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

  • Andrej Likeb
  • Nenad GubeljakEmail author
  • Yury Matvienko


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.


Stress intensity factor Pipe-ring specimen (PRS) Finite element analysis 

List of symbols

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)


\({K_\mathrm{I}}\)  (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


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


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


Modified crack shape function from SENB specimen

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

Coefficient of stress intensity shape function



Stress intensity factor


Single-edge-notched bending specimen


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


Crack opening displacement


Finite element analysis


Equivalent deformation


Apparent stress–strain curve


Limit load


Material resistance curves


J-integral of material


Stress intensity factor of material


Crack tip opening displacement of material


Slovenian Research Agency



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of MariborMariborSlovenia
  2. 2.Mechanical Engineering Research InstituteRussian Academy of SciencesMoscowRussia

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