PSI - Issue 54

T. Fekete et al. / Procedia Structural Integrity 54 (2024) 314–321 T. Fekete, D. Antók, L. Tatár, P. Bereczki Structural Integrity Procedia 00 (2019) 000–000

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Theory on the diagram represents the theoretical framework that determines the physical quantities of interest. Reality is the external world where the processes are performed; Digital Twin symbolizes the digital equivalent of the measurements, positioned between Theory and Reality. The Theory Digital Twin Reality → → sequence expresses the fact that the types of material tests are determined by theory, but the theoretical investigation for specific cases –e.g., the development of the geometry of a MO – is carried out by investigations in the DT layer. In the Theory layer, MOS T means that the theoretical model of the given type MO has to be created; in the Reality layer, MOS R represents that the MO must be prepared for measurement; in the Digital Twin layer, MOS DT denotes that the DT of the MO has to be developed for simulations. T X , DT X and R X describe the sets of possible states of a MO. Preparation of each MO for measurement is described by the map : Init Prep X MO → in Theory , : Init T T T Prep X MO → means that specimen preparation must be designed using theoretical considerations; these considerations should be implemented in Digital Twin , where the process is described by : Init DT DT DT Prep X MO → ; the process in the Reality layer is symbolized by : Init R R R Prep X MO → . : Init Fin Meas MO MO → represents the measurement process performed on each sample. Meas expresses the evolutionary process by which a sample evolves from its initial to its final state. In Theory , the measurement process is represented by : Init Fin T T T Meas MO MO → , which is expressed by : Init Fin DT DT DT Meas MO MO → in Digital Twin . The measurement process is illustrated by : Init Fin R R R Meas MO MO → in Reality ; its complex internal structure is highlighted separately at the bottom of the diagram showing that measurement is an incremental process. The T DT Meas Meas  arrow represents that the measurement process formulated in Theory should be implemented in Digital Twin faithfully, so that simulations can reproduce the process accurately. The arrow expresses the requirement that measurement information must be provided to the Digital Twin that T DT Assess Assess  arrow indicates that the assessing process formulated in Theory must be implemented properly in Digital Twin , so that the computations follow the theoretical scheme faithfully. In the Reality layer, the : Fin R R R Assess MO Y → map refers to the processing of raw data, whose relevant results are compared with corresponding results of DT simulations. T Y , DT Y and R Y denote the set of actual measurement results in the Theory , Digital Twin and Reality layers, respectively. The R DT Y Y ←→ arrow indicates that corresponding results of experiments and simulations are compared during the evaluation. Mapping : Ev Eval Y V → describes the process of evaluating physical quantities that are indirectly determined. In Theory , : Ev T T T Eval Y V → represents the theoretical evaluation scheme, while : Ev DT DT DT Eval Y V → in Digital Twin represents the specific computations. R DT Meas Meas  allows to track the measurement process in a reliable way, i.e., with the required precision. Mapping : Fin Assess MO Y → represents the assessing process. The methodological basis for assessment is designed within Theory ; this is expressed by the : T T Assess MO Y → mapping. The assessing methodology is Fin T implemented in Digital Twin by : DT DT Assess MO Y → . The Fin DT

3. Measurement and evaluation framework

The measurement and evaluation framework of tensile tests is based on the conceptual schema described in Figure 2. and is built up of the subsystems Theory , Digital Twin and Reality . The theoretical model used to describe the measurement process is presented in Fekete et al. (2022). The Digital Twin subsystem was constructed on a High Performance Computing server using FE software. The Reality subsystem is based on a conventionally instrumented universal testing machine, supplemented by an optics-based data acquisition system.

3.1. Preparation and execution of tensile tests

Fig. 3 Specimen used for the experiments