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Physically appropriate characterization of fatigue crack propagation rate in elastic–plastic materials using the \(J\)-integral concept

Abstract

The current paper discusses the physically correct evaluation of the driving force for fatigue crack propagation in elastic–plastic materials using the \(J\)-integral concept. This is important for low-cycle fatigue and for short fatigue cracks, where the conventional stress intensity range (\(\Delta K\)) concept cannot be applied. Using the configurational force concept, Simha et al. (J Mech Phys Solids 56:2876–2895, 2008) , have derived the \(J\)-integral for elastic–plastic materials with incremental theory of plasticity, \(J^{\mathrm{ep}}\), which is applicable for cyclic loading and/or for growing cracks, in contrast to the conventional \(J\)-integral. The variation of this incremental plasticity \(J\)-integral \(J^{\mathrm{ep}}\) is studied in numerical investigations conducted on two-dimensional C(T)-specimens with long cracks under cyclic Mode I loading. The crack propagates by an increment after each load cycle. The maximum load is varied so that small- and large-scale yielding conditions prevail. Three different load ratios are considered, from pure tension to tension-compression loading. By theoretical considerations and comparisons with the variation of the crack tip opening displacement \(\delta _{\mathrm{t}}\), it is demonstrated that the cyclic, incremental plasticity \(J\)-integral \(\Delta J_{\mathrm{actPZ}}^{\mathrm{ep}}\), which is computed for a contour around the active plastic zone of the growing crack, is physically appropriate to characterize the growth rate of fatigue cracks. The validity of the experimental cyclic \(J\)-integral, \(\Delta J^{\mathrm{exp}}\), proposed by Dowling and Begley (ASTM STP 590:82–103, 1976), is also investigated. The results show that \(\Delta J^{\mathrm{exp}}\) is correct for the first load cycle, however, not fully appropriate for a growing fatigue crack.

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Notes

  1. For the mathematical expressions in this paper the direct (coordinate-free) notation is used as in Gurtin (2000). The notation is specified in Ochensberger and Kolednik (2014).

  2. For generating Fig. 6, the simulation was repeated with a FE-mesh size of \(m = 0.033\,\hbox {mm}\).

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Acknowledgments

Financial support by the Austrian Federal Government and the Styrian Provincial Government within the research activities of the K2 Competence Center on “Integrated Research in Materials, Processing and Product Engineering”, under the frame of the Austrian COMET Competence Center Programme, is gratefully acknowledged (strategic Project A4.20-WP3).

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Ochensberger, W., Kolednik, O. Physically appropriate characterization of fatigue crack propagation rate in elastic–plastic materials using the \(J\)-integral concept. Int J Fract 192, 25–45 (2015). https://doi.org/10.1007/s10704-014-9983-z

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  • DOI: https://doi.org/10.1007/s10704-014-9983-z

Keywords

  • Configurational force concept
  • Crack driving force
  • Cyclic \(J\)-integral
  • Low-cycle fatigue
  • Fatigue crack growth
  • Overload effect