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Numerical, experimental, and analytical modelling of impact on multi-layer E-glass fibre composite

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

Energy-related models are among the most common and precise approaches to investigating collision and bullet penetration into composite specimens. By exploring various models, this study is an attempt to modify and complete the already existing models. This collision model investigates the energy absorption mechanisms and compares them with the total energy of the bullet upon collision to examine their ability or inability to pass the target. It also predicts the residual energy of the bullet upon its exit from the target. For experimental analysis, a glass/epoxy container was subjected to spherical bullets at different velocities to validate the proposed model. In this model, the contribution of each energy absorption mechanism was determined at various speed. Moreover, the ballistic velocity of the bullet upon its collision with the composite target was estimated with proper precision. In comparison with the previous models, the presented model included the highest number of energy absorption mechanisms and tried to add new ones (for instance, the energy absorbed due to displacement of the cone under bullet force, energy absorbed in the elastic-plastic deformation of the primary fibers and the energy absorbed due to the bullet-composite target friction) to offer the best energy absorption model with the highest accuracy. This model was finally compared with the finite element results obtained through the ANSYS Ls-Dyna module.

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Data availability

The data that support the finding of this study are available based on the request from the corresponding author.

Abbreviations

A ql :

Pseudo-ribbon area decrease coefficient

a p :

Deceleration of the bullet upon collision with the target

D :

Bullet diameter

E c :

Energy absorbed at the tensile failure of the composite per unit of volume

E Dl :

Energy absorbed due to the delamination

E Dis :

Energy absorbed due to displacement of the cone vertex as a result of bullet force

E EP :

Energy absorbed due to the elastic-plastic deformation of the primary fibers

E ED :

Energy absorbed due to the elastic deformation of the secondary fibers

E El :

Energy absorbed by the primary fibers due to elastic deformation

E Fr :

Bullet-target friction energy

E KE :

Kinetic energy formed at the back of the composite under ballistic collision

E l :

Energy dissipated during the collision

E mt :

Energy absorbed by the matrix per unit of volume

E Mc :

Energy absorbed due to matrix cracking

E Pl :

Energy absorbed by the secondary fibers due to plastic deformation

E Sp :

Energy absorbed due to shear-plug

E Tf :

Energy absorbed due to tensile failure of the primary fibers

E Total :

The sum of energy absorbed by the composite target

F pn :

Energy applied by the bullet to the composite at normal direction

G t :

Shear modulus of the thickness

G Пcd :

Rate of increase in the critical dynamic strain energy in mode II

l :

Equivalent length of the beam

M :

Composite tensile modulus

m c :

Mass of the moving cone

m p :

Bullet mass

N :

The number of shear-plug layers

P :

Load applied to the target by the bullet

P d :

Delamination percentage

P m :

Radius of the cone formed at the back of the composite plane (ellipse radius at each arbitrary angle of θ)

R c max :

Large ellipse-shaped radius

R c min :

Large ellipse-shaped radius

S sp :

Shear-plug strength

T l :

Layers thickness

T :

Composite target thickness

V :

Strain volume of the composite for tensile failure

v :

Bullet velocity at the time of colliding with the target

v c :

The velocity of the moving cone

v n :

The normal exit velocity of the bullet

v n0 :

Initial normal velocity of the bullet at the time of colliding with the target

v 0 :

Ballistic velocity limit

V tΔ:

Variation in the tangential velocity

v nΔ:

Variation in the normal velocity

tΔ:

Duration of the bullet passage through the target

t :

Time spent on passing the bullet through the composite target

w :

Maximum rise of the equivalent beam

δ :

Displacement of the cone vertex formed at the back of the target

ε :

Strain

θ :

Angle of collision

μ :

Bullet-target friction

ρ :

Density of the composite target

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Semnan University, Semnan, Iran

    Jaber Mirzaei & Meysam Nouri Niyaraki

  2. School of Engineering, Damghan University, P.O. Box: 3671641167, Damghan, Iran

    Alireza Albooyeh

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Correspondence to Jaber Mirzaei.

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Mirzaei, J., Albooyeh, A. & Niyaraki, M.N. Numerical, experimental, and analytical modelling of impact on multi-layer E-glass fibre composite. J Braz. Soc. Mech. Sci. Eng. 44, 603 (2022). https://doi.org/10.1007/s40430-022-03915-y

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