A Critical Review of Crack Tip Stress Intensity Factors for Semi‐elliptic Cracks*

Scott, Peter; Thorpe, T.W.

doi:10.1111/j.1460-2695.1981.tb01127.x

Cited by 119 publications

(56 citation statements)

References 29 publications

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“…Short crack growth rates were plotted against crack length as well as against ΔK. Stress intensity factor K values were calculated from the half surface crack length using the empirical formula of Scott and Thorpe [24]. All K calculations assumed a crack depth to half surface crack length ratio (a/c) of 1.…”

Section: Methodsmentioning

confidence: 99%

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Effects of microstructure on room temperature fatigue crack initiation and short crack propagation in Udimet 720Li Ni-base superalloy

Pang

Reed

2008

International Journal of Fatigue

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An assessment of the effects of microstructure on room temperature fatigue crack initiation and short crack propagation in a Ni-base superalloy is presented. The assessment was carried out on microstructural variants of U720Li, including as-received U720Li, U720Li-LG (large grain variant) and U720Li-LP (large intragranular coherent γ′ variant). Fatigue tests were carried out at room temperature using a 20Hz sinusoidal cycling waveform on plain bend bars. Tests were conducted in 3-point bend under load control with an R-ratio of 0.1. A maximum load of 95% σ y was used in all tests. Room temperature fatigue crack initiation was noted to occur due to slip band cracking and from porosity on or just beneath the surface in all materials. Crack propagation was noted to be highly faceted (due to planar slip band cracking) immediately after crack initiation followed by a transition to a flatter Stage II type crack path as crack length increases.U720Li-LP was noted to show the longest fatigue lifetime, followed by U720Li-LG while U720Li shows the shortest life. The longer lifetime of U720Li-LP was linked to a higher resistance to both fatigue crack initiation and short crack propagation. U720Li and U720Li-LG show approximately similar crack initiation resistance although U720Li-LG showed slightly improved short crack growth resistance. The observations have been rationalised in terms of the microstructural characteristics of the materials, and it is believed that larger grain size, larger coherent γ′ precipitate size and higher volume fractions of both coherent and primary γ′ precipitates will improve overall fatigue * Now at Dept. of Materials Science & Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK lifetimes in PM Ni-base alloys which exhibit planar slip characteristics at room temperature.

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Section: Methodsmentioning

confidence: 99%

“…When calculating the ΔK values using the empirical formula of Scott and Thorpe [24], it was assumed that the crack depth is equivalent to half the surface crack length, i.e.…”

Section: Short Crack Propagationmentioning

confidence: 99%

Effects of microstructure on room temperature fatigue crack initiation and short crack propagation in Udimet 720Li Ni-base superalloy

Pang

Reed

2008

International Journal of Fatigue

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“…Scott and Thorpe [31] considered the case of a semi-elliptical crack of length 2c and depth a in a plate of thickness t. For the case of pure bending the two main expressions used to calculate the Mode I stress intensity factors at the surface (θ = 0) and at maximum depth (θ = π/2) in the present paper are: …”

Section: Appendix Bmentioning

confidence: 99%

“…The crack growth rate da/dN was then taken to be half the surface crack growth rate d(2c)/dN. ΔΚ at maximum depth for the short cracks was calculated using the equations outlined by Scott and Thorpe [31]. Instead of using the nominal far-field bending stress range to calculate ΔΚ, the local bending stress range in the notch root predicted by an elastic-plastic FE model was used.…”

Section: Short Crack Growth Interaction and Coalescencementioning

confidence: 99%

Short crack initiation and growth at 600°C in notched specimens of Inconel718

Connolley¹,

Reed²,

Starink³

2003

Materials Science and Engineering: A

113

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The natural initiation and growth of short cracks in Inconel ® 718 U-notch specimens has been studied at 600 o C in air. U notches were introduced through broaching, and hardness traces and optical microscopy on cross sections through the U notch broaching showed that the broaching process had introduced a deformed, work hardened layer. Fatigue tests were conducted under load control using a 1-1-1-1 trapezoidal waveform, on specimens with as-broached and polished U-notches. Multi-site crack initiation occurred in the notch root. Many of the cracks initiated at bulge-like features formed by volume expansion of oxidising (Nb,Ti)C particles. In unstressed samples, oxidation of (Nb,Ti)C particles occurred readily, producing characteristic surface eruptions. Scanning electron microscopy on metallographic sections revealed some sub-surface (Nb,Ti)C oxidation and localised matrix deformation around oxidised particles. A mechanism for crack initiation by carbide expansion during oxidation is discussed. Surface short crack growth rates in the notch root of polished specimens were measured using an acetate replica technique. Observed short crack growth rates were approximately constant across a wide range of crack lengths. However, there was a transition to rapid, accelerating crack growth once cracks reached several hundred microns in length. This rapid propagation in the latter stages of the fatigue life was assisted by crack coalescence. Polishing the U-notch to remove broaching marks resulted in a pronounced increase in fatigue life. IntroductionNickel-base superalloys like Inconel ® 718 (IN718) are used extensively for turbine discs and other components in industrial and aerospace gas turbines. Since turbine discs are safety-critical components, considerable effort is expended in determining their safe operating life. The lifing procedure adopted must enable the reliable prediction of the safe life of the disc, without being overly conservative. Once engines are in service, regular inspection of the engines and refinements of lifing models may enable life-extension programs to be considered. In the traditional predicted safe life philosophy, the life is declared based on laboratory specimen and component testing. In recent years a damage-tolerant approach to lifing has been adopted, in which it is accepted that components contain defects or inhomogeneities from which cracks can initiate. Assuming an initial flaw size c o , the fatigue life is determined as the number of cycles required to propagate the crack to some critical size c c . The initial size c o can be based on the maximum defect size present in the material, or on the minimum defect size detectable by nondestructive testing (NDT) [1]. Selection of c c is based on knowledge of the fracture toughness of the material, the limit load, the maximum allowable strain or maximum permitted compliance change for a particular component. Damage-tolerant lifing requires accurate information on fatigue crack initiation and growth rates. Fatigue lives are determi...

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“…A Linear Elastic Fracture Mechanics (LEFM) calculation of K-equilibrium around the crack front was conducted based on Scott and Thorpe's review paper [39] and the fatigue crack propagation rate da/dN is plotted against stress intensity factor range ΔK depth in Figure 17 (b). In the present research, da/dN was based on the observed evolution of crack aspect ratio [35] as well as dc/dN (calculated by the secant method).…”

Section: Discussionmentioning

confidence: 99%

3-D analysis of fatigue crack behaviour in a shot peened steam turbine blade material

Katsamenis

Mellor

et al. 2015

Materials Science and Engineering: A

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Serial mechanical sectioning and high resolution X-ray tomography have been used to study the three-dimensional morphology of small fatigue cracks growing in a 12 Cr tempered martensitic steam turbine blade material. A range of surface conditions has been studied, namely polished and shot peened (with varying levels of intensity). In the polished (unpeened) condition, inclusions (alumina and manganese sulphide) played an important role in initiating and controlling early fatigue crack behaviour. When fatigue cracks initiated from an alumina stringer, the crack morphology was normally dominated by single stringers, which were always in the centre of the fatigue crack, indicating its primary role in initiation. Manganese sulphide inclusion groups however seemed to dominate and affect the crack path along both the surface and depth crack growth directions. The more intensely shot peened condition did not however evidence inclusion or stringer affected fatigue crack initiation or growth behaviour; sub-surface crack coalescence being clearly observed by both serial sectioning and CT (computed tomography) imaging techniques at a depth of about 150 ~ 180 μm. These sub-surface crack coalescences can be linked to both the extent of the compressive residual stress as well as the depth of the plastic deformation arising from the intense shot peening process. Shot peening appears to provide a different defect population that initiates fatigue cracks and competes with the underlying metallurgical defect populations. The most beneficial shot peening process would in this case appear to "deactivate" 2 the original metallurgical defect population and substitute a known defect distribution from the shot peening process from which fatigue cracks grow rather slowly in the strain hardened surface layer which also contains compressive residual stresses. A benefit to fatigue life in bending, even under Low Cycle Fatigue (LCF) conditions, has been observed in these tests if a sufficiently severe shot peening condition is applied in a constrained notch configuration.

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A Critical Review of Crack Tip Stress Intensity Factors for Semi‐elliptic Cracks*

Cited by 119 publications

References 29 publications

Effects of microstructure on room temperature fatigue crack initiation and short crack propagation in Udimet 720Li Ni-base superalloy

Effects of microstructure on room temperature fatigue crack initiation and short crack propagation in Udimet 720Li Ni-base superalloy

Short crack initiation and growth at 600°C in notched specimens of Inconel718

3-D analysis of fatigue crack behaviour in a shot peened steam turbine blade material

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