SCIENCE CHINA Technological Sciences, Volume 61 , Issue 4 : 542-550(2018) https://doi.org/10.1007/s11431-017-9186-9

Calculation of stress intensity factor in two-dimensional cracks by strain energy density factor procedure

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  • ReceivedSep 15, 2017
  • AcceptedDec 19, 2017
  • PublishedFeb 1, 2018


In order to calculate the stress intensity factor (SIF) of crack tips in two-dimensional cracks from the viewpoint of strain energy density, a procedure to use the strain energy density factor to calculate the SIF is proposed. In this paper, the procedure is presented to calculate the SIF of crack tips in mode I cracks, mode II cracks and I+II mixed mode cracks. Meanwhile, the results are compared to those calculated by traditional approaches or other approaches based on strain energy density and verified by theoretical solutions. Furthermore, the effect of mesh density near the crack tip is discussed, and the proper location where the strain energy density factor is calculated is also studied. The results show that the SIF calculated by this procedure is close to not only those calculated by other approaches but also the theoretical solutions, thus it is capable of achieving accurate results. Besides, the mesh density around the crack tip should meet such requirements that, in the circular area created, the first layer of singular elements should have a radius about 0.05 mm and each element has a circumferential directional meshing angle to be 15°–20°. Furthermore, for a single element around the crack tip, the strain energy density factor is suggested to be calculated in the location where half of the sector element’s radius from the crack tip.

Funded by

the National Natural Science Foundation of China(Grant,No.,51438002)


This work was supported by the National Natural Science Foundation of China (Grant No. 51438002).


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  • Figure 1

    (a) Traditional approach using extrapolation procedure; (b) J-integral; (c) averaged SED approach.

  • Figure 2

    (a) Mode I crack; (b) mode II crack; (c) mixed-mode crack.

  • Figure 3

    (Color online) (a) Global view of mesh style in the mode I crack; (b) mesh style in averaged SED approach in the mode I crack; (c) mesh style in SEDF procedure in the mode I crack.

  • Figure 4

    (Color online) (a) Mesh density near the crack tip in SEDF approach; (b) mesh density near the crack tip in average SED approach.

  • Figure 5

    (a) Singular elements with nodal displacement; (b) non-singular elements without nodal displacement.

  • Figure 6

    (Color online) (a) Change of the SIF with the radius of sector elements; (b) change of the SIF with the circumferential directional meshing angle; (c) change of the SIF with the distance value.

  • Table 1   SIF results


    Theoretical solution

    Traditional approach

    J-integral approach

    Averaged SEDapproach

    SEDF procedure

    Mode I crack







    Discrepancy (%)






    Mode II crack






    Discrepancy (%)





    Mixed mode crack





    Discrepancy (%)








    Discrepancy (%)




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