Mean stress effects on fatigue crack growth and failure in a rail steel

Over a limited range, the effect of mean stress has been studied on fatigue crack propagation and on the critical fatigue crack size associated with sudden fast fracture in centre-notched plate specimens of a rail steel under pulsating loading. The results have been presented in terms of the stress intensity factor range $\text{ΔK}$ and the ratio $\text{R}$ of the minimum to maximum stress. Increasing $\text{R}$ was found to both accelerate cracking and reduce the critical crack size at instability. The data have been correlated with three crack growth equations currently used in the literature and it was found that the equation of Forman et al. relating crack growth rate to $\text{ΔK}$ and $\text{R}$ gave the best fit. This equation was used to predict life in the finite range of the S-N curve. Fractographic examination revealed that the fracture surfaces were complex and a number of fracture modes contributed to cracking.     

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.     

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.     

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.     

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.     

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.     

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 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.     

The effect of an irregular crack front on fatigue crack growth

Crack growth was initiated in 7075-T6 specimens from slits of different shapes in order to produce irregular and wavy crack fronts. Lower crack rates were found for more wavy crack fronts. Crack opening was also lower then, indicating that longer crack fronts produced lower $\text{K}$ values. Part of the environmental effect on crack growth is due to irregular crack fronts. The significance of fatigue fracture morphology for understanding certain influences and improving fatigue crack growth resistance is emphasized.     

The retardation phenomenon of fatigue crack growth in HT80 steel

The fatigue crack growth behavior resulting from single and multiple applications of overload was investigated for HT80 steel. A peak load was found to cause retardation of the crack growth rate, which becomes stronger with increasing the peak/baseline stress ratio or with decreasing baseline stress intensity. Multiple overloads resulted in additional retardation. These experimental data were explained according to a new model based on crack closure conception, being correlated with the residual plastic zone size ahead of crack tip induced by the peak overload(s). The proposed formulation of retardation was expressed simply as a function of peak/baseline stress ratio, $\text{r}$, and two material parameters, $\text{m}$ and β. $\text{m}$ the exponent parameter in Paris equation and β is the ratio of crack distance at the maximum retardation to the residual plastic zone size. The retardation was predicted to increase with increasing $\text{r}$ and $\text{m}$ and with decreasing β. It was suggested that the parameter, β, reflects the change in the morphology of crack tip resulted from the application of overload, which determines the shape of the curve for retarded crack growth rate vs crack distance.     

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.     

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.     

On the fatigue crack growth behaviour of selective laser melting fabricated Inconel 625: Effects of build orientation and stress ratio

The building of Inconel 625 material was carried out using the selective laser melting method, and its fatigue crack growth property at ambient temperature was experimentally investigated. Compact‐tension specimens with different building orientations were utilized to determine the stress intensity factor threshold and fatigue crack growth rate curves at different stress ratios (R). The results indicated that the fatigue crack growth properties in the near threshold stress intensity factor and Paris regions were greatly affected by the loading factor, as well as the orientation of the alloy. The mechanism of fatigue crack growth at different stages was observed and discussed using scanning electron microscopy. Finally, based on the framework of the linear elastic fracture, a new and applicable effective driving force factor range was introduced to replace the traditional stress intensity factor range (ΔK) with good accuracy for all of the fatigue crack growth test data, considering both the stress ratio and orientation.     

Fatigue and fracture of a Ni–P amorphous alloy thin film on the micrometer scale

Fracture and fatigue tests have been performed on micro‐sized specimens for microelectromechanical systems (MEMS) or micro system technology (MST) applications. Cantilever beam type specimens with dimensions of 10 × 12 × 50 μm³, approximately 1/1000th the size of ordinary‐sized specimens, were prepared from a Ni–P amorphous thin film by focused ion beam machining. Fatigue crack growth and fracture toughness tests were carried out in air at room temperature, using a mechanical testing machine developed for micro‐sized specimens. In fracture toughness tests, fatigue pre‐cracks were introduced ahead of the notches. Fatigue crack growth resistance curves were obtained from the measurement of striation spacing on the fatigue surface, with closure effects on the fatigue crack growth also being observed for micro‐sized specimens. Once fatigue crack growth occurs, the specimens fail within one thousand cycles. This indicates that the fatigue life of micro‐sized specimens is mainly dominated by a crack initiation process, also suggesting that even a micro‐sized surface flaw may be an initiation site for fatigue cracks which will shorten the fatigue life of micro‐sized specimens. As a result of fracture toughness tests, the values of plane strain fracture toughness, K_IC, were not obtained because the criteria of plane strain were not satisfied by this specimen size. As the plane strain requirements are determined by the stress intensity, K, and by the yield stress of the material, it is difficult for micro‐sized specimens to satisfy these requirements. Plane‐stress‐ and plane‐strain‐dominated regions were clearly observed on the fracture surfaces and their sizes were consistent with those estimated by fracture mechanics calculations. This indicates that fracture mechanics is still valid for such micro‐sized specimens. The results obtained in this investigation should be considered when designing actual MEMS/MST devices.     

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.     

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 growth of surface cracks in nickel-based superalloys

The fatigue growth of surface cracks in three nickel-base superalloys has been monitored using a DC electrical potential-drop technique at both 200°C and 600°C in air. A three dimensional finite element analysis stress intensity calibration has enabled these growth rates to be compared with standard data obtained from though-cracked compact tension specimens. Good agreement has been found between surface and through-crack growth rates over the range from threshold to $\text{～25}\text{MNm}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ although for applied stress intensity ranges in excess of this the surface cracks propagated more slowly than expected, particularly at 200°C. This retardation has been suggested to arise from the increased proportion of a plane stress crack growth for the shorter surface cracks leading to both increased closure effects and a change in the crack growth mechanism.     

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.