Fatigue crack propagation behaviour of rotor and wheel materials used in steam turbines

The fatigue crack propagation characteristics of several rotor and wheel materials that are commonly used in rotating components of steam turbines were investigated. Particular emphasis was placed on the behaviour at near-threshold growth rates, ie below 10^?5 mm/cycle, approaching the fatigue-crack propagation threshold, $\text{ΔK}{}_{\mathrm{<mtext>th</mtext>}}$. The lifetimes of the cracks of interest lie mostly in this region, and it is also the region where few data are available.The effects of load ratio on the fatigue crack growth rates were examined, as well as the tensile, Charpy V-notch and fracture toughness properties of the rotor and wheel materials. The relationship between fatigue crack propagation behaviour and fractographic features was examined. Fatigue crack growth rate data, $\text{da/d}\text{N}$ vs stress intesity range $\text{ΔK}$, were fitted with a four parameter Weibull survivorship function. This curve fitting can be used for life estimation and establishment of $\text{ΔK}{}_{\mathrm{<mtext>th</mtext>}}$. The results show that load ratio and microstructure play a role in determining the fatigue crack threshold and fatigue crack growth behaviour.     

Fatigue crack propagation in steels

From previous investigations of the mechanisms of both fracture and fatigue crack propagation, the static fracture model proposed by Lal and Weiss may be thought as reasonable for describing fatigue crack propagation in metals at both low and intermediate stress intensity factor ranges $\text{ΔK}$. Recent progress in fatigue crack propagation indicates that it is not only possible, but also necessary, to modify this static fracture model. Based on the modified static fracture model, the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$, which is defined as the difference between $\text{ΔK}$ and the fatigue crack propagation threshold value $\text{Δ}{}_{\mathrm{th}}$, is taken as the governing parameter for fatigue crack propagation. Utilising the estimates of the theoretical strengths of metals employed in industry, a new expression for fatigue crack propagation, which may be predicted from the tensile properties of the metals, has been derived. The correlation between the fatigue crack propagation rate and the tensile properties is thus revealed. The new expression fits the test results of fatigue crack propagation of steels below 10^?3 mm/cycle and indicates well the effect of stress ratio on the fatigue crack propagation rate.     

Condition for stable growth of branched cracks

In order to clarify the reason why the stable growth of branched cracks occurs in delayed failure, while not in other subcritical crack propagation process such as fatigue, the stress intensity factor after crack branching in delayed failure was dropped to various values, and the propagation behavior of both cracks was investigated.The well balanced growth of branched cracks in delayed failure occurs only when the crack propagation velocity after crack branching belongs to the region II where the crack propagation velocity is constant independently of $\text{K}$. The fatigue cracks at the tips of artificially branched cracks, on the other hand, can not propagate stably, and only either crack propagates preferentially.The exponent in the crack propagation law ($\text{d}\text{a/}\text{d}\text{t =}\text{c}{}_1\text{K}{}^{\mathrm{<mtext>m</mtext>}}\text{or}\text{d}\text{a/}\text{d}\text{N =}\text{c}{}_2\text{(ΔK)}{}^{\mathrm{<mtext>m</mtext>}}$) expresses the degree of unbalance growth of branched cracks. The stable growth of branched cracks occurs only when the crack propagation velocity is constant independently of $\text{K}$ or $\text{ΔK}$, i.e. $\text{m}\text{= 0}$.     

Effects of temperature,initial stress intensity factor and loading speed on the crack branching in delayed failure

The relation between diffusion behavior of hydrogen atoms and crack branching in delayed failure was discussed.The hypotheses that diffusion paths of hydrogen atoms at crack tip broaden with increase of stress intensity factor $\text{K}$, and that crack branching occurs when hydrogen atoms diffuse through the position where stable cracks are to nucleate, can well explain the facts that crack branching occurs when $\text{K}$ reaches to a certain value, $\text{K}{}_{\mathrm{IB}}$, and that $\text{K}{}_{\mathrm{IB}}$ increases with increase of temperature. The initial stress intensity factor and loading speed do not actually influence $\text{K}{}_{\mathrm{IB}}$, which can also be explained by the above hypotheses.     

Crack closure in 2219-T851 aluminum alloy

The effects of specimen thickness, stress ratio ($\text{R}$) and maximum stress intensity factor ($\text{K}{}_{\max }$) on crack closure (or opening) were studied using a 2219-T851 aluminum alloy. The crack length and the occurrence of crack closure were measured by an electrical potential method. The experimental work was carried out within the framework of linear-elastic fracture mechanics.The experimental results show that the onset of crack closure (or opening) dependes on $\text{R, K}{}_{\mathrm{<mtext>max</mtext>}}$), and specimen thickness. In terms of the “effective stress intensity range ratio” ($\text{U}$), as defined by Elber, the results show that $\text{U}$ tends to increase for increasing $\text{R}$, decrease for increasing $\text{K}{}_{\max }$, and decrease with increasing specimen thickness. From these trends, it is shown that the “effective stress intensity range” ($\text{ΔK}{}_{\mathrm{<mtext>eff</mtext>}}$) does not always increase with increasing stress intensity range ($\text{ΔK}$).The experimental results show that crack closure cannot fully account for the effects of stress ratio, specimen thickness and $\text{K}{}_{\max }$ on fatigue crack growth. The use of $\text{ΔK}{}_{\mathrm{<mtext>eff</mtext>}}$ as a parameter for characterizing the mechanical driving force for fatigue crack growth is questioned.     

Studies on crack growth rate under high temperature creep,fatigue and creep-fatigue interaction—I: On the experimental studies on crack growth rate as affected by aσg,σg and temperature

Many experimental studies have been reported on the measurements of crack growth rate and the observation of crack growth behaviour under high temperature creep, fatigue and creep-fatigue interaction in literatures. However, many of them have been done in air atmosphere. Furthermore, in many of them the measurements of the crack growth rate have been carried out by interrupting intermittently the running of the testing machine. In such experiments the complex effects due to the atmosphere, the interruption period and the corresponding unloading operation for the crack length measurement might have been involved.In the present paper in order to eliminate such effects, series of experimental studies on the crack growth behaviour under creep, fatigue and creep-fatigue interaction conditions on 304 stainless steel have been carried out by using high temperature microscope and observing the crack length continuously during running the test without interruption in vacuum of 10^?5mm Hg.Among the results, it was found that crack growth rates on a time basis, $\text{da/dt}$, under high temperature creep and creep-fatigue interaction conditions can not be described in terms of solely elastic stress intensity factor $\text{k}{}_{\mathrm{i}}$ or only net section stress σ_net, both independent of gross section stress σ_g. The relation between crack growth rate and stress intensity factor under high temperature fatigue condition changes with some trend according to gross section stress at lower $\text{K}{}_{\mathrm{I}}$ level and it can be approximately described in terms of stress intensity factor $\text{K}{}_{\mathrm{I}}$ only, at higher $\text{K}{}_{\mathrm{I}}$ level. The threshold stress intensity factor and the threshold net section stress under high temperature creep, fatigue and creep-fatigue interaction conditions appears to be almost independent of temperature.     

Prediction of threshold and ultra-low fatigue crack growth rates

A model was derived to predict the true threshold value for fatigue crack growth in the absence of crack closure. The model, based only on the tensile and cyclic properties of the material, was successfully verified against a set of experimental data on medium and high strength steels and one aluminium alloy. Good agreement with experimental results was also obtained for Region I of the $\text{d}\text{a/}\text{d}\text{N vs ΔK}$ curve using a fatigue crack growth rate equation based on the same model.Fatigue crack growth data obtained from the medium strength steel CK45 in the normalized state and two heat-treated conditions were analysed. Good data correlation was shown using a previously developed normalizing parameter, $\text{φ = (ΔK}{}^2\text{?ΔK}{}^2{}_{\mathrm{<mtext>th</mtext>}}\text{)/(K}{}^2{}_{\mathrm{<mtext>c</mtext>}}\text{?K}{}^2{}_{\mathrm{<mtext>max</mtext>}}\text{)}$, in the entire range of fatigue crack growth rates and for stress ratios ranging from 0.1 to 0.8.     

Effect of stress wave shape on the crack propagation velocity in cyclic delayed failure

Crack propagation velocity in delayed failure under superposed repeating load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{R}}$, was compared with that under static load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$Two peaks appear on the relation between decreasing rate of crack propagation velocity, $\text{1-β = 1 ? (}\text{d}\text{a/}\text{d}\text{t))}{}_{\mathrm{R}}\text{/(}\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$ and frequency, ?, both under sinusoidal and square load. By changing the ratio of holding time at maximum stress intensity factor to that at minimum stress intensity factor in square load, it was deduced that the existence of two peaks on the 1 ? β vs $\text{f}$ curve was caused by an asymmetric interaction between hydrogen atoms and cyclic moving of the position with triaxial tensile stress at crack tip. Moreover, the relation between 1 ? β and $\text{f}$ under the positive or negative saw tooth load could be well explained by the interaction model.     

Crack closure studies under constant amplitude loading

Crack closure experiments were performed on 6063-T6 Al-alloy using a COD-gauge for various load ranges and stress ratios. Experimental results show that for a given stress ratio, $\text{R}$, the crack closure load goes on decreasing as crack length increases (or $\text{K}{}_{\max }$ increases) and reaches even below minimum load level at higher values of stress ratios. On the basis of these experimental results, a model for effective stress intensity range ratio $\text{U}$, which is found to be a function of stress ratio $\text{R}$ and $\text{k}{}_{\max }$, is developed.     

Studies on crack growth rate under high temperature creep,fatigue and creep-fatigue interaction—II: On the role of fracture mechanics parameter aeffσg

For high temperature creep, fatigue and creep-fatigue interaction, several authors have recently attempted to express crack growth rate in terms of stress intensity factor $\text{K}{}_{\mathrm{I}}\text{= α}\text{aσ}{}_{\mathrm{g}}$, where a is the equivalent crack length as the sum of the initial notch length a₀ and the actual crack length $\text{a}{}^1$, that is, $\text{a = a}{}_0\text{+ a}{}^1$. On the other hand, it has been shown by Yokobori and Konosu that under the large scale yielding condition, the local stress distribution near the notch tip is given by the fracture mechanics parameter of $\text{aσ}{}_{\mathrm{g}}\text{?(σ}{}_{\mathrm{g}}$), where a is the cycloidal notch length, σ_g is the gross section stress and $\text{?(σ}{}_{\mathrm{g}}$) is a function of σ_g. Furthermore, when the crack growth from the initial notch is concerned, it is more reasonable to use the effective crack length a_eff taking into account of the effect of the initial notch instead of the equivalent crack length a. Thus we believe mathematical formula for the crack growth rate under high temperature creep, fatigue and creep-fatigue interaction conditions may be expressed at least in principle as function of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}\text{, σ}{}_{\mathrm{g}}$ and temperature.In the present paper, the geometrical change of notch shape from the instant of load application was continuously observed during the tests without interruption under high temperature creep, fatigue and creep-fatigue interaction conditions. Also, the effective crack length a_eff was calculated by the finite element method for the accurate estimation of local stress distribution near the tip of the crack initiated from the initial notch root. Furthermore, experimental data on crack growth rates previously obtained are analysed in terms of the parameter of $\text{a}{}_{\mathrm{eff}}\text{σ}{}_{\mathrm{g}}$ with gross section stresses and temperatures as parameters, respectively.     

Effect of loading history on stress corrosion cracking in high strength steel

The effect of preloading on crack nucleation time was examined with compact tension specimens having various notch radius in 0.1N-H²SO⁴ aqueous solution for 200°C tempered AISI 4340 steel. Crack nucleation time t_n increases by preloading for a given apparent stress intensity factor K_p2. The curve K_?2 vs. t_n deviates upward from the curve for the non preloading case. A linear relationship between the crack nucleation time and parameter is seen in semi-log diagram, where is taken as the value at t_n=α due to preloading. The apparent threshold stress intensity factor increases with K_?2 which is the apparent stress intensity factor of preloading. A detached crack is nucleated at some distance from the notch root and extends in a form of circle. This distance increases with increasing K_?2. The effect of load reduction during crack growth was examined. When the K-value was reduced from K₁ to K₂, an incubation time was observed before the crack started growing under the K₂-value. The incubation time t_m tends to increase with increasing ΔK = K₁-K₂. The threshold stress intensity factor was also found to increase for high load reduction.In order to explain these experimental results, a new dislocation model is proposed on the basis of stress induced diffusion of hydrogen in high stress region ahead of the notch root or a crack. This model suggests that the change in the crack nucleation time and the increase of the incubation time due to preloading or load reduction are caused by reducing the hydrostatic pressure and by spreading the hydrogen saturated region which requires more time for the hydrogen accumulation due to preloading or load reduction. The theory predicts the experimentally observed relations between and t_n and between log t_in and ΔK.     

Nucleation mechanism of stress corrosion cracking from notches

Crack nucleation mechanism of hydrogen assisted cracking at notched cracks in aqueous solutions is investigated, using the compact type specimens with various notch radius in low-tempered 4340 steel. A detached crack initiates at some distance ahead of the notch root. The crack nucleation at the notched root is determined by the electrical potential method. When the crack initiates, the voltage difference starts to increase. The crack nucleation site is examined by SEM. The time for crack nucleation increases with the notch root radius, ρ, and decreases with the apparent stress intensity factor K_ρ. A linear relationship between the crack nucleation time, t_n, and the parameter ${}^2\text{K}{}_{\mathrm{\rho }}\text{/(πρ)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-(2K}{}_{\mathrm{\rho }}\text{/(πρ)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{th}}\text{}}$ is seen in semi-log diagram, where $\text{(2K}{}_{\mathrm{\rho }}\text{/(πρ)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{th}}$ is almost equal to the yield shear strength.In order to explain these experimental results, a new model of micromechanics is proposed on the basis of stress induced diffusion of hydrogen in the high stress region ahead of the notch root. This model suggests that the detached crack initiates at the elasto-plastic boundary where the hydrogen concentration is from 2 to 5 times higher than that of the notch root surface. The theory agrees with experiments with respect to $\text{{2K}{}_{\mathrm{\rho }}\text{/(πρ)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-(2K}{}_{\mathrm{\rho }}\text{/(πρ)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{th}}\text{}}$ vs t_n and t_n vs ρ.The empirical equation holds under constant t_n, K_ρ = K_o(ρ/ρ_eff)^m where K₀ is the stress intensity factor with ρ ≈ 0 under the present environment, ρeff is the effective notch radius and m is constant. The value of m is 0.25 for the crack nucleation time (t_n)_th corresponding to the threshold stress intensity factor (K_ρ)_th, 0.5 for t_n < (t_n)_th and 0 for ρ ≦ ρ_eff. The above equation agrees with the theoretical equation proposed by Tanaka and Mura for any t_n and ρ_eff.     

On crack opening stress level in fatigue by Eddy current technique

Linear elastic fracture mechanics relates fatigue crack growth with the stress intensity factor at the crack tip. Presence of residual deformations at the tip of a fatigue crack reduces the crack tip stress intensification such that effective stress intensity range $\text{ΔK}{}_{\mathrm{e}}\text{= U · ΔK}$. In this paper use of eddy current technique is exhibited to find the values of test value of effective stress range factor $\text{U}{}_{\mathrm{test}}$. A reasonable comparison between computed and experimental results of $\text{U}{}_1$ and $\text{U}{}_{\mathrm{test}}$ on two Al alloys 6061-T6 and 6063-T6 has recommended the Eddy Current Technology for finding out the values of crack opening stress level under given loading conditions.     

Fatigue crack propagation from a crack inclined to the cyclic tensile axis

Cyclic stresses with stress ratio R = 0.65 were applied to sheet specimens of aluminium which have an initial crack inclined to the tensile axis at angles of 30°, 45°, 72° or 90°. The threshold condition for the non-propagation of the initial crack was found to be given by a quadratic form of the ranges of the stress intensity factors of modes I and II. The direction of fatigue crack extension from the inclined crack was roughly perpendicular to the tensile axis at stress ranges just above the threshold value for non-propagation. On the other hand, at stress ranges 1.6 times higher than the threshold values the crack grew in the direction of the initial crack. The rate of crack growth in the initial crack direction was found to be expressed by the following function of stress intensity factor ranges of mode I, K₁, and mode II, K₂: $\text{dc}\text{dN}\text{= C(K}{}_{\mathrm{eff}}\text{)sum}$, where $\text{K}{}_{\mathrm{eff}}\text{= [K}{}_1{}^4\text{+ 8K}{}_2{}^4\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$. This law was derived on the basis of the fatigue crack propagation model proposed by Weertman.     

Some formulas for the crack opening stress level

Crack growth data for 2024-T3 sheet material were analysed with different formulas for $\text{ΔK}{}_{\mathrm{eff}}$ as a function fo the stress ratio $\text{R}$. The data covered $\text{R}$ values from ?1.0 to 0.54. A good correlation was obtained for $\text{ΔK}{}_{\mathrm{eff}}$/$\text{ΔK}$ = 0.55 + 0.33$\text{R}$ + 0.12$\text{R}{}^2$ The relation between log $\text{d}\text{a/}\text{d}\text{n}$ and log $\text{ΔK}{}_{\mathrm{eff}}$ was non-linear for high crack rates (> 1 μm/c).     

A simple model of stress intensity range threshold and crack closure stress

The cyclic stress intensity threshold (Δ$\text{K}{}_{\mathrm{TH}}$) below which cracks will not propagate varies with length for short cracks. A model is proposed which relates Δ$\text{K}{}_{\mathrm{TH}}$ to the crack closure stress arising from fracture surface roughness. This is used to predict a variation in Δ$\text{K}{}_{\mathrm{TH}}$ with crack length for surface cracks in Ti 6Al-2Sn-4Zn-6Mo alloy, based upon measured values of crack opening displacement arising from roughness. The predicted variation in Δ$\text{K}{}_{\mathrm{TH}}$ with crack length is found to be similar to that obtained from the empirical model of Δ$\text{K}{}_{\mathrm{TH}}$ proposed by El Haddad et al.[5]. The application of the new model to estimate the value of crack closure stress arising from crack tip plasticity for short surface cracks is also discussed.     

The condition of fatigue crack growth in mixed mode condition

The condition of the initiation of fatigue crack growth in mixed mode conditions has been investigated by using precracked low carbon steel specimens.It is pointed out that, firstly, the critical condition of crack growth should be defined with regard to the modes of fatigue crack growth, i.e. shear mode and tensile mode. Secondly, it is proposed that the critical condition of fatigue crack growth is given by the local tensile stress and shearing stress at the notch tip determined by stress intensity factors $\text{K}{}_{\mathrm{I}}$ and $\text{K}{}_{\mathrm{II}}$, and that this criterion is generally applicable to in-plane-loading conditions, i.e. Mode $\text{I}$, Mode $\text{II}$ and Mixed Mode conditions.     

Growth of fatigue cracks in metals and polymers

Empirical data on the propagation of tensile fatigue cracks in metals and thermoplastics have been examined. It was found that a cyclic crack propagation relationship, based on the stress intensity factor concept, exists which can be successfully utilised for both types of materials.The proposed equation has a form $\text{/.a}{}_{\mathrm{x}}\text{= MA}{}^{\mathrm{n}}$ where $\text{A}$ is a function of$\text{ΔK}$ and mean $\text{K}$. The analysis of results suggests that this equation incorporating the influence of mean stress intensity factor provides an excellent fit to the investigated data. The possible modified forms of such a relationship in terms of strain energy release rate, the crack tip yielding and the crack opening displacement concepts are also indicated.     

Cyclic analysis of a propagating crack and its correlation with fatigue crack growth

Stress and strain field of a propagating fatigue crack and the resulting crack opening and closing behavior were analysed. It was found that a propagating fatigue crack was closed at tensile external loads due to the cyclically induced residual stresses. Strain range value $\text{Δ?}{}_{\mathrm{y}}$ in the vicinity of the crack tip was found to be closely related with the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$ which was determined on the basts of the analytical crack opening and closing behavior at its tip. Application of this analysis to the non-propagating fatigue crack problem and the fatigue crack propagation problems under variable stress amplitude conditions revealed that both $\text{Δ?}{}_{\mathrm{y}}$ and $\text{ΔK}{}_{\mathrm{eff}}$ were essential parameters governing fatigue crack growth rate.     

An analysis of reported fatigue crack growth rate data with special reference to Ti-6A1-4V

A review of the published literature on fatigue crack growth suggests that power-law growth in Ti-6A1-4V is sensitive to microstnictural changes which result in variations in the fatigue mechanism. Microstnictures which promote secondary cracking along α/β interfaces display slow growth rates while microstructures which promote dimpled rupture display fast growth rates. Examples of similar effects are found in other alloy systems.Typically, the power-law growth are found in other alloy systems. It is also suggested that the power-law regime begins at $\text{ΔK ～- 13 MNm}{}^{\mathrm{<mtext>?</mtext><mtext>case3</mtext><mtext>2</mtext>}}$, coinciding with the lower limit of striation formation on the fracture surface. The upper limit occurs at about $\text{K}{}_{\max }\text{= 1/2K}{}_{\mathrm{c}}$. At higher growth rates, the Forman equation appears to be adequate.The normalized stress intensity factor, $\text{ΔK/E}$, required to produce a given growth rate in Ti-6A1-4V is on the order of that for other Ti-base alloys, ferritic steels, martensitic steels and aluminum alloys. Austenitic steels, which deform by planar slip are much more resistant to crack growth over much of the stress intensity range normally encountered.