Numerical simulation of stress-strain state near crack tip in a compact tensile specimen

A computational scheme has been developed and a numerical simulation of the stress-strain state near the crack tip is performed at different levels of the stress intensity factor using a compact tensile specimen as an example. The authors analyze the influence of the finite element size near the crack tip and compare the results obtained in different codes (software packages) for different crack geometries. __________ Translated from Problemy Prochnosti, No. 1, pp. 134–140, January–February, 2009.     

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.     

Effect of a variation in material properties on the crack tip opening displacement

This paper investigates the effect of a variation in material properties on the crack tip opening displacement, a parameter often used in the prediction of fatigue and fracture. This situation is typical when a component is subjected to a relatively slow temperature fluctuation or the material properties undergo direct changes, such as due to a phase transformation. An analytical strip‐yield model is developed using the small‐scale yielding assumption and theory of complex potentials. Four cases of crack tip plasticity behaviour are identified for the different combinations of parameters controlling the variation in material properties. Results of calculations over a wide range of material properties are presented and show a significant effect on the crack tip opening displacement. Finite element simulations are conducted to verify the analytical findings. The implications of the outcomes in relation to several practical situations are also discussed.     

An integral associated with the state of a crack tip in a non-elastic material

An integral has been proposed for a non-elastic material whose value is determined by the magnitude of the singularities at the tip of a crack but which may be evaluated mainly far away from the crack, where the state of deformation may be determined numerically with higher accuracy than near the crack. The integral is intended for situations when plasticity is too great for linear elastic fracture mechanics to be appropriate, but may be related to the stress intensity factors in the linear elastic case. Its value has been calculated for a central or edge crack in a uniformly loaded and unloaded plate with a non-work-hardening elastic plastic material when the loading is either tension or longitudinal shear. It has also been calculated for a non-work-hardening material for a central sloping crack under tension and for a central crack under a quadratic temperature gradient for which previously suggested contour integrals are no longer path independent even in the linear elastic case.

---

Résumé On propose une intégrale, applicable à un matériau non élastique, dont la valeur est déterminée par la grandeur des singularités à la pointe d'une fissure, mais dont l'évaluation peut être faite en grande partie assez loin de la fissure, c'est-à-dire en une zône où l'état de déformation peut être établi par voie numérique avec une précision meilleure qu'au voisinage de la fissure. Cette intégrale est d'application lorsqu'il se trouve que la plasticité est trop importante pour que soit applicable la mécanique de la rupture linéaire et élastique, et où elle peut cependant être associée aux facteurs d'intensité des contraintes correspondant au cas linéaire et élastique.On a calculé sa valeur pour une fissure centrale ou latérale située dans une plaque soumise à chargement ou à déchargement uniforme-il s'agit de tension ou de cisaillement longitudinal-constituée d'un matériau élastique plastique non sujet à l'écrouissage.On a également considéré le calcul d'un tel matériau comportant une fissure inclinée par rapport à la direction des efforts, ou comportant une fissure centrale soumise à un gradient quadratique de températures, cas pour lesquels les intégrales de contour qui avaient été précédemment suggérées s'avérent ne plus être indépendantes du chemin parcouru, même en conditions élastiques.

     

Room-temperature creep behavior on crack tip of commercially pure titanium

The room-temperature creep behavior on crack tip of compact tensile (CT) specimen for commercially pure titanium (CP-Ti) was studied by experiment and finite element (FE) simulation in this paper. The experimental results indicated that the time-dependent deformation was observed on the crack tip of CP-Ti CT specimen at room temperature, which agreed with the primary creep, and crack propagation was not observed. In order to consider the creep behavior on crack tip, time-dependent J-integral was used to characterize the stress fields near crack tip. The room-temperature creep behavior on crack tip was analyzed by FE simulation, which was verified by experimental results. Then, the strain fields under different stress states were analyzed by FE simulation. The influences of the locations to crack tip and load on the room-temperature creep were analyzed, which shows that the creep significance on crack tip is enhanced with increasing of load and decreasing of distance to crack tip. The estimation formula of creep strain value along ligament direction of CP-Ti CT specimen was established and verified by FE simulation results.     

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.     

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.     

Stress, deformation and damage fields near the tip of a crack in a damaged nonlinear material

The stress, strain, displacement and damage fields near the tip of a crack in a power-law hardening material with continuous damage formation under antiplane longitudinal shear loading are investigated analytically. The interaction between a major crack and distributed microscopic damage is considered by describing the effect of damage in terms of a damage variable D. A deformation plasticity theory coupled with damage and a damage evolution law are formulated. A hodograph transformation is employed to determine the singularity and angular distribution of the crack-tip quantities. Consequently, analytical solutions for the antiplane shear crack-tip fields are obtained. Effects of the hardening exponent n and the damage exponent m on the crack-tip fields are discussed. It is found that the present crack-tip stress and strain solutions for damaged nonlinear material are similar to the well-known HRR fields for virgin materials. However, damage leads to a weaker singularity of stress, and to a stronger singularity of strain compared to that for virgin materials, respectively. The stress associated with damage always falls below the HRR field for virgin material; but the distribution of strain associated with damage lies slightly above the HRR field for r/(J/0) > 1.5 while the difference becomes negligible when r/(J/0) > 2. The limiting distributions of stress and strain may indeed be given by the HRR field.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

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.     

Model of fatigue crack propagation by damage accumulation at the crack tip

Modelling fatigue crack propagation by damage accumulation at the crack tip originally proposed by McClintock is reworked out using metallurgical considerations. On a physical basis it is shown that the validity of such models is actually confined to the low crack growth rate range corresponding to stage I growth such as along crystallographic planes. At higher crack growth rates there is a transition to plastic stretching mechanisms which could be described by crack opening displacement models. An evaluation of two models has been carried out on a ³³Co Ni alloy where extensive information was available: both are based on the strain singularity as computed by Tracey from a finite element analysis of plane strain small scale yielding and as adapted to cyclic loading under Rice's hypothesis and taking the grain as the critical element below which size continuum mechanics do no longer apply. It is pointed out that the use of this strain singularity which is not able to account for crack closure, renders models unable to predict experimental crack growth rates curves but only intrinsic curves relating the growth rate to the effective stress intensity amplitude as defined by Elber. The first model which assumes fatal cracking of a grain with an average uniform cyclic equivalent strain, underestimates the crack growth rates and in addition it yields results very sensitive to the shape and size of the grain. The second model which assumes progressive cracking in a grain with a cyclic equivalent strain gradient is able to predict the intrinsic crack growth rate curve in the ³³Co Ni alloy and to yield predictions consistent with other experimental data.     

X-ray method of evaluating local state of stress of material at crack tip in one-time loading

The article deals with the fractographic traits of failure and the regularities of the formation of zones of plastic deformaton in materials with bcc lattice (steels 20, 40, 45, St. 3, 15Kh2MFA) and with fee lattice (alloy D16 and the austenitic steels 40G18F, 40Kh4G18F, 03Khl3AG19) under different kinds of one-time loading: static, impact, high-speed impulsive. It is shown that the local state of stress of the material at the crack tip with all the mentioned kinds of loading can be evaluated by the single criterion h_max/t (the ratio of the maximal depth of the zone of plastic deformation under the fracture surface to the thickness of the specimen). Three regions of local state of stress are identified: h_max/t < 10^–2 close to plane strain (PD), h_max/t > 10^–1 close to plane stress (PD), and 10^–2 < h_max/t < 10^–1 the transient region from PD to PS. In static crack resistance tests of materials the known criterion t(k/_0.2)² 2.5 separates PS from the transient region in materials with fee lattice, and in materials with bcc the transient region from PD. In materials not undergoing phase transformations at failure, the correlation of the criterion h^max/t and the ratio /₀ is described by a single curve, independently of the form of loading. In regions close to PD and PS the ratio /₀ can be used for evaluating the local state of stress of the material at the crack tip.Translated from Problemy Prochnosti, No. 11, pp. 25–32, November, 1991.     

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.     

A damage model for creep crack growth

A model is developed for damage produced by the growth of isolated grain boundary cavities under power law creep. This damage model is combined with the small scale yielding stress and strain fields to predict the damage ahead of a stationary and a steadily propagating crack tip in an elastic-power law creeping material. A failure criterion, based upon the damage ahead of the crack tip attaining a critical value, is invoked. This criterion leads to predictions for the incubation time prior to initiation of crack growth and for the relationship between the remote stress intensity factor and the steady state crack speed. Results are presented for both elastic-primary and -secondary creep crack growth. In either case, there exists a minimum stress intensity factor below which steady state crack growth is not possible. Comparisons of the predictions of this model with others for steady state crack propagation in elastic-secondary creeping materials are also made.

---

Résumé On développe un modèle décrivant le dommage produit par la croissance de cavités isolées aux frontières des grains sous l'effet d'un fluage selon une loi parabolique. Ce modèle d'endommagement est combiné aux champs de contrainte et de déformation conduisant à une plastification à petite échelle, en vue de prédire le dommage qui se produit en avant de l'extrémité d'une fissure stationaire et en propagation lente, dans un matériau soumis à fluage selon une loi élastique. On invoque un critère de rupture basé sur la valeur critique atteinte par le dommage en avant de l'extrémité de la fisure. Ce critère conduit à prédire le temps d'incubation avant amorçage de la croissance d'une fissure, ainsi que la relation entre le facteur d'intensité des contraintes appliquées à une certaine distance et la vitesse de croissance stable de la fissure.On présente les résultats dans les cas de croissance d'une fissure de fluage au stade secondaire. Dans les deux cas, il existe un facteur d'intensité de contrainte minimum en dessous duquel une croissance stable de la fissure n'est pas possible. On procède également à des comparaisons des prédictions données par ce modèle avec d'autres, pour la propagation en état stable d'une fissure dans des matériaux soumis à fluage secondaire élastique.

     

Mechanism and stages of the electrochemical dissolution of metals in the vicinity of the crack tip

We study the behavior and stages of electrochemical processes in the vicinity of the tip of a statically loaded nonpropagating corrosion crack in 20 steel. By using voltammetric methods, we showed that the initial stage of the process of electrochemical dissolution of the metal (immediately after the appearance of a corrosive medium in the crack) is controlled by oxygen depolarization and proceeds with the assistance of OH^– ions. In the course of time, the process becomes autocatalytic and the principal role is played by Fe^2– ions.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 3, pp. 57–62, May – June, 1995.