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.     

The effect of repeating load on the crack growth initiation and crack propagation in delayed failure

The delayed failure test under repeating load was carried out with pre-cracked specimen. The incubation time and the crack propagation rate were correlated with the stress intensity factor K.

The incubation time is decreased by the superposition of repeating load, as the range of stress intensity factor ΔK or the repeating frequency f increase. The reason can be explained by the promotion of corrosion reaction due to, e.g. the destruction of oxide film on the crack tip, which facilitates the invasion of hydrogen atoms into the material.

The crack propagation rate da/dt is decreased by the superposition of repeating load, and there exist two valleys of crack propagation rate minima on the da/dt vs f and da/dt vs ΔK curves. One valley corresponds to the interaction between the cyclic movement of the region with tri-axial tensile stress and the hydrogen atoms diffused from crack tip, which disturbs the concentration of hydrogen atoms. Another seems te correspond to the generation of retained compressive stress which reduces the effective stress intensity at crack tip and supresses the invasion and diffusion of hydrogen atoms.     

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.     

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-growth characteristics of two magnesium alloys

Magnesium alloys are being increasingly used for engineering applications. Fatigue crack-growth data have therefore been obtained for a high strength magnesium-Zr alloy and a medium strength, weldable magnesium-Mn alloy. The results of tests on sheet material are presented in terms of the range of stress intensity factor ΔK. Critical values of ΔK necessary for fatigue crack growth ΔK_c were also obtained. The behaviour of the two alloys was similar; both rates of crack growth and ΔK_c were sensitive to mean stress. Fatigue crack growth was entirely on a 90° plane with no sign of the transition to crack growth or 45° planes usually observed in sheet materials. This was ascribed to the effects of preferred orientation of the crystal structure.     

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.     

Relation between fatigue threshold and fatigue limit for surface-rolled specimens

After cylinder notch fatigue specimens of 40 CrNiMo steel were rolled, their fatigue limit increased by 41%. The rolled specimens did not fracture, even though they had been loaded for 10⁷ cycles under fatigue limit stress, but a non-propagating fatigue crack was generated. Thus the value of the fatigue limit depends on the fatigue threshold value ΔK_th of the metal of the rolled layer. Plastic deformation increased ΔK_th in these experiments. It can be inferred that ΔK_th of the rolled layer increases from the occurrence of plastic deformation and microvoids on the layer. Calculation of the effect of residual stress in the crack wake on the stress intensity factor ΔK indicates that residual compression stress decreases ΔK by 21.5 MPa √M. It was calculated that rolling induced both the length of the non-propagating crack and the increase of fatigue limit. The calculated values are in accord with experiment. Analysis and calculations indicate that the non-propagating crack is generated on the rolled layer. Thus the fatigue limit is improved because rolling produces residual compression stress in the layer (which decreases the stress intensity factor), and increases ΔK_th of the layer.     

Plastic zone formation and fatigue crack extension during high cyclic bending of steels

In repeated high cyclic bending, with constant load amplitude, the size and the shape of the plastic zone preceding the propagating crack is controlled by local structural conditions near the tip rather than by stress intensity. No significant correlations were found between the experimentally determined sizes of plastic zone and the theoretically predicted values of Liu and Rice. The plastic zone sizes ahead of the propagating crack cannot be simply expressed as proportional to the rate of fatigue crack propagation, though a simple relationship exists between the rate and the stress intensity factor. The relationship given by Paris, dl/dN = QΔKⁿ, describes the rate of crack propagation only in a limited range of relative crack length, x < 0.5. The extent of this range depends on the structure and on the level of applied cyclic stress. Beyond this range, the Paris equation could not be applied and the crack propagation cannot be related to the stress intensity factor.     

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.     

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.     

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.     

The growth of fatigue cracks through particulate sic reinforced aluminum alloys

Crack growth rates for large fatigue cracks in 12 variations of particulate silicon carbide reinforced aluminum alloy composites have been measured. Composites with seven different matrix alloys were tested, four of which were of precipitation hardening compositions, and those were tested in both as-extruded and peak aged conditions. Five of the materials were made by casting, ingot metallurgical methods and two of the alloys by mechanical alloying, powder metallurgical methods. For both manufacturing methods, primary fabrication was followed by hot extrusion. The fatigue crack growth curves exhibited an approximately linear, or Paris law, region, fitting the function da/dN = BΔK^s, and a threshold stress intensity factor, ΔK_th. As has been found for other materials, the coefficients B and s are correlated; for these composites In B= −16.4−2.1s. A correlation was also found between ΔK_th and s, and it was found possible to compute the magnitude of ΔK_th using a simple model for the threshold together with yield stress and SiC size and volume fraction. These results were explained using a relationship between ΔK_th and crack closure determined previously for unreinforced aluminum alloys. The path of fatigue crack growth is through the matrix for these composites, and SiC has the effect of altering the slip distance, therefore, the plasticity accompanying fatigue cracks. It was shown that all the crack growth rate curves were reduced to one equation having the form da/dN = B'ΔK_eff^s' where B' = 6.5 × 10^-9m/cy and s' = 1.7. A partly theoretical method for predicting fatigue crack growth rates for untested composites is given. Fatigue crack surface roughness was measured and found to be described by a fractal dimension, but no correlation could be obtained between surface roughness parameters and ΔK_th.     

Fatigue crack growth behavior of cracked aluminum plate repaired with composite patch

In this study, we investigated the fatigue crack growth behavior of cracked aluminum plate repaired with bonded composite patch especially in thick plate. Adhesively bonded composite patch repair technique has been successfully applied to military aircraft repair and expanded its application to commercial aircraft industry recently. Also this technique has been expanded its application to the repair of load bearing primary structure from secondary structure repair. Therefore, a through understanding of crack growth behavior of thick panel repaired with bonded composite patch is needed. We investigated the fatigue crack growth behavior of thick panel repaired with bonded composite patch using the stress intensity factor range (ΔK) and fatigue crack growth rate (da/dN). The stress intensity factor of patched crack was determined from experimental result by comparing the crack growth behavior of specimens with and without repair. Also, by considering the three-dimensional (3D) stress state of patch crack, 3D finite element analyses were performed to obtain the stress intensity factor of crack repaired by bonded composite patch. Two types of crack front modeling, i.e. uniform crack front model and skew crack front model, were used. The stress intensity factor calculated using FEM was compared with the experimentally determined values.     

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.     

Automatic near-threshold fatigue crack growth rate measurements at liquid helium temperature

The development of a fully automated test apparatus for near-threshold fatigue crack growth rate measurements in a liquid helium environment is described, and some initial results for AISI 300 series stainless steels are presented. The experimental apparatus consists of a servohydraulic test machine and a cryostat, complete with a minicomputer, a programmable arbituary waveform generator, a programmable digital oscilloscope and a fully automatic liquid helium refill system. The technique uses 6.4 mm thick compact specimens subjected to systematically decreasing loads, with 24 h operation at 40 Hz, the crack growth being continuously monitored by specimen compliance measurements. The results presented in this study include da/dN vs ΔK curves and threshold fatigue stress intensity factors, ΔK_th, at 4 K for AISI 304L, 304LN and 316 stainless steels. The near-threshold fatigue behaviours of these materials are similar, and the fatigue crack growth rate trends at intermediate ΔK levels nearly agree with published results.     

The solution of a displacement discontinuity for an anisotropic half-plane and its applications to fracture mechanics

By imaginal method the solution of displacement discontinuity for anisotropic half-plane is derived in this paper. According to the Betti's reciprocal theorem, the relationship between the stress intensity factor K_I and the increment Δv/Δa is established and numerical results of K_I are obtained by the twice calculation method. Furthermore, the problem of edge crack chopping is studied in great detail, and the area of contaction and stress intensity factor K_I are found. These results are very worthwhile for research of chopping fracture in theory.     

Depth of intergranular oxygen diffusion during environment-dependent fatigue crack growth in alloy 718

The elevated-temperture fatigue crack growth behavior in alloy 718, when subjected to a loading frequency lower than the transitional frequency of this alloy, is viewed as fully environment dependent. In this process, the crack growth increment per loading cycle is assumed to be equal to the intergranular oxygen diffusion depth at the crack tip during the cycle effective oxidation time. In order to identify the trend of this diffusion depth an experimental program was carried out on compact tension specimens made of alloy 718 at 650 °C in which fatigue crack growth measurements were made for cyclic load conditions with and without hold time periods at minimum load level. This work resulted in establishing a relationship correlating the intergranular oxygen diffusion depth and the value of the stress intensity factor range ΔK. This relationship, when integrated over the cycle effective oxidation time, results in a closed-form solution describing the environment-dependent fatigue crack growth rate. A comparison is made between the results of this solution when applied to different loading frequencies and the corresponding experimental results. This comparison shows good agreement between the two sets of results. Furthermore, by combining the parabolic rate law of diffusion and the equation for the intergranular oxygen diffusion depth, an explicit expression for the oxygen diffusivity of grain boundaries is derived. It is found that this diffusivity is both a ΔK- and a frequency-dependent parameter.     

Long crack growth behavior of implant material Ti–5Al–2.5Fe in air and simulated body environment related to microstructure

The fatigue crack propagation behavior of Ti–5Al–2.5Fe with various microstructures for biomedical applications was investigated in air and in a simulated body environment, Ringer's solution, in comparison with that of Ti–6Al–4V ELI and that of SUS 316L stainless steel. The crack propagation rate, da/dN, of Ti–5Al–2.5Fe in the case of each microstructure is greater than that of the Widmanstätten structure in Ti–6Al–4V ELI in air whereas da/dN of Ti–5Al–2.5Fe is nearly equal to that of the equiaxed structure in Ti–6Al–4V ELI in air when da/dN is plotted versus the nominal cyclic stress intensity factor range, ΔK. da/dN of the equiaxed structure and that of the Widmanstätten structure in Ti–5Al–2.5Fe are nearly the same in air when da/dN is plotted versus ΔK. da/dN of Ti–5Al–2.5Fe is nearly equal to that of SUS 316L stainless steel in the Paris Law region, whereas da/dN of Ti–5Al–2.5Fe is greater than that of SUS 316L stainless steel in the threshold region in air, when da/dN is plotted versus ΔK. da/dN of Ti–5Al–2.5Fe or Ti–6Al–4V ELI is nearly the same in air and in Ringer's solution when da/dN is plotted versus the effective cyclic stress intensity factor range, ΔK_eff, whereas da/dN of Ti–5Al–2.5Fe or Ti–6Al–4V ELI is greater in Ringer's solution than in air when da/dN is plotted versus ΔK.     

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.     

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.