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446 Applications Intermediate improvements in fatigue performance were observed on Ti-6-7/AC. Marked changes in the slope of the S–N curves were observed in Ti-6-7/WQ owing to pronounced lifetime improvements in the HCF regime while finite life was only slightly improved. These results serve to illustrate the complex nature of the effect of surface treatments on fatigue behavior, particularly in the HCF regime, and the dependence of such behavior on the characteristics of the specific material such as strain hardening/softening. The ability of a surface treatment, and the resulting residual stresses that are produced, to slow or stop a fatigue crack is probably the most important aspect in fatigue life improvement, particularly in the HCF regime where complete crack arrest defines the condition for determining an endurance limit. Guagliano and Vergani [59] address the problem of predicting the conditions for non-propagation of cracks in shot-peened speci- mens. They adopt the premise that fatigue alleviation due to shot peening is mainly due to the ability of the residual stresses to stop crack propagation and not in preventing fatigue crack initiation. Their approach is based on fracture mechanics and the existence of a threshold for crack propagation, K th . With the aid of an FEM model which considers both the applied loading and the compressive residual stress field, and taking into account crack closure and contact between crack faces, they are able to explain the presence of non-propagating cracks with typical depths from 0.15 to 0.3 mm in a low alloy steel. They note that the depth at which the cracks have stopped is entirely dependent on the residual compressive stress field induced by shot peening. Such a finding can be used as motivation for the use of other surface treatments that provide greater depths of residual compressive stresses. The control of the initiation and early phase of crack propagation of surface cracks is considered to be paramount for prolonging the fatigue life and improving the HCF strength of engineering components subjected to cyclic loading. The extensive use of shot peening to achieve these purposes through the development of near-surface plastic deformation is based on the widely accepted concepts that work hardening and high magnitude compressive residual stresses are responsible for these benefits. Work hard- ening is expected to increase the resistance to flow in the material while compressive residual stresses can reduce the mean stress for crack initiation or produce closure to retard subsequent crack propagation. For many years, the benefits of the residual stresses were used as motivation for shot peening, and methods for optimizing the depth and magnitude of these stresses were sought after. While many of the approaches have been highly empirical and dependent upon large databases, work such as that by Rodopoulos et al. [60] has endeavored to develop scientifically based optimization procedures for shot peening of aluminium alloys. Their approach treats residual stress profiles, work hardening profiles, and surface roughness as the major parameters which control the final fatigue life improvements. The methodology also predicts crack-closure stress profiles to address the early statges of crack propagation [61]. The surface roughness due to shot peening is treated in terms of elastic stress concentration based on surface roughness HCF Design Considerations 447 measurements. The authors also acknowledge that shot peening has been reported to pro- duce distortion of the near surface microstructure, but such an effect was not considered in their process optimization modeling. The results of the optimization process produced shot-peening conditions that showed a significant improvement in the fatigue life of a 2024-T351 aluminium alloy, but the benefits were mainly in the LCF regime. The life improvement was attributed to a prolonged period of crack arrest. The benefits in the HCF regime, where crack growth is a go, no-go situation, were much less obvious. As pointed out previously, “beneficial effects” have to be examined in terms of the life range in the S–N curve where such observations are made. One of the more significant observations in [60] is the relaxation of the residual stresses during fatigue cycling. An example of such reduction for two values of applied stress under the same shot-peening conditions is shown in Figure 8.60 from that reference. It is noted in this and other examples given in [60] that the relaxation of the residual stresses seems to depend on the applied stress while the basic shape of the residual stress profile remains unaffected. The authors caution, therefore, that credit for residual stresses as a far-field parameter in terms of eff should be avoided since it will overestimate the true effect of the residual stresses because of the relaxation of the stress field. 8.6.3. Deep residual stresses The realization that a compressive residual stress layer at the surface can improve the fatigue properties of a material, particularly by retarding crack growth, has encouraged the development of processes where the depth of the layer has been increased over that obtained with conventional shot peening. The concept of a deeper layer is related to the length of crack that may be retarded by having residual stresses that go deeper into the material. In airframe applications where holes are expanded in order to produce a compressive residual stress field around the hole, the length of crack that has to be considered in a damage tolerant analysis can be increased over that used in analysis on an untreated hole. Thus, as compressive residual stresses are imparted deeper into a material, the resistance to crack propagation is improved for longer crack lengths. An investigation into the fatigue behavior of Ti-6Al-4V subjected to deep rolling and laser shock processing (LSP) was conducted by Nalla et al. [62] at both ambient and elevated temperatures. Deep rolling, as used in that investigation, involved high pressures on a spherical rolling element that produces surface plastic deformation from which deep compressive residual stresses and a work-hardened surface layer are induced. LSP, another method of inducing deep compressive residual stresses, is discussed in more detail below. For both procedures, the residual stress field was more than 0.5 mm deep. For the specific process parameters and test specimen geometry used, deep rolling produced more intense compressive residual stresses as well as a higher degree of work hardening. Both processes produced enhanced HCF resistance at ambient temperature that was attributed 448 Applications –200 –160 –120 –80 –40 0 40 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0% of life 25% of life 50% of life 75% of life Residual stress (MPa) Depth (mm) σ max = 240 MPa σ max = 270 MPa (a) –200 –160 –120 –80 –40 0 40 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0% of life 25% of life 50% of life 75% of life Residual stress (MPa) Depth (mm) (b) Figure 8.60. Residual stress relaxation pattern in an aluminium alloy at a maximum stress of (a) 240 MPa, (b) 270 MPa (from [60]). to both the deep residual stress field and the formation of a work-hardened near-surface layer. At elevated temperature, the near-surface compressive residual stresses were almost completely relaxed, but the fatigue properties were still enhanced, although not as much as at ambient temperature. The authors believe that the benefit at elevated temperature 450 C is associated primarily with the induced work-hardening near-surface layer that is particularly stable, even at high temperature. In this particular example, as well as in carbon steel discussed earlier [53], the beneficial effects of surface treatments are not associated solely with the residual stress fields that are produced in shallow as well as deep layers near the surface. HCF Design Considerations 449 It is of interest to note that processes such as laser shock processing (LSP), where deep compressive residual stresses are induced into the surface region of a material, were originally thought to derive their benefits from changes in the material. Early theories assumed that the increases in fatigue performance were due to work hardening effects, but gradually it became apparent that LSP-induced compressive residual stresses were also a contributing, if not dominating, factor [63]. In the discussions above, no mention has been made of the effects of defects on the fatigue properties in surface-treated specimens or components. It has been noted that fatigue failures in compressively loaded components such as ball or roller bearings can be traced to the presence of defects such as slag inclusions in steels. Almen and Black [50] comment on this type of failure in the following: From previous experience, it is known that fatigue cracks could be caused only by tensile stresses, but the tensile stress in bearing contacts, as calculated by the Hertzian equation, was too low to cause fatigue cracks. …it became clear that microresidual tensile stresses of great magnitude were developed in the steel adjacent to the slag inclusions, voids, and similar defects. … Residual tensile stress develops in such local, compressively deformed metal because the adjacent sound metal does not suffer such plastic deformations and therefore recovers elastically when the elastic load is removed. The drastically deformed metal does not so recover but is forceably restored to nearly its original dimensions by the greater volume of elastically recovered metal. The result is high-magnitude residual tensile stress adjacent to the inclusion. The stress in this small volume of steel ranges from high-magnitude residual tensile stress when no external load is acting to compressive stress when external load is applied. These repeated tensile stresses eventually result in fatigue cracks that grow at acute angles to the surface and form the well-known but variously named pits, flakes, spalls, or cavities that destroy ball bearings, roller bearings, cams, railroad rails, and probably gear teeth. 8.6.3.1. Application to an airfoil geometry In recent years, surface treatments that impart residual stresses much deeper into the surface than conventional shot peening have been studied in specific geometries and applications. The approaches in both understanding and modeling have followed much of the work on shot peening, described above in Section 8.6.2. For example, the beneficial effects of LSP in a simulated airfoil geometry were demonstrated in a study on Ti-6Al-4V [64, 65]. The results of those investigations are presented here in detail because they provide a representative example of many features that are involved in the use of deep compressive residual stress fields, irrespective of the process used to induce them into a component. In the investigations of Ruschau et al., LSP, developed in the 1970s as a fatigue-enhancement surface treatment for metallic materials (see [66] for example), was used as the method for introducing deep compressive residual stresses into a simulated 450 Applications 0.90 0.20 R Notch details 102 63.5 9.5 19.0 11.4 0.75 6.4 R 77.0 Figure 8.61. Geometry of 3-point bend airfoil specimen (dimensions in mm). airfoil leading edge geometry. A unique 3-point bend test specimen, shown in Figure 8.61, was designed and employed to study the effect of LSP on the FCGR properties of Ti-6Al- 4V. The specimen had a typical airfoil leading edge thickness of 0.75 mm and an overall cross section that included sufficient area to counterbalance the residual compressive stresses that developed due to the LSP treatment along part of the leading edge. The back edge of the sample (opposite the leading edge) was considerably thicker to provide constraint as well as to prevent buckling during the 3-point bend loading. Finally, the cross section of the sample was sufficiently tapered so that fatigue crack growth information could be obtained both from regions containing through-thickness residual compressive stresses, as well as in sections where the compressive stresses were not completely through the thickness. This is of particular concern in airfoil applications because, as the thickness increases away from the edge, a tensile residual stress or reduced compressive stress region may be present near the centerline, possibly compromising any benefits created by LSP. The actual shock processing, conducted by LSP Technologies, Inc., consisted of approx- imately 13 hits or strikes that produced a laser spot pattern as shown in Figure 8.62. The resulting surface residual stress field is shown in Figure 8.63 as a function of dis- tance from the leading edge in the direction of crack growth (y). These measurements were made using conventional X-Ray diffraction (XRD) techniques and, in the case of titanium, interrogate a surface layer of approximately 10m thickness. The average com- pressive stress in the x direction x , perpendicular to the crack plane, is approximately 850 MPa at the specimen surface and is reasonably constant throughout the LSP processed region over an area beginning ≈ 1–2 mm back from the leading edge. Near the leading HCF Design Considerations 451 5.6 mm spot Dia. (13 total) 2.0 mm 3.9 mm 3.9 mm Figure 8.62. Laser spot pattern. –1000 –800 –600 –400 –200 0 200 02468101218 σ x (MPa) Distance from edge, y (mm) Edge of LSP region Figure 8.63. Surface residual stresses for an LSP sample along the direction of crack growth (at x = 0). edge, the residual surface stresses are significantly lower as a result of lack of constraint at the free edge of the sample. Likewise at the back edge of the LSP region y ≈7mm, the compressive surface stresses drop rapidly to zero, and become tensile just outside of the LSP processed region. The compressive surface stresses measured well outside the LSP region (i.e. 8–14 mm from edge) are believed to be attributable to low stress grinding operations used in specimen fabrication. Residual stresses measured at the surface in the direction perpendicular to the direction of loading y were minimal due to the narrow LSP processed region as well as the lower constraint at the leading edge where the free surface requires y 0. Residual stress into the depth was examined at two locations in the LSP processed area, and the resulting stress profiles are shown in Figure 8.64 for two locations, 0.5 and 5 mm from the leading edge. A compressive stress field is evident throughout the sample thickness at both locations, dropping from a peak compression of 600–800 MPa at the surface to a minimum compressive stress of 200MPa at the interior. Notice that at both locations the peak compression at the surface decays to the lesser value over a depth of 452 Applications –800 –700 –600 –500 –400 –300 –200 –100 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 σ x (MPa) Depth (mm) Specimen CL 0.5 mm from L.E. –800 –700 –600 –500 –400 –300 –200 –100 0 σ x (MPa) 0 0.5 1 1.5 2 Depth (mm) Specimen CL 5 mm from L.E. (a) (b) Figure 8.64. Through-thickness residual stress profile for an LSP sample as a function of depth; (a) stress profile 0.5 mm from leading edge; (b) stress profile 5 mm from leading edge. approximately 0.2 mm. At the 5 mm location where the sample thickness is approximately 2 mm, the magnitude of the compressive stress field increases slightly at the center of the sample. To compare crack growth characteristics of a treated sample with those of an untreated sample, fatigue testing of the simulated airfoil samples was carried out under 3-point bend, constant amplitude (CA) loading (see Figure 8.61). To examine mean stress effects, two stress ratios R were examined: R = 01 and 0.8. Crack initiation and growth was monitored on all samples using an electric potential difference (EPD) technique where crack length changes of typically 2–3 m were readily detected. HCF Design Considerations 453 An equation was developed using the results from a 3-dimensional elastic finite element analysis of the geometry and loading conditions shown in Figure 8.61 and is valid for all a/W ≤06. Using the strength of materials equation for bending stress, =Mc/I (8.11) where M = bending moment (one-half of the applied load × one-half the support span), c = distance from the centroid of the cross section to the leading edge, and I = moment of inertia of the specimen cross section. The K solution for this specimen is found to be: K = √ afa/W (8.12) fa/W = 11215−50402a/W +144979a/W 2 −220211a/W 3 +129270a/W 4 1−a/W 3/2 (8.13) where a is the crack length measured from leading edge, and W is the total height of the specimen (19 mm). The crack growth response of a non-processed airfoil sample, as well as from a standard C(T) sample, were obtained at both R =01 and R =08. The results from the two sample types agreed reasonably well and are denoted as “baseline” hereafter. The FCGR results for the LSP samples at R = 01 are presented in Figure 8.65 (solid symbols), along with the curve representing the baseline data and closure-corrected data (open symbols), discussed later. Data obtained from the LSP samples clearly demonstrate a significant advantage in FCGR resistance over baseline material when plotted as a function of applied K. Growth rates for the LSP samples in the range of K of 30–40 MPa √ m are nearly three orders of magnitude slower than for the unprocessed material; however, as the applied maximum stress intensity factor approaches the fracture toughness of the material the two data sets appear to converge. For the purpose of comparing results from baseline and LSP samples, compliance measurements were made to evaluate crack closure levels and thus compute the effective crack driving force. For the baseline samples, the compliance traces appear linear over a wide range of crack lengths, indicating no apparent evidence of crack closure. The compliance traces for LSP samples, on the other hand, displayed clear evidence of crack closure. For the tests at R = 01, the opening load value, P open , corresponding to the fully opened crack tip was approximately 80% of the maximum applied load throughout the LSP region. Outside the LSP region (corresponding to crack lengths in excess of 7 mm) the closure levels began to drop off drastically. The magnitude of the residual compressive stress field is directly responsible for the degree of crack closure observed. 454 Applications 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 110 100 ΔK applied ΔK effective da/dN (m/cycles) Baseline R = 0.1 Ti-6Al-4V R = 0.1 ΔK (MPa√m) Figure 8.65. The FCGR data for LSP samples at R =01 as a function of K and K eff . Using this opening load and conventional closure concepts to define an effective stress intensity range, K eff , the da/dN data for different stress ratios can be consolidated into a single curve. This value of K eff is defined simply as: K eff =K maxapplied −K open (8.14) In the absence of closure, K open equals the minimum applied K, and hence the applied K is equal to K eff . The LSP crack growth data in Figure 8.65 were corrected for crack closure by using the experimentally measured values of P open . The data then shift to the left and fall reasonably along the baseline curve at R = 01 which displayed little or no closure. The enhanced FCGR resistance for LSP processed material can be attributed to a superimposed residual stress field shielding the crack tip, producing crack closure. The results of LSP samples tested at R = 08 are presented in Figure 8.66 along with the baseline curve for the same stress ratio. Advantages in the FCGR resistance of LSP at this higher value of R clearly diminish and, in fact, disappear completely since the data fall along the trend line for the baseline material. Compliance traces obtained at R =08 were linear throughout the entire loading range, suggesting that no closure is present. The advantages of LSP do not appear at the higher stress ratio since, for any stress ratio, once HCF Design Considerations 455 10 –9 10 –8 10 –7 10 –6 10 –5 1 10 100 ΔK applied da /dN (m/cycles) Baseline R = 0.8 Ti-6Al-4V R = 0.8 ΔK (MPa√m) Figure 8.66. The FCGR data for LSP samples at R =08. the minimum stress in the loading cycle equals or exceeds the stress due to the residual stress field created in the LSP process, crack growth rates are unaffected. It must be noted that in correcting crack growth rate data for closure, it is inherently assumed that stress ratio has no measurable effect on the growth rate, that is K is the sole correlating parameter. Thus, for the case of an applied K at R = 01inanLSP sample, closure at 80% of maximum load would correspond to an effective R = 08. The data obtained in the reported investigation, represented by the baseline curves in Figures 8.65 and 8.66, show that tests at either R =01orR =08 produce no significant degree of closure and produce comparable growth rates, thereby validating the use of a closure correction for the LSP data. The beneficial effects of surface treatments can be quantified with the aid of fracture mechanics. If residual stresses are present, they produce a residual stress intensity factor, K res , at the crack tip that can be calculated using methods such as weight functions (see below). In the absence of other closure-related mechanisms, the effective values of K at maximum and minimum loads are given by: K maxeff =K maxapplied +K res K mineff =K minapplied +K res (8.15) . near-surface layer that is particularly stable, even at high temperature. In this particular example, as well as in carbon steel discussed earlier [53], the beneficial effects of surface treatments are. tolerant analysis can be increased over that used in analysis on an untreated hole. Thus, as compressive residual stresses are imparted deeper into a material, the resistance to crack propagation. increases slightly at the center of the sample. To compare crack growth characteristics of a treated sample with those of an untreated sample, fatigue testing of the simulated airfoil samples was
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