Influence of R on effective stress range ratio and crack growth

The influence of stress ratio R and stress intensity range ΔK on crack closure and fatigue crack growth were studied. Crack closure and crack growth experiments were performed on 6063-T6 Al alloy. Crack closure stresses were measured using a surface-measurement technique with a COD gauge. The gauge was placed at different locations behind the crack tip, and it was found that the location of the gauge does not influence the closure load. The closure load was however found to be a function of R and ΔK. Fatigue crack growth rate is found to depend upon R, U and ΔK. A model for both U and da/dN has been developed.     

A microcomputer control system for the measurement of fatigue crack growth data

A microcomputer-based system for the measurement of fatigue crack growth da/dn versus cyclic stress intensity factor ΔK data using compact-tension test specimens is described. The procedure has been developed to allow automatic measurement of crack growth rate under any specified combination and sequence of load conditions, i.e. ΔK and R (stress ratio) and includes the capability of establishing the threshold cyclic stress intensity factor ΔK₀. Crack extension measurement is effected from the elastic compliance evaluated from the AC component of the load and displacement signals to an accuracy of -3 μm every 1000 load cycles. Results from a typical low-alloy-steel rotor forging are presented to illustrate the use of the system.     

Fatigue properties of ultrafine grained low carbon steel produced by equal channel angular pressing

Ultrafine grained low carbon (0.15 wt.% C) steel produced by equal channel angular pressing (ECAP) was tested for investigating fatigue properties, including cyclic softening and crack growth rate. Emphasis was placed on investigating the effect of load ratio on the fatigue crack growth rates of ultrafine grained microstructure. The ECAPed steel exhibited cyclic softening. After the first cycle, the tension and compression peak stresses decreased gradually with the number of cycles. Fatigue crack growth resistance and the threshold of ECAPed ultrafine grained steel were lower than that of an as-received coarse grained steel. This was attributed to a less tortuous crack path. The ECAPed steel exhibited slightly higher crack growth rates and a lower ΔK_th with an increase in R ratio. The R ratio effect on growth rates and ΔK_th was basically indistinguishable at a lower load ratio (R>0.3) compared with other alloys, indicating that the contribution of the crack closure vanished. This was explained by the fact that finer grained materials produce a lower opening load P_op due to a relatively less serrated crack path. Consequently, K_min can reach K_op readily with a smaller increment of load ratio. The crack growth rate curve for the ECAPed ultrafine grained steel exhibited a linear extension to the lower growth rate regime than that for the coarse grained as-received steel. This behavior can be explained by a reverse crack tip plastic zone size (r_p) that is always larger than the grain size.     

Study of crack tip opening under cyclic loading taking into account the environment and R ratio

This study involves the R effect and environment effect on crack closure mode, in 7175 T 651 aluminium alloy. To obtain one of the selected objectives, it was necessary to use a clip gauge located at the notch of the compact specimen and a C.T.O.D. gauge located at the crack tip. The crack opening phenomena observed in our tests depends on the applied method which accounts for the differences in ΔK_eff found in the literature. The systematic use of the two methods allowed us to bring to light common features permitting the calculation of ΔK_eff according to Elber's criteria. The concept of ΔK_eff does not fully explain the influence of R ratio and the environment effect.     

Fatigue crack closure study based on whole-field displacements

This study is concerned with crack tip strain field fluctuations at loads below the point of crack closure in fatigue cycling. Moiré interferometry was used to investigate crack tip fields in compact tension specimens, cracked under constant stress intensity range and fixed R-ratio conditions. An elastic-plastic finite element model of simulated closure was developed to provide a theoretical cross-reference for the moiré studies. The ‘stretched zone’, which is believed to be the most significant source of closure effects, was simulated by inserting a constant thickness strip of elements into the crack before unloading from the maximum load point. Analysis of the crack tip fields in the experimental and theoretical cases was made in terms of crack face opening profiles, compliance changes and elastic stress intensity parameters. The latter were inferred through stress and displacement measurements made along circular and radial paths relative to the crack tip. Closure on the stretched zone was found to generate non-proportional loading in the crack tip field, so that the resulting stress changes were not well characterized by the asymptotic elastic equations. It is concluded firstly, that significant strain fluctuations occur below the point of closure load and that these should not be ignored in crack propagation studies. Secondly, the effective stress intensity range in fatigue cycling is not simply related to the open-crack stress intensity range and the need therefore remains for R-ratio and geometry effects to be treated as variables in crack propagation data collection programmes.     

Modelling and measurement of crack closure and crack growth following overloads and underloads

Ignoring crack growth retardation following overloads can result in overly conservative life predictions in structures subjected to variable amplitude fatigue loading. Crack closure is believed to contribute to the crack growth retardation, although the specific closure mechanism is debatable. The delay period and corresponding crack growth rate transients following overload and overload/underload cycles were systematically measured as a function of load ratio (R) and overload magnitude. These responses are correlated in terms of the local “driving force” for crack growth, i.e. the effective stress intensity factor range (ΔK_eff). Experimental results are compared with the predictions of a Dugdale-type crack closure model and improvements in the model are suggested.     

The effect of the stress ratio on fatigue crack growth in a 3% NaCl solution

Corrosion fatigue crack growth tests have been carried out at various stress ratios for a low alloy steel SNCM 2 and type 304 stainless steel.

Measurements of the effective stress intensity factor range ratio U were performed to explain the effect of stress ratio R.

The corrosive environment decreased da/dN at R = 0.1, 0.4 and little affected da/dN at R = 0.9 for SNCM 2 and increased da/dN at all R ratios for SUS 304.

It was confirmed that there exists a threshold stress intensity factor ΔK_thCF in 3% NaCl solution for both materials tested.

The corrosive environment decreased ΔK_thCF for all conditions tested except at R = 0.1 and 0.4 for SNCM 2, where ΔK_thCF-values were nearly equal to ΔK_th-values in air. ΔK_thCF/ΔK_th was 0.6 at R = 0.9 for SNCM 2 and 0.8, 0.5 and 0.7 at R = 0.1, 0.7 and 0.9 for SUS 304, respectively.

It was shown that the complicated effect of stress ratios on crack growth for SNCM 2 can be explained using effective stress intensity factor ΔK_eff.     

A study of the effects of mechanical and environmental variables on fatigue crack closure

Using the potential drop technique, fatigue crack closure has been monitored in pin loaded SEN specimens of -titanium, a titanium alloy and EN24 steel. The specimens were tested in tension-tension under conditions closely approximating to plane strain, and closure was only detected in vacua of better than 133 mN m⁻² (10⁻³ torr). No significant closure was detected in air. The extent of the crack area closed at minimum load varied with air pressure, applied stress, R ratio (R = L_min/L_max), crack length, material, and loading mode. Additional experiments made with a dip gauge showed that the COD/applied load response of the crack was non-linear in vacuum above minimum load in the fatigue cycle confirming that crack closure was occcurring. It is shown that for a given material, loading mode and air pressure, the effect of loading and crack length variables on crack area closed at minimum load can be characterised in terms of the parameter (K²_min-ΔK², this being proportional to the calculated COD at minimum load. The extent of closure in vacuum is influenced extensively by this parameter.     

Fatigue crack growth thresholds-the influence of Young''s modulus and fracture surface roughness

In the present investigation it is shown that the effective fatigue threshold is uniquely correlated to the Young's modulus for a wide range of metallic and composite materials (ΔK_th,eff=1.64·10⁻²·E). It is also demonstrated that the crack closure level K_cl increases with increased roughness of the fracture surface . K_cl and are quantitatively related via the equation for steels with widely different mechanical properties and grain sizes (120 MPa<R_p<1100 MPa, 1 μm<λ<100 μm). This relation can be extended to materials other than steels (e.g. aluminium and WC-Co alloys) by normalising against Young's modulus. The roughness value represents the standard deviation of height of the fracture surface and is shown to be simply related to the length and angle distributions of the linear length elements constituting the fracture profile.     

Fatigue crack closure

A loading stage for the scanning electron microscope has been used in conjunction with the stereoimaging technique to study fatigue crack closure for a center notched specimen of an aluminum alloy. The results are compared to similar measurements from single edge notched specimens of the same alloy and other materials. The magnitudes of closure loads were found to be different for these two specimen designs, but the dependence on stress intensity factor (ΔK) is the same. Comparison of experiments is made with a finite element model simulation of crack opening, a simple model is developed which simulates the observed opening behavior, and a method is given for estimating threshold ΔK from materials parameters and crack opening behavior in the near threshold region.     

The use of ΔK when examining microstructural effects on small fatigue crack growth

The behaviour of small fatigue cracks has been studied in the Al---Li---Cu---Mg---Zr alloy 8090. It was found that the crack inclination normal to the surface of the specimen made crack deflections and kinking in the plane of the specimen surface irrelevant to the crack driving force. The low closure levels associated with small fatigue cracks reduce the effect of microstructure on crack growth but this does not affect the ability of ΔK (stress intensity factor range) to detect microstructural influences. The use of ΔJ (J-integral range) as a correlating parameter reduced the differences between the data for long and short fatigue cracks. However, there was no evidence that ΔJ was superior at identifying microstructural effects. Similarly the effect of the higher-order terms on the value of ΔK was found to be minor. It is concluded that the use of ΔK is not likely to bias the microstructural effects and so ΔK may be used when examining microstructural effects on small fatigue crack growth.     

Evaluation of fatigue crack growth behavior of GLARE3 fiber/metal laminates using a compliance method

The objectives of this study were to investigate the effectiveness of a compliance method for analyzing the fatigue crack growth of GLARE3 fiber/metal laminates. The materials tested were GLARE3-5/4 (2.6 mm thick) and GLARE3-3/2 (1.4 mm thick). Centrally notched specimens with two kinds of notch length and two kinds of fiber orientation were fatigue tested under constant amplitude loading. The expression of the experimental stress intensity factor, K_exp, for the 2024-T3 aluminum-alloy layers of a GLARE3 is formulated and K_exp were obtained from the relationship between crack length and specimen compliance. The test results clarified the following: (1) da/dN–ΔK_exp relationships roughly show the linear relationship independent of the maximum stress level, specimen thickness, notch length, and fiber orientations, (2) the da/dN–ΔK_exp relationships approximately agree with the linear part and its extension of Paris–Erdogan’s law obtained for the da/dN–ΔK relationship of the 2024-T3 aluminum-alloy, (3) the compliance method is effective for analyzing fatigue crack growth in GLARE3 laminates.     

Fatigue threshold and crack growth in an electron beam weld made of steel and bronze

In this research topic some experimental tests with single-edge notched beams were performed to determine the threshold load value for fatigue crack growth and to characterize fatigue crack behaviour of an electron beam weld made of steel and bronze. Subsequently, numerical analyses were done to estimate the threshold value ΔK_th and to simulate the fatigue crack growth. The calculated crack path was compared to those determined experimentally. The objective was to find out the necessary fracture properties for an analysis of an electron beam welded worm wheel and to asses the capability of usual fracture analysis software to simulate fatigue crack growth in welds.     

Statistical evaluation of fatigue crack propagation properties including threshold stress intensity factor

The relationship between fatigue crack propagation rate, da/dn, and range of stress intensity factor, ΔK, including threshold stress intensity factor, ΔK_th, is analyzed statistically. A non-linear equation, da/dn = C{(ΔK)^m-(ΔK_th)^m}, is fitted to the data by regression method to evaluate the 99% confidence intervals. Several experimental results on fatigue crack propagation properties of welded joints are compared by using these confidence intervals.     

Fatigue crack initiation and growth under mixed mode loading in aluminum alloys 2017-T3 and 7075-T6

Fatigue crack initiation and growth characteristics under mixed mode loading have been investigated on aluminum alloys 2017-T3 and 7075-T6, using a newly developed apparatus for mixed mode loading tests. In 2017-T3, the fatigue crack initiation and growth characteristics from a precrack under mixed mode loading are divided into three regions—shear mode growth, tensile mode growth and no growth—on the ΔK_I-ΔK_II plane. The shear mode growth is observed in the region expressed approximately by ΔK_II > 3MPa√m and ΔK_II/ΔK_I > 1.6. In 7075-T6, the condition of shear mode crack initiation is expressed by ΔK_II > 8 MPa√m and ΔK_II/ΔK_I > 1.6, and continuous crack growth in shear mode is observed only in the case of ΔK_I/ΔK_II, 0. The threshold condition of fatigue crack growth in tensile mode is described by the maximum tensile stress criterion, which is given by Δσ_θmax √2πr 1.6MPa√m, in both aluminum alloys. The direction of shear mode crack growth approaches the plane in which K_I decreases and K_II increases towards the maximum with crack growth. da/dN-ΔK_II relations of the curved cracks growing in shear mode under mixed mode loading agree well with the da/dN-ΔK_II relation of a straight crack under pure mode II loading.     

On the calculation of closure-free fatigue crack propagation data in monolithic metal alloys

A computational method is described for the determination of ΔK_b, corresponding to a fatigue crack growth rate of b/cyc, where b is the Burgers vector for a monolithic metal alloy. ΔK_b is found to be numerically equal to E√b for the case of closure-free crack growth behavior. Given that the closure-free FCP rate of many monolithic metals varies with ΔK³, the growth rate of metal alloys at ΔK ΔK_b is given by da/dN = (ΔK/E)³(1/√b. Excellent agreement is found between experimental and computed FCP data for the case of monolithic metal alloys. The limits of these relations for metal-matrix composites and ceramics are discussed.     

Effects of welding residual stresses on fatigue crack growth behaviour in butt welds of a pipeline steel

In the present test the fatigue crack growth rate in the parent plate, weld and cross-bond regions was measured and the results were correlated with the stress intensity range ΔK and the effective stress intensity range ΔK_eff. It is indicated that the welding residual stresses strongly affect the crack growth rate. For the weld metal and cross-bond compact tension specimens in which crack growth is along the weld line the fatigue crack growth rate increases as the crack grows. However, for the T compact tension specimen in which crack growth is perpendicular to the weld line at a constant value of applied ΔK the crack growth rate initially decreases as the crack grows. Particularly, at a low constant value of applied ΔK the crack growth rate obviously decreases and the crack fails to grow after short crack growth. When the crack grows to intersect the welded zone, the fatigue crack growth rate gradually increases as the crack grows further. It is clear that the effect of welding residual stresses on the crack growth rate is related to the position of the crack and its orientation with respect to the weld line. Finally, the models of welding residual stress redistribution in the compact tension specimens with the growing crack and its influence on the fatigue crack closure are discussed. It appears that for a butt-welded joint one of the crack closure mechanisms may be considered by the bend or rotation deformation of crack faces due to the welding residual stress redistribution as the fatigue crack grows in the welded joint.     

Fatigue crack growth characteristics of rotor steels

Room temperature fatigue crack growth rate data were generated for Ni-Mo-V (ASTM A469, Cl-4), Cr-Mo-V (ASTM A470, Cl-8) and Ni-Cr-Mo-V (ASTM A471, Cl-4 and a 156,000 psi yield strength grade) rotor forging steels. Testing was conducted with WOL type compact toughness specimens and the results presented in terms of fracture mechanics parameters. Data show that the Ni-Cr-Mo-V steels exhibit slower fatigue crack growth rates at a given stress intensity range (ΔK) than do the Ni-Mo-V steels. In addition, the Cr-Mo-V steel was found to exhibit slower growth rates than the other alloys at ΔK levels below 40 ksi √in but somewhat foster rates at ΔK levels in excess of 45 ksi √in. The fatigue crack growth rate properties of the alloys studied conform to the generalized fracture mechanics crack growth rate law where da/dN = C₀ΔK^R. It was noted that the fatigue crack growth rate parameters n and C₀ tend to decrease and increase, respectively, with increasing material toughness, K_ic.     

Effect of fiber bridging on the fatigue crack propagation in carbon fiber-reinforced aluminum laminates

A superior crack propagation resistance was observed on various carbon fiber-reinforced aluminum laminates (CARALL) under tension-tension fatigue. It might be attributed to the restraint on the crack opening imposed by intact fibers in the crack wake. These fibers bridging the crack could reduce the effective stress intensity factor actually experienced by the crack tip. Based on the measurement of crack length and delamination size, the effective stress intensity range, ΔK_eff, of fatigue-damaged CARALL laminate was calculated by using a simplified analytical model. It was shown that the fatigue crack propagation rate in CARALL could be expressed as a unique function of the calculated ΔK_eff, which agree well with the Paris equation for the unreinforced aluminum alloy. This result confirmed the applicability of this simplified analytical model in CARALL laminates.     

A study of fatigue crack growth of 7075-T651 aluminum alloy

Both standard and non-standard compact specimens were employed to experimentally study the crack growth behavior of 7075-T651 aluminum alloy in ambient air. The effects of the stress ratio (R), overloading, underloading, and high–low sequence loading on fatigue crack growth rate were investigated. Significant R-ratio effect was identified. At the same R-ratio, the influence of specimen geometry on the relationship between crack growth rate and stress intensity factor range was insignificant. A single overload retarded the crack growth rate significantly. A slight acceleration of crack growth rate was identified after a single underload. The crack growth rate resumed after the crack propagated out of the influencing plastic zone created by the overload or underload. A parameter combining the stress intensity factor range and the maximum stress intensity factor can correlate the crack growth at different stress ratios well when the R-ratio ranged from −2 to 0.5. The parameter multiplied by a correction factor can be used to predict the crack growth with the influence of the R-ratio, overloading, underloading, and high–low sequence loading. Wheeler’s model cannot describe the variation of fatigue crack growth with the crack length being in the overload influencing zone. A modified Wheeler’s model based on the evolution of the remaining affected plastic zone was found to predict well the influence of the overload and sequence loading on the crack growth.