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.

     

Instability of plastic flow in mild steel

Plastic flow localization in the yielding of mild steel is theoretically studied in terms of the instability of the uniform mode of yielding. The instability is judged by the small perturbation theory in which the development of non-uniform modes superimposed upon the basic uniform mode is examined. The constitutive equation of rate-dependent type and the criterion of yield initiation at the plastic-zone front are employed as the constitutive relations of mild steel. The results of the analysis show the relation between the instability and the characteristic nature of mild steel.     

The form of crack tip plastic zones

The “radius” of the plastic zone at a crack tip is a parameter that has numerous applications in fracture mechanics. However, attention is drawn here to the confusion that is apparent, even in text-books, concerning the calculation of the plastic zone “radius” under plane strain conditions. The aim of this work has been to resolve this point, to determine the actual shape and size of the zone and to investigate the influence of stress state and other factors.The plastic zone dimensions have been simply calculated, over a range of values of Poisson's ratio, for isotropic materials subjected to loading under plane stress and plane strain conditions; the analysis has been further extended to cover some effects of anisotropy. It has been demonstrated that, for isotropic materials, the maximum extent of the plastic zone directly ahead of, and in the plane of, a crack is ($\text{K}{}_{\mathrm{I}}\text{/Y)}{}^2\text{18π}$ under plane stress loading and is ($\text{K}{}_{\mathrm{I}}\text{/Y)}{}^2\text{18π}$ under plane strain loading. This latter result is smaller, by a factor of $\text{1}\text{3}$ than the plastic zone “radius” under plane strain conditions that is widely quoted in fracture mechanics texts. That “radius”, ($\text{K}{}_{\mathrm{I}}\text{/Y)}{}^2\text{6π}$ is, in fact, the maximum size of the zone parallel to, but not in, the plane of the crack, if Poisson's ratio is taken to be $\text{1}\text{3}$.A lower value of Poisson's ratio or an increased material anisotropy can lead to an enlarged plastic zone; this latter conclusion suggests that test-pieces for valid fracture toughness measurements on anisotropic materials could be required to be larger than defined in the relevant British Standard.     

An experimental study on the cyclic crack resistance of steel 20

The crack resistances of 10 and 20 mm thick compact samples of steel 20 are presented. The amount of plastic deformation which occurs at both the cyclic elastoplastic and quasistatic stages are taken into consideration.Translated from Problemy Prochnosti, No. 6, pp. 34–38, June, 1990.     

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.     

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.     

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.     

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.     

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.     

A numerical and experimental study of crack tip shielding in presence of overloads

The mechanism underlying plasticity-induced shielding of a crack tip under fatigue loading has been already experimentally investigated by means of photoelasticity using a recently-developed mathematical model which considers stress field near the crack tip and along the flanks. Stress intensification factors have also been defined to describe shielding effects on the applied elastic field. In this paper a new application of this model is developed through a numerical simulation of the experimental tests, which were previously performed.The study is aimed to analyze the shielding effect related to constant amplitude cycling loading and a single overload peak, considering numerical simulation. By means of the models developed by XFEM technique, the plastic region is reproduced finding a good agreement with the experimental data, and a systematic procedure is proposed to evaluate the stress intensity factors.A good correspondence is found by comparing the numerical with the experimental parameters, obtained from the mathematical model.     

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.     

Structure of the plastic zone at the crack tip and the endurance of steel during low-cycle loading

From microhardness, metallographic, and also layered and sight x-ray analyses, the mechanisms controlling changes in the phase composition, structure, and size of the plastic zone at the crack tip during low-cycle loading of steels 12Kh18N10T and Kh11N10M2T have been established. These steels had various initial structures due to directional changes in their strength and ductility. It was shown that with increase in the maximum uniform elongation, there is an increase in the amount of intense structural changes in the plastic zone, an increase in the number of load cycles to failure, and a decrease in the rate of stable crack growth. These mechanical effects can be explained by the positive influence of the martensitic transformation and of dislocation mobility on the energy intensity of failure activation in the plastic zone. In particular, dislocation mobility leads to a partial relaxation of microdistortion in the crystallographic lattice of the matrix phase.Translated from Problemy Prochnosti, No. 8, pp. 23–31, August, 1993.     

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.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.     

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.     

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.