PSI - Issue 18

Rainer Wagener et al. / Procedia Structural Integrity 18 (2019) 490–500 Rainer Wagener, Andreas Maciolek, Heinz Kaufmann/ Structural Integrity Procedia 00 (2019) 000–000

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increasing level of automation, a continuous method from the Low Cycle Fatigue up to the Very High Cycle Fatigue regime is required to consider the cyclic material behaviour in order to derive the maximal benefit out of a digital twin. Digital twins, as used in the context of Industry 4.0, refer to digital replicae of physical assets, process and system, which can be used for various purposes according to GE Digital (2017). Corresponding to Wikipedia (2018) and IBM Watson Internet of Things (2017), the digital representation provides both the elements and the dynamics of how a component or a system behaves throughout its life cycle. To develop a new product, a digital twin must contain a method to handle the effects of service loading conditions and their impact on the material behaviour. Therefore, many different methods have been proposed regarding the assessment of fatigue strength. Together, they pursue the goal of evaluating the component behaviour under service loading, which means randomised variable amplitudes, using the cyclic material behaviour under constant amplitude loading. Most commonly, the linear damage accumulation rule according to Palmgren-Miner and its modifications by Palmgren (1924), Langer (1937), Miner (1945) and Haibach (1970) are used to accumulate the damage for different service load sequences, although non-linear damage accumulation rules have also been developed. Regardless of whether a linear or non-linear damage accumulation is applied, a Wöhler-curve, representing the fatigue strength, is required. In terms of fatigue and in addition to the geometry of the component, a digital twin must represent the main influences on the cyclic material behaviour as well as the loading conditions, including the load time history. Consequently, the quality of these digital twins is directly linked to the material model and properties used. Due to the inhomogeneous microstructure, Hell et al. suggest the usage of a local fatigue concept such as the local strain concept or the material based fatigue approach. One of these should be the first choice for the fatigue design. Hence, the foundation of a digital twin should be a local strain-based fatigue approach concept, which enables the description of the cyclic material behaviour using stress-strain and strain-life curves. In order to qualify a digital twin for a fatigue assessment, a method including a continuous Wöhler-curve from the Low Cycle Fatigue up to the Very High Cycle Fatigue is required, because a prediction, as to whether the next cycle will be a part of the standard service load, an overload or a misuse, is not possible. The digital twin must handle this. To manage the different types of loads means to handle different amounts of plasticity. The amplitudes of standard service loads are related to the High Cycle Fatigue (HCF) regime and, in parts, to the Very High Cycle Fatigue (VHCF) regime. Especially, if extended service life is in the focus of interest. From the macroscopical point of view, the local stress-strain state is linear elastic. On the other hand, the amplitudes of overloads and of misuse will lead to elastic plastic material behaviour, at least at the root of a notch. Therefore, these amplitudes are related to the LCF regime. Depending on the component, its usage and service loading conditions, the different regimes of the Wöhler-curve become the focus of interest. For components such as crankshafts, the damage mechanism of the VHCF regime is important. On the other hand, for consideration of the service loading of the chassis and its components, such as steering knuckles, knowledge of the damage mechanisms in all three regimes is necessary. Beside the technical aspects, economic issues, such as the effort required to determine the Wöhler-curve, should be economically justifiable. Furthermore, and with reference to advancing digitisation, methods are required to validate the test results and derive material properties, before they are stored in databases. 2. Stress-strain behaviour Usually, the formula developed by Ramberg and Osgood (1943) is used to describe the cyclic stress-strain behaviour, eq 1. This equation contains the sum of the elastic and plastic strain proportions. Therefore, the elastic strain amplitude  a,e is equal to the quotient of the stress amplitude  a and the Young’s modulus E. The plastic strain amplitude  a,p is calculated by a power function with quotient of stress amplitude divided by the cyclic strengthening coefficient K’ as the basis of the power of the reciprocal cyclic strengthening exponent n’ as the exponent. ��� � ��� � ��� � � � � � � � � � � � � � � � (1)