Influence of thickness and projectile shape on penetration resistance of the compliant composite

Vishws Mhesh .Shrnpp Joldrshi .Stybodh M.Kulkrni

a Department of Mechanical Engineering.National Institute of Technology Karnataka Surathkal.Mangalore 575025.India

b Department of Industrial Engineering and Management.Siddaganga Institute of Technology.Tumakuru 572103.Karnataka.India

Keywords: Flexible composite blocks Jute Rubber High velocity Projectile shapes Thickness Damage resistance Penetration depth

ABSTRACT The present study deals with development of conceptual proof for jute rubber based flexible composite block to completely arrest the projectile impacting the target at high velocity impact of 400 m/s through numerical simulation approach using finite element (FE) method.The proposed flexible composite blocks of repeating jute/rubber/jute (JRJ) units are modelled with varying thickness from 30 mm to 120 mm in increments of 30 mm and impacted by flat (F).ogival (O) and hemispherical (HS) shaped projectiles.All the considered projectiles are impacted with proposed flexible composite blocks of different thicknesses and the penetration behaviour of the projectile in each case is studied.The penetration depth of the projectile in case of partially penetrated cases are considered and the effect of thickness and projectile shape on percentage of penetration depth is statistically analyzed using Taguchi’s design of experiments(DOE).Results reveal that the though proposed flexible composite block with thickness of 90 mm is just sufficient to arrest the complete penetration of the projectile,considering the safety issues.it is recommended to use the flexible composite with thickness of 120 mm.The nature of damage caused by the projectile in the flexible composite is also studied.Statistical studies show that thickness of the block plays a prominent role in determining the damage resistance of the flexible composite.

1.Introduction

Last few decades have witnessed the usage of composite materials as the substitutes for conventional metals and alloys in many engineering applications.Composites used for structural engineering applications are subjected to various types of static and dynamic loadings out of which dynamic loading seem to be more dangerous.Composite materials are more sensitive to impact loading compared to their metallic counterparts.This makes it necessary to study the impact behaviour of the composites.Various studies have been carried out on the impact response of the composites under low and high velocity impact regimes with both low and high velocity impact loadings having their own importance of study.In case of high velocity impact.the kinetic energy of the projectile is absorbed by the composite laminate due to shear deformation between the layers and delamination[1].

Along with the conventional stiff composites used for structural applications subjected to high velocity impact.flexible fabric composites also find their usage as body armours where damage due to high velocity impact loading is a primary concern.In applications where stiffness is not an area of concern such as claddings and acoustics.flexible composite find their wide application since they can be tailor made to meet the various requirements[2].

PMCs exhibit varied mechanical properties and damage behaviour based on the type of matrix used [3].Vieille et al.[4,5]conducted a comparative study on carbon fiber reinforced PMCs with epoxy and PPS as the matrices.This study revealed that PMC making use of PPS exhibited almost same energy dissipation capability compared to PMC making use of epoxy.There exists an argument referring to the study carried out by Lee et al.[6]that the energy absorption capability of composite that are stiffer are better than the composites that are flexible.On the other hand various other researchers Gopinath et al.[7],Wang et al.[8]argued that the flexible composites are better energy absorbers compared tocomposites that are stiffer.

Concerned to the type of damage the PMCs undergo.various researchers studied the damage behaviour of composites making use of thermoset (TS) [9-14]and thermoplastic [4,15-21]as the matrices.The outcome of which led to the conclusion that TP when used as matrix in PMC leads to minimal damage compared to TS matrix.Also.it was found that TP when used as matrix in PMC provides higher impact force withstanding ability along with energy absorption ability compared to TS [19].Thus it is clearly evident from the studies carried out till date that selection of matrix is one of the important criteria in deciding the impact properties of the PMCs.

Different approaches such as experimental.empirical.semi empirical and finite element(FE)based numerical approaches have been adopted by various researchers to assess the impact response of PMCs[22-27].Various factors such as reinforcement used,type of reinforcement.form of reinforcement.arrangement of plies in the composite combined with the shape of impacting object decides the impact response of the PMCs [28,29].Stiffer composites obviously provides curious engineering properties for structural application.However.their pitfall in terms of hardness and flexibility makes them non potential candidates for impact applications when compared to flexible composites.

Natural rubber which belongs to the class of elastomers strikes to the mind of researcher when a substitute for TS matrix is thought of due to its complaint nature.It was proved by Vishwas et al.[27]that making use of rubber as a constituent in PMC enhances the energy absorption capability of the composite.Wide variety of elastomers are available for use in different engineering applications like shock absorbers.impact resistance panels etc [30-32].Rubber coated fabrics were studied by Ahmad et al.[33,34].Roy et al.[35]and was concluded that rubber coated fabrics resulted in better energy absorption compared to neat system.A study carried out by Stelldinger et al.[36]proved that inclusion of EPDM rubber layer resulted in control of damage in the composites.Biodegradable material which is naturally available is natural rubber (NR)which provides more compliance and thus considered as a suitable constituent of flexible composite which is subjected to impact loading [37].Authors in their previous study [27]have shown the potential of rubber in enhancing the energy absorbing behaviour of the composite subjected to low velocity impact loading.

Natural fibers (NF) are being treated as potential replacements for synthetic fibers (SF) in composites used for many engineering applications due to fact that they are abundantly available at low cost and also provide the mechanical properties just sufficient to meet the requirements of the final product intended to be used[38-42]and Out of all the various natural fibers available for use,it is found that jute has emerged as the most promising fiber owing to its better mechanical property and density compared to other fibers[43].In addition to these advantages.natural fibers are also biodegradable resulting in ‘green’ composites.

There are various factors that influence the damage resistance of energy absorption of the composites subjected to impact loading.In case of composites proposed to be used for high velocity impact applications,study of the damage resistance is of prime importance since the non penetration of the projectile through the thickness of the composite is utmost essential to protect the object or the person behind the target.Thus,the thickness of the laminate is one of the significant factors affecting the impact response of the composites.Deciding the optimal thickness of the composite laminate required for arresting the completing penetration of bullet is thus very essential before production of the final product.

Projectile shape is another factor that plays an important role in deciding the mechanism involved in deformation of the composite laminates.Numerous studies are reported till date aimed at assessing the contribution of different shapes of projectiles on the impact response of the target.In case of aluminium target.flat shaped projectile can penetrate through the target more effectively compared to conical and hemispherical projectile according to the study carried by Wingrove [44].

Various different approaches are used by many researchers to solve both static and dynamic problems numerically.The study carried out by Rabczuk et al.[45]showed that cracking particle method without enrichment can be effectively used to solve various two and three dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any “mesh” orientation bias.A simplified mesh free method for arbitrary evolving cracks was adopted by Rabczuk and Belytschko [46]to solve various two dimensional problems.A new approach of three dimensional large deformation mesh free method for arbitrary evolving cracks was described and applied to various three dimensional problems by Rabczuk and Belytschko [47].An approach of dual horizon peridynamics formulation was used by Ren et al.[48,49]which showed that dual horizon peridynamics is less sensitive to the spatial than the original peridynamics formulation.

Prior to finalizing the material for any applications.their suitability has to be checked.However,large amount of time,effort and cost are involved in deciding the optimal thickness of the composite laminate experimentally.which may be greatly reduced through use of computational simulations [50-53].Also.the numerical modeling gives the insight into mechanisms that lead to the damage and fracture of composites.The study carried out by Hamdia and Rabczuk [54,55]showed that the key parameters influencing the fracture toughness of polymer composite can be determined by numerical modeling and influence of input parameter uncertainties on fracture toughness of polymer nano composites was also studied.

Thus the present study aims at determining the optimal thickness of the flexible composite block necessary for arresting the complete penetration of the projectiles of different shapes(F,O and HS)impacting the target at high velocity and proposing a thickness of the flexible composite for the purpose of fabrication of end product along with assessing the significance of projectile shape and thickness of the proposed flexible blocks on the penetration depth using Taguchi’s design of experiments (DOE).

2.Modeling and simulation

The ballistic impact study of the proposed flexible composites are carried out using commercially available software and flexible composites are modelled with a thickness of 30 mm-120 mm in increments of 30 mm.Projectiles of different shapes are modelled as rigid bodies as shown in Fig.1 and are used for impacting thetargets at an impact velocity of 400 m/s.

Fig.1.Projectiles used in FE analysis.

The modelled and assembled view of composite laminate and bullet are presented in Fig.2 along with the applied boundary condition and Fig.3 provides the meshing details of the flexible composite blocks and projectiles where R3D4(A 4 node 3 D bilinear rigid quadrilateral) element type are used to mesh the projectile and SC8R type shell element with element deletion enabled is used for meshing flexible composite block.The material data pertaining to jute and rubber are tabulated in Table 1.

Boundary conditions are applied to the target such that the degrees of freedom in all the six directions are restricted(Ux=Uy=Uz=URx=URy=URz=0)and the bullet is constrained to move only in Z direction with the assigned velocity.To maintain the integrity between the layers,interaction properties are defined for each layer in the interaction module of the software.Penalty contact algorithm was used to define the contact between the projectile and the top surface of the laminate with hard contact and pressure over closure and friction coefficient of 0.3 and the contact between the laminates was defined using general contact algorithm based on the reported studies [58].The time step of 0.005 with interval of 500 is used for the purpose of analysis and is found to be quite suitable and element deletion was carried out based on the study carried out by Sharma et al.[59]where elements were removed once the damage variable reached a value close to unity so that the collapse of whole structure due to absence of residual stiffness does not happen.

Before the actual FE study.a mesh convergence study is performed on the similar grounds as carried out by Nair and Rao [60]and a mesh division of 60×60 showed good convergence as shown in Fig.4 and hence the same has been used in the actual FE study.

2.1.Governing and constitutive equations

The non linear stress strain relationship of the materials under larger deformation can be described by Neo-Hookean material model [61,62].The constitutive equations for stretching and bending in case of hyper elastic material models are derived from strain energy function W from Eq.(1).

Fig.2.Modelled and assembled view of laminate and projectile with(a)flat;(b)ogival and (c) hemispherical shape.

Fig.3.Meshing of the flexible composite and projectile with(a)flat;(b)ogival and(c)hemispherical shape.

The Cauchy stress tensor for incompressible material is explained as in Eq.(2)

Where.I1and I2are principal invariants of the left Cauchy-Green deformation tensor.defined by Eq.(3)-Eq.(4).

The failure modes in the material damage model are represented by Eq.(5)-Eq.(8)

In Eqs.(5)-(8).^σij(i.j = 1.2) represents the effective stresstensor components.The tensile and compressive strength of the laminate are represented by Xt.Xcin longitudinal direction and Yt,Ycin transverse direction.The in plane and out of plane shear strength of the laminate are represented by Sj(j=L,T).The material,before initiation of damage will behave linear elastic during which the stress-strain can be related as ｛σ｝ =[C]｛εε｝ where [C]is the elasticity matrix which changes to damage elasticity matrix [Cd]once the damage is initiated.The damage elasticity matrix is defined as in Eq.(9) below

Table 1 Material properties of jute and natural rubber (NR) [56,57].

Fig.4.Mesh convergence plot for different mesh size (Thickness of compliant composite block = 120 mm).

3.Results and discussions

3.1.Penetration behaviour

The penetration behaviour of the projectiles of different shapes and the effect of thickness of the proposed flexible composite blocks are presented in Fig.5.It can be seen from the extent of damage the projectile has created in the proposed flexible composite blocks that the blocks with thickness of 30 mm and 60 mm does not restrict the penetration of projectile of any shape considered in the present study.Thus the blocks of thickness 30 mm and 60 mm are found to be not suitable for ballistic impact applications at the impact velocity considered.The blocks with 90 mm and 120 mm thickness restricts the penetration of all three types of projectiles considered.However,the extent of penetration of the projectiles vary.It can be seen that the ogival projectile induces damage up to the last layer in the proposed flexible composite block of 90 mm thickness.But.this is not the case with projectile with flat and hemispherical shapes.Thus it is conclusive that,if the projectile is ogival,then the flexible composite block of 90 mm is not safe to be used.

It can be seen that when the thickness of the proposed flexible composite blocks are increased to 120 mm,all the three projectiles considered are completely arrested by the target and hence the shape of the projectile determines the resistance of proposed flexible composite block.Along with this,the extent of penetration as shown in Fig.6 for any of the projectile considered in the present study shows that the thickness of the target is another factor that influences the damage resistance of the target.Hence,considering both the factors.it is conclusive that the proposed flexible composite block of 120 mm thickness is suitable for protection against high velocity impact considered in the present study.

3.2.Depth of penetration

The approximate depth of penetration of the different projectiles into the flexible composite of 60 mm,90 mm and 120 mm thickness are tabulated in Table 2.It can be seen that ogival projectile penetrates more into the proposed flexible composite bock followed by hemispherical and flat projectiles.This shows that the proposed flexible composite block is more and least prone to complete penetration when impacted by ogival shaped projectile and flat shaped projectile respectively.

From the application point of view a comparative study has been carried out between the present study and the experimental study carried out by Doddamani and Kulkarni [63]and presented in Table 3.

An experimental study carried out by Doddamani and Kulkarni[63]showed that the sandwich composite made of jute epoxy skin and functionally graded core having a total thickness of 120 mm can effectively restrict the bullet penetration impacting at velocity of 350 m/s.However,in the present study,it was able to achieve the complete penetration restriction with a compliant composite block of 90 mm in case of flat and hemispherical projectile and 120 mm in case of ogival projectile with an impact velocity of 400 m/s,which is higher than the impact velocity considered in the study carried out by Doddamani and Kulkarni [63]indicating that the proposedcompliant composite blocks exhibit better penetration resistance compared to conventional stiff composites.

Fig.5.Penetration behaviour of proposed flexible composite of different thicknesses for different projectiles.

Fig.5.(continued).

Fig.5.(continued).

Fig.5.(continued).

3.3.Taguchi method

Taguchi’s L9 orthogonal array is used to predict the effect of projectile shape and thickness of the proposed flexible composite block on the percentage of penetration depth.The factors and levels used are tabulated in Table 4.

Fig.7 shows the effect of projectile shape and thickness on percentage of penetration depth in terms of signal to noise (SN)ratio.It can be observed that the thickness has significant effect on the response compared to projectile shape.The SN ratios are calculated with “Smaller the better” criteria using Eq.(10).

Where.where ‘y’ is the responses for the given factor level combination and ‘n’ is the number of responses in the factor level combination.

Since the percentage of penetration depth is smaller the better type characteristics.projectile with flat shape (Level 1) and a flexible composite block of thickness 120 mm (Level 3) results in minimal percentage of penetration depth which indicates higher resistance to damage.Where.Delta is the difference of maximum value and minimum value of SN ratio.

The response for SN ratios for percentage of penetration depth provided in Table 5 shows that thickness is the significant factor influencing the percentage of penetration depth (damage resistance) in case of proposed flexible composite blocks subjected to high velocity impact.

ANOVA provides the quantitative results of the present analysis and is tabulated in Table 6.It can be observed from the ANOVA analysis that thickness has highest F value indicating that thickness is the significant factor influencing percentage of penetration depth compared to projectile shape.This is supported by the percentage contribution values.When 95% confidence level is considered(p ＜0.05).it is found that percentage of penetration depth is affected by thickness.

Fig.6.Extent of projectile penetration in flexible composite of (a) 90 mm and (b) 120 mm thickness for different projectiles considered.

Table 2 Details of penetration depth of projectiles.

The regression equation for percentage of penetration depth obtained statistically is shown in Eq.(11).

The contour plot for the present analysis is presented in Fig.8.It is evident from the contour plot that percentage of penetration depth is maximum at Level 1(60 mm)and least at Level 3(120 mm)of thickness.This means that as the thickness of the proposed flexible composite block increases.the resistance to damage is enhanced and the projectile is arrested within the block.

Table 3 Comparison of thickness of composite for complete restriction of projectile penetration.

Table 4 Factors and levels used for Taguchi analysis.

Table 5 Response table for SN ratios.

Table 6 ANOVA analysis.

Fig.7.Main effect plot for SN ratio.

4.Conclusions

Fig.8.Contour plot of percentage of penetration depth v/s projectile shape and thickness.

The FE analysis has been carried out in the present study to propose conceptual proof of jute-rubber based flexible composite block of optimal thickness to arrest the penetration of projectiles of different shapes.Taguchi’s DOE is carried out to find the effect of thickness and projectile shape on the penetration depth of the projectile which indicates the damage resistance of the proposed flexible composite block.Following are the conclusions drawn from the study:

· A conceptual proof of flexible composite blocks for ballistic impact application within impact velocity of 400 m/s is successfully proposed.

· The proposed flexible composites with thickness of 30 mm and 60 mm are found to be not suitable for ballistic protection from the projectiles of any shape since they allow complete penetration of the projectile through the thickness of the block.

· The penetration of the projectiles of all the shapes considered in the present study is completely arrested by proposed flexible composite blocks of thickness 90 mm and 120 mm.However,in case of ogival shaped projectile.it is found that the damage propagates till the last layer of the composite and hence block of 90 mm is not considered to be safe for ballistic impact applications.

· It is found that with increase in thickness,the damage resistance of the proposed flexible composite block is enhanced and a block of 120 mm thickness is considered to be safe from all aspects for ballistic impact application within impact velocity of 400 m/s.

· Among the different shapes of projectiles considered in the present study.it is found that ogival projectile causes more damage leading to maximum penetration inside the proposed flexible composite blocks followed by hemispherical and flat shaped projectiles.

· Statistical analysis carried out using Taguchi method (DOE)shows that thickness is the major factor influencing the percentage of penetration depth in the proposed flexible composite block compared to projectile shapes.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.