Ballistic resistance and energy dissipation of woven-fabric composite targets: Insights on the effects of projectile shape and obliquity angle

Ibrahim Goda

Universit′e Bourgogne Franche-Comt′e, FEMTO-ST Institute, D′epartement M′ecanique Appliqu′ee, 24 Rue de L’E′pitaphe, 25000, Besan?on, France

Keywords:Ballistic resistance Numerical modeling Fiber reinforced composite Energy dissipation Oblique impact Angle of incidence Failure mechanisms

ABSTRACT This study aims at investigating the ballistic resistance and energy absorption in woven E-glass composite panels, considering different projectile nose shapes and oblique incidence angles. To that scope,three-dimensional finite element(FE)models of both projectiles and the laminated target are developed and numerical investigations are carried out using Abaqus Explicit solver.The composite damage model's constitutive law encompasses nonlinear material response, material properties degradation,progressive failure, and an element deletion strategy. The cohesive surface technique is used to represent the interface between two adjacent plies in the laminate, and the traction-separation law is used to characterize the behaviors of interlaminar degradation and failure. Material responses attributable to fiber rupture, matrix cracking, and plasticity caused by micro-matrix cracking due to shear loading are taken into account with suitable damage evolution laws. The computational framework is first validated against the experimental results reported in the literature by performing ballistic impact tests on the target laminate with conical, hemispherical and blunt-ended projectile, and the numerical results showed a good comparison in terms of residual velocity. Subsequently the framework is explored in simulating more complex failure mechanisms, with particular emphasis on the influence of the impact angle of obliquity,a parameter that is not usually analyzed in the literature.In that regard,the effects of normal and oblique impact on the damage morphologies and ballistic behavior of the fabric composite target in terms of energy absorption,impact contact force,and projectile residual velocity are conducted and analyzed,comparatively.The findings showed that the ballistic impact behavior of target composite is substantially influenced by projectile nose shape and incidence angle obliquity.

1. Introduction

Under some circumstances,the polymeric composite structures are bound to experience impact by foreign object projectiles [1].Understanding how these structures respond to localized impact is a significant and extremely complicated issue, with the degree of complexity increasing as the impact velocity increases. In some cases, structural materials must demonstrate substantial impact resistance to high velocity impact, since this is a key need during ballistic impact[2].The ballistic impact is a low-mass,high velocity impact caused by a projectile onto a target. The mechanism of ballistic impact is much more complex than that of impact mechanism. The ballistic impact load that involves penetration and perforation of targets by projectiles is one of the crucial situations that the composite structure may experience.Thus,the penetration and perforation resistance of laminated component is one of the most important criteria to ensure,particularly when used in area of defense, military, aerospace and marine applications. With regard to the safety of aircrafts during flight, take-off or landing, damage from impact has become an extremely severe and devastating problem.Runway debris,hailstones and bird strikes are the types of impacts that are most likely to occur, and they can cause serious damage to the aircraft structure, occasionally resulting in perforations [3].

The projectile nose shape and the angle of obliquity are significant considerations that could affect the ballistic resistance of composite laminates. In the literature, there is a large amount of work related to the investigation of the ballistic impacts of composite materials [3-17]. However, ballistic impact research detailing the influence of projectile nose geometry and incidence angles on fabric-laminated composites is still in its infancy stage. It is noteworthy that numerous contact forms from foreign objects could lead to different impact responses and failure mechanisms within the composite structure.Therefore,it is particularly imperative to investigate the influence of projectile nose shape on the ballistic performance of the composite panels and the failure mechanisms associated with the impact.

To the best of knowledge, the studies in the literature have shown that the contact shape between the projectile and structure has a discernible effect on the impact response of general structures, including composite laminates [18-26]. Mitrevski et al. [18]investigated experimentally the influence of impactor shape on the damage resistance and tolerance of woven carbon/epoxy laminates.It is found that the conical impactor causes the highest energy absorption and produces the largest indentation/penetration depth. Sevkat et al. [19] investigated the drop-weight impact response of two hybrid composites struck by impactor of different geometries.The contact area between impactor and composite has been reported to be critical for the response of composites.Kursun et al. [20] studied by experimental and numerical techniques the effect of impactor shape on the low-velocity impact performance of aluminum sandwich composite plates. Their results revealed that for the same impact energies, the maximum deflection in composite laminate is greater when the impactor and plate make less contact. Icten et al. [21] examined the effect of impactor diameter on the impact response of woven glass-epoxy composite plates.The results indicated that the projectile diameter highly affects the impact response of composite materials. De Cicco et al. [22] performed low-velocity impact tests on fiberglass/AZ31B-H24 magnesium fiber-metal laminates (FMLs) with different configurations in order to investigate the effect of impactor size and shape on the response of this type of FML.It is found that the larger is the size of the impactor,the lower is the impact energy absorbed by the FML.Mitrevski et al.[23]investigated the low-velocity impact tolerance of carbon/epoxy laminates to various impactor shapes. It is found that the hemispherical impactor produced the largest damage area in all instances. Ben-Dor et al. [24] presented a model for the description of fiber reinforced plastic (FRP) laminate penetration and perforation by a non-deformed projectile with an arbitrary shape. It has been shown that the projectile with the maximum ballistic limit velocity is a flat-nosed cylinder. Ulven et al. [25]investigated the perforation and damage development in carbon/epoxy laminates induced by different impactor shapes. They reported that the conical shaped projectile resulted in the greatest amount of energy absorbed at ballistic limit followed by the flat,hemispherical, and fragment simulating. Kumar et al. [26] used a cylindrical-shaped flat-ended projectile to model the ballistic impact behavior of a Kevlar/epoxy plate in order to investigate the effect of projectile diameter on ballistic limit velocity. When the mass is constant, the ballistic limit velocity of the laminate increases with increasing diameter. From the above researches, it becomes evident that the projectile shape is directly connected to the impact responses and damage patterns of components. It can also be noted that most existing studies are restricted to the effect of projectile shape on the low-velocity impact.Presently,there is a lack of evidence on the effect of projectile shape on the ballisticvelocity impact behavior of laminated composites. Consequently,it is essential to examine the ballistic-velocity impact response of laminates under various projectile shapes in order to improve the design and optimize of laminated composite structures.

A major concern with ballistic impact is the alteration in obliquity angle of the projectile during impact.Because the target is struck at some obliquity in most practical instances,oblique impact is an essential feature of ballistic contact events.The obliquity angle can be defined as the angle formed between the projectile's initial velocity vector and the normal to the target's surface.Based on this angle, ballistic impacts can be classified into normal impact when the target is struck at 0°obliquity and oblique impact otherwise.A substantial amount of scientific effort has been done in the past to describe the ballistic impact behavior of composite targets. However, the majority of these research deal with normal impact and how the projectile's kinetic energy is dissipated during the collision with the target. In practical situations, normal impacts are infrequent since targets are more commonly struck at some incidence angle. In this study, the effect of the obliquity of ballistic velocity impacts on the behavior of composite plates is focused with considerable concern on their energy dissipation characteristics and damage mechanisms under oblique impact.

The works available in the literature reveal that there are few researches in which oblique impact and penetration of composite laminates have been explored. One of the earliest attempts to investigate the oblique ballistic impact of composites is conducted by Kumar and Bhat [27]. They experimentally investigated the influence of angle of impact on energy dissipation and damage area of glass fiber-reinforced composite laminates. In 2007, Chu et al. [28]investigated the ballistic resistance behavior of basket fabric aramid laminate composite materials subjected to oblique impact test. The results indicated that aramid laminates have a higher degree of ricochet than metal.Pernas-Sanchez et al.[29]conducted experimental tests to investigate the high velocity impact phenomena on carbon/epoxy composites, as well as how obliquity influences laminate response. Recently, Xie et al. [30] investigated experimentally the impact perforation behavior of carbon fiber reinforced laminates impacted at different angles. Interestingly,Meyer et al.[31]used numerical simulations to investigate the high and hypervelocity normal and oblique impacts on unidirectional S2 glass fiber reinforced SC15https://www.sciencedirect.com/topics/engineering/epoxy-composite laminates. Key and Alexander [32],on the other hand, studied the oblique impact experimentally and numerically to evaluate the response and damage evolution of an S2 glass/SC15 epoxy woven fabric composite panel. Compared to the researches on oblique ballistic impacts of composite materials,there has been significant progress in studying the ballistic resistance of metallic materials at oblique impact. Goldsmith and Finnegan [33] experimentally investigated the effect of the angle of incidence on the responses of metallic targets. Gupta and Madhu[34,35] investigated the normal and oblique impact of armorpiercing projectiles on single and layered plates of mild steel,RHA steel and aluminum. Roisman et al. [36,37] proposed a theoretical model for the oblique impact of a rigid projectile on an elastic-plastic target. Chen et al. [38,39] examined the oblique penetration of thick metallic plates by rigid projectiles. To predict the ballistic limit and change in projectile obliquity, an analytical model is developed.Zhou and Stronge[40]investigated the ballistic perforations of monolithic, two-layered and sandwiched steel plates struck by flat and hemispherical nosed projectiles at angles of obliquity 0-45°. Khan et al. [41] developed an analytical model to predict the residual velocity of the projectile and ballistic limit of thin aluminum plates in oblique impact. In addition, experiments are carried out to validate the analytical model by impacting aluminum plates of varying thicknesses with hardened cylindrical steel projectiles at different angles.

For a comprehensive thoughtful of damage mechanism and energy distribution characteristics, which are the main governing parameters considered while designing a laminated composite structure, experimental and analytical approaches inevitably need to be supplemented with appropriate numerical simulations. In spite of years of intensive research efforts on impact, a thorough and trustworthy approach for assessing the damage behavior of laminated composites has not so far been fully realized.This is due chiefly to the complexities of the physical phenomena implicated in impact events, such as laminate-projectile contact, failure modes,projectile geometry,lamination sequence and interactions between plies within the laminate. Additionally, several complex damage mechanisms, such as fiber rupture, matrix cracking, inelastic deformation, interfacial delamination between different oriented fabric reinforced plies, can be presented in composite laminates during impact events. Because of these complicated damage patterns,characterizing the ballistic-velocity impact behavior of fabric composite plates becomes increasingly challenging.In this context,considerable focus has turned from laboratory experiments to numerical schemes due to the high expenses of physical testing and the difficulties to accurately observe the damage degree,especially for ballistic velocity impacts that can cause damage that is virtually imperceptible.

Among the relevant numerical methods, the progressive damage model has emerged as the most prominent modeling strategy for accounting for damage initiation and subsequent damage progression. Nonetheless, the implications of different failure criteria and damage evolution laws on ballistic impact prediction of composite materials have not been well investigated and require additional investigation.

In this work, we aim at developing a nonlinear dynamic FE simulation model in combination with a progressive damage formulation to comprehensively investigate the ballistic perforation behaviors of woven-fabric composite panels when impacted by projectiles of different nose shapes and oblique incidence angles.For such analyses, ballistic impacts simulations are performed considering a progressive damage analysis model based on continuum ply damage along with a surface-based cohesive zone method (the shape and extent of individual delaminations at different interfaces) to properly capture the detailed throughthickness distribution of damage induced by high velocity impact in thin composite laminates. The use of surface based cohesive framework to represent interlaminar behavior has a less severe impact on the total computational effort required for the simulation. The FE analyses are conducted in ABAQUS/Explicit environment using VUMAT subroutine, which accounts for various failure patterns of composite laminates as well as interfacial debonding damage. At first, a comparison between the FE model and experimental results in the literature is performed with different projectile nose geometries in terms of residual velocity. Afterwards,substantial insights into perforation resistance, damage propagation mechanisms and energy dissipation for the composite laminate's oblique ballistic impact are acquired using the developed progressive damage model. In this regard, the woven laminated target is impacted at 15°, 30°and 45°obliquity and the ballistic performance in terms of residual velocity at each angle of incidence is obtained. The contribution of this study is consequently to provide an efficient and robust model for studying many aspects of the oblique ballistic impact behavior of composites under diverse projectile nose shapes, which might offer principles for better designing and protecting laminated composite structures.

2. Geometrical modeling and analysis procedure

The current research is based on a numerical analysis of the normal and oblique ballistic impact of 1.8-mm-thick plain woven Eglass/polyester composite targets by 7.85 mm diameter projectile of different nose shapes. The 3D finite element models of the projectiles and targets are generated in the preprocessing ABAQUS/CAE. The projectiles are modeled as a rigid body with the discrete rigid element (R3D4) due to minimal deformation encountered during impact, whereas the targets are modeled as a deformable body. Because there is little deformation observed in the experiments [42-44], the projectiles in the present study are modeled as rigid body to minimize the simulation computing time.The target plate is restrained at its boundary with “encastre”boundary condition to restrict all degrees of freedom and the projectile is given an initial velocity. The contact between target and projectile and between the delaminated plies is modeled using the general contact algorithm available in ABAQUS/Explicit. In this way,the contact scenarios that could occur between the projectile and target, among individual layers of laminate, and among the newly-generated fragments are contemplated, thus preventing element interpenetration. In the entire interaction computation,the contact is accomplished utilizing the penalty and hard contact formulation approaches. After delamination occurs between adjacent plies, the general contact definition is systematically updated to take into account for possible post delamination contact. The effect of friction is considered between the contact surfaces of projectile and target, and delaminated woven plies with a friction coefficient of 0.3 [45].

The modeling of the laminate-based structure is a complicated phenomenon because of the inclusion of two or more constituents,the orthotropic character of the material, and the necessity to account for delamination behavior induced by interlaminar damages.To account for this tendency, the composites are modeled by treating the fibers and matrix as a single laminate and attributing the overall characteristics to that laminate. This method is frequently used in composite modeling where delamination between layers may be modeled to mimic the real failure pattern.When creating the composite laminate,it should be noted that the laminate is built as a stack of laminae connected by zero thickness interfaces; this is a more physical method that is closer to the real build up lamination. This method accurately represents the laminate layup, especially in terms of contact interactions. In the present study, the size of the composite target plate is maintained at 80×80 mm2.It comprised of 4 layers built up of woven fibers.Each layer is 0.45 mm thick and meshed with 8-node reduced integration continuum shell element type SC8R. The kinematic and constitutive features of these continuum-based shell elements imitate those of 3D continuum solid elements, but they are based on the shell theory. When compared to solid elements, they are more computationally efficient and can typically correctly capture the bending deformation induced by the impact [46,47]. A mesh convergence study is carried out in the present numerical simulations to identify an appropriate mesh size in order to balance between computational accuracy and cost.The residual velocity of the projectile is the parameter taken into account for this evaluation.A mesh size of 0.5 mm by 0.5 mm with two elements in the thickness for each ply is shown to be a reasonable balance between accuracy and computational time.

Fig.1 depicts the geometry, mesh structure and boundary conditions of the system. In addition, the FE model of the three different projectile geometries i.e.,blunt,hemispherical and conical that are investigated in present study is demonstrated in Fig.1.The geometry and mass of these projectiles are kept identical to those of the projectiles used in Muhi et al. [43].

3. Constitutive material modeling

Having heterogeneous nature, distinct material characteristics,sensitivity towards reinforcement directions, and interaction between intralaminar and interlaminar failure results in a complex form of damage at micro and macro level in the composites. Two failure models are employed in this work to describe the damage phenomenon of the composites.The first model is the intralaminar damage model on the basis of the continuum damage mechanics.It accounts for fiber breakage in the warp, weft directions as well as matrix micro-cracking considering plasticity.This damage model is implemented in ABAQUS using a user-defined material subroutine VUMAT, and the model is regulated by various material characteristics and coefficients for the ply damage response. Second, between the interfaces,the interlaminar damage model based on the cohesive zone approach is utilized to account for delamination between plies. The constitutive material models used to simulate the behavior of composite and cohesive damage are triggered via compatible and appropriate input parameters,as will be illustrated in the sequel.

Generally, FRP composites exhibit mechanical behavior depending on strain rate.However,there is no direct consent on the degree of sensitivity of the individual mechanical in the literature,see, e.g., the literature review carried out in Ref. [48] where the results of several experimental investigations are summarized. In our view,consideration of strain rate sensitive materials would not result in more accurate predictions because of the uncertainty in determining the strain rate dependent material parameters. Additionally, the number of material parameters needed to determine the constitutive response must be maintained reasonably low, as the models become less useable as the material input complexity increases. Consequently, strain rate independent constitutive behavior of composite plies and interfaces between individual plies is modeled in the present work.

3.1. Intralaminar damage model

The composite material model consists of three phases: (1)initial undamaged response,(2)damage initiation and (3)damage evolution as a result of damage progression. Typical material behavior describing these concepts are schematically represented in Fig. 2 (right).In continuum damage mechanics, a homogeneous continuous structure with heterogeneous stationery and growing damage entities such as cracks can be described by a collection of scalar damage variables di. The current woven fabric reinforced composites damage model mainly focuses on three damage modes with the following damage variables: (i) d1, fiber failure along 1-direction (or warp direction), (ii) d2, fiber damage along 2-direction(or weft direction),and(iii)d12,fiber-matrix degradation due to shear deformation.

Note that the rupture in the warp and weft directions are considered fiber dominated and can occur either in tension or compression, whereas in shear loading, damage is considered matrix dominated, including stiffness degradation as well as inelastic (plastic) deformation.

For the plain woven composite plies concerned here(Fig.2,left),the properties along the fiber directions are assumed to be orthogonal linear elastic. The stress-strain relations of the initial(undamaged) state of composite ply are defined as

Once the damage initiates in the material, the stress-strain relations coupled to damage can be derived as

where E1, E2,v12and G12are the in-plane orthotropic elastic constants. These material constants can also be degraded analogously to stress in the manner as depicted in Fig.2(right)for the young's modulus Ei.d1and d2are the scalar damage variables denoting the current state of fiber fracture in the warp and weft directions,respectively,d12is the shear damage variable reflecting the current state of matrix micro-cracking due to shear deformation. These damage variables take the value of 0 in case of virgin undamaged material and 1 in case of complete damage; they portray the material degradation induced by different loading situations. The damage variable di(i = 1, 2) is further differentiated by the subscripts + and - to distinguish between the damage caused by tensile (+) and compressive (-) fiber failure modes. Like so, the crack closure effect which may occur upon compression is taken into account. Hence, the formulation of fiber damage variables is defined as follows

Fig.2. Constitutive description of the implemented progressive damage model:undamaged elastic law(OA),damage onset by loading function(point A)and damage progression(path A-C).

where angle bracket x refers to the Macaulay operator, defined as x = （x + |x|)/2. This operator allows to address tension-related damage independently from compression-related damage.

The damage variables'onset and evolution are described in the sequel as a function of the corresponding effective stress,defined as (i = 1, 2)

The damage onset is described in terms of damage activation functions Fi+, Fi-and F12as (i = 1, 2)

In Eq.(5),the loading functions/Xi±(i=1,2)used to predict failure are on the basis of the maximum principal stress criterion.Similar to fiber dominated failure modes,the loading function/S12is introduced to provide a criterion for damage initiation owing to matrix cracking based on maximum shear stress criterion.When they reach 1, the material loses its elasticity and damage will initiate. Xi+and Xi-are the ultimate tensile and compressive strengths in the ith directions (i = 1, 2), and S12is shear stress required for initiation of matrix damage.λi+,λi-and λ12are tensile,compressive and shear damage thresholds, respectively. The damage thresholds are initially set to 1 and after damage initiation(Fi±= 1 or/and F12= 1) they increase with respect to damage progress in accordance with

When the damage initiation condition is fulfilled,the associated damage evolution begins, and the damage variables (di±, d12) exercise a significant influence on the degradation process of the integration point. For fiber damage, the exponential damage evolution law is adopted, which is written as (α = 1±, 2±) [49].

where gα0is the elastic strain energy density at the point of damage initiation under uniaxial tensile or compressive loading expressed as gα0= X2α/2Eα. Gαfis the fracture energy per unit area under uniaxial tensile or compressive loading, and Lcis the characteristic length of the finite element.

The above formulation ensures that the damage variables are monotonically increasing quantities, such that ˙dα≥0. It also guarantees that, regardless of the element size, when the ply is subjected to uniaxial loading conditions in the warp and weft, the correct amount of energy is dissipated during the material fracture[50].This is accomplished by include the characteristic length Lcin the damage evolution law, whereby a constraint on the maximum element size Lc

Based on the work in Johnson and Simon[50],the shear damage variable d12is thought to rise with the logarithm of λ12until it reaches a maximum value of dm12ax; it is expressed as

wi th β12>0 shear damage parameter and dm12ax≤1 the maximum shear damage.

As mentioned previously, the in-plane shear response is predominated by the nonlinear behavior of the matrix, which comprises both plasticity and stiffness degradation owing to matrix micro-cracking. For the subsequent inelastic behaviors before complete failure, the classical plasticity model and hardening law are adopted for the damaged material, which are represented as

For the plain woven E-glass/polyester plies employed in this work, the elastic constants and properties describing the damage initiation along the warp and weft directions are taken from previous relevant literature[51]and tabulated in Table 1.The fracture energies per unit surface for failure in warp and weft due to tension and compression are chosen based on physical considerations of other composite material parameters, specifically E-glass/epoxy,which are available in the literature [52]; the values are given in Table 1. Table 2 also includes the parameters determining the plastic properties and failure behaviors due to shear loading [53].

Table 2 Damage evolution parameters and plasticity coefficients under shear loading[53].

During the ballistic impact simulation,the mesh near the impact area can usually get distorted and affect the progress of the numerical calculation.Therefore,element removal is necessary for the stability of the numerical solution and deal with the fully damaged elements so that simulations do not terminate prematurely. To delete totally damaged elements,a damage-based element deletion scheme is used in this study. When any one tensile/compressive damage variable in the warp and weft achieves the predefined maximum value,d1or d2=dmax=1,the damage-based criterion is triggered.

3.2. Interlaminar damage model

For laminated composites that comprise plies, delamination always happens between two adjacent layers, and separates the laminate into sublaminates along the thickness direction.If no precracks are present, cohesive crack model in the framework of damage mechanics is found to be a robust method in capturing delamination. The constitutive law of the surface-based cohesive zone method(CZM)is used to account for the cohesive connections between adjacent fabric layers and to describe the interlaminar delamination phenomena. The constitutive response used here is controlled by a traction-separation law as depicted in Fig. 3. This law is based on the assumption of initially linear elastic behavior,followed by damage initiation (point A), and evolution of damage(path A-B). The initial elastic response prior to damage onset is characterized by three stiffness parameters relating nominal stress(ti) to displacement across the interface (δi) through the following relationship

The normal and shear stresses are considered uncoupled in initial elastic regime and hence the stiffness tensor Kij=0,if i≠j.In Eq. (11), the subscripts n, s and t stand for the normal, first shear,and second shear directions, respectively, as illustrated in Fig. 3(left). The damage onset for delamination () is considered to initiate when the quadratic interaction function reaches 1;it takes the following form

timax(i=n,s,t)represents the interfacial strength in the normal n and first and second shear directions(s,t)and the Macaulay bracket(〈 〉)is used to signify that a pure compressive deformation or stress state does not contribute to damage initiation.

Once the damage initiation criterion is satisfied,the progression of damage is governed by the interlaminar fracture toughness GCvia the Benzeggagh-Kenane(BK)fracture criterion.An exponential softening law is adopted here to model the evolution of the damage from damage initiation to final failure.To simulate the progression of damage from damage initiation to eventual failure, an exponential softening law is used. The critical mixed-mode energy behavior,which can be described as follows,is utilized according to BK law.

with G the current fracture energy, the superscript C denotes the critical fracture energy,GCstands for the total critical mixed-mode fracture energy and η represents the cohesive property parameter adopted as 1.75. Table 3 summarizes the relevant material parameters used for the interlaminar damage model,which can be found in Ref. [53].

Table 3 Material properties describing the surface-based cohesive model [53].

4. Results and discussion

Mesh convergence is performed prior to running the simulations on the E-glass/polyester composite targets to guarantee that the findings are mesh independent. The goal is to attain a compromise between mesh accuracy and computing time. The element size is varied from 0.3 to 2.5 mm,with two elements across the thickness of each ply. The target is struck with a blunt-ended projectile at incident velocity of 150 m/s, and the residual velocities for different element sizes are obtained as shown in Fig.4.An element size of 1 mm produces convergent residual velocities,and additional refinement has no major influence on the numerical results of the residual velocities. As a result, for the current study and subsequent numerical modeling,a mesh size of 0.5 mm is used.

Fig. 3. Traction-separation response for the used cohesive zone method.

Fig. 4. Mesh convergence results.

To explore the effects of projectile shape and incidence angle obliquity on the ballistic impact behavior of woven laminates,normal and oblique impact simulations with blunt-ended, hemispherical and conical projectiles are performed on E-glass/polyester composite targets under initial impact energy of 115.4 J(176 m/s). Through numerical simulations, important insights are further gained on perforation resistance,dissipation of energy and failure propagation mechanisms for the ballistic impact of the woven composite laminates. Meanwhile, the results from numerical simulations and experimental tests are initially compared.

4.1. Validation of the FE model

Relying on the constitutive models exposed in Section 3, numerical simulations are performed for each experimented test situation reported in Muhi et al. [43] with identical geometry,boundary and loading conditions.The simulations are carried using three types of projectiles,namely,blunt-ended,hemispherical and conical (30°half-angle) projectiles at an initial velocity of 176 m/s as illustrated in Fig. 1. Quantitatively, Table 4 demonstrates the validity of the current FE model in terms of residual velocity with experimental data. From Table 4, it can be seen that the findings obtained from the current model match quite well with those obtained from the experimental tests, with a percentage error of 0.3-1.2%.

Table 4 Validation of residual velocity for the three projectile nose shapes.

With the confidence acquired from the residual velocity validation,the current FE model is further extended to characterize the normal and oblique ballistic perforation behaviors and failure modes of the underlying composite laminate.

4.2. Effect of projectile nose shape

A detailed simulation study regarding the influence of projectile shape on the normal ballistic impact response of woven laminate is explored in this section.Besides,the impact behaviors and damage patterns of laminate subjected to different projectile shapes are displayed and analyzed.

4.2.1. Load-time, velocity-time and energy-time histories

The impact load-time, residual velocity-time and absorbed energy-time curves of the woven fabric laminate under 115.4 J impact energy for different projectile shapes are illustrated in Fig.5.As seen, the impact energy of 115.4 J is sufficient enough to easily perforate the laminate,so the contact duration is greatly shortened.In the case of blunt nosed projectile,the impact load increases more quickly in the rising phase, declines abruptly after the peak value and then decreases gradually, and eventually remains constant at zero during the penetration period(Fig.5(a)).The impact load-time curves for both hemispherical and conical nosed projectiles are dominated by the loading rising and unloading descendent phases.For the hemispherical nosed projectile, it can be seen that in the beginning, the load increases significantly until it reaches the first peak, where severe failures and fractures occur on the front side.Following that,a sudden decrease in the impact load-time curve is observed,which might be attributable to the abrupt damage in the laminate as the impact energy increases.The resistive load ascendsto the second peak in the last phase before decreasing completely throughout the full penetration time. Notably, the impact load curve of the laminated target impacted by hemispherical projectile has a relatively lengthy load plateau spanning from 12 to 22 μs?Particularly, for the conical projectile, the lengthy load plateau happens after the first peak load at time 10 μs and continues until time 58 μs?This can be explained by the fact that the projectile load is no longer increasing after the initiation of damage in the composite, and hence the development of internal damage, as well as the propagation of cracks and fiber breakage be able to significantly lengthen the loading time at a comparatively stable impact load before the projectile perforates the laminate completely.

Fig. 5. History curves of(a) impact load, (b) residual velocity and (c) absorbed energy during ballistic impact of woven laminate at initial strike velocity of 176 m/s.

The occurrence of the projectile's peak load value signifies a partial or total material failure, and after this time, penetration resistance drops suddenly or gradually until it reaches zero at complete perforation, and therefore the projectile's impact force becomes zero. As can be seen from Fig. 5(a), the laminated target impacted by the blunt projectile is the first to reach the maximum contact impact force,while the laminate impacted by the conical is the last.The time it takes for the projectiles to reach their first peak load is found to be 2 μs for blunt,6 μs for hemispherical,and 10 μs for conical. When compared to other projectiles, a lesser value for the time of occurrence of peak load for blunt-ended projectile implies that material failure in the target laminate happens more quickly.Prior to the peak impact load,it is found that the slopes of impact force-time curves rise, as the projectile shape gets flatter.During ballistic impact, the blunt projectile generates the largest impact force and the shortest contact time, whereas the conical projectile results in the lowermost impact force and the lengthiest contact time.These occurrences may be explained by the fact that the higher the contact area between the projectile and the laminate,the greater the impact load and the shorter the contact period.Additionally, as shown in Fig. 5(b), the residual velocity of the blunt-ended projectile is lower than that of the other nosed projectiles(spherical and conical).As a result,energy absorption in the laminate increases with the changing of the projectile nose shape from conical (or hemispherical) to blunt, or, to put it another way,as the projectile’s contact surface area at the impact zone with the target laminate increases.The energy absorbed by the laminate can be defined as the projectile's loss of kinetic energy, and it is calculated by subtracting the projectile's residual kinetic energy from its initial kinetic energy,as depicted in Fig.5(c).This absorbed energy appears in the form of damage. It can be seen from the absorbed energy history curves that the absorbed energies increase with impact time and have no downward trend after the peak value, indicating that the projectiles totally perforated the target.Besides,the final energy absorption reveals that the laminate target struck by a conical projectile and a blunt projectile absorb the minimum and maximum impact energy,indicating that the blunter projectile can cause more significant impact damage.

4.2.2. Failure mechanisms and damaged surface

Although impact load and residual velocity of the projectile or energy absorption by laminate point out the ballistic resistance of the target under different projectile shapes, these quantitative quantities do not provide a qualitative depiction of fracture mechanisms.Therefore,the damage and stress distributions of the laminated target at different time steps upon projectile impact are examined in the sequel to gain a better and clearer comprehension of fracture patterns in composite material.

Fig. 6 shows the progression of through-thickness damage as a function of time for an impact of 176 m/s. The laminate is fully penetrated by different projectile nose shapes in a very short time,as depicted in these figures, with the blunt projectile taking the least amount of time, followed successively by the hemispherical and conical projectile. In consequence of ballistic impact, stress waves are created inside the laminate along the thickness and radial direction. A compressive wave propagates along the laminate's thickness since the impact path is normal to the target,whereas tensile and shear waves propagate along the radial direction.Given the impact case under blunt projectile in Fig.6(a),the total ballistic impact event may be split into two main stages.During the first stage (0< t ≤10 μs), upon the collision with the laminate, the material underneath the projectile compresses, and as the projectile advances, the material flows in the thickness direction.Due to the further advancement of the projectile owing to the compression of the layers,it causes a bulging formation on the target's rear face. The second stage (t > 10 μs) is illustrated by stretching-shearing deformation and localized bending of the individual delaminated layers.At t=20 μs,the plug formation as well as the failure due to tensile of delaminated layers ahead of the projectile are observed. Continuous penetration during the time period t = 40-80 μs results in full plugging shear out of the laminate.

Moreover,Von Mises stress contour plots in Fig.6 reveal that the impact behaviors of distinct projectile cases are highly correlated with impact duration. It exhibits divergent stress propagation on the surface of the target laminate struck by the blunt projectile(Fig.6(a)),while conical and hemispherical projectiles respectively display a relatively concentrated stress propagation (Fig. 6(b) and Fig.6(c)).Transverse shear damage happens in the laminate for the blunt projectile when the stress reaches the critical value,whereas tensile tearing fracture occurs in the laminate for hemispherical and conical projectiles as depicted in Fig.6(b)and Fig.6(c).What's more,the interlaminar delamination may be viewed as the driving force that leads certain layers to pull out ahead of others and subsequently fracture because of the projectile's stretching force.As a result, the entire composite layers are fully fractured around the impact region and,at the end of the impact process,perforated.Furthermore, the laminate struck by the blunt projectile has a larger deformation area (Fig.6(a)) than the laminate struck by the hemispherical and conical projectiles(Fig.6(b)and Fig.6(c)).It also demonstrates that the flatter projectile, as opposed to the sharper projectile, might cause a broader collateral damage zone in the target. The deformation zone is greatly reduced as the projectile gets sharper, which corresponds to the profounder and tighter deformation for the conical projectile situation illustrated in Fig. 6(c).

Fig.6. Effect of projectile nose shape on damage evolution and stress propagation:(a)Blunt projectile; (b) Hemispherical projectile; (c) Conical projectile.

Fig. 7. (continued).

Fiber fracture in tension and compression, matrix cracking,matrix plasticity, and interlaminar delamination are all common damage and failure mechanisms that the composite laminate exhibits in general. During the ballistic impact, all of these damage modes are likely to occur. It is therefore convenient to use the damage evolution variables previously presented in Section 3 to describe the damage modes retrieved in the composite during the ballistic impact under different nose projectiles. These variables include tensile damage (d1+, d2+), compressive damage (d1-, d2-),shear damage (d12) and delamination damage between ply interfaces.They are depicted for the three projectile cases in Fig.7.As illustrated in the damage distribution maps, red zones reflect the most extensive damage,green zones stand for partial damage,and blue color represents no damage. Simultaneously, the completely failed materials are eliminated from the model using the previously discussed element removal scheme. As displayed in Fig. 7, regardless of projectile shapes, tensile and compressive damages along warp and weft directions occur significantly around the impact zone while the matrix shear damage variable d12is comparatively insignificant since 0

4.2.3. Energy-balance model

The validation of the energy conservation concept is an important consequence of impact dynamics using FE simulation code with an explicit integration method.On the basis of energy balance principle, the current numerical models are being exploited to provide a precise knowledge of how the projectile's kinetic energy is being dissipated and which dissipation mode prevails over the others. The following provides the energy balance between the projectile's kinetic energy and the energy absorbed by the different mechanisms

where mpis the mass of the projectile, Viis the projectile's initial velocity, Vr(t) is the residual velocity of the projectile, 1/ 2mpV2istands for the initial kinetic energy of the projectile, 1/ 2mpV2r（t)represents the projectile residual energy (ERK), EPK is the kinetic energy of composite laminate, EVD is the energy dissipated by viscous effects including viscous regularization(except for cohesive elements and cohesive contact), not inclusive of energy dissipated by automatic stabilization and viscoelasticity, EFDis the energy dissipated through frictional effects, Epwis the work done by contact and constraint penalties,and EIE denotes the system's total internal energy, which may be further subdivided into the following components

with ESE the elastically stored energy, EAE the artificial strain energy associated with constraints used to remove singular modes(such as hourglass control),EPD the energy dissipation by inelastic deformation and EDD the energy dissipation through delamination.

In order to determine whether the total energy of the system(ETE) remains constant during the computation, Fig. 8 depicts the energies variation during the normal impact of the structural model by different projectile shapes.From this,it can be seen that the total energy remains constant throughout the analysis for all projectile shape impacts at any time step of the simulation. This validates the concept of energy conservation balance in the system,as well as the models' adaptability for impact investigation with various projectile shapes.Furthermore,the artificial strain energy is checked to ensure that it remains very low for all projectile cases.It corresponds to less than 2.5%of the internal energy,indicating that the numerical model is adequate and produces stable results.From the observation of energy evolution curves in Fig. 8 regardless of the shapes of projectile, it can be concluded that initially,the total energy is only given by the kinetic energy of the projectile.As soon as the projectile begins to penetrate the composite laminate, the kinetic energy of the projectile (ERK) decreases considerably,indicating that some impact kinetic energy is absorbed. This reduction in kinetic energy results in an increase in the target's total internal energy (EIE). Thereby the penetration resistance of the composite can be measured by the decrease in projectile kinetic energy. When compared to other projectiles, the blunt projectile has the greatest drop in kinetic energy,indicating the higher energy absorbed by the laminate impacted by this projectile.

The contribution of various energy absorbing mechanisms ascribed to the laminated target is a vitally important issue that should be quantified. Fig. 9 describes the energy absorbed in various deformation modes when projectiles of different nose shapes impact with the target at normal incidence angle. Overall,the majority of the energy dissipated due to impact is in the form of elastic strain energy,followed successively by the energy dissipated owing to the inelastic deformation in the system, kinetic energy corresponding to the laminate vibration, frictional dissipation,dissipation due to interlaminar delamination, and dissipation of other lower energies in the form of viscous and artificial strain energy.By a careful inspection of each individual energy absorbing mechanism,it is evident that when the target laminate is impacted by blunt-nosed projectile,the energy dissipated due to vibration is very high compared to the other projectile shapes.This increase in target kinetic energy can be explained by the increase in the contact area between projectile and target and hence the amount of damage caused by the blunt projectile.Further,the target impacted with conical nosed projectile exhibits a higher frictional dissipation energy than that of the blunt and hemispherical nosed projectile.This due to the large amount of friction between the projectile's and target's contact surfaces,as the conical projectile results in a longer contact duration during impact, as exhibited in Fig. 5(a).

Fig.8. Energy evolution histories during ballistic impact with different projectile nose shapes.

Fig.9. Individual energy absorption mechanisms at the end of the impact event under different projectile shapes.

Fig. 10(a) and Fig. 10(b) depict the energy distribution in different absorption mechanisms as a function of contact time for the target impacted by the blunt and conical projectile, respectively. The dissipation mechanism in the form of target kinetic energy because of its vibration(EPK),the total internal energy(EIE)and its dissipation into ESE, EPD, EDD, and EAE are illustrated in these figures. The findings show that almost all mechanisms keep increasing with contact time during the initial stage of contact.After some time (this time is short in case of blunt and long for conical projectile),the kinetic energy due to target vibration(EPK)declines while other dissipation mechanisms continue to increase.When complete penetration occurs, all energies remain almost unchanged.

In the light of all the above investigations, it is possible to deduce that the projectile shape has a substantial impact on the energy absorption, stress distribution and fracture patterns. The blunt nosed projectile was the one which gave rise to the highest absorbed energy by the laminate, followed by hemispherical, and lastly the conical.This order in terms of energy absorption capacity is related to the area of impact of each projectile. The blunt projectile has a higher impact area, so the target impacted by this projectile absorbs more energy, on the contrary, the conical projectile has a smaller contact area,so the energy absorption capacity is the smallest. As the energy absorption capacity increased with the increase in the damaged area,the target impacted by the blunt projectile was evidently having a higher damaged area,followed by the same order mentioned previously.

4.3. Influence of incidence angle of impact

With the blunt and conical nosed projectile,the influence of the projectile impact angle is investigated. The angle of incidence can be defined as the angle between the projectile and the normal direction to the laminate(represented as θ in Fig.11).The distribution of impact velocity over the laminate as a result of the oblique impact is schematized in Fig.11.The total velocity vector,v,is split into directions z and x as follows vz= vcosθ, vx= vsinθ, where v is the total impact velocity along impact direction, vzand vxare the impact velocity component along target thickness and target surface, respectively.

4.3.1. Residual velocity and energy absorption capacity

The perforation behavior of the woven laminated composite under oblique impact is investigated, considering three impact angles of 15°,30°,and 45°besides normal impact.Fig.12 explores the effect of obliquity on the velocity time curves of blunt and conical projectiles at incidence velocity of 176 m/s. In general, the resultant velocity of the projectile is found to decrease as the oblique angle increases from 0°to 45°for both blunt and conical projectiles.Particularly in the case of blunt projectile,it can be seen that there is a substantial drop in the velocity of the projectile under normal impact compared to oblique impact,and the drop of the velocity-time profile diminishes as the angle of contact increases (Fig.12(a)). This might be because, under normal impact,the projectile's contact surface with the laminate has been at its maximum since the onset of penetration, and therefore experiences greater penetration resistance.

Fig.10. Energy time history of total internal energy and its dissipation terms when the target impacted by (a) blunt and (b) conical nosed projectile.

Fig. 11. Angular impact of the projectile and the components of the impact velocity along x and z-axis.

Fig.12. Comparison of velocity-time histories at different oblique incidence angles of (a) blunt and (b) conical projectile.

In addition, for both blunt and conical nosed projectile, Fig.13 depicts the trend of alteration in residual velocity as well as energy absorbed by the target as a function of incidence angle.At low obliquity,the resistance of the target under conical impact is found to be nearly identical to that of normal impact.Up to 15°obliquity,the projectile's velocity decrease is nearly identical (Fig.13(a)). At higher obliquity however, the resistance augmented significantly.At 30°and 45°obliquity, the velocity is reduced by 1.7 m/s and 4.9 m/s,respectively,as compared to the normal impact.In the case of blunt projectile, the residual velocity decreases, increases and then decreases with increasing obliquity(Fig.13(a));this variation may be due to the change in failure mode.The overall decline in the residual velocity shown in Fig. 13(a) implies that the penetration resistance provided by the laminate rises against the projectile as the angle of impact increases, as shown in Fig. 13(b). For blunt nosed projectile, the velocity decreases by about 4.6 m/s as the incidence angle increases from 0°to 45°. This indicates that the influence of the projectile's incidence angle on the perforation behavior of the woven laminate is almost the same for both impact situations, i.e.the conical and blunt projectile, in terms of residual velocity and absorbed energy.

As shown in Fig.14 in terms of load-time curves, obliquity is a critical factor in the responses of woven laminate targets under ballistic impact loadings. With the analysis of projectile impact load-time histories for the blunt and conical cases, Fig. 14(a) and Fig. 14(b), respectively, the influence of incidence angle on the perforation resistance of target laminate is clearly depicted.As the incidence angle increases from 0°to 45°, the force-time history of the blunt projectile gets flatter, implying that the projectile with a greater impact angle experiences higher penetration resistance offered by the target laminate(Fig.14(a)).For the conical projectile case,there is a general tendency of increasing peak load as impact angle increases, as seen in Fig.14(b). As well, the time required to perforate the target laminate rises with the projectile's incidence angle. It is evident from Fig. 14(a) and Fig. 14(b) that the timing generated by the oblique impact is extended when compared with the normal impact.The time it takes for the blunt projectile to move with zero acceleration or at constant velocity is found 32 μs in the case of normal impact (θ = 0°) and 100 μs for the inclined impact(θ=45°).On the other hand,the conical projectile exhibits a longer perforation time than that of the blunt projectile, i.e., 70 μs for normal impact (θ = 0°) and 108 μs in case of inclined impact(θ = 45°).

Fig.13. Computed projectile's residual velocity (a) and energy absorbed by the laminate (b) at varying angle of obliquity.

Fig.14. Resultant impact load-time histories of (a) blunt projectile (b) conical projectile at different incidence angles.

4.3.2. Perforation behavior and global deformation

The effect of impact angle on the damage morphology in the laminated target is investigate at incidence velocity of 176 m/s.Fig.15(a) and Fig.15(b) respectively portray the predicted damage patterns as a function of time when the target laminate is struck by conical and blunt projectile at different obliquities. For both projectile cases, it can be seen that the perforation time of the target increases with the projectile impact angle. Moreover, the failure pattern of the laminate is significantly affected by the angle of obliquity. For better illustration, Fig.16(a) and Fig.16(b) show the damage patterns on the back sides of target laminate at the same time instant of 140 μs, when impacted at 0°, 15°, 30°and 45°incidence angle by conical and blunt projectile, respectively. The findings in Fig. 16(a) demonstrate that the laminate failure is occurred through petal formation (triangle-shaped pieces) at each angle of impact in the case of the conical projectile. Under normal impact, four equal petals (triangles) are formed, whereas oblique impact results in four petals of different sizes. Due to obliquity,when the angle of impact increases from 0°to 45°, the size of the two petals decreases which ultimately leads to an increase in the size of the other two petals.At 45°obliquity,the two smaller petals came close to each other while the two larger petals are excessively deformed and ruptured.

Fig.15. Temporal evolution of damage status in the laminate when impacted by (a) conical projectile (b) blunt projectile at different obliquities.

What's more, when the laminate is exposed to a blunt shaped projectile,failure is occurred owing to shearing and plug formation as illustrated in Fig.16(b).However,when the laminate is struck by an oblique projectile,shearing and tearing of the laminate are seen,and the plug remains connected to the laminate. Some fragmentations of the laminate material are also observed.For 30°and 45°obliquity, the formation of the plug did occur, but it remained attached to the laminate.

As illustrated earlier,as the projectile incidence angle increases,more energy is lost and thus the composite laminate becomes more resistant. This signifies that the laminate absorbs more energy through multiple energy absorption mechanisms. Fig. 17 graphically summarizes the quantitative contribution of individual mechanisms to the total energy absorbed by the laminate when impacted by conical and blunt projectile at varying obliquities. In general, the majority of the energy due to oblique impact is dissipated as elastic strain energy (ESE), inelastic deformation energy(EPD)and frictional energy (ESE)in the case of a conical projectile(Fig.17(a)).For the blunt projectile scenario(Fig.17(b)),the most of energy absorption takes the form of laminate kinetic energy corresponding to vibration (EPK), permanent inelastic deformation(EPD) and elastic strain energy (ESE). More specifically, under conical impact,the frictional dissipation,elastic strain and inelastic energy all increase continuously with increasing the incidence angle of impact from 0°to 45°.On the other hand,with increase in the angle under impact by blunt projectile, both the inelastic deformation and the frictional energy increase continuously while the other contributing mechanisms do not follow the same trend.This points out that regardless of projectile shape, the energy dissipation in the form of frictional, inelastic and elastic strain energy is more influenced by impact angle of the projectile compared to the other energy contributions.

So far, the use of such a numerical modeling approach has allowed the interpretation and analysis the influences of normal and oblique impact under various projectile nose shapes on the damage responses and behaviors of fabric composite targets. This results in an effective design for an improved ballistic resistant composite laminate.

5. Conclusions and final remarks

Presently, there is still a lack of knowledge on the effect of projectile nose shape and impact angles on the ballistic velocity impact behaviors of woven fabric composite materials.Therefore,it was necessary to investigate the ballistic impact behavior and damage morphology in the target laminate under projectile impact at different obliquity angles and with varied nose shapes for improved design and protection of woven laminated structures.Consequently, the goal of this research was to propose a computational framework for simulating the normal and oblique ballistic impact behavior of woven composite materials. Using different projectile nose geometries, this approach addressed the failure mechanisms and damage behavior in laminated composites due to normal and oblique perforation impact. Fiber damage, matrix cracking, and plasticity effects because of micro-matrix cracking due to shear stress were all taken into consideration in the material responses with significant nonlinear behavior. The material behavior of composite and interlaminar region was modeled using the appropriate constitutive material model for each constituent.To this end, two constitutive models have been implemented: the first, a homogeneous orthotropic elastic model based on stiffness degradation concept for intralaminar behavior of the composite plies,and the second,a traction separation law for cohesive model to capture interlaminar damage in composite interfaces. Initially,the residual velocities for different projectile nose shapes were compared with the experimental measurements reported in the literature and a good agreement was found between the two sets of results.Based on the adopted progressive damage model,the effect of projectile nose shape and impact angle on the residual velocity,energy absorption, and failure mechanisms has been investigated.The angle of incidence has been varied as 0°,15°,30°,and 45°.For each projectile shape(blunt,conical,and hemispherical)and angle of incidence, the corresponding residual velocity and damage morphology were obtained. The following conclusions may be derived regarding the effect of projectile nose geometry and obliquity on the laminated composite target's ballistic performance:

Fig.17. Individual energy absorption mechanisms at the end of the impact under (a)conical and (b) blunt impact with different incidence angles.

- According to the ballistic impact response of varied projectile nose shape examples, the sharper projectile (conical) has generated prolonged contact time,lesser peak impact load,and lesser initial slope of impact load curve. The blunter projectile,on the other hand, resulted in the greatest impact load and quickest contact period during ballistic impact. These occurrences may be explained by the fact that the larger the contact area between the projectile and the laminate, the greater the impact force and the shorter the contact period.

- From the final energy absorption,it was revealed that the target laminate impacted by conical projectile and blunt projectile absorbed the minimum and maximum impact energy, respectively. The blunt shape projectile resulted in higher energy absorbed by the laminate, and higher damaged area, followed by the hemispherical and conical shapes. This was attributable to the fact that the impact area of the blunt projectile was higher compared to the remaining two.

- From the stress propagation,it was found that a diverging stress propagation occurred on the surface of target laminate when struck by blunt projectile, while a concentrated stress propagation exhibited for conical and hemispherical projectiles.Furthermore,the deformation area of the laminate impacted by the blunt projectile was larger than that of the hemispheric and conical projectiles. In comparison to the sharper projectile, the flatter projectile caused a greater collateral damage zone in the target.

- Regardless of projectile shape, the composite damage response revealed interlaminar delamination,fiber and matrix damage as potential mechanisms of material failure under ballistic impact.The fiber tensile rupture along warp and weft directions was the most prevalent failure mode, followed by the mechanism of fiber failure caused by compressive loading,and the matrix shear damage mode was comparably small. On the other hand, the amount of delamination in the laminate was noticed to increase as the projectile shape altered from conical to flat.

- Regarding the damage morphology under different projectile shapes, it was observed that for hemispherical and conical projectiles, petaloid penetration of four symmetrically shaped triangular pieces resulted from tensile tearing.However,for the blunt projectile case,the damage propagated more peripherally along the lateral region resulting in fragmented plies due to shearing failure mechanism.

- The total energy variation in the course of the ballistic impact of the structural model remained constant throughout the analysis for all projectile nose shapes.As a result,the concept of energy conservation in the system was confirmed as well as the applicability of the created models for impact analysis under different projectile shapes.

- The majority of the energy dissipated as a result of impact was in the form of elastic strain energy, followed by energy dissipated as a result of inelastic deformation in the system,kinetic energy corresponding to the target vibration, frictional dissipation,dissipation due to interlaminar delamination, and less other energies dissipated as viscous and artificial strain energy.

- The load-time history of the blunt projectile became flatter as the impact angle increased from 0°to 45°, which implies that the projectile with a greater angle of impact experiences more penetration resistance provided by target laminate. For the conical projectile case, there was a general tendency of increasing the peak load with increasing the angle of impact.

- It was evident from the load-time history that the timing under oblique impact was extended when compared to the normal impact. The time it takes a blunt projectile to move with zero acceleration or at a constant velocity was found to be 32 μs under normal impact and 100 μs in the case of oblique impact(θ = 45°). Oppositely, the conical projectile exhibited a longer perforation time than that of the blunt projectile, that is, 70 μs for normal impact and 108 μs for the oblique impact (θ = 45°).

- Oblique impact has affected the mechanism of failure of the target laminate; particularly, the damage morphologies on the front surfaces differed between normal and oblique impact.The size of two petals generated in the laminate in the case of a conical projectile was reduced, resulting in two lengthy petals that were deformed and ruptured. In the case of a blunt projectile, however, the plug was only partially sheared.

- Most of the energy due to oblique impact under conical projectile was dissipated as elastic strain energy, inelastic deformation and frictional dissipation. For the laminate impacted with blunt projectile,the most of the energy absorbed takes the form of laminate's kinetic energy, elastic strain and inelastic deformation energy.Further,regardless of projectile nose shape,the energy dissipation in the form of frictional, inelastic and elastic strain energy is more affected by projectile oblique angle compared to the other energy contributions.

Declaration of competing interest

The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.