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Research Papers: Design and Analysis

The Accounting for Geometrical Nonlinearity for Thin-Walled Pressurized Elastic Pipe With Long Axial Surface Crack

[+] Author and Article Information
Andrii Oryniak

IPP-Centre, Ltd.,
8, Strutyns'kogo Street,
Kyiv 01014, Ukraine
e-mail: oryand@ipp-centre.com

Igor Orynyak

Institute for Problems of Strength of
Academy of Science of Ukraine,
2, Tymiryazevska Street,
Kiev 01014, Ukraine
e-mail: igor_orinyak@yahoo.com

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received January 19, 2016; final manuscript received May 17, 2016; published online January 11, 2017. Assoc. Editor: Kunio Hasegawa.

J. Pressure Vessel Technol 139(2), 021210 (Jan 11, 2017) (8 pages) Paper No: PVT-16-1012; doi: 10.1115/1.4033703 History: Received January 19, 2016; Revised May 17, 2016

Consideration of a geometrical nonlinearity is a common practice for thin-walled pressurized structures, especially when their cross section is not a perfectly circular one due to either initial imperfections or distortions caused by the nonsymmetrical loading. The application of inner pressure leads to so-called rerounding effect when decreasing of local flexibilities takes place. The crack can be also treated as the concentrated flexibility, so the goal of this work is the investigation of dependence of stress intensity factor (SIF) on applied pressure. Two cases of SIF calculation for 1D long axial surface crack in a pipe loaded by inner pressure are considered here: (a) cross section of pipe has an ideal circular form and (b) the form has a small distortion and crack is located at the place of maximal additional bending stresses. The theoretical analysis is based on: (a) well-known crack compliance method (CCM) (Cheng, W., and Finnie, I., 1986, “Measurement of Residual Hoop Stresses in Cylinders Using the Compliance Method,” ASME J. Eng. Mater. Technol., 108(2), pp. 87–92) and (b) analytically linearized solution for deformation of the curved beam in the case of action of uniform longitudinal stresses. It is shown that for moderately deep crack (crack depth to the wall thickness ratio of 0.5 and bigger) in thin-walled pipe (radius to thickness ratio of 25–40) and inner pressure which induce hoop stress up to 300 MPa, the effect investigated can be quite noticeable and can lead to 5–15% reduction of calculated SIF as compared with the linear case. The analytical results are supported by the geometrically nonlinear finite element method (FEM) calculations.

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References

Figures

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Fig. 1

Direction of forces and displacements for curved beam element

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Fig. 2

The dependence of the multiplier λ on the dimensionless pressure p¯

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Fig. 3

The dependence of the multiplier F1(α)=YMβN/Y0 on the relative crack depth α

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Fig. 4

The influence of circumferential stresses due to internal pressure on the SIF reduction coefficient for two dimensionless depths of the crack: (a) α = 0.4 and (b) α = 0.6

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Fig. 5

The general FEM model, view of mesh, and boundary conditions

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Fig. 6

Dimensionless SIF dependence for ideal ring with crack

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Fig. 7

Dimensionless SIF dependence versus inner pressure with accounting of additional opening (yellow line) or closing (green line) bending moment due to initial form distortion

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Fig. 8

Comparison of dimensionless SIF values for case (b) obtained by FEM as well as by the present analytical method

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Fig. 9

Comparison of dimensionless SIF values for case (c) obtained by FEM as well as by the present analytical method

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