Wedge crack nucleation in Type 316 stainless steel

Type 316 austenitic steel has been heat-treated to produce a range of grain sizes and then creep-tested at 625° C at various stresses so as to examine the nucleation and the factors which effect the nucleation of grain-boundary triple point or wedge cracks. An internal marker technique was used to evaluate the extent of the grain-boundary sliding in relation to the total creep strain. Triple point crack nucleation occurred over the entire range of grain sizes and stresses examined when the product of the stress and grain-boundary displacement reached a critical value; the effective surface energy for grain boundary fracture, estimated using an expression derived by Stroh, was in approximate agreement with the surface free energy value indicating that only limited relaxation occurred by plastic deformation. The first cracks were observed to form along grain boundary facets perpendicular to the applied stress direction and with the sliding grain boundaries at high angles (60 to 80°) to the crack growth direction. Subsequent cracking occurred under conditions which deviated slightly from this initial condition, and the increase in crack density with strain was expressed in terms of geometrical factors which take account of the orientation effects.     

Crack growth by grain boundary cavitation in the transient and extensive creep regimes

Crack growth due to cavity growth and coalescence along grain boundaries is analyzed under transient and extensive creep conditions in a compact tension specimen. Account is taken of the finite geometry changes accompanying crack tip blunting. The material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset and distributed on a given density of cavitating grain boundary facets. The evolution of the stress fields with crack growth under three load histories is described in some detail for a relatively ductile material. The full-field plane strain finite element calculations show the competing effects of stress relaxation due to constrained creep, diffusion and crack tip blunting, and of stress increase due to the instantaneous elastic response to crack growth. At very high crack growth rates the Hui-Riedel fields dominate the crack tip region. However, the high growth rates are not sustained for any length of time in the compact tension geometry analyzed. The region of dominance of the Hui-Riedel field shrinks rapidly so that the near-tip fields are controlled by the HRR-type field shortly after the onset of crack growth. Crack growth rates under various conditions of loading and spanning the range of times from small scale creep to extensive creep are obtained. We show that there is a strong similarity between crack growth history and the behaviour of the C(t) and C _t parameters, so that crack growth rates correlate rather well with C(t) and C _t .A relatively brittle material is also considered that has a very different near-tip stress field and crack growth history.Visiting Professor, Brown University, August 1988 through December 1989.     

Investigation of the crack growth behavior of Inconel 718 by high temperature Moiré interferometry

The effect of environment on creep crack growth behaviors of many nickel-base superalloys is a well-documented and serious problem. Stress accelerated grain boundary oxidation (SAGBO) is accepted as the prior mechanism of the environment effect. In this paper, the crack growth behavior of Inconel 718 was investigated by high temperature moiré interferometry (HTMI), coupled with SEM/EDAX. Based on the results obtained from this research, the mechanism is proposed to be caused by the segregated Nb, which couples with the oxygen diffusing into the grain boundaries in front of the crack tip and forms an NbO layer on the grain boundaries, thereby causing the brittle elastic cracking behavior.     

An elastic-plastic finite element analysis of a blunting interface crack with microvoid damage

A finite strain elastic-plastic finite element analysis is performed on a crack which lies on an interface between two dissimilar materials. The materials above and below the interface are assumed to be different from each other in yield stress or in strain-hardening exponent. Gurson's constitutive equation for porous plastic materials is used in order to take into account the effect of the microvoid nucleation and growth on the fields near the tip of a crack.It is found that the microvoids have larger effects on the crack tip blunting and stress fields for a bimaterial than for a homogeneous material. It is also found that the plastic strain and the microvoid volume fraction localize in a few narrow bands which grow into the softer material from the intersection of the interface and the blunted crack tip at inclinations of about 15° 45°.     

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.     

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.     

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.     

The effect of hold-time on fatigue crack growth behaviors of WASPALOY alloy at elevated temperature

The effect of hold-time on fatigue crack growth behaviors of WASPALOY alloy was investigated. It was found that the role of hold-time depends on the competition between the harmful environmental effect and the beneficial effect of creep. If temperature is not higher than 705 °C, fatigue crack growth rate of WASPALOY alloy increases with hold-time. On the contrary, hold-time plays a beneficial role on steady state fatigue crack growth of WASPALOY alloy at 760 °C and lower stress intensity factor. The beneficial effect of hold-time was attributed to the creep caused stress relaxation during the hold-time. However, accumulated creep damages cause to cavity nucleation and growth at the grain boundaries, and then accelerate fatigue crack growth. Hold-time plays a harmful role during the final stage of fatigue crack growth.     

Time-derivative equations for fatigue crack growth in metals

Predicting fatigue crack growth in metals remains a difficult task because available models are based on cycle-derivative equations, such as the Paris law, while service loads are often far from being cyclic. The main objective of this paper is therefore to propose a set of time-derivative equations for fatigue crack growth. The model is based on the thermodynamics of dissipative processes. For this purpose, three global state variables are introduced in order to characterize the state of the crackthe crack length a, the plastic blunting at crack tip and the intensity of crack opening C. Thermodynamics counterparts are introduced for each variable. Special attention is paid to the elastic energy stored inside the crack tip plastic zone, because, in practice, residual stresses at crack tip are known to considerably influence fatigue crack growth. The stored energy is included in the energy balance equation, and this leads to the appearance of a kinematics hardening term in the yield criterion for the cracked structure. No dissipation is associated with crack opening, but to crack growth and to crack tip blunting. Finally, the model consists in two laws: a crack propagation law, which is a relationship between d dt and da/dt and which observes the inequality stemmed from the second principle, and an elastic-plastic constitutive behaviour for the cracked structure, which provides d dt versus applied-load. The model was implemented and tested. It reproduces successfully the main features of fatigue crack growth as reported in the literature, such as the Paris law, the stress-ratio effect and the overload retardation effect.     

Grain boundary microstructure and fatigue crack growth in Allvac 718Plus superalloy

The correlation between grain boundary microstructure and fatigue crack growth with hold-times was investigated for two conditions of the superalloy Allvac 718Plus; a Standard condition with the recommended distribution of grain boundary phases and a Clean condition with virtually no grain boundary phases. Fatigue testing was performed at 704 °C using 10 Hz cyclic load with intermittent hold-times of 100 s at maximum tensile load. Microstructural characterization and fractography were conducted using scanning- and transmission electron microscopy techniques. Auger electron- and X-ray photoelectron spectroscopy techniques were used for oxide analyses on fracture surfaces. It was found that in the Standard condition crack growth is mostly transgranular for 10 Hz loading and intergranular for hold-times, while for the Clean condition crack growth is intergranular in both load modes. The lower hold-time crack growth rates in the Standard condition are attributed to grain boundary δ-phase precipitates. No effect of δ-phase was observed for 10 Hz cyclic loading crack growth rates. Two different types of oxides and oxide colours were found on the fracture surfaces in the Standard condition and could be correlated to the different loading modes. For cyclic loading a bright thin Cr-enriched oxide was dominate and for hold-times a dark and slightly thicker Nb-enriched oxide was dominant These oxide types could be related to the oxidation of δ-phase and the matrix respectively. The influence of δ-phase precipitates on crack propagation is discussed.     

Oxidation assisted fatigue crack growth under complex non-isothermal loading conditions in a nickel base superalloy

This paper deals with the prediction of fatigue crack growth at high temperatures in the N18 nickel base superalloy, which is employed by Snecma for turbine disc applications. This material and other nickel base superalloys were widely studied in the past under isothermal conditions and constant amplitude fatigue. Dwell time effects are observed which are attributed, in this material, to grain boundary oxidation. The main objective of this research is to use this knowledge to model the fatigue crack growth rate in the N18 nickel base superalloy when complex “missions” are encountered. This implies variable amplitude and non-isothermal loading conditions (450–650 °C). For this purpose, an incremental fatigue crack growth model which was originally developed for isothermal variable amplitude loading conditions was extended so as to be applicable to non-isothermal loading conditions. In addition, the incremental form of the fatigue crack growth law in this model is very useful to account for the coupling effect between fatigue and time-dependent phenomena such as creep or oxidation. In the present case, the effect of the environment was modelled as a competition between two phenomena: a detrimental effect of grain boundary oxidation ahead of the crack tip and a beneficial effect of the growth of a passivation layer of oxides on the freshly created crack surfaces. The model was used to simulate fatigue crack growth under complex cycles at high temperature and the comparisons with experimental results are satisfactory.     

Creep crack growth by grain boundary cavitation: crack tip fields and crack growth rates under transient conditions

Transient creep crack growth due to grain boundary cavitation, and under plane strain and small scale creep conditions, is investigated. Full account is taken of the finite geometry changes accompanying crack tip blunting and the material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset, distributed on a given density of cavitating grain boundary facets. Our analyses show the competing effects of stress relaxation due to creep, diffusion and crack tip blunting, and the stress increase due to crack growth. Another outcome of our analyses is the crack growth rate under various conditions of loading and for various values of material properties and for various characterizations of the failure process. Prior to crack growth, Hutchinson-Rice-Rosengren type singular fields dominate over the crack tip region, outside of a finite strain zone that has dimensions of the order of the crack opening displacement. These singular fields scale with the path integral C(t), which to a good approximation decays as K _I ²/t, with t being the elapsed time since load application and K _Ithe imposed stress intensity factor. When the crack growth rate is faster than the growth rate of the creep zone, our finite element results show that Hui-Riedel singular fields dominate over the crack tip region and the magnitude of the Hui-Riedel fields scales with the crack growth rate. For a crack that grows more slowly than the creep zone, Hutchinson-Rice-Rosengren type fields dominate over the crack tip region. In these circumstances, the crack growth rate is found to scale as C(t) to a power. Regardless of which of the two singular fields dominates for the growing crack, finite strain effects are found to be significant over a size scale of the order of the crack opening displacement at crack growth initiation. The effect of increased mesh refinement is also considered and very little mesh dependence is found.

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Résumé On étudie la croissance d'une fissure en fluage transitoire, associée à la cavitation aux frontières des grains, sous des conditions d'état plan de déformation et de fluage à petite échelle. On tient compte des modifications finies de géométrie accompagnant l'arrondisement de l'extrémité de la fissure, et le matériau suit une loi de fluage elasto-parabolique, avec une contribution additionnelle à la vitesse de fluage venant d'une densité donnée de facettes de joints de grains comportant de la cavitation. On suppose que toutes les cavités sont présentes dès le début, et qu'elles sont distribuées selon une densité déterminée de ces facettes. L'analyse montre les effets rivaux d'une relaxation des contraintes associée au fluage, à la diffusion et à l'arrondisement des extrémités de fissure, et d'une augmentation de contraintes due à la croissance de fissure. Un autre résultat de l'analyse est l'établissement de la vitesse de croissance de la fissure sous diverses conditions de mise en charge, pour diverses valeurs des propriétés du matériau, et pour divers modes de caractérisation du processus de rupture. Avant croissance de la fissure, ce sont des champs singuliers de type Hutchinson-Rice-Rosengren (HDR) qui prédominent sur la région de l'extrémité de la fissure, à l'extérieur d'une zone de déformations finies dont la taille est de l'ordre de grandeur du COD. Ces champs singulier sont proportionnels à l'intégrale de parcours C(t) laquelle, avec une bonne approximation, s'atténue en fonction de K _I ²/t, où t est le temps qui s'est écoulé depuis la mise en charge et K _Ile facteur d'intensité de contraintes imposés. Lorsque la vitesse de croissance de la fissure dépasse la vitesse de croissance de la zone en fluage, les résultats de l'analyse par éléments finis montre que ce sont les champs singuliers de Hui-Riedel qui prédominent sur la zone de l'extrémité de la fissure, et que l'amplitude de ces champs est proportionnelle à la vitesse de croissance de la fissure. Pour une fissure qui croit moins vite que la vitesse de fluage, es champs de type HRR sont prédominants et on trouve que la vitesse de croissance de la fissure est proportionelle C(t) à une certaine puissance. Quel que soit le type de champs singulier qui détermine la croissance de la fissure, on trouve que les effets de déformation finies sont significatifs sur une échelle de dimension de l'ordre du COD à l'amorçage de la fissuration. On considère également l'effet d'un affinage plus important du réseau, et l'on trouve me très faible dépendance par rapport à ce paramètre.

     

Predicting fatigue crack growth under irregular loading

We describe a model for predicting fatigue crack growth (FCG) with the presence in the loading spectrum of peak and block tensile overloads. The model is based on account for the following factors influencing crack growth retardation: change of the quantity K_op as a consequence of the induction of a system of residual compressive stresses at the crack tip and increase of the degree of crack closure that is due to plastic deformation of the material in the wake of the tip of the growing crack; plastic blunting of the crack tip. We propose a technique for quantitative prediction of the residual crack tip opening (radius of the blunted tip) after a peak tensile overload. Experimental verification of the proposed FCG model with differing applied load irregularity showed that the model may serve as the basis of a method for predicting the service life of cracked structural members operating in irregular loading regimes.Translated from Problemy Prochnosti, No. 8, pp. 3–16, August, 1994.     

The structure of slow crack interfaces in silicon nitride

Fracture interfaces formed in silicon nitride at high temperatures were studied using light and electron microscopy. The structure of the fracture interface depended on the type of silicon nitride fractured. High-purity, reaction-bonded silicon nitride always formed flat, relatively featureless, fracture surfaces. Fracture occurred by a brittle mode even at the highest temperature (1500° C) studied. The critical stress intensity factor for reaction-bonded silicon nitride ( 2.2 MN m^–3/2) is relatively low and is insensitive to temperature. By contrast, hot-pressed silicon nitride gave evidence of plastic flow during fracture at elevated temperatures. Crack growth in magnesia-doped, hot-pressed silicon nitride occurs by creep, caused by grain boundary sliding and grain separation in the vicinity of the crack tip. As a consequence of this behaviour, extensive crack branching was observed along the fracture path. The primary and secondary cracks followed intergranular paths; sometimes dislocation networks, generated by momentary crack arrest, were found in grains bordering the crack interface. As a result of the high temperature, cracks were usually filled with both amorphous and crystalline oxides that formed during the fracture studies. Electron microscopy studies of the compressive surfaces of fourpoint bend specimens gave evidence of grain deformation at high temperatures by diffusion and dislocation motion.     

Grain boundary influence on short fatigue crack growth rate

The influence from different grain boundary configurations on the crack growth rate of a microstructurally short edge crack, located within one grain and subjected to remote fatigue loading, is studied. The study is performed using a dislocation formulation, were the geometry is described by dislocation dipole elements in a boundary element approach and the plasticity by discrete dislocations, located along specific slip planes in the material. Plane strain and quasi-static conditions are assumed. The crack is assumed to grow in a single shear mechanism due to nucleation, glide and annihilation of discrete dislocations. Different grain boundary configurations in front of the growing crack are considered, including both high angle and low angle grain boundaries. It is shown that both grain boundary configuration and distance between the crack and a grain boundary has a pronounced influence on the crack growth rate.     

Analysis of creep rupture in a notched tensile bar

For circumferentially notched, round tensile bars the creep rupture behaviour is analysed, based on constitutive relations that account for the nucleation and growth of grain boundary cavities in polycrystalline metals at high temperatures. Both diffusive cavity growth and growth by dislocation creep of the surrounding grains is incorporated in the model, and in some cases free grain boundary sliding is assumed. Failure by cavity coalescence is predicted at small overall strains in the range where cavity growth is constrained by the rate of dislocation creep of the grains, whereas outside this range large occur prior to failure.In the analyses for notched specimens, where the stress fields are strongly non-uniform, first failure occurs at the notch tip, and subsequently a macroscopic crack grows into the material. Various combinations of material parameters are considered, and in most cases the crack is found to grow in the plane of the notch. The results are related to earlier experimental and computational investigations of creep rupture in notched bars.     

Creep fatigue crack growth in 0·5Cr–Mo–V steel

Abstract

An investigation is presented of crack growth in a normalised and tempered 0·5Cr–Mo–V steel under cyclic displacement controlled loading conditions at 565–600°C. A transition from fatigue to creep dominated behaviour was observed as the duration of the tensile dwell period in the cycle was increased. This change was a result of a progressive increase in the extent of crack tip grain boundary damage accumulation which, in the long dwell tests, was sufficient to give rise to crack extension directly. Time dependent crack propagation rates during the dwells of the long dwell tests were found to approach those determined for static load conditions. No evidence was found for a significant creep-fatigue interaction and it appears that overall crack growth rates are determined by crack tip oxidation and damage accumulation processes.

MST/756     

Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains

It is generally accepted that the fatigue crack growth (FCG) depends mainly on the stress intensity factor range (ΔK) and the maximum stress intensity factor (K_max). The two parameters are usually combined into one expression called often as the driving force and many various driving forces have been proposed up to date. The driving force can be successful as long as the stress intensity factors are appropriately correlated with the actual elasto-plastic crack tip stress-strain field. However, the correlation between the stress intensity factors and the crack tip stress-strain field is often influenced by residual stresses induced in due course.A two-parameter (ΔK_tot, K_max,tot) driving force based on the elasto-plastic crack tip stress-strain history has been proposed. The applied stress intensity factors (ΔK_appl, K_max,appl) were modified to the total stress intensity factors (ΔK_tot, K_max,tot) in order to account for the effect of the local crack tip stresses and strains on fatigue crack growth. The FCG was predicted by simulating the stress-strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region. The model was developed to predict the effect of the mean and residual stresses induced by the cyclic loading. The effect of variable amplitude loadings on FCG can be also quantified on the basis of the proposed model. A two-parameter driving force in the form of: was derived based on the local stresses and strains at the crack tip and the Smith-Watson-Topper (SWT) fatigue damage parameter: D = σ_maxΔε/2. The effect of the internal (residual) stress induced by the reversed cyclic plasticity manifested itself in the change of the resultant (total) stress intensity factors controlling the fatigue crack growth.The model was verified using experimental fatigue crack growth data for aluminum alloy 7075-T6 obtained under constant amplitude loading and a single overload.     

Effect of stress ratio on fatigue crack growth in TiAl intermetallics at room and elevated temperatures

The fatigue crack growth behavior of γ-based titanium aluminides (TiAl) with a fine duplex structure and lamellar structure has been investigated by scanning electron microscope (SEM) in situ observation in vacuum at 750°C and room temperature. For the duplex structured material the fatigue crack growth rates are dominated by the maximum stress intensity, particularly at 750°C. The threshold stress intensity range for fatigue crack growth at 750°C is lower than that at room temperature for any corresponding stress ratio. The fatigue crack growth rate at 750°C is affected by creep deformation in front of the crack tip. The severe crack blunting occurs when the stress ratio is 0.5. For the lamellar structured material the scatter of fatigue crack growth data is very large. Small cracks propagate at the stress intensity range below the threshold for long fatigue crack growth. The effects of microstructure on fatigue crack growth are discussed.