Damage mechanics and energy absorption capabilities of natural fiber reinforced elastomeric based bio composite for sacrificial structural applications

Vishwas Mahesh.Sharnappa Joladarashi.Satyabodh M.Kulkarni

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

Keywords: Flexible composite Ballistic impact Energy absorbed Rubber Damage mechanism

ABSTRACT The present study deals with the experimental.finite element (FE) and analytical assessment of low ballistic impact response of proposed flexible ‘green’composite make use of naturally available jute and rubber as the constituents of the composite with stacking sequences namely jute/rubber/jute (JRJ).jute/rubber/rubber/jute (JRRJ) and jute/rubber/jute/rubber/jute (JRJRJ).Ballistic impact tests were carried out by firing a conical projectile using a gas gun apparatus at lower range of ballistic impact regime.The ballistic impact response of the proposed flexible composites are assesses based on energy absorption and damage mechanism.Results revealed that inclusion of natural rubber aids in better energy absorption and mitigating the failure of the proposed composite.Among the three different stacking sequences of flexible composites considered.JRJRJ provides better ballistic performance compared to its counterparts.The damage study reveals that the main mechanism of failure involved in flexible composites is matrix tearing as opposed to matrix cracking in stiff composites indicating that the proposed flexible composites are free from catastrophic failure.Results obtained from experimental.FE and analytical approach pertaining to energy absorption and damage mechanism agree well with each other.The proposed flexible composites due to their exhibited energy absorption capabilities and damage mechanism are best suited as claddings for structural application subjected to impact with an aim of protecting the main structural component from being failed catastrophically.

1.Introduction

Composites used in various engineering applications are prone to different types of impact loadings such as: low velocity impact(below 10 m/s).intermediate impacts (10 m/s to 50 m/s).high velocity impacts (50 m/s to 1000 m/s) and hypervelocity impacts(2 km/s to 5 km/s)[1].Also,within the high-velocity impact regime,the velocities within 350 m/s are classified as low ballistic velocities and velocities greater than 350 m/s are classified as high ballistic velocities [2].High-velocity impact is one of the most adverse loading conditions that any composite structure might be subjected to.and in such structures.the fundamental importance lies in the selection of an appropriate material.The most demanding requirement in the field of high-velocity impact engineering is to combine the requirements of protection.mobility and efficiency.Polymer matrix composites (PMCs) are being extensively used in protective structures owing to their lightweight coupled with the enhanced performance [3,4].From the PMCs point of view.many synthetic fibers such as glass.kevlar and carbon are extensively used in high-velocity impact applications to provide protection against high-velocity impact threats and out of these.Kevlar is popularly used fiber [5-8].However.these synthetic fibers have some disadvantages such as high cost and environmentally nonfriendly which makes the engineers and designers look for an alternative.Natural fibers have emerged as substitutes for the synthetic fibers overcoming their limitations and possessing acceptable mechanical,thermal and chemical properties.Industrial crops which grow in abundance serve as the primary source of natural fibers and thus give a large scope for using the natural fibers in place of synthetic fibers.In engineering applications,apart from primary structures.there are also secondary structures that areeither used to support the primary structures or protect the primary structures.Sacrificial structures such as cladding belong to such class and used to protect the primary structure by cannibalizing itself.It is thus not essential to have very strong mechanical properties in such sacrificial structures.Natural fibers are potential replacements for synthetic fibers in such sacrificial structural applications [9,10].Among the various natural fibers available.jute emerges as the most promising natural fiber due to its better thermo-mechanical properties.economy and availability.Hence,there is a wide scope for using the jute reinforced composites in various engineering applications [11].out of which high-velocity impact applications are one.

Prior to using the PMCs in any high-velocity impact applications,it is very much essential to study their damage tolerance characteristics and high-velocity impact resistance [12].Sacrificial structures which are used to protect the primary structures from impact loading must be capable of absorbing maximum energy and prevent catastrophic failure.To enable this.flexible materials are widely used by designers and engineers [13-15].The energyabsorbing behavior of flexible materials is extensively studied using experimental and analytical techniques by various researchers[16-18].From the viewpoint of transfer of energy.various mechanisms are involved during the kinetic energy dissipation of the projectile when the projectile impacts a fabric.Some of such mechanisms include deformation of fabric.yarn tension.frictional slip and yarn pull out[19-21].The mechanism that dominates the impact process is dependent on various factors such as yarns properties [22,23].projectile shape [24,25]and boundary conditions [26-28].

Numerous efforts have been made by many researchers to produce a sandwich composite capable of absorbing maximum energy.For better energy absorption,nondangerous deceleration in the structure has to be obtained by the sandwich composites [29].In an attempt to enhance the energy absorption capability of the composites various approaches such as modification in the geometry of the core and its sequence of layup have been tried by various researchers[30-37].

It is possible to obtain different impact responses of the PMCs when the fabric is reinforced with different types of matrix and thus the energy absorption and the nature of damage of PMCs when subjected to impact loading depends on the type of matrix used [38].Vieille et al.[39,40]studied various PMCs subjected to impact loading.the outcome of which led to the selection of carbon/epoxy-based PMC with the highest energy dissipation ratio when compared to carbon/PPS composite.However.the study revealed that the energy dissipation capability of carbon/PPS is almost the same as that of carbon/epoxy composite.Lee et al.[12]studied the energy absorption behavior of stiff and flexible composites whose outcome showed that energy is better absorbed by stiff composites rather than flexible composites.However.the studies carried out by Gopinath et al.[41]and Wang et al.[42]proved that energy absorption ability is better in flexible composites coupled with larger deformation in comparison with stiff composites.The study carried out by Wang et al.[42]makes it clear that the resistance against the impact of the PMCs depends on the matrix type used.

Concerned to the damage mechanism of the PMCs.various researchers have put their effort to understand the role of type of matrices including both thermoset(TS)[43-48]and thermoplastic(TP)[39,49-55]and concluded that using TP matrix in PMC results in minimal damage compared to the PMC making use of TS matrix[49].Glass fiber reinforces TP based PMC results in enhanced impact force and energy absorption compared to the same fiberreinforced TS based PMC [53].In order to achieve the required impact response of the PMCs.an appropriate selection of both matrix and reinforcement is essential.

Different approaches such as experimental.analytical and numerical studies have been adopted by many researchers to analyze the impact response of conventional stiff composites [56-59].Many researchers have come with efficient methods for fracture and impact modeling.A simple and robust three-dimensional cracking particle method without enrichment was proposed by Rabczuk et al.[60]for various static and dynamic problems which proved to be nearly comparable with the experimental data with mesh refinement at the crack region.This method was able to capture the failure mechanism in static and dynamic conditions.However.this method could not get the convergent result especially for higher dynamic events.A simplified meshfree method for arbitrarily evolving cracks was studied by Rabczuk and Belytschko[61].This approach is simpler than the methods based on level sets or other explicit crack representations for complex patterns of fracture and at the same time limits the accuracy of the method.A three-dimensional large deformation meshfree method for arbitrary evolving cracks was studied by Rabczuk and Belytschko [62]which proves to be useful for analysis of materials with larger deformations and also suitable for impact problems.Pertaining to fracture modeling in composites,a phase-field approach is adopted to model a fracture in the matrix and interface of polymeric nanocomposite by Msekh et al.[63].A computational library for multiscale modeling of material failure was presented by Talebi et al.[64]through open-source software framework called PERMIX.

There are various factors such as reinforcement and its structure used in the composite.thickness and stacking sequence of the lamina to get the laminates coupled with the shape of the projectile are responsible for achieving the different impact responses of the composites [18,65,66].Despite the fact that conventional stiff composites are capable of producing curious mechanical properties.their rigidity and firmness affect their impact properties adversely.This has raised the need for using flexible matrices in composites where stiffness is not a concern.

Naturally.there are several elastic materials available out of which natural rubber (NR) is the most promising and widely used material in several engineering applications and has the potential to be used as a matrix in place of TS in composites.Several studies have been carried out by researchers [18,38,67-74]where it has been effectively demonstrated that usage of rubber in different forms as one of the constituents of composite results in enhanced impact response of the composites.

To date.researchers have concentrated on the study of stiff PMCs for high-velocity impact applications and flexible fabric composites for body armor applications at high ballistic impact velocities.As far as the author’s knowledge is concerned the use of completely green composite comprising of jute and NR for use as the sacrificial structural application with an aim of eliminating the catastrophic failure when subjected to low ballistic impacts remains an untouched area.Also.the available literature focused on the combination of experimental approach combined with either FE or analytical approach.However.no literature is found concentrating on all three approaches together.Thus,the present work is aimed at studying the low ballistic impact response of such a flexible ‘green’ composite comprising of naturally available jute fiber and NR as the constituents of the composite using the experimental.FE and analytical approach.

2.Experimental.FE modeling and analytical formulation

2.1.Materials and manufacturing

The reinforcement used to fabricate the flexible composites is naturally available jute fiber in the form of woven fabric with adensity of 1450 kg/m3and areal density of 350 g/m2.NR sheets are interleaved and rubber-based flexible matrix (‘B’ stage cured prepegs) are used in the fabrication of the proposed flexible ‘green’composite.The constituents used in the preparation of the composites are shown in Fig.1.

Proposed flexible green composites with different stacking sequences namely JRJ.JRRJ and JRJRJ are fabricated using a compression molding technique with the application of temperature (138°C) and pressure (25 kg/cm2).The desired stacking sequences are obtained by initially placing the layers of jute and natural rubber sheet in the desired order with rubber-based matrix in between each layer.The arrangement is placed in between two plates smeared with high-pressure vacuum grease and compressed in a compression molding machine as shown in Fig.2 by maintaining the desired temperature for 7 min.

The obtained laminates after curing are cut into a 300 mm × 300 mm dimension as shown in Fig.3 with their schematic representation shown in Fig.4.Table 1 provides the necessary information pertaining to the flexible composites used in the present study.

The properties of jute fibers provided by the supplier are provided in Table 2 and that of natural rubber and natural rubber based bonding gum (B stage cured pre peg) in Table 3.

2.2.High-velocity impact testing and setup

High-velocity impact tests were carried out using a gas gun apparatus in the lower range of high-velocity impact regime at 50-120 m/s.The impact velocity of the projectile was measured by means of light-emitting diodes(LED)placed at the point where the projectile leaves the barrel and the residual velocity was measured by means of a chronograph placed immediately after the target.The specimen of size 300 mm × 300 mm was clamped firmly to the fixture and the conical-shaped projectile with a diameter of 12 mm,conical nose angle of 34°,length of 40 mm and mass of 10 gms was used to impact the target.Fig.5 shows the gas gun arrangement and Fig.6 shows the specimen clamped to the fixture and the projectile used to carry out high-velocity impact test.

The energy absorbed by the target is calculated using Eq.(1)

where,Eais the energy absorbed by the target in J,mpis the mass of the projectile in Kgs,viand vrare the impact and residual velocities in m/s.At the ballistic limit.energy absorption is calculated using Eq.(2).Further,the energy absorption percentage(E%)is calculated using Eq.(3).

Fig.2.Flexible green composite fabrication using a compression molding machine.

where.Eiis the impact energy given by Eq.(4)

2.3.Modeling and simulation

The FE simulation is carried out using commercially available FE ABAQUS 6.14/Explicit software.The flexible composites of different proposed configurations and the projectile are modeled and analyzed according to experimental conditions.The proposed flexible composite is modeled as flexible material.projectile as a rigid material.Corresponding material properties are assigned tothe composite plates and mass is assigned to the projectile.The dimensions of the laminates and the projectile are maintained the same as used in experimental conditions.Jute and rubber plates are modeled separately and then assembled together.To maintain the proper interaction among the jute and rubber plates,the surface to surface contact is defined.The boundary condition is applied such that all the four sides of the laminate are restricted for their linear and rotational movement and the projectile movement is allowed in only one direction.The reference point is defined for the projectile at which the velocity is provided.The free mesh is applied for both the laminates and the projectile.Before the actual FE study is carried out,a mesh convergence study is performed on the similar grounds as studied by Ansari and Chakrabarti[75,76],Husain et al.[77]for ballistic impact studies and it was found that a mesh division of 40 × 40 showed good convergence as shown in Fig.7.Thus,the same has been used in the actual FE study.

Fig.1.Constituents of proposed flexible green composite.

Fig.3.Fabricated flexible green composite laminates of different stacking sequences.

Fig.4.Schematic of the proposed flexible composite.

Table 1 Stacking sequence and their designation.

Table 2 Properties of jute fiber.

Table 3 Properties of natural rubber and natural rubber based matrix (B stage cured pre pegs).

The model modeled using the FE method is shown in Fig.8.The number of elements used and the element types used are presented in Table 4.

The properties of the constituent materials are determinedexperimentally and used for FE analysis is presented in Table 5.

Fig.5.Gas gun arrangement used to carry out high-velocity impact test.

Fig.6.(a) Specimen clamped in a fixture and (b) projectile.

Fig.7.Mesh convergence plot for different mesh division (Vi = 80 m/s).

2.4.Analytical formulation

In order to predict the energy absorbed.residual velocity and ballistic limit of the proposed flexible composites.an analyticalmodel based on the simple law of conservation of energy is proposed.The damage mechanisms occurring in the composites are identified and based on that.the analytical formulation is developed in order to predict the energy absorbed.The residual velocity of the projectile is determined based on the concept of the total energy absorbed by the damaged plate is equal to the reduction in kinetic energy of the projectile.The ballistic limit of the composite is obtained when total energy absorbed by the damaged plate equals the projectile’s initial kinetic energy.

Fig.8.Modeling of proposed flexible composite laminates and projectile.

Table 4 Type of elements and number of elements used in composite plate and projectile.

Table 5 Material properties used in FE analysis.

The fibers below the projectile are known as primary yarns and those away from the projectile as known as secondary yarns.Cone is formed on the back face of the composite as shown in Fig.9.

Following assumptions are made for the development of the analytical model:

1.Compared to total energy absorbed,the energy absorbed due to deformation of the projectile is negligible.

2.The loss of energy due to the result of friction between projectile and plate is negligible.

3.The material properties of the constituents used remain the same throughout.

4.Strain rate remains the same during perforation.

5.The projectile remains rigid and nondeformable throughout the impact process.

6.The motion of the projectile remains uniform during penetration.

At the start of an impact event.the initial kinetic energy of the projectile is represented by Eq.(5)

where,mpis the mass of the projectile and viis the initial velocity.The kinetic energy of the projectile will be absorbed by the composite laminate as it undergoes failure by different modes and thus the velocity of the projectile reduces to vr.Thus.according to the law of conservation of energy.we get Eq.(6).

where,Eais the total energy absorbed by various failure modes and kinetic energy of moving cone.

During an impact event,the elastic and plastic waves propagate outwards from the poi nt of impactand thevelocity of elastic (Ce)and plastic wavepropagationis given by Eq.(7) and Eq.(8)respectively.

As the wavelets of strain pass through a particular point of the yarn.there is an inward flow of the material towards the point of impact and transverse waves are developed whose velocity is given by Eq.(9)

The final radius of the cone formed depends on the starting timeof the impact to yarn breakage or stoppage of the projectile and is given by Eq.(10).

Fig.9.Cone formation at the back face of the target.

As the projectile strikes the proposed flexible composite laminate during an impact event,the kinetic energy of the projectile is converted into energy absorption of the proposed flexible composite laminate by various damage mechanisms.In the proposed flexible composites laminates.the following damage mechanisms are identified:

· Tensile failure of primary yarns

· Elastic deformation of secondary yarns

· Matrix/Interleaved NR tearing

Consider a primary yarn under tensile loading.Strain at distance‘x’ from the point of impact is given by ε(x).The strain variation is given by Eq.(11).

where,ε0is the strain at the point of impact;b is a magnitude less than 1;x is the distance and a is the yarn size.Energy absorbed can be represented by Eq.(12)

During an impact event,the fibers which come in direct contact with the projectile undergo elongation in tensile mode and then fail.The volume of such fibers is given by 4Rctd.The area of the composite laminate beneath projectile fails completely due to the tensile mode and the energy absorbed due to this mode is given byThe remaining volume of the primary fibers given byis under tension and experience plastic strain.!Thus energy absorbed by these yarns is given byThus,the energy absorption during tensile failure of primary yarns(ETF) is given by Eq.(13) [78].

where d: projectile diameter; t: laminate thickness; Ec: energy absorbed up to failure i.e.area under the stress-strain curve of the composite; Rc: Radius of cone-formed at back face of laminate; E:Young’s modulus of composite;εp:Plastic strain is given by Eq.(14)obtained on simplification of Eq.(15) [79].

where.viis impact velocity; C is the velocity of waves in the composite given by Eq.(16).

where ρ is the density of composite laminate.

All the other yarns except primary yarns are known as secondary yarns which do not directly come under the projectile.Such yarns undergo some elastic deformation and thereby absorbing some kinetic energy of the projectile.Assuming that within the secondary yarns,there is a linear variation of strain from plastic to zero,boundary conditions as in Eq.(17) are imposed.

where,εfis the failure strain of the composite.The variation of the strain can be expressed by Eq.(18).

The energy absorbed by the secondary yarns per unit volume is given by Eq.(19).

The total energy absorption by elastic deformation of secondary yarns (Eeds) is given by Eq.(20) [78].

The energy absorption by Matrix/Interleaved NR tearing mechanism (Et) is given by Eq.(21) [80].

where λ: critical tearing length where the steady tearing state has been reached.In most practical cases,λ can be taken as a width of tearing object or damage width.If steady-state is not reached.λ is equal to tearing length;σ0:flow stress of material given by Eq.(22)and vt: is the volume of torn material.

where,σy: yield stress and σu: is the ultimate tensile stress.

The total energy absorbed by the flexible composite laminate is the sum of energy absorption during tensile failure of primary yarns(ETF),energy absorption by elastic deformation of secondary yarns (Eeds) and energy absorption by Matrix/Interleaved NR tearing mechanism (Et).Thus.mathematically.it is represented as in Eq.(23).

where.EKEis the kinetic energy of moving projectile given by Eq.(24).

where.mc: the mass of moving cone during perforation given by Eq.(25) obtained after simplification of Eq.(24); viis the impact velocity.

According to the law of conservation of energy.the energy balance can be represented by Eq.(6).

On simplification of Eq.(6),the residual velocity is given by Eq.(26).

For the ballistic limit.the residual velocity of the projectile is zero.Thus.from Eq.(26).the equation for the ballistic limit is derived and presented as Eq.(27).

3.Results and discussion

The addition of the jute layer enhances the mechanical properties of the composite proposed when compared to pure rubber[81].Thus the inclusion of jute layers is justified.Also,since it was established that jute reinforced composites are better than pure rubber in terms of their mechanical properties,the ballistic impact study on pure rubber is eliminated for further studies.

3.1.Ballistic limit velocity

In order to determine the ballistic limit velocities of the proposed flexible composites a minimum of three highest partial penetration velocities and three minimum complete penetration velocities are used and their average provides the ballistic limit velocity of the particular target and projectile combination [82].This approach followed to determine the ballistic limit velocities experimentally and FE approach is in line with the approach followed by Khodadadi et al.[38].Analytically,the ballistic limits are calculated using Eq.(27).Thus obtained ballistic limit values are presented in Table 6.

The ballistic limit velocities of the flexible composites with stacking sequences JRJ.JRRJ and JRJRJ found experimentally as 63 m/s.83 m/s and 88 m/s respectively.It can be seen that the inclusion of an additional layer of rubber(JRJ to JRRJ)enhances the ballistic limit by 32%and the inclusion of an additional layer of jute(JRRJ to JRJRJ)enhances the ballistic limit by 6%.This shows that the rubber layer can significantly enhance the ballistic limit of the flexible composite compared to the jute layer.

The same trend is found in the case of the FE approach with ballistic limit velocities of 61 m/s.82 m/s and 85 m/s for JRJ.JRRJ and JRJRJ respectively.In the case of the analytical approach.the ballistic limits of proposed flexible composites are found to be 65 m/s,86 m/s and 92 m/s for JRJ,JRRJ and JRJRJ respectively which agrees well with the experimental and FE approach.

3.2.Residual velocity

The residual velocity of the projectile after impacting flexiblecomposites of different stacking sequences(JRJ,JRRJ,and JRJRJ)are obtained from chronograph placed immediately after the target in case of an experimental approach.In case of an analytical approach,Eq.(26) is made use of to determine the residual velocities.The residual velocities obtained for different stacking sequences at different impact velocities in all three approaches are tabulated in Table 7.

Table 6 Ballistic limits of proposed flexible composites.

It is evident from Table 7 that JRJRJ exhibits better lower ballistic impact performance followed by JRRJ and JRJ.It can be seen that at all the impact velocities considered in the present study.the residual velocity of JRJ is more compared to JRRJ and JRJRJ indicating that JRJ offers the least resistance to damage compared to JRRJ and JRJRJ.The viscous damping characteristics of rubber enable the flexible composites to absorb larger energy leading to a reduction in the projectile velocity.JRRJ and JRJRJ having two layers of rubber that provide better energy absorption and damage resistance behavior.Rubber being compliant material stretches to a larger extent resisting the projectile penetration.The variation in the residual velocity of the projectiles in experimental,FE and analytical studies are in agreement with each other.

3.3.Energy absorption

The energy absorption of the proposed flexible composites at ballistic limit velocities is calculated using Eq.(2) for all the approaches considering their respective ballistic limits and at other impact velocities.the energy absorbed is determined using Eq.(1)for experimental and FE approach;and Eqs.(6-25)for an analytical approach.The energy absorbed by the proposed flexible composites at their ballistic limits is tabulated in Table 8.Table 9 provides the energy absorption of the proposed flexible composites at impact velocities other than ballistic limit velocity.

It is found that the energy absorption by the flexible composites JRJ.JRRJ and JRJRJ at their respective ballistic limits in case of experimental study is found to be 19.84 J.34.44 J and 38.72 J respectively.The energy absorption of JRJRJ is more compared to JRJ and JRRJ by 95.16%and 12.42%respectively.The energy absorption of JRRJ is enhanced by 73.58%compared to JRJ.Further,in the case of FE and analytical study.a similar trend is observed and the results agree well with each other.This shows that an additional layer of rubber enhances the energy absorption of the flexible composite significantly compared to an additional layer of jute.

Further.the energy absorbed by the flexible composites is calculated for impact velocities of 80 m/s.100 m/s and 120 m/s considering the ballistic limits of the flexible composites to assess the behavior of the composites at enhanced velocities.The majority of the kinetic energy of the projectile during an impact event is absorbed by the primary yarns when the projectile strikes the fabric.Further.the secondary yarns are pulled by the transverse deflection of the primary yarns thereby assisting in the dissipation of the projectile’s kinetic energy.Primary yarns are pulled out significantly as they were directly impacted by the projectile.

In the proposed flexible composites,the elastic nature of rubber aids in better transfer of impact load from primary to secondary yarns which further enables the fabric in resisting and absorbing the kinetic energy of the projectile.Better and consistent fabric arrangement with an integrated and uniform coating of the fabric can be achieved by the rubber matrix.Rubberized matrix also eliminates sliding,extracting,windowing under impact loading.In addition.rubber being a material with good damping properties aids in better absorption of the projectile’s kinetic energy.

In the case of flexible composites,an increase in impact velocity leads to an increase in energy absorption attributing to higher strain rates where the response of rubber varies.During impact loading.the mechanical strain rate dominates the segmentaldynamics of rubber resulting in a changeover to glassy state and further failure leading to sufficiently great energy dissipation resulting in higher energy absorption by rubber at higher impact velocity.Thus.flexible composites absorb higher energy at higher impact velocity.

Table 7 Residual velocities of the proposed flexible composites at different impact velocities.

Table 8 Energy absorption at the ballistic limit.

Among the proposed flexible composites,the energy absorption in case of JRRJ and JRJRJ stacking sequences are same at an impact velocity of 80 m/s in case of experimental and FE approach due to the fact that both the stacking sequences arrest the penetration of the projectile at this impact velocity providing a zero residual velocity.In other words.both these stacking sequences absorb the kinetic energy of the projectile completely at an impact velocity of 80 m/s.In the case of an analytical approach.both JRRJ and JRJRJ provide a negligible amount of residual velocity resulting in energy absorption of 31.8 J and 31.9 J respectively.The deviation of the energy absorbed obtained from the analytical approach is negligible compared to the experimental and FE approach.

However.when the impact velocity is raised to 100 m/s and 120 m/s the JRJRJ absorbs better energy followed by JRRJ and JRJ.At an impact velocity of 80 m/s,the energy absorption of JRRJ and JRJRJ are equal and greater by 38% when compared to JRJ in case of experimental study and 29.13% in case of FE study.However.this increases drastically as the impact velocity increases.The energy absorption of JRJRJ is 76.93%and 77.83%more compared to JRJ at an impact velocity of 100 m/s and 120 m/s respectively for experimental study owing to the more amount of resistance offered by the rubber layers in JRJRJ compared to JRJ.A similar trend is observed for FE and analytical studies.

However.the increase in energy absorption of JRJRJ when compared to JRRJ at 100 m/s and 120 m/s is merely 14% and 9.5%respectively for experimental study,as both JRRJ and JRJRJ stacking sequences has equal amount of rubber layers and addition of one more layer of jute in JRJRJ compared to JRRJ contributes to the marginal increase in energy absorption capability of JRJRJ.FE and analytical approaches follow a similar trend.Considering all these comparisons,it can be said that a flexible composite with the JRJRJ stacking sequence is the better energy absorber in a lower ballistic impact regime.The energy absorption percentage is calculated using Eq.(3)and tabulated in Table 10 at impact velocities of 80 m/s,100 m/s and 120 m/s.

The energy absorption percentage of the flexible composites increases in the order JRJRJ ＞ JRRJ ＞ JRJ.In case of an experimental study.at an impact velocity of 80 m/s.the energy absorption percentage of JRJRJ and JRRJ is 38%more compared to JRJ.As the impact velocity increases to 100 m/s.JRJRJ absorbs 77% more energy compared to JRJ and 14% more energy compared to JRRJ.This increase in energy absorption of JRJRJ is found to be 77.85%and 9.5%more than JRJ and JRRJ respectively at an impact velocity of 120 m/s.The addition of a layer of rubber to JRJ results in JRRJ configuration which provides 55.16% and 62.39% more energy absorption percentage at 100 m/s and 120 m/s respectively compared to JRJ.However.adding a single layer of jute to JRRJ results in JRJRJ configuration which exhibits 14%and 9.5%more energy absorption percentage capability at 100 m/s and 120 m/s respectively compared to JRRJ.This behavior is due to the fact that JRRJ has an additional layer of rubber compared to JRJ which results in significant enhancement of energy absorption percentage compared to an addition of jute layer as in the case of JRRJ to JRJRJ.The same trend is followed for FE and analytical study.

It can be seen that the energy absorption percentage reduces with an increase in impact velocity and as the number of rubber layers increases.the energy absorption percentage increases drastically.This shows that the number of rubber layers plays animportant role in the energy absorption percentage.Thus it is evident that rubber plays a prominent role in deciding the energy absorption of the flexible composite and the role of jute when compared to rubber is negligible.

Table 9 Energy absorption at impact velocity of 80 m/s,100 m/s and 120 m/s.

Table 10 Energy absorption percentage of proposed flexible composites.

Thus.at the lower ballistic impact regime considered in the present study,JRJRJ emerges as a better energy absorber compared to its counterparts.This is due to the more number of rubber layers in combination with the intermediate jute layer and more rubberbased matrix used.

3.4.Specific energy absorption

Specific energy absorption(SEA)provides the energy absorption effectiveness of each stacking sequence of the flexible composite.SEA is calculated using Eq.(28).The areal density of the proposed flexible composites is calculated using Eq.(29) and tabulated in Table 11.The SEA of the proposed flexible composites is calculated using Eq.(28) and tabulated in Table 12 for ballistic impact velocities and in Table 13 for impact velocity of 80 m/s.100 m/s and 120 m/s.nearly the same energy absorption capability.This is due to the fact that the dual-layer of rubber provides more resistance for projectile penetration thereby converting the most of the kinetic energy of the projectile into the absorbed energy of the flexible composite.

Table 12 SEA of the proposed flexible composites at the ballistic limit velocity.

SEA of the considered flexible composite increases with an increase in impact velocity above the ballistic limit.Above the ballistic limit,SEA of the flexible composites follows a similar trend as observed at the ballistic limits (JRJRJ ＞ JRRJ ＞ JRJ).The reason remains the same as explained for SEA at ballistic limit velocity.A good agreement of the SEA values can be observed between experimental.FE and analytical approaches.

where,Eais energy absorbed in J and ρa(bǔ)is the areal density in Kg/m2.

where.ρ is the density of the composite in Kg/m3and t is the thickness of composite in m.

It can be seen that the SEA of the proposed flexible composites increases in the order JRJRJ ＞ JRRJ ＞ JRJ.The SEA of JRJRJ at the ballistic limit obtained experimentally is enhanced by 52%and 2.7%compared to JRJ and JRRJ respectively.The FE and analytical results follow the experimental trend with negligible variation in SEA of JRRJ and JRJRJ indicating that both these flexible composites exhibit

3.5.Study on damage mechanism

The schematic of the proposed damage mechanism in each layer of the flexible composite is represented in Fig.10 along with damages from the experiment visualized through SEM.It is proposed that at the layer containing jute,the damage is dominated by fiber breakage and the mechanism of fiber pull which is common in neat fabrics is eliminated in the jute layer of the flexible composite due to the adherence of the jute to the rubber which is compliant in nature.Whereas.at the layer containing rubber.the damage is dominated by tearing of the rubber where the resistive bands are generated due to compression of the rubber leading to maximum energy absorption and enhanced resistance to damage.

Table 11 The areal density of the flexible composite.

Table 13 SEA of the proposed flexible composites.

As the projectile strikes the front face of the flexible composite laminate,it encounters the jute layer which offers less resistance to the movement of the projectile and gets damaged through fiber breakage mode.As the projectile penetrates further.it encounters the rubber layer where maximum resistance is offered to the movement of the projectile due to their compliant nature.When the impact velocity is not sufficient to overcome the resistive forces induced by the proposed flexible composite.the movement of the projectile is arrested resulting in partial penetration.However,when the impact velocity overcomes the resistive forces.the complete penetration of projectile through the thickness of the proposed flexible composites takes place.The resistive forces are higher at the entry point of the rubber layer since the compliance offered due to the presence of a large amount of rubber and rubberbased matrix and this resistive force gradually reduces through the thickness of the rubber layer in the direction of impact as the tearing of rubber in the flexible composite takes place as shown in Fig.11.The above-described mechanism can be visualized from Fig.10 where it can be seen that at the point of entry of projectile the resistance offered by rubber to the movement of the projectile is more compared to exit.Due to this resistance offered,the rubber stretches along the direction of movement of the projectile up to the point where the velocity of the projectile overcomes the resistance offered by the rubber.

The proposed flexible composites exhibit remarkably highvelocity impact response due to the high damping characteristics of the rubber.Fig.12 shows the comparison of the damage mechanism involved in the proposed flexible composites at ballistic impact velocity and at impact velocities of 80 m/s.100 m/s and 120 m/s obtained through experimentation.The use of rubber matrix results in better attachment of the fabric and interleaving of NR provides better resistance against the movement of the projectile.It is also found that in the case of flexible composites.the main damage mechanisms involved are rubber tearing and fiber breakage.When the fabric reaches the maximum stress during an impact loading.the failure occurs through the fiber breakage mechanism which is shown at the point of impact of the projectile.Failure propagating further leads to tearing of rubber and rubber detachment in some cases.A clear distinction can be observed in the failure pattern of the proposed flexible composites at different impact velocities.At ballistic impact velocity,tearing of rubber and fiber breakage are the only patterns observed.However.as the impact velocity is increased lump formation of the torn out rubber is also observed in addition to tearing of rubber and fiber breakage.With further increase in the impact velocity,the rubber tearing and detachment of the rubber from the rear face of the flexible composite is observed.Thus it can be said that at lower impact velocity,rubber tearing is the only pattern that can be observed in the failed laminate and as the impact velocity increases,rubber tearing,lump formation and detachment are predominantly observed along with fiber breakage.The damage mechanisms explained above are exhibited by the scanning electron microscope images in Fig.13.

The damage mechanism involved in the proposed flexible composites for no complete penetration is shown in Fig.14.No complete penetration of the projectile through the proposed flexible composites results in complete kinetic energy absorption of the projectile by the flexible composites.The proposed flexible composites undergo bending and compression with subsequent shear on the entry side and bending and stretching on the exit side.The projectile penetrates the composite by tearing the rubber and fiber breakage.Further,as the projectile gets struck in the composite the pit formation as a result of bending and compression with subsequent shear can be observed at the front face of the composite.Whereas,at the rear face of the composite,tearing takes place due to bending and stretching.

4.Conclusions

The present study was conducted to investigate the highvelocity impact response of neat jute fabric and jute/natural rubber based flexible composite.Following conclusions are drawn from the present study:

· A novel flexible green composite making use of fully biodegradable materials has been successfully developed and the inclusion of rubber aids in better absorption of energy in the lower ballistic impact regime which also helps in mitigating the failure.

· It is found that the results obtained through experimental.FE and analytical approach pertaining to the lower ballistic impact response of the proposed flexible composites agrees well with each other and thus the proposed analytical approach is valid for lower ballistic impact assessment of such flexible composites.

· It is found that the inclusion of an additional layer of rubber(JRJ to JRRJ)enhances the ballistic limit by 32%and the inclusion of an additional layer of jute (JRRJ to JRJRJ) enhances the ballistic limit by 6%.This shows that the rubber layer can significantly affect the ballistic limit of the flexible composite compared to the jute layer.

· It is found that the residual velocity of JRJ is more compared to JRRJ and JRJRJ indicating that JRJ offers the least resistance to damage compared to JRRJ and JRJRJ.The viscous damping characteristics of rubber enable the flexible composites to absorb larger energy leading to a reduction in the projectile velocity.

· It is found that the energy absorption of the proposed flexible composites at their ballistic limits increases in the order JRJRJ ＞ JRRJ ＞ JRJ with JRJRJ absorbing 95.16% and 12.42% more energy compared to JRJ and JRRJ.The energy absorption of JRRJ is enhanced by 73.58% compared to JRJ.

Fig.10.Proposed damage mechanism represented (a) Schematically; (b) FE simulation and (c) Experimentally.

· The extended energy absorption study of the proposed flexible composites reveals that energy absorption of JRJRJ and JRRJ is greater by 38% when compared to JRJ at an impact velocity of 80 m/s and this increases as the impact velocity increases with JRJRJ absorbing 76.93% and 77.83% more compared to JRJ at impact velocity of 100 m/s and 120 m/s respectively and 14%and 9.5%respectively compared to JRRJ at impact velocity of 100 m/s and 120 m/s respectively.

Fig.11.Schematic of damage resistance distribution in flexible composite.

· The energy absorption percentage of the flexible composites increases in the order JRJRJ ＞ JRRJ ＞ JRJ and as it is found that as the impact velocity increases,the energy absorption percentage reduces.An increase in energy absorption percentage is more from JRJ to JRRJ when compared with JRRJ to JRJRJ due to the fact that JRRJ has an additional layer of rubber compared to JRJ which results in significant enhancement of energy absorption percentage compared to an addition of jute layer as in case of JRRJ to JRJRJ.

· It is found that the SEA of the proposed flexible composites at ballistic limit increases in the order JRJRJ ＞ JRRJ ＞ JRJ with SEA of JRJRJ being enhanced by 52%and 2.7%compared to JRJ and JRRJ respectively.This indicates that JRJRJ is a better energy absorber compared to its counterparts.

Fig.12.Damage mechanism of flexible composites at (a) ballistic limit; (b) 80 m/s; (c) 100 m/s and (d) 120 m/s.

Fig.13.SEM images exhibiting the damage mechanism involved.

Fig.14.Damage mechanism of flexible composites for no complete penetration.

· A damage mechanism is proposed for the flexible composite from which it is found that the rubber layer offers more resistance to the penetration of the projectile through it resulting in higher energy absorption and resistance to damage.It also leads to the elimination of fiber pull out which is found in the case of neat jute fabric.The damage patterns obtained in proposed flexible composites using the experimental and FE simulation approach matches well with each other and are validated.

· The damage mechanism study pertaining to flexible composites reveals that the proposed flexible composites offer higherresistance to the movement of the projectile at the initial stage of impact event compared to a later stage.The presence of rubber layers and the rubber-based matrix offers resistance to the movement of the projectile due to their compliant nature leading to better energy absorption and reduced damage leading to tearing of matrix as opposed to matrix cracking in conventional stiff composites and thus eliminating catastrophic failure which is the major concern in composites subjected to impact.Thus the proposed flexible composite can be a potential material for secondary sacrificial structural applications such as claddings which are used to protect the primary structural components.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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.