PSI - Issue 54

Johannes Kaiser et al. / Procedia Structural Integrity 54 (2024) 26–33 Johannes Kaiser et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Many factors must be taken into account in the design process for a new component. In many applications, plastics are capable of replacing classic construction materials, such as metals or ceramics, because their specific properties often contribute to significant resource efficiency [1]. In order to be able to exploit the full potential of the material, special attention must be paid to a design that is suitable for the plastic. In finite element simulations, usually only material properties obtained from standard test procedures and determined under ideal conditions are used. Although fracture mechanics methods do not provide any direct input parameters for the design process, they can desribe the crack behavior locally very precisely and thus offer the possibility of mapping the failure behavior and internal and external influencing factors. 2. State of the art 2.1. Fracture mechanical failure evaluation In fracture mechanics, the damage behavior and damage mechanisms of cracked components are considered, which have their origin in the fracture of molecular chains, in the pulling out of molecular chains or in the rupture of phase interfaces. Depending on the type of stress, crazes and shear bands, for example, can develop locally in the so-called fracture process zone. In fracture mechanics, a distinction is made between three modes of crack stress [2]. The most relevant is mode I, in which the crack flanks open perpendicular to the direction of loading. Crack opening modes II and III, which are not considered in detail here, describe longitudinal and transverse shear opening modes, respectively. Depending on the categorization of the crack or fracture that occurs, different approaches are available. In the case of a ductile fracture, a lot of energy is expended for the deformation of the material, whereas in the case of a low-deformation or deformationless brittle fracture, the energy is released abruptly. Depending on the type of fracture, a distinction is made between linear-elastic, elastic-plastic and post-yield fracture mechanics. Originally, fracture mechanics tests were developed and validated on metallic materials. In order to be able to characterize plastics with these methods as well, they needed to be adapted. One of these methods is the J-integral, which was independently developed by Rice and Cherepanov [3, 4]. The energy release rate is calculated using a path independent line integral around the plastically deformed crack tip region. For the calculation of the J-integral, this results in the following equation (1) [3]: = 1 (1) U corresponds to the deformation work per unit area, B to the specimen thickness and a to the crack length. However, the evaluation according to this procedure is very time-consuming, since several test specimens with different crack lengths are necessary. For this reason, approximation methods were developed that allow the deformation of the test specimen to be taken into account via a geometry function depending on the type of loading (static or dynamic) and enable characteristic values to be developed with a reduced number of test specimens. Equation (2) according to Bagley and Landes [5] represents a corresponding evaluation method: = ( )∫ ( ) ( − ) (1) F is the force applied to the specimen and s the deformation. The geometry function f (a/b) corresponding to the specimen depends on the quotient of the acting crack length a (force application point to crack tip) and the acting specimen width b (force application point to end of specimen).