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The determination of the stress intensity factor solutions for the new pipe-ring specimen using FEA

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Abstract

For safe transport and reliable supply of petrochemical substances, it is crucial to ensure the structural integrity of the equipment, pipelines in particular. Regarding the large diameters and high mass per distance, pipelines for natural gas are designed as thin-walled cylindrical structures. To ensure the structural integrity of the unknown material means to measure and therefore empirically test the material fracture properties of the laboratory specimen for giving an assessment of the accepted defect size. Compared to standards and regulations, such as the ASTM E-1820, BS 7448 standards and the GKSS procedure, the production of standard specimens for measuring the fracture toughness is commonly very difficult or even impossible for applications. On the basis of the Slovenian–Russian bilateral project, we investigate and propose a solution for this issue with a new kind of specimen, called the pipe-ring specimen. The specimens were made from a segment of the observed thin-walled pipeline from the construction filed or stored in a warehouse. The measurement procedure is similar as for the standard SENB specimens and extensometer because of the geometry of the specimen, which is cut from the pipe and contains only a machine-made notch. The next step is to test specimens axially on the three-point bending load test on the hydraulic machine. Because the ring as the specimen is not standardized, it is necessary to show and prove how, and if it is possible to use ring specimens as an alternative option to the standard specimens for testing and determining fracture properties of testing material for thin-walled pipelines. In the frame of the three main experimental, analytical and numerical approaches, this publication shows the numerical approach of defining the stress intensity factor (SIF) for crack opening mode I with and without prior fatigue pre-cracking. Besides the limit load, the SIF presents one of two main parameters for developing the failure assessment diagram and estimating the possible accepted defects in a material relating to its’ structural integrity.

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Abbreviations

R  (mm):

Outer radius of the ring

W  (mm):

Height of the ring = height of SENB specimen

B  (mm):

Wall thickness of the ring = thickness of the SENB specimen

S  (mm):

Span distance between supports

a / W :

Crack aspect ratio

R / B :

Ratio between outer radius and wall thickness of ring

W / B :

Ratio between height of ring or SENB specimen against wall thickness or with of SENB specimen

J  (N/m):

J-integral

\({K_\mathrm{I}}\)  (MPa\(\surd \) m):

Stress intensity factor for mode I

\(K_{\mathrm{I,PRS}}\)  (MPa\(\surd \) m):

Stress intensity factor for mode I of the pipe-ring specimen

\(K_{\mathrm{I,SENB}}\)  (MPa\(\surd \) m):

Stress intensity factor for mode I of the SENB specimen

F  (kN):

Load and recorded force of testing machine

\(K_{\mathrm{I,PRS}}{/}K_{\mathrm{I,SENB}}\) :

Ratio between SIF of pipe-ring specimen and SENB specimen

\(\sigma _{\mathrm{eH}}\)  (MPa):

Limit yield of material

\(\sigma _{\mathrm{f}}\)  (MPa):

Effective fracture stress

\(\sigma _{m}\)  (MPa):

Linearly approximated fracture stress

n :

Hardening of the material

\(E^{{\prime }}\)  (MPa):

Modulus of elasticity

\(\sigma \)  (MPa):

Nominal stress

\(\sigma _{\mathrm{b}}\)  (MPa):

Bending stress

M  (Nm):

Bending moment

\(W_{t}\)  (mm\(^{3}\)):

Resistance moment of bending

f(a / W):

crack shape function

\(f^{*}(a{/}W)\) :

Modified crack shape function from SENB specimen

\(C_{1}, C_{2}, C_{n }\) :

Coefficient of stress intensity shape function

SIF:

Stress intensity factor

SENB:

Single-edge-notched bending specimen

ARAMIS:

A non-contact and material-independent measuring system based on digital image correlation (DIC)

COD:

Crack opening displacement

FEA:

Finite element analysis

PEEQ:

Equivalent deformation

\(R-e\) :

Apparent stress–strain curve

LL:

Limit load

R-curves:

Material resistance curves

\(J_{\mathrm{mat}}\) :

J-integral of material

\(K_{\mathrm{mat}}\) :

Stress intensity factor of material

\(\mathrm{CTOD}_{\mathrm{mat}}\) :

Crack tip opening displacement of material

ARRS:

Slovenian Research Agency

References

  1. ASTM E-1820.: Standard test method for measurement of fracture toughness. Annual Book of ASTM Standards, vol. 03.01 (2013)

  2. BS 7448.: Fracture mechanics toughness test, Part 1 published in 1991, Part 2: Method for determination of KIC, critical CTOD and critical \(J\) Values of Welds in Metallic Materials. TWI Abingdon Hall, Cambridge (1995)

  3. GKSS-Forschungszentrum Geesthacht GmbH.: EFAM GTP 02—the GKSS test procedure for determining the fracture behavior of materials. GKSS 2002/24 (2002)

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Acknowledgements

The authors would like to acknowledge ARRS (Slovenian Research Agency) for the support provided during this research and funding Ph.D. program for Dr. Andrej Likeb.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Maribor, Smetanova u.17, 2000, Maribor, Slovenia

    Andrej Likeb & Nenad Gubeljak

  2. Mechanical Engineering Research Institute, Russian Academy of Sciences, 4 M.Kharitonievsky Per., Moscow, Russia, 101990

    Yury Matvienko

Authors
  1. Andrej Likeb
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  2. Nenad Gubeljak
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  3. Yury Matvienko
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Correspondence to Nenad Gubeljak.

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Likeb, A., Gubeljak, N. & Matvienko, Y. The determination of the stress intensity factor solutions for the new pipe-ring specimen using FEA. Arch Appl Mech 89, 897–909 (2019). https://doi.org/10.1007/s00419-018-1481-8

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  • DOI: https://doi.org/10.1007/s00419-018-1481-8

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