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.     

On the influence of environment on the load ratio dependence of fatigue thresholds in pressure vessel steel

A study has been made of the influence of load ratio $\text{R}$ on fatigue crack propagation behavior and specifically on the value of the fatigue crack growth threshold, Δ$\text{K}{}_0$, in a bainitic 2.25 Cr-1Mo pressure vessel steel tested at 50 Hz in aqueous, and moist and dry gaseous environments. Data are obtained for crack growth in a distilled water environment and are compared to previously published results in air and hydrogen. It is found that in distilled water the dependence of thresholds Δ$\text{K}{}_0$ values on $\text{R}$ is far less marked than in moist air and dry hydrogen atmospheres where Δ$\text{K}{}_0$ values decrease sharply with increasing $\text{R}$. Furthermore, whereas in air and hydrogen, the threshold condition is characterized by a constant maximum stress intensity at low load ratios, and a constant alternating stress intensity at high load ratios, no such behavior is observed in water. Based on extensive measurements of crack face oxidation products using scanning Auger speetroscopy and on previous crack closure measurements using ultrasonics techniques, the role of load ratio in influencing near-threshold fatigue behavior is ascribed to mechanisms of crack closure specifically plasticity-induced closure and closure arising from crack face oxide debris. The implications of such plasticity-induced and oxide-induced closure to the load ratio-dependence of near-threshold fatigue behavior in various environments are discussed in detail.     

A study of crack closure in fatigue

Crack closure phenomenon in fatigue was studied by using a Ti-6Al-4V titanium alloy. The occurrence of crack closure was directly measured by an electrical potential method, and indirectly by load-strain measurement. The experimental results showed that the onset of crack closure depends on both the stress ratio, $\text{R}$, and the maximum stress intensity factor, $\text{K}{}_{\max }$. Crack closure was not observed for stress ratio, $\text{R}$, greater than 0.3 in this alloy.A two-dimensional elastic model was used to explain the behavior of the recorded load-strain curves. Closure force was estimated by using this model. Based on the estimated closure force, the crack opening displacement was calculated. This result showed that onset of crack closure detected by electrical-potential measurement and crack-opening-displacement measurement is the same.The implications of crack closure on fatigue crack are considered. The experimental results show that crack closure cannot fully account for the effect of stress ratio, $\text{R}$, on crack growth, and that it cannot be regarded as the sole cause for delay.     

The effects of load ratio on environmentally assisted fatigue crack growth

A modification to the model of Weir et al. for surface reaction and transport controlled fatigue crack growth has been developed to explicitly account for the effect of load ratio on environmentally assisted fatigue crack growth. Load ratio was found to affect principally gas transport to the crack tip, and therefore affected only transport controlled crack growth response. Experimental verification of the modified model was made by studying the room temperature fatigue crack growth responses at different load ratios for a 2219-T851 aluminum alloy exposed to water vapor.The results show that the effects of load ratio can be attributed to two different sources—one relating to its effect on local deformation at the crack tip and is reflected through the mechanical component, (d$\text{a}$/d$\text{N}$)₀ and the other on its role in modifying environmental effect and is manifested through the corrosion fatigue component, $\text{(da/dN)}{}_{\mathrm{cf}}$ Furthermore, the results show that the saturation value of corrosion fatigue component, $\text{(da/dN)}{}_{\mathrm{cf,s}}$, is essentially independent of $\text{R}$, and that the exposure needed to produce “saturation response” ($\text{P}{}_0\text{/2f)}{}_{\mathrm{s}}$, as a function of load ratio can be predicted from the modified model. The modified model, therefore, allows one to predict the corrosion fatigue crack growth response for any load ratio on the basis of measurements made at a single load ratio, provided that the values of ($\text{da/dN}$), are known.     

Crack tip closure and environmental crack propagation

Crack propagation rate, da/dN, and crack tip closure stress, σ_cc, in part-through crack fatigue specimens of aluminum alloys are drastically affected by gaseous environments. The present studies indicate that the crack closure reflects the influence of the environment on the plastic deformation at the crack tip, and, therefore, on the crack propagation rates. Postulating that da/dN is mainly determined by $\text{ΔK}{}_{\mathrm{eff}}\text{∝ (σ}{}_{\max }\text{?σ}{}_{\mathrm{cc}}\text{)}$ (instead of $\text{ΔK ∝ (σ}{}_{\max }\text{?σ}{}_{\min }\text{)}$, as is done traditionally) leads to the relationship $\text{da/dN = A(ΔK}{}_{\mathrm{eff}}\text{)}{}^{\mathrm{n}}$ in which $\text{A}$ and $\text{n}$ are virtually independent of the gaseous environment. The exponents are $\text{n ≈ 3.3}$ for Al 7075 T651 and $\text{n ≈ 3.1}$ for Al 2024 T351, respectively.     

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.     

The influence of environment and stress ratio on fatigue crack growth at near threshold stress intensities in low-alloy steels

Fatigue crack propagation at low stress intensities has been studied in two low alloy steels in a variety of environments with particular emphasis being placed on the influence of stress ratio and strength level. It was found that fatigue crack growth rates are lower and threshold stress intensities ($\text{ΔK}{}_0$) are higher in vacuum than in humid, laboratory air but, in dry gaseous environments (argon, hydrogen and air) and at low stress ratio ($\text{R ~ 0.1}$), crack growth rates are faster and $\text{ΔK}{}_0$ values are lower than in laboratory air. However, the influence of stress ratio is considerably greater in laboratory air than in dry gaseous environments with the result that, at high stress ratio ($\text{R ~ 0.8}$) $\text{ΔK}{}_0$ values are similar in all environments examined. Increasing material strength level resulted in higher, near-threshold crack growth rates and a reduction in $\text{ΔK}{}_0$ in both dry and humid air environments. The results are discussed in terms of the influence of crack closure and environmental effects on fatigue crack growth behaviour. The importance of corrosion debris produced in fatigue cracks at low stress intensities is also discussed.     

A synergistic fracture mechanics approach to fatigue life evaluation

A technique for modeling synergistic effects in fatigue crack propagation (FCP) is presented. First, a mission (load/temperature history) is segregated into elemental damage events. A simple three parameter model is then used to describe these events. The model coefficients are seen to be interrelated linear functions of FCP rate controlling variables such as frequency, temperature, stress ratio (σ_min/σ_max), dwell, overload ratio ($\text{P}{}_{\mathrm{overload}}$/$\text{P}{}_{\max }$) and cycles between overload. Finally, integrating event-by-event crack advance gives the expected component crack propagation life under mission cycling. Results of this procedure applied to gas turbine disk materials IN100 and Waspaloy are discussed to examine the accuracy of the model.     

Dynamic stress distribution around the tip of a running crack

The stress distribution is obtained around the tip of a crack running in a brittle material. The stresses are written as the sum of the associated static solution and the wave-effect terms which depend upon the crack speed. The results obtained clearly reduce to the associated static solutions if the crack speed vanishes.Near the tip of the crack, the dynamic stress-intensity factor for the circumferential stress, $\text{σ}{}_{\mathrm{\theta \theta }}$, is written as the product of the associated static stress-intensity factor and the dynamic correction factor which is a nondimensional function of the crack speed, $\text{V}$, the angle from the crack plane, θ, and Poisson's ratio, ν. The value of the correction factor is computed for various values of $\text{V}$ and θ at $\text{ν = 0.25}$. It is shown that the maximum tensile value of $\text{σ}{}_{\mathrm{\theta \theta }}$, occurs on the crack plane for $\text{V}$ less than 0.7 time shear wave speed, $\text{c}{}_2$, and suddenly shifts to the plane of $\text{θ = 55°}$ for $\text{V}$ slightly larger than 0.7 $\text{c}{}_2$. For $\text{V > 0.7}$$\text{c}{}_2$, the angle θ for the maximum $\text{σ}{}_{\mathrm{\theta \theta }}$, θ being larger than 55°, varies continuously with the crack speed, $\text{V}$. The results obtained are used to discuss the growth of branching crack.     

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.     

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.     

A method for determining the stress intensity threshold level for fatigue crack propagation

The influence of a decreasing rate of stress intensity factor with crack propagation, $\text{d}\text{K/}\text{d}\text{a}$, on a stress intensity threshold level, $\text{δK}{}_{\mathrm{th}}$, below which fatigue crack propagation becomes insignificant is investigated. Specimens, 200 mm wide, 10 mm thick with a 40 mm-long central crack, are fatigued at the decreasing rates, $\text{∥}\text{d(δK)}\text{d}\text{a∥}$, of 2,44, 5 and 10 kg/mm^5/2 with a peak load control system and a pair of crack followers. In this range of $\text{d}\text{(δK)/}\text{d}\text{a}$, the stress intensity threshold levels, $\text{δK}{}_{\mathrm{th}}$, have the same value regardless of $\text{d}\text{K/}\text{d}\text{a}$. Therefore, the present method of decreasing the stress intensity factor at a constant rate is suitable for determining the characteristic $\text{δK}{}_{\mathrm{th}}$ of materials. Furthermore, the influence of stress ratio, $\text{R}$, is investigated at the decreasing rate, $\text{∥}\text{d}\text{(δK)/}\text{d}\text{a]}$, of 10 kg/mm^5/2.     

The stress field near the blunt crack tip and the fracture criterion

The asymptotic expansion solution containing two terms for the stress field near the blunt crack tip is obtained. It is proposed that the slit be divided into the ideal crack, blunt crack I, blunt crack II and the notch in accordance with the geometrical structure of the slit tip. Whether the blunt crack can be considered as the ideal crack will depend mainly on the following three factors: $\text{√}\text{2R}{}_0\text{C}$, $\text{√}\text{R}{}_0\text{r}{}_{\mathrm{c}}$ and the profile of the crack. In this paper, the influence of the crack tip radius on the fracture criterion is studied and it is shown that the classical strength theories belong to the unconditional extremum criteria while the S criterion, etc. in fracture mechanics belong to the conditional extremum criteria. A modified maximum tension stress theory is developed, in which the fracture theories of the crack and the notch can be roughly unified.     

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.     

G̃c and R-curve fracture toughness values for aluminum alloys under plane stress conditions

The effect of specimen geometry and subcritical crack growth on the nonlinear energy fracture toughness, $\text{G}\text{?}{}_{\mathrm{c}}$, has been examined for thin, center-cracked sheets of 2024-T3 and 7075-T6 aluminum alloys. The procedure followed was to independently vary the specimen length, L, width, w, andd crack length-to-specimen width ratio and to determine the toughness both at the onset of subcritical crack growth and at the initiation of unstable fracture. Comparisons were also made with the R-curve toughness, G_R, evaluated at unstable fracture from which it was found that both $\text{G}\text{?}{}_{\mathrm{c}}$ and G_R displayed the same trend of change with geometrical variables, with $\text{G}\text{?}{}_{\mathrm{c}}$ consistently higher than G_R. When the nonlinear energy fracture toughness was evaluated at the onset of subcritical crack growth, it was found that the geometry dependence essentially disappeared.Scanning electron microscopic examination of some typical fracture surfaces showed that stable crack growth was accompanied by a gradual change of fracture mode from plane strain to plane stress. An analysis of possible errors in the experimental procedure showed that the scatter observed in $\text{G}\text{?}{}_{\mathrm{c}}$ values was not due to experimental errors, but apparently due to inhomogeneities in the materials. Several techniques were also introduced for the purpose of more directly incorporating crack growth into the $\text{G}\text{?}{}_{\mathrm{c}}$ determination, but it was found that they did not cause significant variation in the toughness values.     

On the cyclic behavior of cast and extruded aluminum alloys. Part A: Fatigue crack propagation

The fatigue crack propagation (FCP) response of a cast and extruded aluminum alloy was examined as a function of mean stress and specimen orientation. The extruded alloy was tested in both the longitudinal and transverse orientation and no difference in FCP response was noted. FCP tests were conducted at R ratios of 0.1, 0.5, 0.65 and 0.8. In the threshold regime, it was seen that as R ratio increased, $\text{Δ}\text{K}{}_{\mathrm{TH}}$ decreased. In addition, ΔK_TH values determined for the cast alloy were superior to those determined for the extruded alloy at all R ratios examined. The threshold regime was also shown to be K_MAX rather than $\text{Δ}\text{K}$ dependent. At intermediate ΔK levels, a mean stress effect was seen for both alloys at R ratios less than 0.5. Crack closure was monitored during testing so that ΔK_EFF values could be determined. $\text{Δ}\text{K}{}_{\mathrm{EFF}}$ was seen to explain mean stress effects at intermediate $\text{Δ}\text{K}$ levels.     

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.     

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.     

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).