PSI - Issue 28

Thomas Bergmayr et al. / Procedia Structural Integrity 28 (2020) 1473–1480 C.V. Thomas Bergmayr et al. / Structural Integrity Procedia 00 (2020) 000–000

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2

1. Introduction

In the last decade, the e ff orts of the aircraft industry to develop lighter structures have increased rapidly, leading to the increased use of fiber reinforced polymers (FRP), due to the great advantages of FRP in strength- and sti ff ness-to weight ratio. However, a major disadvantage of composite materials is the particularly challenging structural inspec tion, caused by its numerous and very complex failure mechanisms that are often not recognizable by sole visual inspection. In aircraft structures, not only impacts like bird strike or tool drop, but also manufacturing defects that propagate during operation can lead to a critical damage. In order to avoid down time and cost expensive inspections with non-destructive testing (NDT) methods to detect damages like delaminations or face layer debondings results into the development of structural health monitoring (SHM) methods. Compared to NDT methods SHM methods have the aim to continuously monitor the integrity of structures during operation by systems of sensors in order to detect dam ages in an early stage. SHM methods can be classified into static and dynamic methods (Giurgiutiu (2014), Kralovec (2020)). Typical dynamic methods are e.g., the electro-mechanical impedance (Rytter (1993), Kralovec (2017)) or the guided waves method (Yeasin Bhuiyan (2017), Gschossmann (2016)). Typical static methods are the electrical impedance tomography (Nonn (2018)) or the strain-based methods (Grassia (2019)). The method presented in this paper counts to the strain-based approaches. Well known strain-based SHM methods are, e.g. rain-flow counting algo rithms for fatigue monitoring. More recent studies evaluate the structural integrity via artificial neuronal network and machine learning algorithms as stated in Farreras-Alcover (2017) and Grassia (2019). Nevertheless, the present paper deals with global strain measurements along zero-strain directions for damage evaluation, which could be realized by distributed fiber optical sensors (FOS) or fiber Bragg grating sensors (FGB). The idea of using strain measurements along zero-strain trajectories as possible SHM-method was first presented in Schagerl (2015). Considering a plain strain state with the components ε xx , ε yy and ε xy the direction α 1 and α 2 of the principal strain components ε 1 and ε 2 , where the shear component vanishes are calculated according to Eq. 1 and illustrated by Mohr’s circle, depicted in Fig.1. ε nm = − ε xx − ε yy 2 sin(2 α ) + ε xy cos(2 α ) ! = 0 (1) However, considering the same plane strain state two directions exist where there is zero-strain if the principal strain directions are tensile and compression (have opposite signs), respectively. This can be shown by solving the Eq. 2 in order to get the angels of the zero-strain directions β 1 and β 2 . Compared to the principal directions not the shear component is set to zero, but therefore the normal component, yielding the following equation to solve for β 1 and β 2 2. Zero-strain trajectories 2.1. Fundamentals

ε xx − ε yy 2

ε xx + ε yy 2

cos(2 β ) + ε xy sin(2 β ) !

= 0

(2)

ε nn =

+

Nevertheless, connecting the zero-strain directions at various points of a structure yields to a zero-strain trajectory (ZST). This task is realized with the same procedure which is used to calculate streamlines of a 2D flow field, because they are defined in the same way. The ZST-lines have to be instantaneously tangent to the direction vectors of a vector field.

2.2. SHM by zero-strain trajectories

The basic idea of the ZST method is to optimially orient a strain-sensor such that it is most sensitive to a change in a known plane strain state, i.e, for the application of the ZST method, structure and loading condition need to be known (Schagerl (2015), Schro¨der (2014), Schaberger (2020)). However, the ZST method can be perfectly combined with the application of fiber-optical sensors (FOS) for the monitoring of large planar structures as they are typical in lightweight design. A major advantage of the ZST method is that for the considered loading of the structure the sensor