PSI - Issue 52

Vitalijs Pavelko et al. / Procedia Structural Integrity 52 (2024) 382–390 Vitalijs Pavelko/ Structural Integrity Procedia 00 (2019) 000 – 000

387

6

4. Prediction of damage development, the fatigue strength distribution function, and estimation of its parameters 4.1. The model of destruction of a perfectly brittle transducer. Results of FEA used for establishing of a model of destruction of perfectly brittle constrained transducer at static loading. This model is useful for further analysis of results of fatigue tests. The model of destruction of perfectly brittle transducer installed to the thin-walled sheet (Fig.2). Assumptions: 1) The material of the transducer is linearly elastic and perfectly brittle, and its tensile strength is constant 0 2) The host sheet is loaded by monotonically increasing quasi-static load. Obviously, the first destruction will occur in the middle cross-section when the stresses reach the tensile strength of the material. The transducer will be divided into two separate parts as the configuration b) in Fig. 3, and the stress distribution in each part corresponds to an orange curve (Fig. 4) with the maximum stress in the middle cross-section. With further loading, the next destruction will be in the middle cross-section of this fragment, and it will be divided into two parts of equal length similarly to configuration c) in Fig. 3, and the stress distribution corresponds to a yellow curve (Fig. 4) with the maximum stress in the middle cross-section of each part. The differences between these stresses are negligible, but it is likely that the subsequent destruction of these parts will occur sequentially. Assuming that first there was a destruction of type d) in Fig. 3, then the stress distribution corresponds to the green line in Fig. 4, and this destruction practically does not affect the stress in the adjacent fragment. It can be argued that at further increase in the load, this fragment will collapse in its middle cross-section. Such a development of the process of multiple destruction can logically be called the process of equi-fragmental crushing (EFC). Easy to see that stable configuration of damaged transducer corresponds to PET crushing to fragments of the same length, and the critical load value corresponds to each configuration. In Fig.5 the normalized mean stress of each fragment of transducer for all configurations (Fig.3). It is seen that the mean stress of all fragments of each stable configuration c) and e) is approximately equal one to other. The transient configuration d) means that if the external load causes crushing of first fragment, then further small increase of load will cause the destruction of the second fragment and the transition to a stable configuration e). The transition to the next stable configuration with two times a greater number of fragments is possible at significant increase of load only. 4.2. General prediction of fatigue fracture of PET The development of PET fracture during panel fatigue testing has a significant similarity with the above model of destruction of the built-in transducer under monotonous panel loading. First, multiple cracks of transducers are observed in tests and predicted in simulation. The crushing features of the transducer follow from the model, and the crushing process in the fatigue test proceeds in a similar way. In both cases, the host structure is loaded with tension. The differences between the model and the experiment are primarily due to the type of loading (cyclic load in the experiment and monotonically increasing load in the simulation). The statistical nature of fatigue is also a significant cause of the differences, but at the same time allows us to give a consistent explanation of the fracture process under cyclic load. Below is proposed a description of the process of development of PET destruction, considering the results of FMA and model of PET destruction under monotonous loading. 1) Fatigue failure starts on the lower surface of the transducer. In contrast to the brittle fracture model described above, it is assumed that several cracks arise in cross-sections with distance up to 20 mm from the middle cross section of PET. This assumption is justified by the fact that the variation of tensile stresses in this interval do not exceed 10%. The second argument in favor of this sentence consists in statistical nature of fatigue fracture. There are many senses of large scattering of fatigue strength of PET. 2) PET first destruction close to middle cross-section is the most probable because here is zone of largest stresses (Fig.4, red curve). It means the transition to configuration b) (Fig.3). This event causes redistribution of