PSI - Issue 32

A.Yu. Iziumova et al. / Procedia Structural Integrity 32 (2021) 93–100 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

99 7

F

  

: . dp

E



(17)

s

p

Heat dissipation was calculated by Eq. (1), (14) and (17). The calculations were carried out in a finite element package Comsol Multiphysics in a plane-stressed formulation. The work of plastic deformation was considered in a stationary setting. For each of the selected crack lengths, three loading cycles were simulated. Then, the integral value of the plastic work for a stabilized cycle was determined. Fig. 5 shows the results of experiment and numerical simulation of the energy dissipation per cycle depends on the crack length for maximum load of 10.5 kN and 11 kN.

Fig. 5. The crack length dependence of heat dissipation per cycle under maximum load of 10.5 kN and 11 kN (experiment and simulation).

The numerical calculation showed satisfactory agreement with the experimental data, especially up to a crack length of 15 mm (Fig. 6). For a crack length more than 15 mm, the simulation shows a sharper increase in heat dissipation value than experimental data. It is caused by an increase in plastic work intensity when the crack approaches the specimen boundary. As a result, the applicability of the mathematical model was limited to the crack lengths of 19 mm (for maximum load of 11 kN) and 17 mm (for maximum load of 10.5 kN). 5. Conclusions An experimental assessment of the energy balance in the CVN-specimens of titanium alloy Ti-0.8Al-0.8Mn under cyclic deformation mode has been carried out. It has been shown experimentally that the critical value of the stored energy tends to a certain general value. It is approximately the same for two different values of loading. Numerical simulation of the dissipated energy during the fatigue crack propagation showed a good agreement between the numerical and experimental data. It allows one not only to verify the used model, but also to establish the limits of its applicability. According to the thermodynamic theory of strength developed by Schipachev (2018) and Fedorov (1979), close to the fracture moment the stored energy reaches a certain critical value, comparable to the enthalpy of material melting. It is obvious that under the mechanical loads the plastic deformation is inhomogeneous over the material volume, and damage process is local. Breaking interatomic bonds and material damage under melting occurs more uniformly. Therefore, the estimation of the material volume with the bonds broken due to the plastic deformations is necessary to compare the obtained critical value of stored energy and the enthalpy of titanium melting. For this, additional structural studies should be carried out. Nevertheless, the steady growth of the stored energy up to a certain critical value, which is approximately the same for different values of loading, allows us to suggest that an analogy between critical value of stored energy and the enthalpy of melting may exist.