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.     

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 effect of temperature and R ratio on fatigue crack growth in A612 grade B steel

Fatigue-crack propagation rates in ASTM$\text{A612}$ Grade B steel were investigated at room temperature and ?100°F (?73°C) with $\text{R}\text{ratio}\text{= ?0.1}\text{and}\text{+0.67}$. The data were evaluated in terms of the crack propagation rates ($\text{d}\text{a/}\text{d}\text{N}$) as a function of the alternating stress intensition ($\text{ΔK}$), according to $\text{d}\text{a/}\text{d}\text{N = e+(v ? e)(? 1}\text{n}\text{(1 ?}\text{Δ}\text{K/K}{}_{\mathrm{b}}\text{))}{}^{\mathrm{t/k}}$. It was found that crack growth rates were increased due to increasing $\text{R}$ ratio. Also the dependence of crack growth rates on $\text{R}$ ratio is strongest at the lowest crack growth rates where a $\text{ΔK}$ fatigue threshold is established. Crack growth rates were decreased due to decreasing test temperature in the slow crack growth region. However, it was found that crack growth rates were increased due to decreasing test temperature in the fast crack growth region near the upper instability asymptote. Decreased test temperature and increased $\text{R}$ ratio interact synergistically to increase crack growth rates for the entire range of $\text{ΔK}$.     

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).     

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.     

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. $\text{m}\text{= 0}$.     

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 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.     

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.     

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.     

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 and fatigue crack propagation in high strength steel from room temperature to −180°c

Fracture toughness under tensile test and fatigue test on high strength steel at temperature ranging from room temperature to ?180°C were experimentally studied. The value of fracture toughness under fatigue test is considerably tower than that obtained under tensile test.Within the range from room temperature to ?100°C the following results were obtained: the power coefficient δ of the fatigue crack propagation rate $\text{[(dc)/(dN)] = AΔK}{}^5$ is related with [(1)/($\text{T}$)] as: $\text{δ = b}{}_1\text{+ [(a}{}_1\text{)/(kT)]}$. $\text{[(dc)/(dN)]}$ shows Arrhenius type, and, however, different equation from usual stress dependent rate process equation. The trend is in good agreement with the dislocation dynamics theory of fatigue crack propagation.     

The crack tip opening angle (CTOA) of the plane stress moving crack

Recently, Crack Tip Opening Angle (CTOA) was proposed by C.F. Shih et al. to describe the instability criterion of ductile crack propagation during plane strain (flat crack) conditions, and was derived by J. R. Rice analytically by means of the slip line field theory and the incremental theory of plasticity. CTOA appears to be applicable in (some or most) cases, but does not accurately describe the plane stress growing crack (slant crack).Unstable ductile crack propagation of the plane stress crack is widely studied for the safe design of highly pressurized gas pipelines. The impact absorption energy of the Charpy test is well correlated to the fracture arresting properties of the structures, but the mechanics of the fracture are not yet well established.In this paper, CTOA of the plane stress growing crack is derived from the plane stress plasticity of perfectly plastic materials by Sokolovsky's approach. Our proposed modification of CTOA expressed as follows: $\text{CTOA}\text{= (α/δ}{}_0\text{)(}\text{d}\text{J/}\text{d}\text{l) + β(δ}{}_0\text{/E)}\text{ln}\text{(eR/r)}$ where $\text{β = 1.40}$ under the plane stress conditions.CTOA in the Dugdale model is also defined and compared with the results of laboratory test. The results show that $\text{α = 0.5}$, and $\text{β = 1.27}$ for plane stress crack growth. These analyses give similar results to those obtained by Rice et al. for CTOA under plane strain conditions, that is, $\text{α = 0.65}$ from the experimental results and $\text{β = 5.08}$ from the slip line theory.The CTOA obtained for plane stress ductile crack growth is applied to the wide plate tensile crack growth test. The results of the present analysis coincide well with those of the plane stress finite element method (FEM) computed by T. Kanazawa et al. The phenomena of plane stress ductile crack propagation are also explained by the CTOA criterion under plane stress conditions.     

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.     

Incipient fracture angle,fracture loci and critical stress for mixed mode loading

A prediction of the direction of incipient crack growth in brittle-like materials and the associated fracture loci under mixed mode loading is proposed. It is postulated that the direction of unstable crack propagation is determined by the “weakest” near-tip element defined as the one which would relax maximum potential energy upon prospective crack extension. Starting from the energy rate principle of crack extension (Eshelby energy-momentum tensor and Rice $\text{J-}\text{internal}$ vector) it is deduced that a crack will extent in the direction along which the following stress criterion is satisfied, $\text{(δ}{}_{\mathrm{\theta \theta }}{}^2\text{? δ}{}_{\mathrm{rr}}{}^2\text{) →}\text{maximum (for}\text{δ}{}_{\mathrm{\theta \theta \; >\; 0)}}$ The fracture angle in pure Mode II (70.4° away from the original straight path) is shown to be unstable in the sense that any slight tension along the crack (non-singular at the crack tip) affects considerably (up to 22%) the directionality of crack extension. It appears to be sensitive to the extent of the near-tip zone ($\text{r}{}_0$) in which linear elasticity does not hold and the non-singular stress term (squared).The fracture loci in mixed mode loading (generated by projecting the $\text{J-}\text{integral}$ vector along the prospective fracture path and letting this scalar function attain a critical value) is quadratic in $\text{K}{}_1$ and $\text{K}{}_2$ with an interactive cross product term $\text{K}{}_1\text{× K}{}_2$.The suggested criterion with its implication in predicting critical fracture load, exhibits behavior which is consistent with experimental observations collected from several sources. The common and uncommon features with respect to other known criteria are compared and 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.     

Effect of some aircraft loading program modifications on the fatigue life of open hole specimens

Flight simulation and program tests were performed with different 2024-T3 sheet specimens containing a central hole. The effect of the peak-load frequency on the damage sum and flight number was investigated. Gust spectrum test results were compared with those of other authors. For sufficiently close spectra with similar log-linear gust load distribution but different GAG cycle distribution, the relative Miner rule yielded satisfactory results. In the case of truncation levels $\text{S}{}_{\max }\text{= 1.84σ}{}_{\mathrm{m}}$ and $\text{S}{}_{\max }\text{= 1.685σ}{}_{\mathrm{m}}$, the investigated change of the frequency of stress cycles at the highest loading level (for cycle numbers smaller than those following from the log-linear gust distribution) had a weak effect on the damage sum, while the effect of decrease of the frequency of the lowest stress amplitude $\text{σ}{}_{\mathrm{a}}\text{= 0.222σ}{}_{\mathrm{m}}$ (MiniTWIST instead of TWIST) was considerable in some cases. It was found that in particular loading program cases, rare load peaks may have not only a beneficial but also a detrimental effect on the number of simulated flights. Truncation had a detrimental effect but the increase of the number of overload peaks above the number of cycles at the truncation level associated with the log-linear gust distribution had also a detrimental effect.     

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.     

Fracture of thin sections containing surface cracks

Surface-cracked specimens of several thicknesses of 7075-T651 and 7075-T6 aluminum were tested in uniaxial tension. For thicknesses t less than 0.25 in., the gross fracture stress σ_f of 7075-T651 Al was empirically related to flaw size by the following expression:

$\text{δ}{}_{\mathrm{f}}\text{σ}{}_{\mathrm{ult}}\text{= 1 + S(}\text{a}\text{φ}{}^2\text{.t}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$

where σ_ult is the ultimate strength, a the crack depth, φ a function of crack shape, and S a proportionality constant equal to ?1.7 in.^{$\text{?1}\text{2}$}. For 0.25-in. thick 7075-T651 aluminum, σ_f was found to obey this relationship only when $\text{a}\text{φ}{}^2$ is less than 0.065 in.; for larger flaws, such that $\text{0.065 <}\text{a}\text{φ}{}^2\text{< 0.11, σ}{}_{\mathrm{f}}$ is better predicted by Irwin's surface-crack equation with an apparent K_IC value of $\text{32.2}\text{ksi-in.}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.Fracture data for thin sections of 2014-T6 and 2014-T651 Al tested at ?423°F are analyzed in terms of the empirical relationship above and are found to be in good agreement. For these alloys, S has a value of ?2.6 in.^{$\text{?1}\text{2}$}.Applicability of the empirical relationship and Irwin's surface-crack analysis to the fracture of thin sections is discussed in terms of crack size, section thickness, and plastic zone size.