13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Figure 3. Temperature evolution versus time Figure 4. Thermal model, geometry at a distance of 5mm from the crack front and boundary conditions In order to determine the heat source associated with the crack propagation. Under plane stress condition the radius of the reverse cyclic plastic zone can be quantified with the relation: 2 2 8 y R K r (1) For a stress intensity factor of 20MPa mthe radius of the reverse cyclic plastic zone is about 130µm. This value remains small compared to the size of the specimen. The heat source distribution will be thus considered as linear and centered in the reverse cyclic plastic zone. For a slow moving crack, the heat source associated with the fatigue crack propagation can be considered to be motionless. This assumption can be justified by the calculation of the Péclet number, noted Pe, which compares the characteristic time of thermal diffusion with the characteristic time associated to the heat source velocity (i.e. the velocity of the reverse cyclic plastic zone at the crack tip). In our case the Péclet number is expressed by Pe =L a v where L is the characteristic length of crack propagation, v the crack velocity and a the thermal diffusivity. For a crack length of around 1mm, a crack velocity of 0.1mms−1 and a thermal diffusivity of 1.4×10−5 m2s−1 the Péclet number is 6×10−3. This value remains small compared to unit and therefore the heat source can also be considered as motionless. In order to identify the heat source a thermal model of the plate was made and solved with the finit element method. The geometry and the thermal boundary conditions are detailed in fig. 4. The heat convection coefficient on the specimen faces and the room temperature are respectively taken equal to 10Wm-2K-1 and 20°C. For C40 mild steel, the thermal and mechanical properties are given in table 1. A unit line heat source (q=1Wm-1) is imposed on the crack front line. For a steady state regime the temperature variation at a distance of 5mm of the crack front is about 0.0163°C. Thanks to the linearity of the heat equation with the heat source, it is possible to deduce a heat source of 153Wm-1 associated with the fatigue crack loaded with a stress intensity factor range of 20MPa m. 3. The stress field and stress intensity factor due to the heterogeneous temperature field near the crack tip 2.2. An infinite plate with a semi-infinite through crack This section is focused on the theoretical problem of an infinite plate with a semi-infinite through
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