Temperature fields near a running crack tip

Near a running crack tip, the plastic work rate is high. According to the theory of irreversible thermodynamics, the plastic work will be almost completely converted into heat which may lead to high temperature rise at the running crack tip. The plastic zone is regarded as the zone of the heat source, and the plastic work rate as the strength of the heat source. In this paper, the plastic work rate is derived from the solution of stress and strain fields obtained by Chitaley and McClintock[1] for a steady state crack growth under anti-plane shear in an elastic perfectly-plastic material. The dependence of the thermal conductivity on temperature has been considered and a non-linear model for temperature fields has been proposed. The numerical results for glass have been given and compared with other papers.     

Nonlocal elastic damage near crack tip

A constitutive modeling for nonlocal elastic damage near crack tip is proposed. A calculation method for nonlocal elastic damage is introduced and the computational results for stress and damage are given by means of finite element method.     

Microscale characterization of granular deformation near a crack tip

This paper presents a study of microscale plastic deformation at the crack tip and the effect of microstructure feature on the local deformation of aluminum specimen during fracture test. Three-point bending test of aluminum specimen was conducted inside a scanning electron microscopy (SEM) imaging system. The crack tip deformation was measured in situ utilizing SEM imaging capabilities and the digital image correlation (DIC) full-field deformation measurement technique. The microstructure feature at the crack tip was examined to understand its effect on the local deformation fields. Microscale pattern that was suitable for the DIC technique was generated on the specimen surface using sputter coating through a copper mesh before the fracture test. A series of SEM images of the specimen surface were acquired using in situ backscattered electronic imaging (BEI) mode during the test. The DIC technique was then applied to these SEM images to calculate the full-field deformation around the crack tip. The grain orientation map at the same location was obtained from electron backscattered diffraction (EBSD), which was superimposed on a DIC strain map to study the relationship between the microstructure feature and the evolution of plastic deformation at the crack tip. This approach enables to track the initiation and evolution of plastic deformation in grains adjacent to the crack tip. Furthermore, bifurcation of the crack due to intragranular and intergranular crack growth was observed. There was also localization of strain along a grain boundary ahead of and parallel to the crack after the maximum load was reached, which was a characteristic of Dugdale–Barenblatt strip-yield zone. Thus, it appears that there is a mixture of effects in the fracture process zone at the crack tip where the weaker aspects of the grain boundary controls the growth of the crack and the more ductile aspects of the grains themselves dissipate the energy and the corresponding strain level available for these processes through plastic work.     

Stress and plane strain fields at the tip of a stationary tensile crack in a creeping material

Approximate steady state stress and strain fields are determined at the tip of a crack in an elastic perfectly-plastic creeping material by matching the far distant creeping field with the Prandtl punch solution. A new path-independent contour integral is formulated and expressions are derived for the size of the plastic regions, the crack opening displacement rate and the transient time.

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Résumé On détermine less champs approximatifs de contrainte et de déformation en état stable à l'extrémité d'une fissure dans un matériau élastique en cours de fluage parfaitement plastique en appliquant la solution ponctuelle de prandtl au champ de déformation par fluage suffisamment lointain de l'extrémité de la fissure. On formule une nouvelle intégrale de contours indépendante du chemin parcouru et on dérive des expressions de la dimension des régions plastiques de l'accroissement du déplacement d'ouverture de la fissure ainsi que de la durée de la période de transition pour atteindre une dimension stable.

     

Stress distribution near a crack tip in an anisotropic plate

The anisotropy of elastic properties of various materials was analyzed and its influence on the stress field near a crack tip under plane stress conditions was investigated. It was shown that this influence is substantial only in the case of sharply pronounced anisotropy.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 5, No. 6, pp. 714–719, November–December, 1969.     

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.     

Dynamic fields near a crack tip growing in an elastic-perfectly-plastic solid

A complete asymptotic solution is given for the fields in the neighborhood of the tip of a steadily advancing crack in an incompressible elastic-perfectly-plastic solid.For Mode I crack growth in the plane strain condition, the following noteworthy results are revealed: (1) The entire crack tip in steady crack growth is surrounded by a plastic region, and no elastic unloading is predicted by the complete dynamic asymptotic solution. Thus, the elastic unloading region predicted by the result of neglecting the important influence of the inertia terms in the equations of motion. (2) Unlike the quasi-static solution, the dynamic solution yields strain fields with a logarithmic singularity everywhere near the crack tip. (3) The stress field varies throughout the entire crack tip neighborhood, but does display behavior which can be approximated by a constant field followed by an essentially centered-fan field and then by another constant field, especially for small crack growth speeds. Indeed, the stress field reduces to that for the stationary crack, as the crack tip velocity - measured by the Mach number, M - reduces to zero; the strain field, however, does not reduce to that for the static solution, as M vanishes. (4) There are two shock fronts emanating from the crack tip across which certain stress and strain components undergo jump discontinuities. The location of the shock fronts and the magnitude of the jumps depend on the crack growth speed. The stress jump vanishes while the strain jump becomes unbounded, as the crack tip speed goes to zero.Finally, the Mode III steady-state crack growth is reviewed and, on the basis of Mode I and Mode III results, it is concluded that ductile fracture criteria for nonstationary cracks must be based on solutions which include the inertia effects, and that for this purpose, quasi-static solutions may be inadequate. Then, a possible ductile fracture criterion is suggested and discussed.One interesting feature of the complete dynamic asymptotic solution is that, unlike the quasi-static solution, it yields the same strain singularity for all three fracture modes.     

Creep crack growth modeling and near tip stress fields

The problem of near tip stress fields in a cracked body subjected to Mode I loading at elevated temperatures is studied. Specifically, the superalloy, IN 718, is examined in the standard compact tension specimen geometry. The simulation is at 650°C. The specimen is assumed to be under dead load conditions. For a stationary crack, the near tip stress fields are calculated and compared with the asymptotic solutions available in the literature. While the results assuming small strains agree very well with the asymptotic solutions, the large strain analysis does not. The results indicate that both the amplitude and the asymptotic exponent are dependent on the applied load level which is in disagreement with the asymptotic predictions. In addition, the zone effected by creep deformation is larger when large strains are considered. An algorithm is developed and tested for the modeling of stable crack growth. Both convergence and stability are investigated. Explicit time integration is used for crack growth studies as it is demonstrated to be computationally more efficient. The algorithm is employed to study the near tip stress fields for a growing crack. The near tip stress fields for a growing crack (with constant velocity) are generated using the developed algorithm. The results demonstrate that the asymptotic behavior of the stress field is load dependent. Comparison is made with the limited analyses available. Recommendations for future research are discussed.     

Large deformation near the tip of a transverse crack in bimaterial infinite sheet

Large deformation near the tip of a transverse crack in bimaterial infinite sheet     

A tensile crack in creeping solids with large damage near the crack tip

An asymptotic analysis of stationary mode I crack in creeping solids with large damage near crack tip is conducted. To consider the damage effect, Kachanov damage evolution law is utilized and incorporated into the power-law creep constitutive equation. With the compatibility equation, a nonlinear eigenvalue problem which can be solved by numerical approaches is established. From this result, the distribution of stress and strain rate are obtained with the coupling effect of damage and creep under plane stress condition. Also the influence of material parameters on the stress is examined. According to the result, it is shown that the creep exponent n and damage parameter (=/(1+k)) have a significant effect on determining the eigenvalue s and angular distribution of stress and strain rate near the crack tip. The creep exponent n plays the role to soften and damage parameter plays the role to harden the material near the crack tip. The stress and strain rate show quite different behavior from those of HRR problem.     

On the dependence of the dynamic crack tip temperature fields in metals upon crack tip velocity and material parameters

Although various approximations have been used to analytically predict the temperature rise at a dynamic crack tip and its relation to the crack tip velocity or the material properties, few experimental investigations of these effects exist. Here, the method of using a high speed infrared detector array to measure the temperature distribution at the tip of a dynamically propagating crack tip is outlined, and the results from a number of experiments on different metal alloys are reviewed. First the effect of crack tip velocity in 4340 steel is investigated, and it is seen that the maximum temperature increases with increasing velocity, the maximum plastic work rate density increases with velocity and the active plastic zone size decreases with increasing velocity. Also, it is observed that a significant change in the geometry of the temperature distribution occurs at higher velocities in steel due to the opening of the crack faces behind the crack tip. Next, the effect of thermal properties is examined, and it is seen that, due to adiabatic conditions at the crack tip, changes in thermal conductivity do not significantly affect the temperature field. Changes in density and heat capacity (as well as material dynamic fracture toughness) are more likely to produce significant differences in temperature than changes in thermal conductivity. Finally, the effect of heat upon the crack tip deformation is reviewed, and it is seen that the generation of heat at the crack tip in steel leads to the localization of deformation in the shear lip. The shear lip is actualy an adiabatic shear band formed at 45° to the surface of the specimen. In titanium, no conclusive evidence of shear localization in the shear lip is seen.     

Near tip damage and subcritical crack growth in a participate composite material

In this study, pre-cracked sheet specimens were used to conduct constant displacement rate crack propagation tests at room temperature. The effects of microstructure on damage accumulation and fracture processes near the crack tip and crack growth behavior were investigated and the results are discussed.     

Characterization of near tip stress and deformation fields in creeping solids

Finite element solutions for near tip stress and deformation fields in elastic-power law creeping solids are used to investigate the dominance of the asymptotic crack tip fields. With geometry changes neglected, the full range from small scale to extensive creep is analyzed. A full finite deformation analysis is carried out under small scale creep conditions. Our analyses show that, in the transient regime, Hutchinson-Rice-Rosengren type singular fields dominate over a region that is about one fifth the extent of the creep zone. Finite deformation effects are found to dominate over a size scale of the order of the crack tip opening as is the case for rate independent solids. Our numerical results for the time dependence of the amplitude of near tip fields are in good agreement with the approximate relation given by Riedel and Rice [7] and Ohji, Ogura and Kubo [5].

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Résumé Pour l'étude de la prépondérance des champs asymptotiques à l'extrémité d'une fissure, on recourt à des solutions par éléments finis relatifs aux champs de contraintes et de déformation au voisinage de cette extrémité, pour des solides soumis à fluage selon une loi élastique. En négligeant les modifications géométriques, on analyse l'entièreté de l'échelle du fluage et l'on montre que, en régime transitoire, il y a prépondérance d'un champ singulier de type Hutchinson-Rice-Rosengren sur une étendue de l'ordre du cinquième de la zone de fluage. On trouve que les effets de déformation finie sont déterminants à une échelle de dimension de l'ordre de l'ouverture de l'extrémité de la fissure, comme c'est le cas des solides dont le comportement mécanique est indépendant de la vitesse. On montre que les résultats numériques relatifs à la dépendance de l'amplitude des champs au voisinage de l'extrémité de la fissure en fonction du temps sont en bon accord avec les relations approchées obtenues par Riedel et Rice d'une part, et Ohji, Ogura et Kubo d'autre part.

     

Stress relaxation around the tip of an open crack in a metallic material

The paper deals with a previously proposed criterion for the occurrence of yield bands, which is based on determining the state of strain from linear elasticity theory.Translated from Problemy Prochnosti, No. 3, pp. 37–43, March, 1994.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Stress and strain fields at the tip of a sharp V-notch in a power-hardening material

The stress and strain fields at the tip of a sharp V-notch in a power hardening material are researched in this paper. It is found that the singularity of strain energy density at the tip is first slightly decreased and then increased when the hardening exponent n increases if the notch angle is not too large. It is also found that the singularity of strain energy density at the tip is nearly the same when n 40 and 45° for fixed . The analytical formula of the strain field at the tip for an ideal plastic material is found. The difference in the distribution of circumferential stresses for various n isn't large when the notch angle 2 is fixed; but the distribution of the radial stresses _r for different n is significantly different.

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Résumé On cherche à établir les champs de contrainte et de déformation à l'extrémité d'une entaille V aiguë dans un matériau sensible à l'écrouissage. On trouve que la singularité de la densité de la densité d'énergie de déformation en cet endroit commence par décroître légèrement, puis s'accroît lorsque croît le module d'écrouissage n, pour autant que l'angle de la fissure ne soit pas trop grand. On trouve également que cette singularité de la densité d'énergie de déformation est sensiblement la même lorsque n < 40 et < 45°. On trouve une formule analytique pour le champ de déformation à l'endroit étudié dans le cas d'un matériauidéalement plastique. Lorsque l'angle 2 est fixé, la différence de distribution des contraintes circonférentielle correspondant á diverses valeurs de n n'est pas grande.Toutefois, cette différence est significative pour la distribution des contraintes radiales _r.

     

Evaluation of crack tip stress and strain fields under nonproportional loading in a viscoelastic material

The crack tip strain and stress fields in a viscoelastic material under nonproportional loading conditions are evaluated. In order to evaluate the strain field, the crack tip displacement field is measured by using the digital image correlation (DIC) technique. This displacement field is then approximated by using the theoretically obtained crack tip displacement field in viscoelastic materials. The result shows that the approximation method can smoothly reconstruct the experimentally obtained displacement field. From the approximated displacement field, the crack tip strain field can be precisely obtained by using the differential form of the theoretical displacement. On the other hand, the crack tip stress field is analyzed by using the stress function. This suggests that the strain and stress fields can be independently evaluated. In addition, different time dependencies between stress and strain fields near the crack tip are observed. Based on this experiment, we can discuss the several criteria for the crack propagation directions in viscoelastic materials.     

Fatigue crack propagation and cyclic deformation at a crack tip

The fatigue crack propagation relation da/dN = f(R)ΔK² can be derived with three assumptions: small scale yielding, material homogeneity and that crack tip stresses and strains are not strongly affected by plate thickness. f(R) is a constant at a given stress ratio, R. The effects of plate thickness and stress ratio on crack tip deformation and fatigue crack growth in 2024-T351 aluminum alloy were studied. High ΔK level in a thin specimen causes crack tip necking. Necking is more pronounced at high stress ratio. Necking causes high maximum strain near a crack tip, ε_max, and fast crack growth rate. In order to avoid the effects of crack tip necking, plates thicker than 2.5 (ΔK/σ_Y(c))² should be used.