PSI - Issue 18

A. Vshivkov et al. / Procedia Structural Integrity 18 (2019) 608–615 Author name / Structural Integrity Procedia 00 (2019) 000–000

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deformation and failure, which is accompanied by accumulation and dissipation of energy. The investigation into thermodynamics of deformation and failure is a key issue of solid mechanics. The analysis of the kinetics of damage accumulation, the process of crack nucleation and kinetics of the crack growth allows specialists to predict the time of structure failure and to perform in proper time a partial replacement or repair of fractured structural elements. Moreover, the repair or replacement of the defective parts on a timely basis is more effective than their complete replacement after mechanical damage. It is therefore very important to know the time during which the flaw size in the ill-behaved areas reach critical values. The actual engineering structures operate under complex types of loading. So, it is of considerable interest to study the behavior of materials under mixed loading conditions that combine mode 1 and mode 2 fractures. In sufficiently plastic structural materials the propagation of the crack begins when the plastic deformation near its tip becomes large (of the order of 10 percent). This irreversible process is accompanied by the release and accumulation of energy, which leads to a local temperature change in the region of the crack tip and the occurrence of a heat flux. Infrared thermography is an efficient method for estimating energy dissipation under mechanical testing [5, 6]. 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. A principal solution to the problem of measuring the energy dissipated in the structure under deformation and failure can be obtained by the development of additional system for direct monitoring of the heat flux [7]. The heat generation process depends on both the thermo elastic effect and plastic energy dissipation. The measurement of heat flux near the crack tip allows one to calculate the energy balance during crack propagation and to develop a new equation for its description. Attempts to develop a new equation for crack propagation were made by many authors. They used such quantities as the J-integral, the work of plastic deformation, the size of the zone of plastic deformation, the amount of dissipated energy and others [8-11]. The classical assumption of almost complete dissipation of the deformation energy into heat [12] has proved to be correct only in a limited number of cases. In this work, we have derived an equation describing the evolution of plastic work at the crack tip. Following the idea given in [14], 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 [11,15]. Analysis of this approximation has shown the independence of heat dissipation in cyclic plastic zone from the crack advance. This dissipation is fully determined by the spatial size of a cyclic plastic zone and characteristic diameter of the yield surface. This approach gives well know correlation between fatigue crack rate and dissipated energy. This equation based the hypothesis about link between the elastic solution and the elastic-plastic deformation in the fatigue crack tip using the Young’s modulus and the secant plasticity modulus [16] and it was originally proposed as an empirical expression for a central crack in a wide sheet loaded in tension normal to the line of the crack. Analysis of the experimental data on crack propagation under biaxial loading has revealed similar qualitative features of energy dissipation [17]. 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. 2. Experimental setup A series of samples made from stainless steel were tested. The geometry of the samples is shown in Figure 1. During tests the samples were subjected to cyclic loading with constant stress amplitude and different biaxial coefficient