Issue 53

A. Chatzigeorgiou et alii, Frattura ed Integrità Strutturale, 53 (2020) 306-324; DOI: 10.3221/IGF-ESIS.53.24 322 From Fig.22, up to (about) 56000 cycles and for crack length about 17mm, the results were identical. After this point, there was a difference in cycle loads. In the experimental procedure, the propagation stops at 58000 cycles, and in FEMAP for the same crack length, the propagation stops at 61900 cycles, which means a difference of 5.99%. C ONCLUSION code was created in order for the FEA program FEMAP 11.3.2, to be able to study fracture mechanics problems. In order to verify the results produced by the proposed code in FEMAP, analytical calculations and experimental results were used. From the analysis it is observed: (i) At first, the comparison of the calculated SIFs from FEMAP and the analytical method shows a difference of 0.90% for K I and 4.92% for K II . (ii) Secondly, the trajectories from all cases from FEMAP were checked with experimental results. They show almost identical behavior. (iii) Finally, the estimation of the fatigue lifetime was also checked with experimental results. The results were identical up to a certain point. After that, a difference of 5.99% occurred. The differences of the calculations for the SIFs are small, and possibly can be reduced, replacing the COD method with the J integral method, which introduced by James Rice [33]. It is more complicated to apply this method to the FEA, but many studies in the bibliography show that using this method better results can be produced. For the crack propagation criteria already used, Diaz [34] found that SED, although is computationally more expensive, it describes the processes of the calculation of the Keq and the kinking angle, very well for ductile materials. Moreover, the problem with the selected Keq criteria is that negative K II has the same effect as a positive one. Rozumek and Macha [35], have published a comprehensive review on the calculation of the Keq. Finally, the path of the crack and the estimation of the lifetime which produced by the proposed code in FEMAP, are almost identical with the experimental results. The deviation at the end of the calculation of the lifetime is considered small. A cause of this deviation can be the difference of the calculations for the K II , as was mentioned previously in (i) or even in an internal defect of the material of the specimen which used in the experiment. According to Diaz [34], the difference between experimental and numerical results in the modified compact specimen may also be attributed to crack closure and roughness. Consequently, the proposed code gives reliable results and can be used in order to study cracked surfaces. Furthermore, apart from the simple cases of cracked surfaces, this code can be used as a base for more complicated and complex studies. Two examples of these studies can be the study of Crack Growth Behavior of Welded Stiffened Panel, and the effects due to overloads (for example [36,37]). In addition, out-of-plane sliding mode III crack problems may be also studied with the proposed code. The procedure proposed by this code is the capability of the finite element program FEMAP to confront successfully crack mechanics problems. In addition, the proposed code has the possibility with a computational effort to study cracked problems with no built-in tools. N OMENCLATURE α crack length a 1 material property in the Richard’s criterion for the Keq C fatigue parameter in the Paris-Erdogan law. d α /dN fatigue crack growth rate E axial modulus of elasticity F applied load K I mode-I stress intensity factor K II mode-II stress intensity factor K III mode-III stress intensity factor K IC fracture toughness K eq equivalent stress intensity factor K max Maximum stress intensity factor K min Minimum stress intensity factor L length of the crack tip element A