PSI - Issue 17

C P Okeke et al. / Procedia Structural Integrity 17 (2019) 589–595

590

C P Okeke et al / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction

The fatigue failure of Polymethyl Methacrylate (PMMA) polymer material components of an automotive lamp is a common occurrence. Lamp assemblies are subjected to accelerated random vibration tests during design to assess their integrity over a life time exposure to random vibration loading. It is a requirement that the lamps must withstand this accelerated random vibration which is normally carried out as specified in the international standard ISO 16750-3 (2012). However, often, the optical components made of PMMA fail by fracturing during accelerated random vibration test. This results in a costly and time-consuming design cycle as design changes and modification of the injection moulding tool are needed. Numerically predicting the fatigue life of this optical component prior to producing an assembly prototype can help to reduce the design cycle. However, there are challenges in numerically predicting the fatigue of polymers. Polymers exhibit complex behavior during deformation - the stress-strain relationship of polymers is notably non-linear within the elastic limit and they also exhibit inter-sample variation due to manufacturing processes. The non-proportionality between the stress-strain leads to variation in the elastic modulus across the strain; this is shown by Okeke et al (2017). Hence, using the initial tensile modulus in the response analysis of a structure with non-linear materials may introduce errors as the stiffness is assumed constant across the strain. This problem has been noted by Bernal (1994) and Zareian et al. (2010). Charney (2008) and Jehel et al. (2014) also presented the same view and suggest using tangent modulus based stiffness instead of initial tensile modulus. The American Society for Testing and Materials (ASTM) International, ASTM D638-02a (2003) suggests using the secant modulus in the event of non-proportionality between material stress-strain. The secant modulus is defined as the ratio of stress (nominal) to corresponding strain at a point of interest on the stress-strain curve. Okeke et al (2018), studied the random vibration response of Polycarbonate/Acrylonitrile Butadiene Styrene (PC-ABS), Polymethyl methacrylate (PMMA) and Polypropylene 40% Talc filled (PPT40) polymer materials using non-linear model and linear model of initial tensile modulus and secant modulus. The result showed that for linear model, secant modulus gives a better representation in material behavior than initial tensile modulus. However, it is worth noting that the results of both moduli will ultimately depend on the extent the material strained under the applied loading. The nonlinear hyperelastic model provided a more accurate representation of the material behavior than both linear models. However, the nonlinear analysis can only be done in transient mode, a time domain analysis and even with a simple beam can take up to 100 times longer to run than the frequency domain analysis of linear model. This is a significant disadvantage of nonlinear analysis – the limited time in product design and development, makes nonlinear analysis undesirable. The objective of this paper is to develop a robust numerical fatigue life prediction model for PMMA polymer material of automotive lamp components subjected to random vibration loading, with consideration for material non linearity. The fatigue life based on initial elastic modulus and secant modulus is predicted using ANSYS software and compared to the experimentally obtained fatigue life. Three fatigue life prediction models, Steinberg, Narrow Band and Wirsching were used. Twelve specimens cut-out from injection moulded optical blades of PMMA were tested to obtain the fatigue life. All the specimens have a double sided u-notch positioned 10mm from the clamp and block steel was bonded to the tip to generate weight. The specimen connected to the test fixture was driven by electrodynamic shaker using standard automotive random vibration loading. The average experimental fatigue life was obtained from the twelve specimens tested and compared to the initial modulus and secant modulus based simulation results. (1) where { } , { ̇} and { ̈} are nodal displacement, nodal velocity and nodal acceleration vectors respectively. [ ] , [ ] and [ ] are mass, damping and stiffness matrices and m, ̈ and are mass of the base, random acceleration input and the applied force. As stress-strain response of polymers is known to exhibit non-proportionality within the elastic limit, it is expected that the elastic modulus which is a measure of stiffness will vary across the stress or strain. The focus of this study is therefore to understand the effect of this stiffness variation in the numerical prediction of fatigue life. 2. Random vibration response analysis The base excited randomly vibrating structure’s response can be written as: [ ]{ ̈} + [ ]{ ̇} + [ ]{ } = − { ̈}