Issue 50

O. Plekhov et alii, Frattura ed Integrità Strutturale, 50 (2019) 1-8; DOI: 10.3221/IGF-ESIS.50.01 2 deformation, the Rise integral, the sizes of plastic deformation zone at crack tip, the dissipated energy were used as the crack propagation control parameters [1-4]. To derive a crack propagation law valid for arbitrary loading conditions we have to consider an energy concept of crack propagation. The current state of development of experimental mechanics allows one to monitor the dissipated part of energy with very high precision using infrared thermography [5-7]. The main problem of application of thermography technique is caused by the uncertainty of the solution to the inverse thermal problem [8]. Few years ago, we proposed an effective chip solution for the problem. We developed an additional system for direct monitoring of a heat flow [9]. To treat the experimental data we need a simple description of elasto-plastic deformation in process zone valid for arbitrary (multiaxial) loading conditions. Following by idea [10], we proposed a model of energy dissipation at crack tip. The key point of this approach is a hypothesis of the link between the elastic and elasto-plastic solutions at the fatigue crack tip proposed by Dixon [11]. In the framework of the model we divided the dissipated energy into two parts corresponding to reversible (cyclic) and monotonic plastic zones. Analysis of this approximation has shown zero effect of fatigue crack advance on the energy dissipation into cyclic plastic zone. This dissipation is a function of spatial size of a cyclic plastic zone and characteristic size of the yield surface. Under isotropic hardening, the change of the applied stress amplitude leads to the change of characteristic size of the yield surface and, as consequence, to the heat dissipation at constant crack rate. The dissipation in monotonic plastic zone is a function of both crack rate and characteristic size of the yield surface. This part of the model gives correlation between fatigue crack rate and power of heat dissipation [4,7]. The previous authors’ investigations were focused on crack growth problems under an opening or mode I mechanism [9] and a relationship was proposed for the growth rate of a fatigue crack based on an analysis of the energy balance at its tip. However, most structures are failed due to mixed mode loading. Many uniaxial loaded materials, structures and components often contain randomly oriented defects and cracks which develop a mixed mode state by rotation of their orientation with respect to the loading axis. For example mixed mode I/II cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces as discussed in the following [12-15]. In this work, we verify the main hypothesis used for our phenomenological description of fatigue crack propagation law and verify the approach for fatigue cracks titanium Grade 2 samples subject to the multiaxial cyclic loading. E NERGY DISSIPATION AT THE CRACK TIP UNDER CYCLIC LOADING n the previous work [9] we obtained the relation to calculate the energy of plastic deformation as a consequence, energy dissipation at fatigue crack tip:     2 2 1 2 , tot p da U W A W A dN     (1) where A τ – stress amplitude. Terms in Eqn. (1) correspond to reversible (cyclic) and monotonic plastic zones. Analysis of this approximation has shown that energy dissipation in a cyclic plastic zone is independent of 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 in the characteristic diameter of the yield surface and, as consequence, to the 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. It was shown by Short [1], that crack growth can be determined by heat generation: p da W dN J      (2) Where W p - hysteresis energy rate, Φ - heat generation rate, J - fracture energy added to V per unit crack advance, Γ - fracture energy required per unit crack advance (original notation are used). We can write the equation for heat generation from (2): I