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 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.     

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.     

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.     

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.     

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.     

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.     

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.     

FATIGUE BEHAVIOR OF A RAIL STEEL

The fatigue behavior of a hot-rolled, control-cooled, plain carbon eutectoid rail steel has been characterized. The data include monotonic and cyclic stress-strain curves, low cycle fatigue data and near-threshold fatigue crack growth rate behavior in air and in vacuo. The effects of environment and mean stress on the near-threshold fatigue crack growth rates of rail steel are significant. At a low stress ratio (R), ΔK_o is lower in vacuum (7 MPa √m) than in moist air (10 MPa √m). At high R, ΔK_o is higher in vacuum (6 MPa √m) than in air (4 MPa √m). The beneficial effect of moist air on FCGR at low ΔK and low R is attributed to an increase in closure due to fracture surface roughness and oxide film.     

Fatigue analysis of an edge crack specimen: Hysteresis strain energy density

Accumulative damage model based on the hysteresis strain energy density is proposed for predicting fatigue crack growth. Investigated is the application of sinusoidal loading on an edge crack whose growth rates are obtained by specifying the number of cycles, Δ$\text{N}$, for each growth step. The corresponding increment of crack growth, Δ$\text{a}$, is calculated by having the accumulated local strain energy density to reach certain critical value, $\text{(dW/dV)}{}_{\mathrm{c}}$. As it is to be expected, each growth increment Δ$\text{a}$ increases up to the point of unstable rapid fracture. The growth rate $\text{da/dN}$ versus a data are generated from the nonlinear incremental theory of plasticity. Because of the complexities involved in the stress and subcritical crack growth analysis, the finite element procedure is adopted such that the grid pattern is readjusted for each step of crack growth. Results for the edge crack specimen are displayed graphically and compared with those for the center cracked specimen made of the same material. The different growth characteristics are discussed and expected because material damage by fatigue is sensitive to changes in load history, specimen geometry and crack configuration. Insight into these nonlinear effects provides a means for establishing the range of applicability of the linear fatigue growth models. Discussed in particular are the $\text{da/dN}$ vs δ$\text{k}{}_1$ and AS relations where the linear theory of elasticity is used to calculate Δ$\text{K}{}_1$ and Δ$\text{S}$.     

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.     

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.     

On the cyclic behavior of cast and extruded aluminum alloys. Part B: Fractography

In a prior study [1], the fatigue crack propagation (FCP) response of a cast and an extruded aluminum alloy was examined as a function of mean stress and specimen orientation while crack closure data were collected. In this work, extensive electron fractographic studies were conducted on the previously generated fatigue fracture surfaces using both scanning and transmission electron microscopy. The threshold micromorphology revealed crisp, cleavage-like facets. Striation spacing measurements at intermediate and high $\text{Δ}\text{K}$ levels were obtained to determine microscopic growth rates; these measurements were seen to vary with $\text{R}$ ratio and were best correlated with $\text{ΔK}{}_{\mathrm{EFF}}$ rather than $\text{Δ}\text{K}{}_{\mathrm{APP}}$. Slope changes in the $\text{da/da-}\text{Δ}\text{K}$ plots were identified and attempts made to establish correlations between the associated plastic zone sizes and microstructural dimensions. Of particular note, a stage IIa to IIb transition in the extruded material was found to correspond to a micromechanism change from faceted growth to striated growth when the reversed plastic zone size was similar to the subgrain dimension.     

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.     

Fracture toughness of H-11 steel and its susceptibility to stress corrosion cracking

The plane strain fracture toughness, $\text{K}{}_{\mathrm{IC}}$, was measured for H-11 steel using compact tension specimens after two separate heat treatments; one to provide good mechanical properties for normal engineering applications. Rc 46, 195 ksi yield strength, and the ofter heat treatment to provide maximum strength, Rc 56, 245 ksi yield strength. The Rc 46 samples exhibited no subcritical crack growth in either steam distilled water or hydraulic oil at $\text{K}{}_{\mathrm{I}}$ levels approaching 95% of the specimens' $\text{K}{}_{\mathrm{IC}}$ with times exceeding 20 hr. The Rc 56 samples under constant displacement loading exhibited subcritical crack growth in steam distilled water with a measured $\text{K}{}_{\mathrm{Iacc}}$ of 17.8 ksi √(in). The specimens were subjected to the environment just prior to loading, subcritical crack growth commenced without an incubation period, and both the $\text{K}{}_{\mathrm{I}}$ and crack growth increased with time. No subcritical crack growth was encountered in hydraulic oil at $\text{K}{}_{\mathrm{I}}$ levels approaching 98% of the specimens' $\text{K}{}_{\mathrm{IC}}$ with times exceeding 24 hr.     

Mechanism of corrosion fatigue crack propagation in high strength steels

The crack propagation velocity in corrosion fatigue $\text{(d a/d N)}{}_{\mathrm{c}}$ were measured on the Ni-Cr-Mo steel quenched and tempered at 473 or 773 K.The steel with high sensitivity to delayed failure reveals the largest $\text{(d a/d N)}{}_{\mathrm{c}}$ under square load and the smaller $\text{(d a/d N)}{}_{\mathrm{c}}$ under positive saw tooth load. The frequency dependency of crack propagation characteristics indicates that the interaction between hydrogen atoms and the cyclic moving of triaxial position at crack tip acts an important role in the crack propagation mechanism, i.e. hydrogen concentration process controls the crack propagation of the steel.The steel with low susceptibility to delayed failure reveals, on the other hand, the largest $\text{(d a/d N)}{}_{\mathrm{c}}$ under the positive saw tooth load but the smallest $\text{(d a/d N)}{}_{\mathrm{c}}$ under the square load, i.e. the stress increasing time is important and the hydrogen invasion process is the controlling factor for the crack propagation.     

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.     

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.     

An evaluation of the crack growth and fracture properties of AISI 403 modified 12 Cr stainless steel

The plane strain fracture toughness, $\text{K}{}_{\mathrm{Ic}}$, and fatigue crack growth rate material properties were developed for three heats of AISI 403 modified 12 Cr stainless steel. Valid (per ASTM requirements) fracture toughness tests were conducted in the temperature range ?200°F to 175°F. In addition, both the room temperature air environment plus 520°F, 1200psi distilled water environment fatigue crack growth rate material properties are presented. Finally, a hypothetical example problem is included which demonstrates the application of fracture mechanics technology to an AISI 403 modified 12 Cr stainless steel turbine rotor.     

An examination of mixed fatigue-tensile surface crack growth in rails

The fracture instability associated with alternating periods of fatigue and tensile growth of surface cracks was investigated in steel rails. Three different steels were tested. The instabilities commenced when the maximum stress intensity factor $\text{K}$ exceeded the fracture toughness $\text{K}{}_{\mathrm{IC}}$ and resulted in crack jump or total rail failure. The conditions for the establishment of fatigue-tensile crack jump and arrest are described. The load level, residual stresses, crack geometry and fracture toughness effects are analysed. The fatigue surface cracks were penetrated in both stress relieved and stress unrelieved rails. The effective stress intensity factors including the contribution of the applied load and residual stresses were calculated. For both the fatigue-tensile and tensile-fatigue transitions the stress intensity factors were almost the same with the value for the tensile-fatigue transition being slightly lower. Both calculated stress intensity factors were close to the fracture toughness $\text{K}{}_{\mathrm{IC}}$.