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.     

A fracture mechanics approach to high temperature fatigue crack growth in Udimet 700

Crack growth behavior under high temperature fatigue in Udimet 700 has been analyzed using both linear and non-linear elastic fracture mechanics concepts. It is shown that crack growth data for various loads in a compact tension specimen correlate well with the stress intensity factor, even at temperatures as high as 850°C. Using these results, a self consistent procedure has been developed for the determination of the $\text{J-}\text{integral}$ parameter under load-controlled fatigue and is shown to be compatible with data based on the stress intensity factor. The spread in the crack growth data is smaller in terms of $\text{J-}\text{integral}$ as compared to stress intensity or crack opening displacement parameters. Also based on a detailed fractographic analysis, it is suggested that the micromechanism of crack growth in Stages I and II is the environmentally assisted cleavage process, whereas in Stage III creep assisted crack growth processes are superimposed on the cleavage mode of crack growth. Effects of stress and temperature on the fatigue crack growth behavior of the Udimet alloy are discussed in detail.     

A cumulative model of fatigue crack growth and the crack closure effect

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated using the local stress/strain at the crack tip by assuming that a small highly strained area $\text{x}{}^1$, existing at the crack tip, is responsible for the fatigue crack growth, and that the fatigue crack growth may be regarded as the cumulation of successive crack re-initiations over a distance $\text{x}{}^1$. It is shown that crack closure can be modelled using the effective contact zone g behind the crack tip. The model allows the fatigue crack growth rate over the near threshold and linear ranges of the general da/dN versus ΔK curve to be calculated. The fatigue crack growth retardation due to overload and fatigue crack arrest can also be analysed in terms of g and $\text{x}{}^1$.Calculated fatigue crack growth rates are compared with experimental ones for low and high strength steel.     

Acoustic emissions of fatigue crack growth

Acoustic emissions of fatigue crack growth have been monitored and quantitatively correlated with growth rate and the applied range of stress intensity for high cycle fatigue of 2024-T851 aluminum alloy. The data suggest a more cogent relationship for acoustic emissions and the applied range of stress intensity rather than between acoustic emissions and the average crack growth rate. Since nearly all crack growth is expected during the maximum load portion of the fatigue cycles, only the emissions from the acoustic events in the vicinity of the peak load were incorporated in correlations with $\text{d}\text{a/}\text{d}\text{n}$ and $\text{ΔK}$. Large amplitude emissions in the proximity of the minimum cyclic load were also detected. Because of their characteristics, these emissions are attributed to crack surface interference and, consequently, were not included in the correlation analyses.     

Mixed mode fatigue crack growth predictions

This work is aimed at developing a predictive capability for the quantitative assessment of crack growth under fatigue loadings. The crack growth rate relation, $\text{Δa}\text{ΔN}$, may involve all three stress intensity factors k₁-k₃ such that the direction of crack growth may not be known in advance and must be predicted from a preassumed criterion. In principle, both the stress amplitude and the mean stress level should be included in the original expression for $\text{Δa}\text{ΔN}$.The strain energy density factor range, ΔS, is found to be a convenient parameter for predicting fatigue crack growth and can be applied expediently to examine the combined influence of crack geometry, complex loadings and material properties. Assumed is the accumulation of energy, $\text{ΔW}\text{ΔV}$, stored in an element ahead of the crack which triggers subcritical crack growth upon reaching a number of loading cycle, say ΔN. The proposed $\text{δa}\text{ΔN}$ relationship includes both the stress amplitude and mean stress effects.     

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 growth retardation inconel 600

The effect of single-cycle overloads on the subsequent fatigue crack growth behavior of Inconel 600 is studied. Overloads ranging from 10 to 50% are applied to a sample undergoing baseline fatigue crack growth at constant Δ$\text{K}$. In all cases, the crack growth rate increases slightly immediately after the overload and then decreases rapidly to a minimum value before later returning to the pre-overload value. The plastic zone size, affected crack length and the crack growth increment at minimum crack growth rate, $\text{a}\text{?}$, are measured for each overload.The affected crack length is considerably larger than the overload plastic zone size for overloads greater than 20%. Consequently, although the minimum crack growth rate occurs within the plane stress overload plastic zone, the effect of the overload extends well beyond the overload region.Within the overload plastic zone, contact occurs between the crack faces due to the excessive deformation produced during the overload cycle. The size of the contact region agrees very well with the overload plastic zone size. Beyond the overload region, Δ$\text{K}{}_{\mathrm{eff}}$ remains less than the applied Δ$\text{K}$ for some time due to the wedge action of the plastically deformed overload region, delaying recovery of the pre-overload crack growth rate. The crack growth rate recovers only after the crack grows out of the region of influence of the wedge.     

Fatigue crack tip strain loop under single overload in Fe3Si steel

For the problem of the retardation of fatigue crack growth caused by single overload, cyclic strain changes in one cycle of the local crack tip region were investigated by using fine-grid-method. From the application of Crack Tip Strain Loop (C.T.S.Loop), the correlation between effective stress intensity factor range (ΔK_eff^T) defined from the stress range of C.T.S.Loop and crack growth rate ($\text{d}\text{a}\text{d}\text{N}$) was discussed. Moreover, from the strain range of C.T.S.Loop, the correlation between crack-tip strain range (Δ_?^T) and $\text{d}\text{a}\text{d}\text{N}$ was also investigated.     

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.     

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.     

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.     

A cumulative model of fatigue crack growth

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated by means of the local stress/strain at the crack tip. The local stress and strain calculations are based on the general solutions given by Hutchinson, Rice and Rosengren. It is assumed that a small highly strained area existing at the crack tip is responsible for the fatigue crack growth. It is also assumed that the fatigue crack growth rate depends mainly on the width, x¹, of the highly strained zone and on the strain range, $\text{Δ?}{}^1$, within the zone. A relationship between stress intensity factor K and the local strain and stress has been developed. It is possible to calculate the local strain for a variety of crack problems. Then, the number of cycles N¹ required for material failure inside the highly strained zone is calculated. The fatigue crack growth rate is calculated as the ratio $\text{x}{}^1\text{N}{}^1$.The calculated fatigue crack growth rates were compared to the experimental ones. Two alloys steels and two aluminium alloys were analyzed. Good agreement between experimental and theoretical results is obtained.     

Fatigue crack growth in PMMA and rigid PVC under biaxial stress

Fatigue crack growth rate results for PMMA and rigid PVC are presented on a fracture mechanics basis. Centre-notched specimens were used to measure the effects of the stress biaxiality factor $\text{B}$, defined as the ratio of load acting in the crack line to that acting on a line normal to it. Variations in $\text{B}$ from 0 (uniaxial) to 2 have little effect on the fatigue crack growth rate in PVC, but reduce that in PMMA by a factor of 2 or 3. If the variation in $\text{B}$ is a stepwise one, this growth rate reduction may be accompanied by a temporary crack arrest period. The observations can be explained for both materials by postulating a direct effect of $\text{B}$ on the stress intensity factor, for which a possible mechanism-using crack closure concepts is suggested. It is shown that the regime of true fatigue crack growth in PMMA, which is investigated here, is limited at its upper end by a sharp transition to a slow-growth dominated crack extension mode.     

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$\text{S}$.     

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 $\text{ΔK}$.     

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.     

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.     

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 theory for fatigue crack propagation

A new continuum mechanics model is developed for predicting fatigue crack propagation rates using a fracture mechanics approach. The model demonstrates the critical dependence of fatigue crack growth on the fatigue ductility exponent, the fatigue ductility coefficient, the elastic modulus and the fracture toughness; it is related to the stress intensity range, implying that fatigue crack growth is critically dependent upon the condition at the tip of the crack.Four materials are studied, namely a creep resistant stainless steels, FV535; a $\text{2}\text{1}\text{2}$ per cent nickel-chromium-molybdenum direct hardening steel, 2S96D; a nickel base heat resisting alloy INCO 901; and a ferrous alloy containing titanium carbide in a medium alloy tool steel matrix, known as Ferrotic C.The developed model provides a means of predicting crack propagation rates based on mechanical properties, and the simplified model provides a fundamental basis for a more general form of the Paris relationship.     

Fatigue crack propagation in an epoxy polymer

This experimental study investigates the fatigue crack growth rate behavior in an epoxy resin polymer using the tapered-double-cantilever-beam (TDCB) specimen in ambient and elevated temperature environments. An empirical crack growth rate model based on the change in crack extension force, Δ?, is proposed. Its relation to current $\text{ΔK}$ models is discussed and observations on the fatigue surface morphology presented.