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The Mechanical Behaviour of Poly(Vinyl Butyral) at Different Strain Magnitudes and Strain Rates

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The Mechanical Behaviour of Poly(Vinyl Butyral) at Different Strain Magnitudes and Strain Rates *Manuscript Click here to download Manuscript: jmatsci_paper.tex Click here to view linked References 1 2 Journal of Materials Science manuscript No. 3 (will be inserted by the editor) 4 5 6 7 8 9 The mechanical behaviour of poly(vinyl butyral) at different 10 11 12 strain magnitudes and strain rates 13 14 15 P. A. Hooper · B. R. K. Blackman · J. P. Dear 16 17 18 19 20 Received: date / Accepted: date 21 22 23 24 Abstract The mechanical behaviour of poly(vinyl butyral) (PVB) at small (< 0.1%) and 25 26 large strains (> 200%) is investigated experimentally over a range of strain rates in order 27 28 to provide data for the development and validation of constitutive models. The small-strain 29 30 response is investigated using dynamic mechanical analysis at frequencies from 1Hz to 31 32 100Hz and temperatures from −80◦Cto70◦C. It is found that a generalized Maxwell model 33 34 adequately describes the material behaviour in the small-strain regime. The large-strain re- 35 36 sponse is investigated using a high-speed servo hydraulic test machine at strain-rates from 37 38 0.2s−1 to 400s−1. It is found that the PVB response is characterised by a time-dependent 39 40 steep initial rise in stress followed by a hyperelastic type response until failure. No current 41 42 material model completely captures this time-dependent behaviour at large-strains. 43 44 45 Keywords PVB · Poly(vinyl butyral) · Laminated glass · DMA · Large strain · High 46 47 strain-rate · Viscoelasticity 48 49 P. A. Hooper · B.R.K. Blackman · J. P. Dear 50 51 Department of Mechanical Engineering, Imperial College London, Exhibition Road, London, SW7 2AZ, UK 52 53 Tel.: +4420 7594 7128 54 E-mail: [email protected] 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 2 5 6 1 Introduction 7 8 9 Polyvinyl butyral (PVB) is primarily used as an interlayer material in the manufacture of 10 11 laminated glass. Its mechanical response is highly non-linear, time dependent and it is capa- 12 13 ble of undergoing extensions to several times its initial length and recovering without signif- 14 15 icant permanent deformation. The behaviour of PVB at two distinct strain magnitudes are of 16 17 practical interest. Firstly, the small-strain behaviour plays an important role in determining 18 19 the bending behaviour of uncracked laminated glass panes. Secondly, the large-strain be- 20 21 haviour is of interest in cracked laminated glass where the PVB acts as bridge between glass 22 23 fragments and can undergo large tensile extensions. The mechanical response at different 24 25 rates of strain is also of significant importance due to applications ranging from quasi-static 26 27 loading through to impact, ballistic and blast loading regimes. 28 29 30 Bennison et al. [1] and van Duser et al. [2] have investigated the small-strain behaviour 31 32 of a Dupont Butacite interlayer in the development of a finite element model to predict the 33 34 behaviour of laminated glass plates subject to wind pressure loading. They included vis- 35 36 coelastic effects by using a generalized Maxwell series to account for the time-dependent 37 38 shear modulus of the interlayer. Terms in the Maxwell model were determined experimen- 39 40 tally using dynamic mechanical analysis. Variation in shear modulus at different tempera- 41 42 tures was also taken into account by using the Williams-Landel-Ferry (WLF) equation [3] 43 44 to shift the time dependent shear modulus curve to a different temperature. The mechanical 45 46 behaviour of PVB at large-strains has not been widely reported in the literature. 47 48 In this paper the behaviour of a single grade of PVB is investigated experimentally over 49 50 a wide range of strain magnitudes and strain rates. The behaviour over these ranges needs 51 52 to be fully understood before physically based models of laminated glass (particularly after 53 54 the glass plies fracture) and other composites containing PVB can be developed. 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 3 5 6 2 Methods 7 8 9 The mechanical behaviour of PVB was investigated using two experimental methods. The 10 11 small-strain behaviour was investigated using dynamic mechanical analysis (DMA) at fre- 12 ◦ ◦ 13 quencies from 1Hz to 100Hz and temperatures from −80 Cto70C. The large-strain be- 14 15 haviour was investigated using a servo hydraulic tensile test machine at displacement rates 16 17 between 0.01 m/s and 15 m/s. The interlayer material tested was Saflex PVB produced by 18 19 Solutia Inc. with product number RB-41. 20 21 22 23 2.1 Small-strain behaviour 24 25 26 The small-strain viscoelastic behaviour of PVB is of interest when considering the response 27 28 of a laminated glass pane to loading before the glass plies fracture. Under these conditions 29 30 the strain in the PVB is limited by the failure strain of the glass plies (typically 0.1%). The 31 32 small-strain viscoelastic response has been investigated using DMA. The following sections 33 34 cover some background information on viscoelasticity, the DMA experimental technique 35 36 and analysis methods used. 37 38 39 Linear viscoelasticity 40 41 42 The viscoelastic properties of a material can be investigated by subjecting a sample to an 43 44 oscillatory load. When a viscoelastic material is subjected to an oscillating load the strain 45 46 ε lags behind the applied stress σ due to the viscous component of the material response. 47 48 Figure 1a shows an applied sinusoidal stress and the resulting out-of-phase strain response 49 50 with a phase angle δ.Itisusefultodefine two moduli which correspond to the elastic 51 52 and viscous components of stress. Figure 1b shows the stress signal decomposed into a 53 54 component in phase with the strain and a component out-of-phase with the strain. 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 4 5 6 Tδ/2π Strain 7 Stress 8 9 10 ε 11 , σ 12 13 14 15 T 16 17 Time 18 19 (a) Lag in stress. 20 21 22 Strain Stress in-phase 23 Stress out-of-phase 24 25 ε 26 , 27 σ 28 29 30 31 32 Time 33 34 (b) Stress components. 35 36 Fig. 1: Sinusoidal stress and strain for a linear viscoelastic material. 37 38 39 40 The amplitude of the stress in-phase with the strain divided by the strain amplitude 41 42 is referred to as the storage modulus and is denoted by E in tension and G in shear. The 43 44 amplitude of the stress out-of-phase with the strain divided by the strain amplitude is referred 45 46 to as the loss modulus and is denoted by E in tension and G in shear. The ratio of the 47 48 moduli is equal to the tangent of the phase angle 49 50 51 52 53 E G 54 = = tanδ (1) 55 E G 56 57 58 59 60 61 62 63 64 65 1 2 3 4 5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Fig. 2: DMA tensile fixture. 27 28 29 30 For tanδ = 0 the stress and strain are in-phase (the loss modulus is equal to zero) and the 31 32 material behaviour is purely elastic. For tanδ = 1 the viscous component of stress is as large 33 ◦ 34 as the elastic component and the stress and strain are 45 out-of-phase. At a phase angle of 35 36 90◦ the storage modulus is equal to zero and the material behaviour is purely viscous. 37 38 39 40 41 Dynamic mechanical analysis 42 43 44 In dynamic mechanical analysis (DMA) a sinusoidal strain is applied to a sample and the 45 46 resulting stress signal is measured in order to calculate storage modulus, loss modulus and 47 48 tanδ. This is usually performed over ranges of frequencies and temperatures to characterise 49 50 a material at different time scales. A TA Instruments Q800 DMA machine was used to 51 52 test the small-strain viscoelastic behaviour of PVB in extension. Figure 2 shows the tensile 53 54 fixture used to apply oscillatory strains to the sample. 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 6 5 6 In this fixture the top of the sample is held stationary between grips and the bottom of 7 8 the sample is connected to a drive shaft which oscillates up and down. The initial length of 9 . 10 the sample l0 was 16mm, the width w was 4 45mm and the thickness was 1 52mm. A small 11 12 preload was applied to the sample to ensure that it did not buckle when oscillated. The stress 13 14 in the sample was then calculated from the cross sectional area and the applied force. The 15 16 strain was found from the original length of the sample and the displacement of the drive 17 18 shaft. The PVB was tested with a strain amplitude of 0.1% at three frequencies; 1Hz, 10Hz 19 20 and 100Hz. 21 22 The test fixture shown in Fig. 2 was enclosed inside a chamber so that the temperature 23 24 could be controlled and varied.
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