13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- On the effect of fatigue crack plastic dissipation on the stress intensity factor Nicolas Ranc1,*, Thierry Palin-Luc2, Paul C. Paris3 1 Arts et Métiers ParisTech, PIMM, CNRS, 151 Boulevard de l’Hôpital, F-75013 Paris, France 2 Arts et Métiers ParisTech, I2M, CNRS, Esplanade des Arts et Métiers, F-33405 Talence Cedex, France 3 Parks College of Engineering, Aviation, and Technology, St. Louis University St. Louis, MO, 63103 USA and visiting professor at Arts et Metiers ParisTech, France * Corresponding author: Nicolas.ranc@ensam Abstract In metals, during plastic strain, a significant part of the plastic energy is converted into heat. This generates a heterogeneous temperature field around the crack tip which depends on the intensity of the heat source associated with the plasticity and the thermal boundary conditions of the cracked structure under cyclic loading. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to stress field around the crack tip. This paper shows how this thermal effect modifies the mode one stress intensity factor for two cases: (i) the theoretical problem of an infinite plate with a semi-infinite through crack and (ii) a finite plate specimen with a central through crack. The comparison of the two cases allows the authors to discuss the effect of convection. The comparison of the simulated and experimental temperature field variation at the specimen surface (infra-red measurement on a mild steel) leads to identify the heat flux in the reverse cyclic plastic zone. This is the key parameter of the problem. Finally, the consequences of the calculation on the range, the ratio and the maximum and the minimum values of the stress intensity factor are discussed. Keywords: stress intensity factor, plastic dissipation, reverse cyclic plastic zone, thermal stress 1. Introduction During experimental study of fatigue crack propagation (for example the characterization of the propagation velocity versus the range of the stress intensity factor) the heating effects associated with the crack propagation are often neglected and the tests are considered as isothermal. This assumption is all the more legitimate when the loading frequency is small. However currently it is increasingly necessary to study the fatigue behavior of materials for long and very long life. Experimental techniques of accelerated tests thus are often carry out in order to reduce test durations : electromagnetic resonance fatigue testing machine with a loading frequency of about hundred Hertz and even ultrasonic fatigue machine with a loading frequency of about several tens of kHz. It is then necessary to know if the assumption of an isothermal process is always valid under these test conditions. In metals, during plastic strain, a significant part of the plastic energy (around 90% [1,2]) is converted in heat. During a cyclic loading of a cracked structure, the plasticity is located in the reverse cyclic plastic zone near the crack tip [3,4]. This heat source generates a heterogeneous temperature field which depends on the intensity of the heat source associated with the plasticity and the thermal boundary conditions of the cracked structure. Due to the thermal expansion of the material, the temperature gradient near the crack tip creates thermal stresses which contribute to the stress field in this region and on the global stress intensity factor. The objective of this communication is to propose a method in order to quantify the thermal contribution on the stress intensity factor. In a first part the identification of the heat source associated with the crack propagation will be detailed. In a second part the estimation of the thermal effect on the stress field near the crack tip and on the stress intensity factor will be made for the two geometries: an infinite plate with a semi-infinite through crack and a finite plate specimen with a central through crack and with convection boundary conditions on all the specimen faces. Finally, in the last part, all these results will be compared and discussed.
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