Journal articles: 'Small Fatigue Crack Growth'

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Goto, Masahiro, Takaei Yamamoto, Junichi Kitamura, Seung Zeon Han, R. Takanami, Terutoshi Yakushiji, and J. H. Lee. "Growth Rate of Small Surface-Cracks in Age Hardening Cu-Ni-Si Alloy under Cyclic Stressing." Key Engineering Materials 827 (December 2019): 216–21. http://dx.doi.org/10.4028/www.scientific.net/kem.827.216.

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Stress-controlled fatigue tests were conducted on round-bar specimens to understand the fatigue behavior of precipitate-strengthened Cu–6Ni–1.5Si alloy. The cracks were initiated at the grain boundaries, followed by growth along the crystallographic slip planes in the adjacent grains. The crack growth data of plain specimens exhibited a large scatter, resulting in a difficulty of the measurement of crack growth rate. To evaluate the small-crack growth rate of the alloy, the plain specimens with a small blind hole as the crack starter were fatigued. The crack growth rate of small cracks from the hole was uniquely determined by a term σanl and the material constant, n, was 5.3. The term σanl with n = 5.3 was applied to the plain specimen, showing good applicability of the term to small cracks in the plain specimen.

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Zhu, Lei, Xuteng Hu, Rong Jiang, Yingdong Song, and Shoudao Qu. "An investigation of small fatigue crack behavior in titanium alloy TC4 under different stress levels." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 15 (June 4, 2019): 5567–78. http://dx.doi.org/10.1177/0954410019852867.

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In this paper, the small fatigue crack behavior in titanium alloy TC4 under different stress levels was investigated. Single-edge-notch tension specimens were axially fatigued with stress ratio of 0.1 at room temperature. Results show that the naturally initiated cracks nucleate from the α/β interfaces. When the crack is below a critical length of ∼200 µm, crack growth rates exhibit large fluctuations and temporary retardations due to microstructure effects. But once the crack length exceeds ∼200 µm, the fluctuations in crack growth rates die down and the crack grows more rapidly. There is no distinct effect of stress level on small crack growth rate. A linear relationship exists between the total fatigue life and crack initiation life.

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Goto, Masahiro, Seung Zeon Han, Yuji Yokoho, Kazuya Nakashima, S. S. Kim, and Kwang Jun Euh. "The Relationship between Shear Bands and Crack Growth Behavior in Ultrafine Grained Copper Processed by Severe Plastic Deformation." Key Engineering Materials 452-453 (November 2010): 645–48. http://dx.doi.org/10.4028/www.scientific.net/kem.452-453.645.

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Fatigue life of smooth specimens is approximately controlled by the growth life of a small crack. This means the growth behavior of small cracks must be clarified to estimate the fatigue life of plain members. However, there are few studies on the growth behavior of small cracks in ultrafine grained (UFG) metals. In the present study, fatigue tests for UFG copper have been conducted. The formation behavior of shear bands (SBs) and growth behavior of a small crack have been monitored to clarify the effect of SBs on the growth behavior of a major crack.

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Lukaszewicz, Mikolaj, Shen Gi Zhou, and Alan Turnbull. "Novel Concepts on the Growth of Corrosion Fatigue Small and Short Cracks." Solid State Phenomena 227 (January 2015): 3–6. http://dx.doi.org/10.4028/www.scientific.net/ssp.227.3.

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Corrosion fatigue small, short and long crack growth rates have been determined for a 12Cr steam turbine steel in aerated 300 ppb Cl- + 300 ppb SO42- solution and in air at 90 °C. The crack growth rate for short and long cracks was monitored by direct current potential drop (DCPD) and for the small cracks by combining high resolution optical microscopy and DCPD. Comparison of the fatigue growth rate demonstrated that in solution the short crack growth rate was remarkably enhanced in comparison to long cracks, when the crack size is smaller than 250 μm. This enhancement was attributed to the electrochemical crack size effect associated with greater anodic polarisation of the short crack in such low conductivity solution. However, such enhanced growth was not observed for small cracks, which was rationalised on the basis of additional contribution of current from the pit limiting crack-tip polarisation.

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Ortiz, K., and A. S. Kiremidjian. "A Stochastic Model for Fatigue Crack Growth Rate Data." Journal of Engineering for Industry 109, no. 1 (February 1, 1987): 13–18. http://dx.doi.org/10.1115/1.3187085.

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This paper summarizes a new approach to the probabilistic modeling of fatigue crack growth. The material’s resistance to fatigue crack growth is modeled as a stochastic process, which varies randomly along the crack path. Model parameters are determined through time analysis of fatigue crack growth rate data. Predictions of the statistics of crack growth are excellent, especially for small cracks.

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Prakash, R. V. "Fatigue crack growth at stress concentrators under spectrum loading." Journal of Strain Analysis for Engineering Design 40, no. 2 (February 1, 2005): 117–27. http://dx.doi.org/10.1243/030932405x7764.

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Fatigue cracks initiate at stress raisers such as notches, discontinuities, and surface defects. Many of the field failures that indicate the presence of a fatigue crack at failure can be traced to crack initiation from one or more crack initiation sites and merger of cracks over a period of service. Substantial service life is spent in the growth of small cracks from an initial size of few micrometres before they coalesce and grow to critical dimensions that cause fracture. This paper summarizes research that was carried out in order to understand the kinetics of crack growth of small cracks at notches under simulated FALSTAFF service loading. This paper also presents a method used to understand crack growth kinetics in a pin-loaded lug joint through a crack-front-mapping technique.

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Burchill, Madeleine, Simon Barter, Lok Hin Chan, and Michael Jones. "Microstructurally small fatigue crack growth rates in aluminium alloys for developing improved predictive models." MATEC Web of Conferences 165 (2018): 13004. http://dx.doi.org/10.1051/matecconf/201816513004.

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The fatigue or durability life of a few critical structural metallic components often sets the safe and/or economic useful life of a military airframe. In the case of aluminium airframe components, growth rates, at or soon after fatigue crack nucleation are being driven by near threshold local cyclic stress intensities and thus are very low. Standard crack growth rate data is usually generated from large cracks, and therefore do not represent the growth of small cracks (typically <1mm). Discussed here is an innovative test and analysis technique to measure the growth rates of small cracks growing as the result of stress intensities just above the cyclic growth threshold. Using post-test quantitative fractographic examination of fatigue crack surfaces from a series of 7XXX test coupons, crack growth rates and observations of related growth phenomenon in the threshold region have been made. To better predict small crack growth rates under a range of aircraft loading spectra a method by which standard material data models could be adapted is proposed. Early results suggest that for small cracks this method could be useful in informing engineers on the relative severity of various spectra and leading to more accurate predictions of small crack growth rates which can dominate the fatigue life of airframe components.

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Potirniche, G. P., M. F. Horstemeyer, P. M. Gullett, and B. Jelinek. "Atomistic modelling of fatigue crack growth and dislocation structuring in FCC crystals." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2076 (July 5, 2006): 3707–31. http://dx.doi.org/10.1098/rspa.2006.1746.

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Fatigue damage in face-centred cubic crystals by dislocation substructuring and crack growth was computationally simulated at the atomic scale. Single-crystal copper specimens with approximately 200 000 atoms and an initial crack were subjected to fatigue loading with a constant strain amplitude of ϵ max =0.01 and a load ratio of R = ϵ min / ϵ max =0.75. Cyclic plastic deformation around the crack tip is the main influencing factor for the propagation mechanisms of nanocracks. The main crack-propagation mechanisms occurred either by void nucleation in the high-density region near the crack tip or by fatigue cleavage of the atomic bonds in the crack plane. Fatigue crack growth at grain boundaries was also studied. For high misorientation angle grain boundaries, the crack path deviated while moving from one grain to another. For low crystal misorientations, the crack did not experience any significant out-of-plane deviation. For a large crystal misorientation, voids were observed to nucleate at grain boundaries in front of the crack tip and link back with the main crack. During fatigue loading, dislocation substructures were observed to develop throughout the atomic lattices. Fatigue crack growth rates for nanocracks were computed and compared with growth rates published in the literature for microstructurally small cracks (micron range) and long cracks (millimetre range). The computed growth rates for nanocracks were comparable with those for small cracks at the same stress intensity ranges and they propagated below the threshold for long cracks.

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Wang, Xi Shu, and Jing Hong Fan. "Growth Rate of Small Fatigue Cracks of Cast Magnesium Alloy at Different Conditions." Materials Science Forum 546-549 (May 2007): 77–80. http://dx.doi.org/10.4028/www.scientific.net/msf.546-549.77.

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Some differences between the growth behaviors of small fatigue crack of cast AM50 magnesium alloy at different elevated temperature and at open and closed states were investigated based on in-situ observations with scanning electron microscope (SEM). These results indicate that the growth rates of small fatigue cracks depend on not only the stress levels but also the elevated temperature and crack states. The fatigue crack growth rates were estimated based on novel and conventional methods.

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Knorr, Alain Franz, and Michael Marx. "Microstructural Barriers against Fatigue Crack Growth." Materials Science Forum 783-786 (May 2014): 2339–46. http://dx.doi.org/10.4028/www.scientific.net/msf.783-786.2339.

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Fatigue induced fracture is the number one reason for failure of technical systems. However, in the stage of small crack growth grain or phase boundaries lead to a fluctuating crack propagation rate near the obstacle. Sometimes the cracks stop completely for a large number of cycles resulting in an additional number of life time cycles. However, so far it is not clear, what actually determines the resistance of a grain boundary against fatigue cracks. Therefore we developed a systematic experimental technique based on in-situ imaging in the scanning electron microscope and focused ion beam (FIB) crack initiation which gives detailed information on the interaction of short fatigue cracks with microstructural elements. We investigated the mechanisms of crack transmission in the neighbouring grain on the microscopic scale and identified different useful aspects of the interaction between microcracks and microstructural barriers. The 3D-tomographs revealed by serial sectioning an FIB give information about the transition process from one grain to the neighbouring one. The result is a purely geometrical consideration leading to a quantitative description of the blocking effect of grain boundaries on short fatigue crack growth. The results include useful aspects for fatigue life calculation and to make materials more fatigue resistant.

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van Kuijk, Jesse, René Alderliesten, and Rinze Benedictus. "Fatigue crack surface area and crack front length: new ways to look at fatigue crack growth." MATEC Web of Conferences 165 (2018): 13009. http://dx.doi.org/10.1051/matecconf/201816513009.

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This paper discusses the appropriateness of crack length as a reference dimension for fatigue damage. Current discussion on short crack versus long crack data is still divided between various approaches to model small crack growth. A proper physical explanation of the probable cause of the apparent differences between short crack and long crack data is not yet provided. Long crack data often comprises crack growth in constant thickness specimens, with a through crack of near constant crack front geometry. This is not true for corner cracks or elliptical surface crack geometries in the small crack regime where the crack front geometry is not symmetric or through-thickness. This affects similitude parameters that are based on the crack length. The hypothesis in this paper is that a comparison between long crack data and short crack data should be made using similar increments in crack surface area. The work applied to the specimen is dissipated in generation of fracture surface, whereas fracture length is a result. The crack surface area approach includes the two-dimensional effect of crack growth geometry in the small crack regime. A corner crack and a through crack are shown to follow the same power law relationship when using the crack area as base parameter. The crack front length is not constant, and its power law behaviour for a corner crack is shown.

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12

Chan, K. S., J. Lankford, and D. L. Davidson. "A Comparison of Crack-Tip Field Parameters for Large and Small Fatigue Cracks." Journal of Engineering Materials and Technology 108, no. 3 (July 1, 1986): 206–13. http://dx.doi.org/10.1115/1.3225868.

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A comparison of the elastic-plastic crack-tip fields of large and small fatigue cracks has been made using the ΔJ-integral approach. Using experimental strain and displacement range measurements obtained by means of the stereoimaging technique, the ΔJ-integral has been computed for an aluminum alloy containing either large or small fatigue cracks, by performing line-contour integration along a variety of rectangular paths around the crack tip. These calculations reveal that for both large and small cracks the ΔJ-integral is path-dependent, and that the value of ΔJ increases with decreasing distance from the crack tip. Using an average local ΔJ or one estimated from the CTOD, the enhanced crack growth rates associated with small fatigue cracks can be explained on the basis of the large average ΔJ-integral within the cyclic plastic zone. The effect of crack closure on the computed local ΔJ (or ΔK) and crack growth is discussed.

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SHOJIMA, K., K. YANASE, and M. ENDO. "PREDICTION FOR FATIGUE CRACK GROWTH IN NOTCHED PLATES." International Journal of Modern Physics: Conference Series 06 (January 2012): 269–74. http://dx.doi.org/10.1142/s2010194512003297.

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The notch is usually unavoidable in designing various mechanical components. As well known, those notches significantly influence the fatigue life and fatigue strength of materials. In addition, most fatigue cracks spend the vast majority of their lives as short cracks, and the behavior of such flaw is of significant importance in determining the fatigue lifetime of notched components. Correspondingly, in this research, we investigate the fatigue crack growth behavior and fatigue strength of notched plates. For the proposed method, the elastic-plastic behavior, the Kitagawa effect and the crack closure are taken into account as the major factors responsible for the peculiar behavior of small fatigue cracks emanating from notches. Regarding the experiment, the fatigue tests were conducted using the plates with a circular notch under uniaxial loading condition. The proposed approach is validated by comparing the predicted results to the experimental data.

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Kamaya, Masayuki. "Evaluation of Fatigue Crack Growth of Interacting Surface Cracks." Advanced Materials Research 33-37 (March 2008): 187–98. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.187.

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Since mechanical interaction between multiple cracks affects the rate of crack growth due to fatigue and stress corrosion cracking, it is important to consider its influence when predicting growth. In this study, a procedure predicting the growth of interacting surface cracks was developed. First, using the results of fatigue crack growth tests performed in a previous study, the transient growth behavior during coalescence and growth under interaction was evaluated based on area of crack face. It was shown that the area is a representative parameter of the growth of interacting surface cracks as well as independent cracks. The growth in area showed good correlation with the crack driving force defined using size of area. Then, in order to investigate the relationship between growth of interacting cracks and their relative spacing, crack growth simulations were carried out. The body force method was used to evaluate the change in stress intensity factors (SIF) during crack growth under interaction, and the simulation could reproduce the crack configurations obtained in the fatigue crack growth test. SIF of an interacting crack tip converges to that of a coalesced crack as the distance between cracks decreases. It was concluded that when the distance between cracks is small enough, the cracks can be replaced with a semi-elliptical crack of the same area of crack face for a growth evaluation. The threshold offset distance for the replacement was suggested to be less than 0.1Rx, where Rx is the span length of two cracks on the surface.

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Sakamoto, Junji, Yoshimasa Takahashi, and Hiroshi Noguchi. "Small Fatigue Crack Growth Behavior from Artificial Notch with Focused Ion Beam in Annealed 0.45% Carbon Steel." Key Engineering Materials 488-489 (September 2011): 319–22. http://dx.doi.org/10.4028/www.scientific.net/kem.488-489.319.

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The aim of this study is firstly to investigate the applicability of a sharp notch with Focused Ion Beam (FIB) as a crack for fatigue limit evaluation. Secondly we investigate a condition in which artificial defects (drilled hole, FIB notch) can be used as a crack for fatigue limit evaluation. To achieve the aim, the growth behaviors and the non-propagating crack sizes of small fatigue cracks initiated from a FIB notch and a drilled hole are carefully compared with those of an annealed fatigue crack which imitates an ideally sharp crack. The results show that a FIB notch can be used as a crack for fatigue limit evaluation under some conditions. The results also show that the condition which controls the applicability of an artificial defect as an ideal crack for fatigue limit evaluation is strongly dependent on the relation between (i) the length of a non-propagating fatigue crack and (ii) the crack length when the small fatigue crack growth behaviors from an artificial defect and an ideal pre-crack become almost the same. It is found that the length of (ii) can be obtained by the analyses using the number of cycles from a certain crack length to failure.

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Lados, Diana A. "Fatigue Crack Propagation Mechanisms of Long and Small Cracks in Al-Si-Mg and Al-Mg Cast Alloys." Materials Science Forum 618-619 (April 2009): 563–74. http://dx.doi.org/10.4028/www.scientific.net/msf.618-619.563.

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Fatigue crack growth of long and small cracks was investigated for various Al-Si-Mg and Al-Mg cast alloys. Low residual stress was ensured during processing to concentrate on microstructural effects on crack growth. Compact tension and single edge tension specimens were fatigue crack growth tested at room temperature and stress ratio, R = 0.1. Microstructure related mechanisms were used to explain the near-threshold behaviour and crack growth response in Regions II and III for each material considering relevant microstructural features such as SDAS, grain size, and volume fraction and morphology of eutectic Si. Threshold behaviour of long cracks is attributed to closure-dependent mechanisms. In Regions II and III, the changes in crack growth mechanisms were explained through correlations between the extent of the plastic zone ahead of the crack tip and material-specific microstructural damage. Threshold behaviour of small cracks is explained through closure-independent mechanisms, specifically through the barrier effects of controlling microstructural characteristics specific to each material. Recommendations for integrating materials knowledge in structural design for fatigue performance are given.

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Wang, Y., and J. Pan. "Analysis of Small Edge Cracks and Its Implications to Multiaxial Fatigue Theories." Journal of Pressure Vessel Technology 123, no. 1 (October 20, 2000): 2–9. http://dx.doi.org/10.1115/1.1342012.

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The near-tip fields of small edge (Case B) cracks in power-law hardening materials are investigated under generalized plane strain, mixed mode, and general yielding conditions by finite element analyses. The results of the J integral from the finite element analyses are used to correlate to a fatigue crack growth criterion for Case B cracks. The trend of constant J contours on the Γ-plane is compared reasonably well with those of the experimental results of constant fatigue life and constant fatigue crack growth rate under multiaxial loading conditions.

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Newman, James C. "Fatigue and Crack Growth under Constant- and Variable-Amplitude Loading in 9310 Steel Using “Rainflow-on-the-Fly” Methodology." Metals 11, no. 5 (May 15, 2021): 807. http://dx.doi.org/10.3390/met11050807.

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Fatigue of materials, like alloys, is basically fatigue-crack growth in small cracks nucleating and growing from micro-structural features, such as inclusions and voids, or at micro-machining marks, and large cracks growing to failure. Thus, the traditional fatigue-crack nucleation stage (Ni) is basically the growth in microcracks (initial flaw sizes of 1 to 30 μm growing to about 250 μm) in metal alloys. Fatigue and crack-growth tests were conducted on a 9310 steel under laboratory air and room temperature conditions. Large-crack-growth-rate data were obtained from compact, C(T), specimens over a wide range in rates from threshold to fracture for load ratios (R) of 0.1 to 0.95. New test procedures based on compression pre-cracking were used in the near-threshold regime because the current ASTM test method (load shedding) has been shown to cause load-history effects with elevated thresholds and slower rates than steady-state behavior under constant-amplitude loading. High load-ratio (R) data were used to approximate small-crack-growth-rate behavior. A crack-closure model, FASTRAN, was used to develop the baseline crack-growth-rate curve. Fatigue tests were conducted on single-edge-notch-bend, SEN(B), specimens under both constant-amplitude and a Cold-Turbistan+ spectrum loading. Under spectrum loading, the model used a “Rainflow-on-the-Fly” subroutine to account for crack-growth damage. Test results were compared to fatigue-life calculations made under constant-amplitude loading to establish the initial microstructural flaw size and predictions made under spectrum loading from the FASTRAN code using the same micro-structural, semi-circular, surface-flaw size (6-μm). Thus, the model is a unified fatigue approach, from crack nucleation (small-crack growth) and large-crack growth to failure using fracture mechanics principles. The model was validated for both fatigue and crack-growth predictions. In general, predictions agreed well with the test data.

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SUH, CHANG-MIN, and SEON-GAB KIM. "SURFACE FATIGUE CRACK GROWTH BEHAVIOR FROM SMALL NOTCH IN WASPALOY." International Journal of Modern Physics B 24, no. 15n16 (June 30, 2010): 3112–17. http://dx.doi.org/10.1142/s0217979210066173.

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We investigated the surface fatigue crack behaviors including initial surface crack appearances depend on three artificial notch lengths applied with the axle load level of the maximum load, 1,103 MPa and minimum load 55.3 MPa at the stress ratio of 0.05. This load level is the F100 engine's maximum operation condition of Waspaloy. The initial cracking site in depth is started from multi-origin. The effectiveness of crack growth rate by ductile striation space measurement on the fractured surface is confirmed by the working load and the stress intensity factor range. The surface cracks of Waspaloy at room temperature in air follow the ΔK vs da/dN and db/dN relation, even though the crack length initiated early in notch size 1 mm and initiated very late in notch size 4 mm. And the ΔK vs da/dN and db/dN relation have similar slope at 3 kinds of notches.

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Itoga, Hisatake, Hisao Matsunaga, and Saburo Matsuoka. "Effect of Hydrogen Gas on the Growth of Small Fatigue Crack in JIS-SCM435." Advanced Materials Research 891-892 (March 2014): 942–47. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.942.

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The fatigue crack growth (FCG) from a small hole in a low alloy steel JIS-SCM435 round bar was investigated using tension-compression fatigue tests in 0.7 MPa hydrogen gas and ambient air. In the higher FCG rate regime (e.g. da/dN > 108 m/cycle), FCG was accelerated in hydrogen gas compared to in air. On the other hand, in the lower FCG rate regime (e.g. da/dN < 108 m/cycle), FCG in hydrogen was rather slower than that in air. There was no noticeable difference in fatigue limits between these two atmospheres. The FCG in the respective atmospheres showed a typical small crack behavior, i.e. the da/dN for small cracks were much greater than those for large cracks obtained by compact tension (CT) specimen when they were compared at the same ΔK level. In order to unify such a discrepancy of FCG behavior between small crack and large crack, the strain intensity factor range ΔKε was adopted. As a result, the da/dN data for various crack sizes was gathered in a narrow band, i.e. the small crack effect was successfully evaluated with the strain intensity. Moreover, the crack growth life was predicted based on the da/dN-ΔKε relation. The reproduced S-N curve showed a conservative agreement with the fatigue life obtained by experiments.

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Jin, Huijin, Bing Cui, and Ling Mao. "Fatigue Growth Behaviour of Two Interacting Cracks with Different Crack Offset." Materials 12, no. 21 (October 28, 2019): 3526. http://dx.doi.org/10.3390/ma12213526.

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Under cyclic fatigue load, multiple cracks would significantly deteriorate the service life of the components with respect to the case of a single crack owing to the crack interaction. The present study aims to explore the effect of crack interaction on the fatigue growth behaviour of samples with different crack offset. In this study, fatigue crack growth tests were performed for samples containing a single crack and non-collinear cracks of different crack offset in an aluminum–lithium alloy. It was shown that the two facing non-collinear cracks changed their growth direction when the cracks were overlapped, resulting in load mode transfers from mode I to I + II mixed mode. Then, the interaction behaviour was studied by establishing the finite element models to calculate the stress intensity factor K of samples with different crack offset. The results indicated that the K decreased, largely owing to the shielding effect as the two cracks overlapped, leading to retardation of crack growth in the position of overlap, especially for the specimens with a small crack offset. It was also shown that the interaction effect could change from positive to negative during the process of the multiple cracks’ growth, thus leading to the acceleration or deceleration of crack growth rates, suggesting that the influence of interaction on cracks’ growth behaviour could vary with the different stages of crack growth.

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Lin, X. B., and R. A. Smith. "Fatigue Growth Prediction of Internal Surface Cracks in Pressure Vessels." Journal of Pressure Vessel Technology 120, no. 1 (February 1, 1998): 17–23. http://dx.doi.org/10.1115/1.2841878.

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Fatigue crack growth was numerically simulated for various internal surface cracks with initially either semi-elliptical or irregular crack fronts. The simulation was directly based on a series of three-dimensional finite element analyses from which the stress intensity factors along the front of growing cracks were estimated. The fatigue crack growth law obtained from small laboratory specimens was incrementally integrated at a set of points along the crack front, and a new crack front was then re-established according to the local advances at this set of points by using a cubic spline curve. This method enabled the crack shape to be predicted without having to make the usual assumption of semi-elliptical shape. Fatigue analysis results are presented and discussed for fatigue shape developments and deviations from the semi-elliptical shape, aspect ratio changes, stress intensity factor variations during crack growth, and fatigue life predictions. Some of the results were also compared with those obtained by two simplified methods based on one and two degree-of-freedom models, respectively.

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Buffière, Jean Yves, Emilie Ferrié, Wolfgang Ludwig, and Anthony Gravouil. "Characterisation and Modelling of the Three Dimensional Propagation of Short Fatigue Cracks." Materials Science Forum 519-521 (July 2006): 997–1004. http://dx.doi.org/10.4028/www.scientific.net/msf.519-521.997.

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This paper reports recent results on the characterisation and modelling of the three dimensional (3D) propagation of small fatigue cracks using high resolution synchrotron X ray micro-tomography. Three dimensional images of the growth of small fatigue cracks initiated in two Al alloys on natural or artificial defects are shown. Because of the small size of the investigated samples (millimetric size), fatigue cracks grown in conventional Al alloys with a grain size around 100 micrometers can be considered as microstructurally short cracks. A strong interaction of these cracks with the grain boundaries in the bulk of the material is shown, resulting in a tortuous crack path. In ultra fine grain alloys, the crack shapes tend to be more regular and the observed cracks tend to grow like ”microstructurally long cracks” despite having a small physical size. Finite Element meshes of the cracks can be generated from the reconstructed tomographic 3D images. Local values of the stress intensity factor K along the experimental crack fronts are computed using the Extended Finite Element method and correlated with the crack growth rate.

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Newman, J. C. "Fatigue-Life Prediction Methodology Using a Crack-Closure Model." Journal of Engineering Materials and Technology 117, no. 4 (October 1, 1995): 433–39. http://dx.doi.org/10.1115/1.2804736.

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This paper reviews the capabilities of a plasticity-induced crack-closure model and life-prediction code, FASTRAN, to predict fatigue lives of metallic materials using small-crack theory. Crack-tip constraint factors, to account for three-dimensional state-of-stress effects, were selected to correlate large-crack growth rate data as a function of the effective-stress-intensity factor range (ΔKeff) under constant-amplitude loading. Some modifications to the ΔKeff-rate relations were needed in the near-threshold regime to fit small-crack growth rate behavior and endurance limits. The model was then used to calculate small- and large-crack growth rates, and to predict total fatigue lives, for notched specimens made of several aluminum alloys and a titanium alloy under constant-amplitude and spectrum loading. Fatigue lives were calculated using the crack-growth relations and microstructural features like those that initiated cracks for the aluminum alloys. An equivalent-initial-flaw-size concept was used to bound the fatigue lives for the titanium alloy. Results from the tests and analyses agreed well.

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Gupta, A., W. Sun, and C. J. Bennett. "Simulation of fatigue small crack growth in additive manufactured Ti–6Al–4V material." Continuum Mechanics and Thermodynamics 32, no. 6 (March 25, 2020): 1745–61. http://dx.doi.org/10.1007/s00161-020-00878-0.

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Abstract Additive manufacturing (AM) offers design freedom and ability to fabricate parts of complex shapes which are not often possible with the conventional methods of manufacturing. In an AM part, even with optimum build parameters, a complete elimination of defects is not possible and this makes it hard to fully deploy the AM technology to build load bearing parts operating under cyclic loading conditions. Many of these defects are < 1 mm in size and are categorised as ‘small cracks’. Local interaction of cracks with microstructural features and closure effects at the wake of the crack tip are some of the factors which make the growth behaviour of small and long cracks different. A crack growth life prediction method, which effectively considers the small crack growth behaviour, has been discussed in this paper. This proposed method includes a detailed finite element-based crack growth simulation using the ANSYS SMART fracture technology. The lifing calculations utilise the modified NASGRO equation and small crack growth data which was obtained from the published long crack growth data, corrected for closure effects. The predicted stress versus number of cycles curves were compared against the fatigue test results for the AM specimens in Ti–6Al–4V material. A good correlation between the predictions and test results suggests that the proposed method can be used to assess the small crack growth life of AM parts where the fatigue effects of cyclic loading can be quite significant.

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Wang, Y., and J. Pan. "A Plastic Fracture Mechanics Analysis of Small Case B Fatigue Cracks Under Multiaxial Loading Conditions." Journal of Engineering for Gas Turbines and Power 120, no. 4 (October 1, 1998): 796–800. http://dx.doi.org/10.1115/1.2818470.

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The near-tip fields of small Case B cracks in power law, hardening materials are investigated under generalized plane-strain and general yielding conditions by finite element analyses. The results for two different crack orientations are examined and compared. The results indicate that the plastic deformation patterns near the tips of the cracks of two different orientations are remarkably similar in terms of the global coordinates. The results of the J-integral from the finite element analyses are used to correlate to a fatigue crack growth criterion for Case B cracks. The trends of constant ΔJ-contours on the Γ-plane for two cracks of different orientations are virtually the same. Further, the trends are compared reasonably well with those of the experimental results of constant fatigue life and constant fatigue crack growth rate.

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27

Ikeda, Yuichi, Kiyotaka Munaoka, Takashi Matsuo, and Msahiro Endo. "OS8-16 Development of Testing Machine for Small Shear-Mode Fatigue Crack Growth Test(Fatigue crack propagation,OS8 Fatigue and fracture mechanics,STRENGTH OF MATERIALS)." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2015.14 (2015): 126. http://dx.doi.org/10.1299/jsmeatem.2015.14.126.

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Zhu, C. "A MODEL FOR SMALL FATIGUE CRACK GROWTH." Fatigue & Fracture of Engineering Materials and Structures 17, no. 1 (January 1994): 69–75. http://dx.doi.org/10.1111/j.1460-2695.1994.tb00773.x.

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29

McDowell, David L. "Multiaxial small fatigue crack growth in metals." International Journal of Fatigue 19, no. 93 (June 1997): 127–35. http://dx.doi.org/10.1016/s0142-1123(97)00014-5.

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30

Furuya, Y. "Visualization of internal small fatigue crack growth." Materials Letters 112 (December 2013): 139–41. http://dx.doi.org/10.1016/j.matlet.2013.09.015.

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31

Lu, Zizi, and Yongming Liu. "Small time scale fatigue crack growth analysis." International Journal of Fatigue 32, no. 8 (August 2010): 1306–21. http://dx.doi.org/10.1016/j.ijfatigue.2010.01.010.

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32

Shamsaei, Nima, and Ali Fatemi. "Small fatigue crack growth under multiaxial stresses." International Journal of Fatigue 58 (January 2014): 126–35. http://dx.doi.org/10.1016/j.ijfatigue.2013.02.002.

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33

Edwards, L., and Y. H. Zhang. "Investigation of small fatigue cracks—II. A plasticity based model of small fatigue crack growth." Acta Metallurgica et Materialia 42, no. 4 (April 1994): 1423–31. http://dx.doi.org/10.1016/0956-7151(94)90161-9.

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34

Zhu, Lei, Xu Teng Hu, Rong Jiang, Ying Dong Song, and Shou Dao Qu. "Initiation and Propagation Behaviors of Small Fatigue Crack in Titanium Alloy TC4." Key Engineering Materials 795 (March 2019): 9–14. http://dx.doi.org/10.4028/www.scientific.net/kem.795.9.

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The initiation and propagation behaviors of small fatigue crack in TC4 were investigated in the present work. Surface replication on the basis of a two-part silicon mixture and confocal laser scanning microscope were used to record and observe the small crack initiation and growth processes at room temperature in air. Results showed that surface cracks initiated from the interfaces between α and β phases. When the crack lengths were below ~200 μm, the crack growth rates exhibited large oscillations and temporary retardations due to the presence of α/β interfaces. The corner crack propagated much faster and might have shielding effect on the surface crack.

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35

Knorr, Alain Franz, and Michael Marx. "Calculating the Resistance of a Grain Boundary against Fatigue Crack Growth." Advanced Materials Research 891-892 (March 2014): 929–35. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.929.

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One problem of the quantitative description of small fatigue crack propagation is the fluctuating crack growth rate induced by obstacles like grain or phase boundaries. Sometimes cracks stop completely for a large number of cycles sometimes cracks only decelerate, both resulting in an additional number of life time cycles. However, so far it is not clear, what actually determines the resistance of a grain boundary against fatigue cracks. Therefore we investigate small crack propagation through grain boundaries systematically by in-situ imaging in the scanning electron microscope and focused ion beam (FIB) crack initiation. By this unique technique, artificial stage I cracks with constant crack parameters can be observed while interacting with different grain boundaries which gives detailed information on the interaction mechanisms. We identified different useful aspects of the interaction between microcracks and microstructural barriers on the microscopic scale. 3D-tomographs revealed by serial sectioning and FIB give information about the transition process from the initial grain to the neighbouring one. The resulting purely geometrical consideration leads to a quantitative description of the blocking effect of grain boundaries and can be used to calculate the probability of a crack transfer from the orientation data of two neighboring grains only.

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Hu, B. R., J. Z. Liu, B. Chen, L. F. Wang, and Xue Ren Wu. "Fatigue Behavior and Life Prediction for Argon-Arc Weld Joints Based on Small Crack Methodology." Key Engineering Materials 306-308 (March 2006): 157–62. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.157.

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Experimental and analytical studies were made on the fatigue behavior and life prediction for argon-arc welded titanium alloy joints, TA15. High cycle fatigue tests at two stress ratios, R=0.5 and 0.06, were carried out on smooth specimens with the argon-arc weld joint located at the specimen center section. Through macroscopic observation and SEM fractographic analysis, it was found that most of the cracks were initiated at weld defects such as voids and inclusions at the edge of weld and in the heat affected zone (HAZ). A small crack methodology based on the plasticity-induced crack-closure concept and the effective stress intensity factor range, ΔKeff , was used to predict the total fatigue life of the weld joints. Large crack growth curve for cracks in the HAZ area was employed as the da/dN-ΔKeff base-line of the TA15 alloy. From fractographic measurements, an average defect size of 100 microns was assumed as the initial small crack size in the life predictions. Predicted total fatigue life by solely considering small crack growth stage agreed well with the experimental data.

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Wang, Qing Yuan, Norio Kawagoishi, Nu Yan, and Q. Chen. "Super-Long Life Fatigue Behavior of Structural Aluminum Alloys." Key Engineering Materials 261-263 (April 2004): 1287–94. http://dx.doi.org/10.4028/www.scientific.net/kem.261-263.1287.

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The objective of this study is to determine very long life fatigue and near threshold fatigue crack growth behaviors of 7075/T6 and 6061/T6 Al-alloys using piezoelectric accelerated fatigue at 19.5KHz. The experimental results show the fatigue failure can occur beyond 107, even 109 cycles, and endurance limits could not be obtained in the Al-alloys until 109 cycles. Fatigue voids are noticed on fatigue fracture in both alloys. By using scanning electron microscopy (SEM), the crack initiation and propagation behaviors have been examined. Fatigue crack growth rates of small cracks in the Al-alloys are found to be greater than those of large cracks at the same stress intensity factor range.

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Murakami, Yukitaka, Junichiro Yamabe, and Hisao Matsunaga. "Microscopic Mechanism of Hydrogen Embrittlement in Fatigue and Fracture." Key Engineering Materials 592-593 (November 2013): 3–13. http://dx.doi.org/10.4028/www.scientific.net/kem.592-593.3.

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The microscope mechanism of hydrogen embrittlement (HE) is overviewed from the viewpoint of Mechanics-Microstructure-Environment Interactions. The plastic deformation (Mechanics) at crack tip for low strength steel is controlled by hydrogen concentration (Environment) to crack tip, eventually resulting in very strong time dependent phenomenon in static fracture and fatigue crack growth. Various typical phenomena in low strength steels which can be understood from the viewpoint of Mechanics-Environment Interactions will be presented. Fracture and fatigue of high strength steels (Microstructure) are strongly influenced by hydrogen. Especially, fatigue crack growth is remarkably accelerated by hydrogen-induced deformation twins. The HE phenomemon of the high-strength steels was applied to a newly inclusion rating method. Hydrogen trapped by nonmetalliec inclusions causes the elimination of fatigue limit at very high cycle fatigue. The values of threshold stress intensity factor KTH in hydrogen for small cracks are much smaller than those for long cracks measured by the standard WOL or CT specimens, which are eventually unconservative for the design of hydrogen components. This phenomenon is similar to the small crack problem in fatigue.

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White, Paul, and David S. Mongru. "Fractographic Study on the Use of Rainflow Counting for Small and Long Cracks in AA7050." Advanced Materials Research 891-892 (March 2014): 687–92. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.687.

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Using ada/dNequation to predict fatigue crack growth for a variable amplitude loading sequence, requires converting the sequence into an equivalent series of constant amplitude cycles, which is sometimes achieved using the rainflow cycle counting technique. Rainflow counting views small intermediate cycles as an interruption to a larger cycle, in effect, the crack tip remembers the state of the larger cycle. This has been shown to be an effective technique in predicting fatigue growth rates for long cracks, but has not been extensively investigated for use in predicting the growth of small cracks. An investigation was made into the applicability of rainflow cycle counting for predicting the crack growth of small and long cracks created with variable amplitude fatigue loading in AA7050-T7451 plate, a common modern aircraft material. A series of coupons were tested with a number of different variable amplitude loading sequences which had distinct marker bands inserted to separate the individual segments of loading and enable them to be identified fractographically. For the sequences examined, which covered varying numbers of interrupted cycles and a staircase of three steps, the baseline and the rainflow loading segments within each sequence showed effectively the same rate of growth for the same stress intensity range in both the small and long crack coupons, demonstrating that rainflow cycle counting was a suitable cycle counting technique for both small and long cracks.

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40

He, Yu Ting, Wen Jun Shu, Rong Hong Cui, Li Ming Wu, and Jin Qiang Du. "Total Fatigue Life Prediction under Constant Amplitude Loading." Materials Science Forum 704-705 (December 2011): 636–40. http://dx.doi.org/10.4028/www.scientific.net/msf.704-705.636.

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This paper applies the fracture-mechanics-based analysis and the crack-closure concept to naturally occurring small cracks and large crack growth, and to make total fatigue life predictions solely based on crack growth from the assumed initial materials defect. The equation of total fatigue crack propagation life under constant amplitude loading is presented. And the total fatigue propagation lives of LY12-BCZYU aluminium alloy SENT specimens by this equation and validated by experimental results. Validation against calculations by the model and experimental data shows a good agreement.

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41

Takeuchi, Yushi, Hiroyuki Akebono, Masahiko Kato, and Atsushi Sugeta. "OS8-15 AFM Observation of Small Fatigue Crack Growth Behavior in extruded Mg-Alloy AZ31(Fatigue crack propagation,OS8 Fatigue and fracture mechanics,STRENGTH OF MATERIALS)." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2015.14 (2015): 125. http://dx.doi.org/10.1299/jsmeatem.2015.14.125.

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42

Liaw, P. K., and W. A. Logsdon. "Crack closure: An explanation for small fatigue crack growth behavior." Engineering Fracture Mechanics 22, no. 1 (January 1985): 115–21. http://dx.doi.org/10.1016/0013-7944(85)90164-x.

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43

Tokaji, Keiro, Yoshihiko Uematsu, and Mitsutoshi Kamakura. "Effect of Powder Size on Fatigue Behaviour in Mg₂Si-Dispersed Magnesium Alloys Produced by Solid-State Synthesis." Key Engineering Materials 345-346 (August 2007): 315–18. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.315.

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The fatigue behaviour of newly developed Mg2Si-dispersed magnesium (Mg) alloys produced by solid-state synthesis was studied. Rotary bending fatigue tests have been performed using smooth specimens of materials produced with fine and coarse AZ31 alloy powders. Both Mg2Si-dispersed Mg alloys exhibited lower fatigue strength than a conventional extruded AZ31 alloy and the powder size dependence of fatigue strength was clearly recognized, where the material produced with fine alloy powder showed considerably higher fatigue strength than the counterpart. Fatigue cracks invariably initiated at large Mg2Si particles immediately after cyclic loading was applied and subsequent small crack growth was faster than the extruded AZ31 alloy. It was concluded that the lower fatigue strength of Mg2Si-dispersed Mg alloys was attributed to premature crack initiation at Mg2Si particles and faster small crack growth, and the observed powder size dependence of fatigue strength was due to difference in the size of the particle from which the crack initiated.

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44

Wang, Weihan, Weifang Zhang, Hongxun Wang, Xiaoliang Fang, and Xiaobei Liang. "Influence of Grain Boundary on the Fatigue Crack Growth of 7050-T7451 Aluminum Alloy Based on Small Time Scale Method." Advances in Materials Science and Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/7671530.

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Based on the small time scale method, the influence of grain boundary on the fatigue crack growth of 7050-T7451 has been investigated. The interaction between fatigue crack and grain boundary was investigated by in situ SEM testing. Results showed that the fatigue crack growth will be retarded by grain boundary when the angle between fatigue crack and grain boundary is greater than 90 degrees. Mechanism analysis showed that the fatigue crack tip would not be able to open until the loading reached the 55% of maximum load, and the fatigue crack had been closed completely before the loading was not reduced to the minimum value, which led to the crack growth retardation. When the 7050-T7451 aluminum alloy suffered from fatigue loading with constant amplitude, a behavior of unstable fatigue crack growth could be observed often, and results indicated that the bridge linked mechanism led to the behavior. The grain boundary was prone to fracture during fatigue loading, and it became the best path for the fatigue crack growth. The fatigue crack tip would be connected with fractured grain boundary eventually, which led to the fast crack growth in different loading stage.

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45

Qi, Shuang, Li Xun Cai, Kai Kai Shi, and Chen Bao. "A Prediction Model for Mode-III Fatigue Crack Growth." Applied Mechanics and Materials 853 (September 2016): 41–45. http://dx.doi.org/10.4028/www.scientific.net/amm.853.41.

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In the fracture mechanics, the failure of mode-III crack belongs to the anti-plane shear (also called out-plane shear or longitudinal shear). Fatigue crack growth (FCG) behavior under mode-III reversed load (load ratio R=-1) was studied by using 30Cr2Ni4MoV rotor steel with types of circumferential notches. Under the remote cyclic torsional load, the precrack process was applied to specimens with notch in the round bar, and the ideal sharp-crack was obtained. Then, mode-III FCG test under the remote cyclic torsional load and the axial constant small load was carried out until to fatigue failure. The axial constant small load is aimed at reducing the cracks interaction in the mode-III FCG experiment. Due to experimental data of 30Cr2Ni4MoV rotor steel, the mode-III FCG rate in the range of KIII from 12MPa·m1/2 to 40 MPa·m1/2 and the threshold value were got. Furthermore, a prediction model for mode-III FCG is proposed with considering the small scale yield of plane stress crack tip zone and the plastic strain energy density failure criteria. The predicted mode-III FCG rate is found to agree well with the experimental curves of 30Cr2Ni4MoV rotor steel.

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46

De Iorio, Antonio, Marzio Grasso, George Kotsikos, F. Penta, and G. P. Pucillo. "Development of Predictive Models for Fatigue Crack Growth in Rails." Key Engineering Materials 488-489 (September 2011): 13–16. http://dx.doi.org/10.4028/www.scientific.net/kem.488-489.13.

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Fatigue failures of rails often occur at the rail foot, since the geometry of this zone gives rise to stress concentrations under service loads or defects during rail manufacture and installation. In this paper, the fatigue behavior of cracks at the web/foot region of a rail is analyzed numerically. Analytical models in the literature for a semi-elliptical surface crack in a finite plate assume that the geometry of the front remains semi-elliptical during the whole propagation phase and the ellipse axes do not undergo translations or rotations. Fatigue tests show that this is not the case for such cracks in rails. A predictive model for crack growth has been developed by assuming an initial small crack at one probable initiation point between the web and foot of the rail in reference to a service condition loading. SIF values have been estimated by means of the finite element method and the plastic radius correction. The results attained were compared with crack growth experimental data.

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47

Shaari, Mohd Shamil, Sylvia Urai, Akiyuki Takahashi, and Mohd Akramin Mohd Romlay. "Predicting Fatigue Crack Growth Behavior of Coalesced Cracks Using the Global-Local Superimposed Technique." Frattura ed Integrità Strutturale 16, no. 62 (September 22, 2022): 150–67. http://dx.doi.org/10.3221/igf-esis.62.11.

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The S-version Finite Element Method (FEM) is known as a global-local superimposed approach that consists of two separate meshes referred to as global and local cracks. The relationship between the energy release rate and the Stress Intensity Factor (SIF) is evaluated to characterize the growth behavior of the fatigue cracks. The SIF is determined using the Virtual Crack Closure Method (VCCM). The cracks propagated in the direction of the loading before coalescing into a single crack. Each crack begins with a length of 10mm and a depth of 3mm. After the crack coalesces, the diameter of the surface crack before it breaks is 28mm, whereas the depth of the crack is 5.3mm. The V-shaped surface crack forms quickly after coalescence occurs and continues to propagate into a massive semi-elliptical surface crack before finally breaking. The result was validated and compared between S-version FEM and the analytical solution. The behavior of the fatigue crack growth shows a good agreement between both methods with small errors. The result indicates that the Root Mean Square Error (RMSE) values before coalescing are 0.1496 with 0.6, and after coalescing is 0.4, the RMSE value is 0.1665. Therefore, it can be stated that the S-version FEM approach can predict the growth of fatigue cracks.

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48

Gavras, Anastasios, Anthony Spangenberger, and Diana A. Lados. "Fatigue Crack Growth in Cast and Wrought Aluminium Alloys." Materials Science Forum 765 (July 2013): 574–79. http://dx.doi.org/10.4028/www.scientific.net/msf.765.574.

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Fatigue crack growth (FCG) behaviour of cast aluminium alloys with different strengthening mechanisms (A535, 319, A356, A390) and wrought aluminium alloys (6061) was investigated in this study. Among the various parameters that can affect the propagation of fatigue cracks, the initial flaw size and microstructure were studied and correlated. Long and small FCG tests at low and high positive stress ratios were conducted on these materials in room temperature air. The mechanisms of FCG at the microstructural scale were identified and will be compared and discussed. In addition, two-parameter design diagrams were constructed to link loading conditions to microstructural response and fracture modes determined from fractographic observations. Finally, a new methodology and tools that can be used to bridge the differences between small and long fatigue cracks were developed and will be presented.

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Okazaki, Saburo, Atsushi Kusaba, Hisao Matsunaga, and Masahiro Endo. "Investigation for Small Shear-Mode Fatigue Cracks in Bearing Steels." Materials Science Forum 750 (March 2013): 236–39. http://dx.doi.org/10.4028/www.scientific.net/msf.750.236.

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Flaking and spalling caused by rolling contact fatigue associate with a small crack, and a special testing method and machine are required to study the small fatigue crack behavior under shear mode loading. It was found by authors that the behaviors of small shear-mode fatigue cracks from the inclusions and the artificial defects could be successfully observed by applying the fully-reversed torsion coupled with static axial compressive stress. However, the servo-hydraulic fatigue testing machine is quite expensive for purchase and maintenance, and large installation space is necessary for the hydraulic and cooling systems. Moreover, the presence of axial compression significantly lowers the frequency of torsional loading, which consequently results in low testing speed. In this study, a cost-effective, space-saving and high-speed fatigue testing method was newly proposed, and the shear-mode fatigue crack growth tests were carried out by using the developed machine. Based on the obtained experimental data, the potential of the new testing machine is discussed.

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50

Burchill, Madeleine, Simon A. Barter, and Michael Jones. "The Effect of Crack Growth Retardation when Comparing Constant Amplitude to Variable Amplitude Loading in an Aluminium Alloy." Advanced Materials Research 891-892 (March 2014): 948–54. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.948.

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It has often been observed that the growth of short fatigue cracks under variable amplitude (VA) cyclic loading is not well predicted when utilising standard constant amplitude (CA) crack growth rate/stress intensity data (da/dN v DK). This paper outlines a coupon fatigue test program and analyses, investigating a possible cause of crack growth retardation from CA-only testing. Various test loading spectra were developed with sub-blocks of VA and CA cycles, then using quantitative fractography (QF) the sub-block crack growth increments were measured. Comparison of these results found that, after establishing a consistent uniform crack front using a VA load sequence, the average crack growth rate then progressively slowed down with the number of subsequent CA load cycles applied. Further fractographic investigation of the fracture surface at the end of each CA and VA sub-block crack growth, identified significant crack front morphology differences. Thus it is postulated that a variation or deviation from an efficient crack path is a driver of local retardation in short crack growth during CA loading. This may be a source of error in analytical predictions of crack growth under VA spectra loading that may need to be considered in addition to other potential effects such asless closure whilst cracks are small. For aircraft designers, using solely CA data for fatigue life predictions this may result in non-conservative estimates of total crack fatigue life, producing unexpected failures or an increased maintenance burden.

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Journal articles on the topic 'Small Fatigue Crack Growth'

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