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Configurational force based analysis of creep crack growth

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Abstract

Based on the concept of configurational forces, the driving force of cracks in elastic–plastic, creeping materials is derived. In a numerical study, the variation of the crack driving force with increasing creep time is compared to the behaviors of different parameters that have been used in literature to describe the tendency to creep crack growth. This is performed for the assumption of stationary cracks in C(T)-specimens made of Waspaloy at 700 °C. The loading conditions are varied so that small-scale creep, transition creep, or extensive creep conditions prevail. Either the load or the load-point displacement are held constant. It is demonstrated that, for the considered cases, the conventional creep crack growth parameters do not reflect the crack driving force, but qualitatively follow a behavior similar to the (absolute value of the) time derivative of the crack driving force.

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Notes

  1. A difference occurs only regarding the surface configurational force at the location of a traction vector t at a boundary, but the effects of opposite traction vectors compensate, see Fischer et al. (2012).

  2. The path independence of \(J^{{{\text{nle}}}}\) is valid for an ideally sharp crack. If the crack blunts, a process zone appears at the crack tip where non-proportional loading conditions can prevail. This leads to a decrease of \(J^{{{\text{nle}}}}\) near the crack tip, \(J_{{\Gamma_{{\text{r}}} }}^{{{\text{nle}}}} \to 0\) for \(r \to 0\), see e.g. McMeeking (1977), Rice (1979), and Kolednik et al. (2014).

  3. Note that the meaning of the term “crack driving force” differs for a cyclically loaded crack; its purpose is to allow the prediction of the crack propagation rate of a fatigue crack (Paris and Erdogan 1963).

  4. In ABAQUS, the C*-integral according to Eq. (2) is denominated as Ct-integral. It is stated that Ct becomes path independent and is known as C*-integral for steady-state creep conditions. As for the computation of the computational J-integral, JVCE, the line integral of Eq. (2) is transformed into a domain integral for the evaluation.

  5. A comparison of the strain energy density rate \(\dot{\phi }\) in the cases of F = 1 kN (Sect. 5.1) and V = 0.030 mm shows that, for F = 1 kN where the C*-integral is always positive, \(\dot{\phi }\) is always positive in front of the crack tip and decreases with increasing creep time. For V = 0.030 mm, negative \(\dot{\phi }\)-values appear in two regions near the back face of the specimen, above (and below) the crack plane. The expansion of these regions becomes smaller with increasing creep time. These findings explain why negative values of the C*-integral can appear for large contour radius R, compare Eq. (2).

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Acknowledgements

The authors acknowledge very helpful discussions with Professor F.D. Fischer, Institute of Mechanics, Montanuniversität Leoben. A.T. acknowledges discussions with Professor A. Saxena, School of Materials Science and Engineering, Georgia Institute of Technology. Financial support by the Austrian Federal Government (in particular from Bundesministerium für Verkehr, Innovation und Technologie and Bundesministerium für Wissenschaft, Forschung und Wirtschaft) represented by the Österreichische Forschungsförderungsgesellschaft mbH and the Styrian and the Tyrolean Provincial Government, represented by Steirische Wirtschaftsförderungsgesellschaft mbH and Standortagentur Tirol, within the framework of the COMET Funding Programme is gratefully acknowledged (Strategic Project P1.3-WP3).

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  1. A. Tiwari

    Present address: Metallurgical & Materials Engineering Department, Indian Institute of Technology Ropar, Ropar, Punjab, 140001, India

Authors and Affiliations

  1. Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, 8700, Leoben, Austria

    O. Kolednik & A. Tiwari

  2. Materials Center Leoben, 8700, Leoben, Austria

    A. Tiwari & C. Posch

  3. Faculty of Mechanical Engineering, University of Maribor, 2000, Maribor, Slovenia

    M. Kegl

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  1. O. Kolednik
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Correspondence to O. Kolednik.

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Kolednik, O., Tiwari, A., Posch, C. et al. Configurational force based analysis of creep crack growth. Int J Fract 236, 175–199 (2022). https://doi.org/10.1007/s10704-022-00645-z

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