PSI - Issue 47

G. Morettini et al. / Procedia Structural Integrity 47 (2023) 296–309 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Regardless of the simplification of stress, due to the specific condition under examination, defining the value of the stress state around the notch remains a very complex operation. Various authors have proposed, with different approaches, such definition (Berto at al. (2014)). These solutions are condensed in a more general expression proposed by Lazzarin Filippi (Filippi at al. (2002)) in which a series of parameters dependent on the geometry of the notch and fracture toughness � describe the stress state of the notch under examination. Therefore, we can evaluate the total deformation energy associated with a generic volume of radius � thanks to the assumptions made: � ����� � � � ������ � �� � (7) The strain energy density is obtained by dividing by the considered volume. Under the above assumptions, the value of � can be calculated from an expression that is a function only of material parameters, through the following equation, whose derivation is discussed in (Yosibash at al. (2004)): � � ���� � � � ����� � � �� � ��� � � (8) It should be noted that, for the considered notch geometry, to obtain the geometric radius of the control volume, visible in Fig.1, the value of � must be added to a purely geometric length function � , which depends only on the notch geometry and is equal to: � � � � � � � � � � � (9) 2.2. The Equivalent Material Concept (EMC) To apply the ASED criterion, a stringent assumption must be verified: linear behavior of the material. This assumption mainly affects the evaluation of the Critical Strain Energy and consequently the definition of the material's mechanical properties ( , ��� , �� … ). From the graph in Fig.2 (a), it can be seen that the lost energy contribution (red Area) is not balanced by the energy considered with the standard ASED approach (green Area). The approximation of the material's behavior as linear elastic leads to an underestimation of the energy required to cause PLA failure. Furthermore, a second consideration must be made: the engineering stress-strain curve derived from the real tensile test, as can be seen from Fig.2 (b), underestimates the energy that can be stored in the material. This occurs for both ductile and brittle materials, although in the latter case, it is less compromising on the final prediction.

Fig. 2. Considerations on the Energy contribution due to the scenario considered.