Issue 48

O. Plekhov et alii, Frattura ed Integrità Strutturale, 48 (2019) 451-458; DOI: 10.3221/IGF-ESIS.48.43 452 Many authors proposed other correlations between the fatigue crack rate and different mechanical-structural parameters. For instance, the J-integral, the work of plastic deformation, the size of plastic deformation zone, the amount of dissipated energy were used as a parameter determining the crack propagation rate [1-4]. The propagating crack interacts with the material which can be considered as a complex hierarchical structure. Mechanical behavior at different spatial levels can be described in terms of energy concepts. Monitoring of energy dissipation during fatigue crack propagation can give significant information about the kinetics of deformation processes and the current crack propagation rate [5-8]. Infrared thermography is an efficient method for estimating energy dissipation under mechanical testing. The main difficulty associated with application of this technique to the study of energy dissipation is related to the uncertainties in the solution of the inverse problem. The determination of energy dissipation under deformation can be obtained by the development of an additional system for direct monitoring of a heat flow. Such a system based on the Seebeck effect was developed at ICMM UB RAS [9]. In this work, we have derived an equation describing the evolution of plastic work at the crack tip. Following the idea given in [10], we have divided the plastic work and, as a consequence, energy dissipation at crack tip into two parts corresponding to reversible (cyclic) and monotonic plastic zones. Analysis of this approximation has shown the independence of energy dissipation in cyclic plastic zone from the crack growth. This dissipation is fully determined by the spatial size of a cyclic plastic zone and the characteristic diameter of the yield surface. For isotropic hardening materials, the change of the applied stress amplitude leads to the change of the characteristic diameter of the yield surface and, as consequence, to energy dissipation at a constant crack rate. Dissipation in the monotonic plastic zone is a function of both crack rate and characteristic diameter of the yield surface. This gives a well know correlation between fatigue crack rate and dissipated energy [4,7]. To confirm the proposed approximation, we have compared it with the results of two fatigue crack propagation tests (uniaxial loading with constant stress intensity factor and biaxial loading with different biaxial coefficients). The experiments with constant stress intensity factor were reported in [11] for the first time. The main unexpected results of these experiments have shown that the energy dissipation measured by the contact heat flux sensor decreases during the crack propagation with the constant stress intensity factor. The proposed approximation demonstrates good qualitative agreement with the experimental data obtained during the uniaxial test. The developed approach gives us an opportunity to generalize it for complex loading conditions. Analysis of the experimental data on crack propagation under biaxial loading has revealed similar qualitative features of energy dissipation [8]. We observed two stages of energy dissipation: constant value at the first stage and sharp increase at its final stage. The comparison of the phenomenological predictions and the obtained experimental results shows good qualitative agreement as well. E XPERIMENTAL SETUP wo types of experiments were carried out to analyze energy dissipation under fatigue crack propagation in metals. We conducted uniaxial tests at constant stress intensity factor and tests on biaxial loading with a constant stress amplitude. Fig. 1 shows the geometry of samples examined during the tests. Samples for uniaxial testing were made of stainless steel AISE 304. The experiments were carried out at Bundeswehr University Munich. The samples were subjected to cyclic loading of 20 Hz at constant stress intensity factor and at loading ratio R = -1. The crack length was measured by the potential drop method. The electrical potential drop method has been chosen due to its ability to monitor fatigue crack propagation and to set the stress intensity factor controlling a feedback. In this case, the potential method provides sensitivity up to 0.02 mm for a d.c. (direct current) of 5 A. The experimental program includes four tests with constant stress intensity factor. The constant stress intensity factors are 15 MPa m 1/2 , 17.5 MPa m 1/2 , 20 MPa m 1/2 and 22.5 MPa m 1/2 , and the crack rates are 2.0076e-08 m/cycle, 6.6391e-08 m/cycle, 1.0245e-07 m/cycle, and 1.7177e-07 m/cycle, respectively. The first part of each experiment was performed subject to loading with a constant stress amplitude to initiate a 1 mm long fatigue crack, and the second part – at constant stress intensity factor until a 8 mm long crack was obtained. A similar experimental program was realized at ICMM UB RAS. The detailed description of the mechanical properties, geometry of the samples and corresponding test conditions are given in [9]. The Russian steel analogous to that used to prepare samples of different geometries was tested for the loading ratio R=0. The stress intensity factors were equal to 25 MPa m1/2 and 30 MPa m1/2 (for crack rates of 1.4e-07 m/cycle, 1.65e-07 m/cycle, respectively). The results of both experimental programs are similar. In the future analysis, we are going to use the results obtained for the AISE 304 T