PSI - Issue 33

Riccardo Caivano et al. / Procedia Structural Integrity 33 (2021) 1095–1102 Riccardo Caivano et al./ Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction In recent years, the development of additive manufacturing (AM) technologies for metal alloys has seen a significant growth [1–4]. The main reason lays in the fact that AM allows the creation of extremely complex geometries and features with fewer manufacturing constraints compared to traditional processes as reported by [5]. Indeed, thanks to AM, it is possible to manufacture the complex optimised geometries provided by the topology optimisation (TO) algorithms [6–8], and even more complex features such as lattice structures and metamaterial cells [9,10]. In particular, TO permits to find the most performant material distribution in terms of maximised stiffness or minimised mass employment under different constraints [11–13]. Recently, the research community developing TO algorithms has focused on imposing fatigue-driven constraints in the optimisation formulation [13-24]. Most of them are based on the classical fatigue theory of cumulative damage evaluation which is effective for a wide number of industrial applications. However, it is well known that the fatigue response of AM components is controlled by the manufacturing defects that form during local process instabilities [26–29]. For this reason, the analysis of the fatigue response of AM parts must be conducted employing different and more appropriate theories, such as that by Murakami [30]. With the aim of reliably design AM parts, Gao et al. [31] developed an algorithm, named TopFat, that permits to include the influence of defects on the fatigue response as a constraint in the TO. Nevertheless, the use of this defect-driven TO algorithm may be crucial for many industrial applications. Indeed, the diffusion of AM parts in primary structural applications, such as components in engines, turbines, spacecraft, or aeroplanes, relies on the possibility to safely design them against fatigue failures. In this sense, a single proprietary code is not enough for the wide number of possible industrial applications. The present paper shows how to apply the TopFat algorithm to a commercial Finite Element Analysis (FEA) software for the design against fatigue failures of components under different loading conditions and stress ratios. 2. Method According to [31] and to Murakami formulation [30], it is possible to express the fatigue limit in presence of defects as a limit on the first principal alternate stress. Indeed, the first principal stress is related to the critical tensile load that allows a single critical defect to propagate. In Eq.(1) the relationship between fatigue limit ̄ � and the material and load properties are reported [31]. ̄ � � � ∙ � � �2�� �√ � � � ∙ � � � 2 � ��������∙�� �� (1) being � a constant parameter depending on the defect location, the Vickers hardness of the material, the stress ratio, i.e., the ratio between the minimum and the maximum stress during the cyclic load history and √ the square root of the area of the defect measured in a plane perpendicular to the maximum applied stress. For its application, Eq.(1) requires the information about the defect population, namely √ , within the material to properly evaluate the first principal alternate stress limit. This information is available only after the component realization for example thanks to non-destructive inspection techniques. Therefore, the limit would be evaluable only after the component realization when no further modifications are practicable. To overcome this issue, the defect population can be estimated a-priori. It has been demonstrated in [30] that the defect size is a random variable that follows the Largest Extreme Value Distribution (LEVD). Therefore, the probability √� to find a defect with size below √ can be expressed as in Eq.(2): √� �√ � � � �� �� √� � � √ � � √� � (2) where √� and √� are the location and the scale parameters of the defect size distribution which can be estimated experimentally within a defined test value, named reference volume � . Reversely, it is possible to employ Eq.(2) to calculate the expected defect size √ given a certain probability. Therefore, it is possible to combine Eq.(1) and Eq.(2) to estimate the fatigue limit in presence of defect before the component realization, as expressed in Eq.(3).