to the family of slip plane traces that are stressed to yield levels by the local stresses. In the latter case the mode of concentrated shear along a ray of discontinuity is of kink type. Some consequences of this are discussed in terms of the dislocation generation and motion necessary to allow the flow predicted macroscopically.     

Transient effect on ideally plastic stationary crack tip fields

This paper analyses the transient effect on ideally plastic stationary crack tip fields under mode I plane strain conditions, when the inertial forces are not negligible. It is shown that the governing equation for such a problem can be expressed in formal simplicity when referred to a system of moving curvilinear coordinates, which is a generalization of the system defined by the slip-line field in quasi-static plasticity. A perturbation method of solving the equations is described and illustrated by application to problems of ideally plastic stationary crack tip fields when the inertial forces are not negligible.     

On the size of plastic zone ahead of crack tip

A method for the crack tip analysis of a tensile loaded crack (mode I) due to yielding of the material is developed. The stress/strain distribution within the plastic zone, as well as size of the plastic zone are presented. The development is based on the energy interpretation of the strain hardening exponent, and an analogy between mode III and mode I for the case of small scale yielding. Predictions of the proposed method are compared with the experimental results, and a fairly good agreement is observed. A number of proposed methods to estimate the plastic zone size for ductile materials are also discussed.     

Numerical simulations of crack tip fields in polycrystalline plastic solids

In this paper, modes I and II crack tip fields in polycrystalline plastic solids are studied under plane strain, small scale yielding conditions. Two different initial textures of an Al-Mg alloy, viz., continuous cast AA5754 sheets in the recrystallized and cold rolled conditions, are considered. The former is nearly-isotropic, while the latter displays distinct anisotropy. Finite element simulations are performed by employing crystal plasticity constitutive equations along with a Taylor-type homogenization as well as by using the Hill quadratic yield theory. It is found that significant texture evolution occurs close to the notch tip which profoundly influences the stress and plastic strain distributions. Also, the cold rolling texture gives rise to higher magnitude of plastic strain near the tip.     

Fatigue crack growth by crack tip cyclie plastic deformation: the unzipping model

A fatigue crack may propagate by the mechanism of crack tip cyclic plastic deformation, by the mechanism of fracture of brittle particles and embrittled grain boundaries,or, often, by a combination of both. Neutnann and Vehoff have made in situ observations of alternate shear decohhesions on two intersecting conjugate slip bands at a crack tip as the basic mechanism of fatigue crack growth. It is a mechanism by plastic deformation. A micro-mechanism based finite element model is made to simulate the unzipping process of the crack tip shear decohesion mechanism. The calculated crack growth rates by the finite element model agree very well with the measured rates in the intermediate K region of a number of materials

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Résumé La propagation d'une fissure de fatigue peut être due au mécanisme de déformation plastique cyclique de l'extrémité de la fissure, au mécanisme de rupture de portions fragiles et de frontières de grains fragilisées ou, souvent, à une combinaison de ces deux mécanismes.Neumann et Vehoff ont procédé à des observations in situ des décohésions par cisaillement alterné dans deux bandes de glissement s'intersectant à l'extrémité d'une fissure, et ont décrit ce mécanisme par déformation plastique comme un mécanisme de base de la propagation d'une fissure de fatigue.En vue de simuler le processus d'ouverture qui régit le mécanisme de décohésion par cisaillement à l'extrémité dame fissure, on élabore un modèle par éléments finis basé sur un mécanisme à échelle microscopique. On trouve que les vitesses de propagation d'une fissure calculées grâce à ce modèle par éléments finis sont en très bon accord lvee les vitesses mesurées dans la zone des K intermédiaries et pour plusieurs matériaux.

     

Analysis of crack growth rate based on rotation at the crack tip plastic zone

The crack growth rate of a line crack is obtained from a linear elastic analysis of work required in the formation of a crack tip plastic zone. Equations of crack growth rate are derived from rigid body rotation at the root of Dugdale's plastic zone. The proposed relations are used to study the fracture behaviour of materials in tension tests and the three point bending tests. This revised version was published online in August 2006 with corrections to the Cover Date.     

Plane stress dynamic plastic field near a propagating crack tip

In this paper the asymptotic solution to the plane stress dynamic plastic field surrounding a propagating crack tip is given. The perfectly plastic model and Mises yield condition as well as J₂ flow theory are adopted. The force of inertia is considered in the equations of motion. The asymptotic expansions of displacements, strains and stresses are given and solved for the dominant terms. The results show that strain possesses ln (A/r) singularity at the crack tip. Finally, the stress distribution surrounding the crack tip are given numerically.

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Résumé On fournit dans cette étude une solution asymptotique pour le champ de déformations pastiques dynamiques sous contraintes planes qui entoure l'extrémité d'une fissure au cours de sa propagation. On adopte comme hypothèse un modèle parfaitement plastique, la conditions de passage en plasticité de von Mises et la théore de l'écoulement J₂. Dans les équations de mouvement, on considère la force d'inertie. Les développements asymptotiques des déplacements, des déformations et des contraintes sont fournis et résolus pour leur termes principaux. Les résultats montrent qu'à l'extrémité d'une fissure, la déformation présente une singularité de caractère ln A/Y. Enfin, on fournit une expression numérique de la distribution des contraintes dans la zone enrobant l'extrémité de la fissure.

     

Asymptotic fields near the crack tip in elastic-perfectly plastic crystals

The basic equations of plane strain problem for the elastic-perfectly plastic crystals with double slip systems have been presented in the basis of three dimensional flow theory of crystal plasticity. Using these equations the stationary crack tip stress and deformation fields are analysed for tensile load. The fields involve an elastic angular sector and are fully continuous. An asymptotic solution is also obtained for the steadily growing crack that consists of five angular sectors: two plastic angular sectors in the front of the crack tip connected with the boundary on which the associated velocity field has discontinuities; a secondary plastic angular sector near the crack face; two elastically unload angular sectors connected with the boundary on which the discontinuity of the associated velocity field occurs. The asymptotoic solution is not unique. A family of solutions is obtained. Finally, the application of these solutions on both FCC and BCC crystals is discussed.     

Calculation of crack tip phase transformation zones with the weight function method

Stabilized Zirconia ceramics can undergo a stress-induced tetragonal-to-monoclinic phase transformation. This way, a transformation zone with compressive stresses develops around crack tips, leading to an increase in fracture toughness. The increase in fracture toughness depends on the size of the transformation zone. Therefore, the ability to compute the phase transformation zone at a crack tip is crucial to determine the transformation toughening due to phase transformation. In the case of subcritical phase transformation, the crack tip phase transformation zone has been calculated using the finite element method. In some Zirconia ceramics, such as ceria-stabilized TZP Zirconia ceramics, an autocatalytic phase transformation takes place, leading to large, elongated transformation zones. As this supercritical phase transformation cannot be computed with finite elements, several methods for investigating supercritical phase transformation have been developed. In this paper, a method based on the weight function method will be described.