Effects of Impactor Geometry on the Low-Velocity Impact Behaviour of Fibre-Reinforced Composites: An Experimental and Th
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Effects of Impactor Geometry on the Low-Velocity Impact Behaviour of Fibre-Reinforced Composites: An Experimental and Theoretical Investigation Haibao Liu 1 & Jun Liu 1 & Yuzhe Ding 1 & Jin Zhou 2 & Xiangshao Kong 3 & Bamber R.K. Blackman 1 & Anthony J. Kinloch 1 & Brian G. Falzon 4 & John P. Dear 1 Received: 3 April 2020 / Accepted: 11 May 2020/ # The Author(s) 2020
Abstract
Carbon-fibre/epoxy-matrix composites used in aerospace and vehicle applications are often susceptible to critical loading conditions and one example is impact loading. The present paper describes a detailed experimental and numerical investigation on the relatively lowvelocity (i.e. > > > > > > > 6 −ν 12 =E22 dε > > 22 > > = 6 < 6 −ν =E dε33 ¼ 6 13 33 0 > 6 > dε12 > > 6 > > > 4 > 0 > > > dε13 > ; : dε23 0
−ν 21 =E11 1=E22 −ν 23 =E33 0 0 0
−ν 31 =E11 −ν 32 =E22 1=E33 0 0 0
0 0 0 1=G12 0 0
0 0 0 0 1=G13 0
9 8 p 9 38 dσ11 > dε11 > 0 > > > > > > > > > > > > > 7 0 7> dσ dεp22 > > > > 22 > > > > = = < < p 0 7 dσ dε 33 33 7 þ ð1Þ p 7 0 7> dσ12 > dε12 > > > > > > > > > > p 0 5> dσ > > > > > > dε13 > > ; > ; : 13 > : p > dσ23 1=G23 dε23
where dεij (i, j = 1, 2, 3) are the incremental total strain tensors and dσij (i, j = 1, 2, 3) are the incremental stress tensors. The parameters νij (i, j = 1, 2, 3, i ≠ j) are the Poisson’s ratios, Eii (i, j = 1, 2, 3) are the Young’s moduli either for tension or compression loading, which are generally considered to be similar for composite laminates [29], and Gij (i, j = 1, 2, 3, i ≠ j) are the shear moduli. The parameters dεpij ði; j ¼ 1; 2; 3Þ represent the incremental plastic strain tensors, which are related to the effective stress, σeff, and effective plastic strain, εpeff . The effective stress, σeff, is given by [30, 31]: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 σ22 þ σ233 −3σ22 σ33 þ 3a66 τ 213 þ τ 212 þ τ 223 σeff ¼ ð2Þ 2 where the value of a66 can be readily determined from off-axis experiments conducted at different values of the off-axis angle using a unidirectional composite [27, 31–33]. The relationship between the effective stress, σeff, and the effective plastic strain, εpeff , can be expressed as a power-law function, given by [31–33]: εpeff ¼ Aσeff n
ð3Þ
where A and n are nonlinear coefficients, which are determined by fitting to the σeff versus εpeff data, again as obtained from the off-axis experiments when different off-axis angles are employed using a unidirectional composite [27, 31–33]. The determination of the parameter, a66, and the nonlinear coefficients, A and n, allow the calculation of the incremental plastic strain tensors, dεpij ði; j ¼ 1; 2; 3Þ, as given by: 9 8 p 9 8 0 dε11 > > > > > > > > > > p > > 3ðσ −σ Þ=2σ > > > > dε > > > > 22 33 eff > > > = = < 22 < p > An 3ðσ33 −σ22 Þ=2σeff dε33 ¼ dσeff ð4Þ p 3a66 τ 12 =2σeff > dε12 > > σeff n−1 > > > > > > > > > p > > > dε > > 3a66 τ 13 =2σeff > > > > > > > ; ; : 13 : 3a66 τ 23 =2σeff dεp23 The three-dimensional (3D) Northwestern University (NU) damage criteria were
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