Elsevier

Composites Part B: Engineering

Volume 143, 15 June 2018, Pages 292-300
Composites Part B: Engineering

Analytical models for the perforation of thick and thin thickness woven-laminates subjected to high-velocity impact

https://doi.org/10.1016/j.compositesb.2018.01.030Get rights and content

Abstract

This paper deals with the problem of high-velocity impact of a low-mass projectile on woven composite plates. A nondimensional formulation of two analytical models has been developed (one for thin laminates and the other for thick ones). Both analytical models are based on energy conservation and have been applied for the ballistic impact on E-glass woven fibres/polyester composite plates. The results of the models (mainly the ballistic limits) have been compared with experimental results. The value of the ratio target thickness/projectile diameter determining whether the laminate behaves as thick or thin has been established.

Introduction

For their stiffness, strength, and light weight, woven laminates are commonly used in the aeronautic, maritime, and ground-transport industries as well as in civil infrastructures. These laminate structures are usually designed to withstand common loads although in some cases, they may be subjected accidentally to impact loads caused by foreign bodies. Such problems may lead to structural failure due to the low transverse stiffness that composite structures show under impact loads [1,2]. The impact velocity may vary from a few meters per second up to several hundred meters per second [3]. For instance, in the case of low-mass high-velocity projectiles striking a structure, the damage varies from indentation to perforation [4,5]. These impacts may compromise the mechanical properties of a structural element [6,7]. Therefore, engineers need predictive tools to check the structural behaviour under impact conditions. Thus, the development of analytical models, which provide sufficient accuracy for predicting the response of a composite panel under impact loads, is a hot topic.

Many previous works have examined the impact behaviour of composite laminates by means of experimental tests [4,[8], [9], [10], [11], [12], [13]]. Although such tests are costly and time consuming, they are valid only for the configuration (plate and projectile) tested [15]. Numerical simulations have been applied successfully for modelling the perforation process of composite structures subjected to ballistic impacts [[13], [14], [15], [16], [17], [18]]. Such approaches require considerable computing time. However, analytical models can be useful to provide a sufficiently accurate solution with a lower computational cost than with numerical methods [9,[17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27]].

As a consequence of the above, there is continual interest in developing analytical models to predict the ballistic limit of laminate plates. This parameter is useful to define the condition of the perforation of a structure. The ballistic limit can be defined as the minimum velocity that a particular projectile needs to consistently penetrate the component [28].

From experimental, analytical and numerical studies, many authors have demonstrated that a fundamental parameter in the performance of a laminate plate is its thickness [4,[24], [25], [26], [29], [30], [31], [32], [33], [34], [35], [36],[29], [30], [31], [32], [33], [34], [35], [36]]. Some authors show a non-linear relationship between the ballistic limit and the plate thickness for E-glass plates [24,31,32]. By contrast, Zhu et al. [29] contended that there is a linear relationship between the ballistic limit and the thickness for Kevlar/polyester laminates under impact by flat-faced projectiles. Buitrago et al. [4] and Naik et al. [33] found the same behaviour for E-Glass woven laminates subjected to high-velocity impact with spherical and flat-faced projectiles, respectively. Additionally, these studies show that there is a certain controversy regarding how to consider a laminate as being thick or as thin. For example, the work by Caprino et al. [34] shows that laminates of less than 6 mm may be considered as thin for graphite/epoxy laminates, in agreement with García-Castillo et al. [17,36] but for E-Glass laminates. On the other hand, there are works where laminates are considered thick when exceeding 2 mm [32] for E-Glass/polyester or 4 mm [30] for graphite/epoxy laminates. The works by Naik et al. [33,35] have demonstrated that the thickness of a laminate determines the energy-absorption mechanisms to consider for the analytical models. Therefore, definition of laminates as thin or thick is a key issue in high-velocity impacts.

In the present study, the objective is to estimate the threshold thickness that determines the behaviour of a laminate plate as thin or thick. This threshold is important because it establishes the energy-absorption mechanisms to consider. To reach this goal, a nondimensional formulation of the two models was developed.

Section snippets

Model description

Two analytical models for woven laminates (thin and thick) of glass fibres in polymer resin used in previous works [17,35] were modified in this study. Both models considered that the kinetic energy of the projectile impact is consumed during the perforation process by several energy-absorption mechanisms. In the case of thin laminates, the energy-absorption mechanisms are: tensile failure of fibres, elastic deformation of fibres, acceleration of the laminate in the back-side of the plate,

Materials and experimental procedures

In this study, E-glass/polyester woven laminates were considered. These laminates are widely used in naval and ground-transport industries because of their good mechanical properties, low manufacturing costs and permeability to electromagnetic waves. Although these kinds of structures are not designed as armour, they could be subjected to high-velocity impacts of low-mass fragments, and this requires fuller knowledge of their response to impacts of this type. In this work, impact tests were

Model verification

For the validation of the analytical models, the ballistics of the laminates made of E-glass/polyester woven plies of various thicknesses (3 mm, 6 mm, 9 mm, and 12 mm) were analytically determined and then compared with those experimentally measured. For the case of the impact on the laminate plate 9 mm thick, experiments were carried out in this work and, for the cases of 3 mm, 6 mm, and 12 mm the results were taken from previous experiments for the same projectile and conditions as found in

Results

The ratio of laminate thickness/projectile diameter (herein called the geometry ratio) is a parameter to consider in the high-velocity-impact studies, as demonstrated by other studies [39]. Therefore, in this work the results of this ratio are discussed.

Fig. 4 shows the variation of the ballistic limit regarding the geometry ratio from both analytical models mentioned above. As reflected in this figure the intersection between the two curves occurs for a geometry ratio equal to 0.94. Therefore,

Conclusions

In this paper a nondimensional formulation of two different analytical models has been developed, one for thin and another for thick woven E-Glass/polyester laminates, both impacted by a foreign object. The application of the two models enabled the establishment of the threshold from which a laminate behaving as a thin one begins to perform as a thick composite. As in problems of impact on metal targets, when the geometry ratio (laminate thickness/projectile diameter) reaches a value near one,

Acknowledgements

The authors are indebted to the project “Acción Estratégica en Materiales Compuestos y Análisis Numérico simplificado de Estructuras y protecciones ligeras sometidas a impacto balístico” (2010/00309/002) of the University Carlos III of Madrid for the financial support of this work.

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