Low-velocity impact behaviors of sandwich composites with different structural configurations of foam core: numerical study and experimental validation

Sandwich composites have very weak properties as well as superior properties. Damages will be invisible and may create huge problems due to the high strength difference of composite components. To investigate sandwich composites, numerical studies’ importance is so high because experimental studies require high labor and are time-consuming. In this study, low-velocity impact properties of the configurations of sandwich composites with E-glass fiber/epoxy and PVC foam core are investigated numerically, and the results are compared with experimental results. Reference sandwich composite, and four different types of configurations are modeled with homogenized properties. Numerical simulations are performed using the material models of rigid impactor, foam core, and composite material models of LS-DYNA software. Numerical and experimental results of these sandwich composites are compared in terms of contact force-time and contact force-displacement curves, core/facesheet debonding areas, peak contact forces, absorbed energy, maximum displacement, and contact time; a good agreement is obtained.


Introduction
Sandwich composites subjected to low-velocity impact have been examined experimentally, analytically, and via numerical methods.Because of the high strength difference between the facesheet and core material, sandwich composites are very susceptible to impact loading.Thus, there have been studies about the failure mechanisms of sandwich composites, the response of the structure, and contact analysis between the impactor and the sandwich composite.The through-thickness reinforcements like stitching, 3D weaving, tufting, and z-pinning had an important role in decreasing core-facesheet debonding in the sandwich composites [1][2][3][4][5].
In some studies, different core materials are compared experimentally and numerically.The low-velocity impact tests were applied to sandwich structures including bonding foams of different densities and good agreement with the FE model and experimental data was observed, and perforation resistance increased by using cores with different densities [6,7].The perforation resistance of plain foams and their sandwich composites were investigated.The numerically obtained results were in good agreement with the experimental results [8].The dynamic response of the foam core sandwich panel was investigated by the analytical model, and the predictions of low-velocity impact results were compared.A reasonable correlation was obtained for the impact damage and energy absorption [9].
The impact behavior of composite materials and the through-thickness reinforcement effect were investigated by some studies.Composites containing glass fiber and epoxy resin were used because of their high impact performance.The effects of impactor mass and impactor velocity were both examined experimentally and numerically in laminated composites.It was found that the high mass impact causes a high delamination area at the same energy level [10].The stitched laminated composites were tested by tensile, bending, and lowvelocity impact tests.The obtained results showed that the stitching process increased the mechanical properties of the laminated composites.By using the stitching process, the resistance of the bonding area in composites could be increased.Thus, stitching parameters; angle of insertion, cord diameter, number of the stitching line, and distance were examined numerically, and optimum parameters were defined [11,12].
Through-thickness reinforcements are not only applied to the laminated composites but also applied to sandwich composites under investigation through different types of tests.Sandwich composite joints were compared experimentally and analytically.A numerical analysis is carried out on stitched sandwich composites.The homogenized mechanical properties were used and the results showed that stresses and displacements could be decreased by stitching [13].Compression after impact test was applied to stitched sandwich composites experimentally and numerically; in densely stitched specimens, impact damage decreased, while stiffness and strength increased [14].Out-of-plane shear and compression properties of sandwich composites were investigated numerically.The stitching angle and stitching step were investigated and the obtained results were in good correlation [15].The effect of shear keys in sandwich composites was investigated under in-plane compression.Sandwich composites were made from E-glass/epoxy and PVC foam core materials.Experimental and numerical results showed that core/facesheet debonding resistance increased [16].Debonding of stitched sandwich composites was investigated.Stitched foam core was defined as homogenized material analytically.Analytical results were compared with the experimental study [17].
As seen in examined previous studies; core stitched sandwich composites and facesheet stitched sandwich composites were not studied before.In this study core stitched and facesheet stitched sandwich composites were compared, numerically.The results of the previous experimental study by the authors [18] were used to compare numerically as a continuation of the study.Additional compression and fracture toughness tests were applied experimentally.These results were used as input for numerical analysis.The sandwich composite was modeled using a continuum damage mechanic composite material model and crushable foam model in LS-DYNA software.Impact experiments was applied 70 J impact energy which was obtained with a hemispherical nose had 4.92 kg and impactor velocity of 5.34 m s −1 .The impact energy was chosen as the energy in which all configurations were perforated.Experimentally and numerically obtained results were plotted with contact force-time and contact force-displacement data.Core/facesheet debonding areas were analyzed by ImageJ program.Absorbed energy, peak contact forces, maximum displacement, and contact time were compared in the tables both experimentally and numerically.

Experimental method
Sandwich composites with different structural configurations of foam core were manufactured [18] and specimen properties are given in table 1.In this table; 'C20' means 'plain core with 20 mm thickness', 'ecC10' means '10 mm thick core material with epoxy columns' and 'st' means 'stitched'.The specimens were manufactured with a vacuum infusion process.Before resin infusion core materials were drilled and 2Scs coded specimens were stitched with two cores and a middle sheet.2Sfs coded specimens were stitched with a top facesheet, middle sheet, bottom facesheet, and two-core all together.The stitching thread was 2400 Tex.Tests were repeated three times to obtain the average and standard deviation values.Alongside the facesheet material, the mechanical properties of the specimen are given in table 2 [19].To obtain compressive properties and stress- strain curves, out-of-plane compression tests were applied where the specimen had facesheet dimensions of 50 mm × 50 mm and the thickness of the structure was about 23 mm.The test was performed with a Shimadzu AG-X Plus 100 kN universal testing machine with a strain rate of 0.25 s −1 .For use in numerical analysis, the specimens were almost completely compressed by the load capacity of the testing machine.Figure 1 shows the universal testing machine with compression plates.
Two different tests were conducted to determine the fracture toughness values of sandwich composites.The specimen preparation, calculations, and evaluations of these tests were made [12,15,20,21].For these tests, appropriate pretreatments were required for the samples.For mode I fracture, an initial crack was created in the specimen and a hinge was attached to the specimen to properly apply the load.The bolted connection was made because the adhesive bonding was separated in the trial tests.Specimens for testing were prepared in dimensions of 25 mm × 150 mm.The test speed was selected as 0.5 mm min −1 [12].In figure 2, the close view of the SCB (single cantilever beam) specimen can be seen from the fixed lower and movable crosshead.Mode I fracture toughness was found using equation (1).2. Mechanical properties of E-glass fiber/epoxy [19].Here, P is the applied load to the specimen by the device, δ is the displacement, b is the width, and a is the crack length at the time of testing.As can be seen in the test setup given in figure 3, for the mode II fracture, firstly, the part that is equal to the thickness of the bottom shell and core material was placed under the left part of the three-point bending test apparatus.25 mm of the lower shell and core material were removed from the left side of the specimen and, an initial crack was formed.Progresses in a crack, opening, and sliding modes in SLB (single leg bend) specimen, the fracture toughness value calculated using equations (2) and (3) was mixed mode value.There was both an opening and shear compound in the calculated total energy.The Mode II value was found by subtracting the value from equation (1) from the value obtained from equations (2) and (3) [20].
Here, P is the applied load to the specimen by the device, δ is the displacement, b is the width, and a is the crack length.D and D S factors of the Equations detailed information is given in Shah and Tarfaoui study [20].

Numerical method
LS-PrePost can be used for pre and post-processor which is provided by LS-DYNA.The structure was modeled, material models, and analysis parameters were defined using pre-processing.The results were evaluated using a post-processor.The modeled sandwich composite structure is given in figure 4. As in the experimental study, numerical impactor diameter and mass were defined as 12.7 mm, and 4.92 kg, respectively.The boundary conditions were defined in the numerical study as the same as in the experimental study.In numerical sandwich composite parts, stiffness-based hourglass control was defined.Hourglass energy should not exceed 10% of the peak internal energy [22,23].Hourglass energy was obtained below 1% of the peak internal energy.To define the impactor and sandwich composite interaction, the contact model 'Contact_ Automatic_ Surface_ to_ Surface' was used [24].The material model for facesheet material, facesheet thickness, and fiber orientations in facesheet was defined in the 'Part_Composite' definition.'MAT020-Rigid' material model was used for modeling the impactor which has steel properties.These were Poisson's ratio of 0.3, and elasticity modulus of 200 GPa.The same material model was also used for the lower and upper supports.Boundary conditions were defined in this material model for the impactor to move only through the vertical axis direction.The density of the modeled impactor was increased so that the weight of the modeled impactor with the impactor used in the experimental study was the same.The friction between the impactor and sandwich composite structure was neglected.The data were obtained from impactor in both experimental study and numerical analysis.MAT063 Crushable_Foam material model was used for crushable foams.The model was one-dimensional because Poisson's ratio was assumed zero.The modulus of elasticity was constant [25,26].
Tensile fiber failure (mode I): σ 11 0; Compressive fiber failure (mode II): σ 11 < 0; Tensile matrix failure (mode III): Compressive matrix failure (mode IV): are the tensile stress in the fiber direction, tensile stress in the transverse direction, in-plane shear stress, tensile strength in the fiber direction, compression strength in the fiber direction, tensile strength in the transverse direction, compression strength in the transverse direction, and inplane shear strength, respectively.
In 'MAT058-Laminated_Composite_Fabric', ERODS is the parameter that controls damage.When the effective strain reaches the maximum value, the element is erased.At the same time, this model uses stress limit factors.These factors limit stresses to an exact value.Thereby, in this factor using equation (8), the stress value remains at maximum, as a result, the model behaves like an elastoplastic.SLIMCx, and SLIMS are recommended as 1.0 [26].SLIMCx: 1.0, SLIMS: 1.0, SLIMTx: 0.5, and ERODS: 0.4 were used for the facesheet material used in this study.Delamination is a very important damage mechanism for composite materials.Delamination occurs due to high interlaminar stresses.Composite material generally has low through-thickness properties.Delamination damage can be caused by; out-of-plane loads, curved shapes, cracks, resin-rich regions, or free edges.The CZM (Cohesive Zone Model) model defines the separation of cracked surfaces at a crack tip or cohesive interface.This definition can be made using cohesive interface elements and a 'tiebreak' connection in LS-DYNA [28].For the delamination modeling of sandwich composite specimens, Automatic_One_Way_Surface_to_Surface_Tiebreak' connection model was used between the facesheet and core materials.There are different options in the tiebreak connection type to model delamination in LS-DYNA.When a critical crack opening reaches the maximum value, the nodes of the tiebreak contact definition are released, and the tiebreak contact definition is deleted.After the software converts the contact definition to 'surface_to_surface' for these nodes that prevents interpenetration of the elements [23].Option 9 was used in the 'Automatic_One_Way_Surface_to_Surface_-Tiebreak' connection model for the analysis of the debonding between the facesheet, and core in sandwich composites.This model includes mixed-mode debonding criteria and a damage formulation [26,28].In this study, the simplified numerical model was used therefore configurations were assumed their effects homogenous [13,14,17,29].The model had homogenized equivalent core and core/facesheet debonding properties defined in the numerical model.The used properties were obtained by experimental studies [18].

Results and discussion
The low-velocity impact performance of configurated sandwich composites is investigated numerically with homogenized properties.Core/facesheet debonding areas, contact force-time curves, contact forcedisplacement curves, and absorbed energies are obtained numerically and compared with experimental results.Impactor velocity of 5.34 m s −1 , and impactor mass of 4.92 kg were used to obtain the energy values of 70 J.The contact force-time curve shows the force relationship between impactor and specimen by time.In this study, the perforation impact energy of 70 J was used, and the obtained curves are given both numerically and experimentally in figure 5.When the impactor starts to move in sandwich composite at the beginning elastic deformation occurs then core buckling and facesheet damage continue up to peak force.At peak sudden force decrease occurs with top facesheet fracture and penetration.Core crushing continues with core densification to the bottom facesheet.Then failure of bottom facesheet ends with fully perforation if the impact energy had enough energy to perforate the specimen.When the curves are examined in detail, both peak contact forces of sandwich composite 'S' are similar.All three peak contact forces of two-core sandwich composites have similar behavior.There is only a slight difference at the 3rd peak contact force curve region of the two-core sandwich composite '2 S'.At the same time, there is a little difference after the perforation of the sandwich composites.This situation is caused by the friction between the sandwich composite and the impactor.In the numerical simulations, the friction was neglected.It is determined that the contact force-time curves of sandwich composites had a good correlation.
The contact force-displacement curve shows the movement of the impactor inside the sandwich composite during the impact test.The sandwich composite structure had relatively strong facesheet material and relatively weak core material.This situation causes three peak forces.Contact force-displacement curves at the impact energy of 70 J are given in figure 6.It is seen from this figure that the contact force-displacement curves of 'S', '2 S', and '2 Sfs' are so close to each other both experimentally and numerically.For '2 Sec' and '2 Scs', there is a little deviation after 3rd peak contact force values.
All peak contact force values are obtained numerically and are compared with experimental results given in table 3.For sandwich composites 'S', two of both contact force values close to each other are obtained with little difference.When the three of peak contact force values for all types of two-core sandwich composites are examined, harmonious values are obtained in all peak contact forces.For two-core sandwich composites, 1st peak forces had similar values because of top facesheet layers had the same thickness and the delamination between the top facesheet and upper core material was nearly the same.2nd peak forces of '2S' and '2Sec' have a higher value.Both sides of the middle sheet had bonded to core materials with epoxy resin during infusion, this situation caused a resin-rich middle sheet thus these sandwich composites had higher 2nd peak forces values.Although '2Scs' and '2Sfs' have lower 2nd peak force values.Lower peak forces may have occurred due to stitches.During stitching, oriented glass fiber is distorted by stitching fiber.As a result, it caused to decrease in middle sheet strength.The boundary condition of the bottom layer affects the impact properties of the structure.With facesheet stitches '2Sfs' had the highest value at 3rd peak contact force.
The comparison of maximum displacement, and contact time values obtained experimentally and numerically is given in table 4. Essentially these values of tables 3 and 4 summarize the contact forcedisplacement and contact force-time curves.Displacement values of two-core sandwich composites with epoxy columns and two-core sandwich composites with core stitches sandwich composites had little deviation.This difference occurred after 3rd peak contact force value.However, displacement values of other sandwich 6  To compare absorbed energy values of sandwich composites together, these values are given in figure 7 both experimentally and numerically for the impact energy value of 70 J.Also, the difference between experimental and numerical results were given in percentage.The configuration of 'S' into '2 S' increased the absorbed energy value under impact conditions.The difference may be caused by the facesheet/core bonding area.The middle sheet is created from top and bottom facesheet layers.The facesheet/core bonding area is doubled.The bonding areas of the sandwich composite are in the top facesheets lower side, middle sheet on both sides, and bottom facesheet upper side.PVC core materials had resin-rich facesheet/core bonding in the sandwich composite structure.Due to this structure, two-core sandwich composites absorbed more energy than one-core sandwich composites.'2Sec' absorbed noticeably more energy than the non-column two-core sandwich composite.In point of absorbed energy, epoxy columns had a favorable effect.'2Scs',which had stitch thread through the holes, absorbed more energy than '2Sec' at 70 J.The stitch threads strengthen epoxy columns, and it caused higher absorbed energy absorption.'2Sfs', which had stitch thread through the glass fiber layers and core materials, absorbs more energy with little difference in the experimental and numerical studies compared to the core stitched one, while it absorbs less energy with a small difference.The stitching process is like rebar in concrete.The concrete is like epoxy resin and the rebar is like stitch thread.
After the experimental tests and numerical simulations of low-velocity impact at 70 J, the damaged images of sandwich composites are obtained.To make clear the damaged area of the sandwich composite, the cross-    that, only '2 Sec' debonding is given in figure 8. Thanks to core stitching configuration debonding area of the '2 Scs' sandwich composite is decreased remarkably.This difference is caused by the stitching thread bonded to the facesheet material by the matter of the stitching process, thus the debonding area was reduced.The debonding area of the '2Sfs' sandwich composite was reduced highly due to facesheet stitches as expected.For core/facesheet debonding the stitching thread must be broken.For a more detailed debonding phenomena explanation, scanning electron microscopy (Zeiss Gemini 500) was used to obtain images which are given in figure 9. To understand the SEM images collected area, crosssection photos of specimens were marked as a red rectangle.As seen in the given figure '2S' specimen debonding failure was acquired inside the PVC core material.Here the phenomenon is glass fiber layer bonded outer surface of the PVC foam with epoxy resin and the crack propagation took place inside the PVC foam as expected.In '2Sec' specimen crack propagation occurred inside epoxy columns which cannot stop the debonding between the facesheet and the PVC core material.But as seen in the given images '2Sec' had less crack width the '2S' specimen.The stitching thread fibers cracked due to impact for '2Scs'.This type of failure caused decrease debonding area and increased absorbed energy.The stitching fibers failure has reduced the crack propagation.In '2Scf' specimens crack width is so small that caused by stitched thread.The stitches over the facesheet block the debonding and as a result debonding area of the impacted specimen was decreased highly compared to other types of specimens.

Conclusion
In this study, the impact behavior of stitched glass fiber/epoxy sandwich composites with PVC foam core is studied numerically.The simulations are based on homogenized properties of different structural configurations of stitched composites on macroscale.In addition to previous study fracture toughness and compression tests were applied.The obtained results are compared with the results of the experimental study.The effect of different configurations through the thickness is examined.LS-DYNA finite element software is used to perform numerical studies.Contact force curves with contact time and displacement had significant harmony both experimentally and numerically.All peak contact forces, absorbed energy, maximum displacement, and contact time values had a good correlation.Also, core/facesheet debonding areas are examined and had an agreement with each other.
The results shows that the fracture toughness of sandwich composites had an important role in core/ facesheet debonding.The least core/facesheet debonding area is obtained in the '2Sfs' facesheet stitched sandwich composite due to the high fracture toughness value.
According to needs these configurations should be used, selectively.As a further study, ballistic impact behaviors of these configurations can be studied.

Figure 1 .
Figure 1.Universal tensile/compression testing machine with compression plates.

Figure 2 .
Figure 2. View of the SCB specimen during testing.

Figure 3 .
Figure 3.View of the SLB specimen during testing.

strength 8 minFigure 4 .
Figure 4. Finite element model of low velocity impact problem.

Figure 7 .
Figure 7.Comparison of experimental and numerical absorbed energy values.
These equations represent Mode I fiber rapture, Mode II fiber buckling and kinking, Mode III matrix cracking under transverse tension and shearing, and Mode IV matrix cracking under transverse compression and shearing.
t X , c Y , t Y , c S c

Table 3 .
The comparison of peak force values.

Table 4 .
The comparison of maximum displacement, and contact time.
sectioned parts are kept in penetrant liquid.Transparency of glass fiber epoxy laminates brought out core/ facesheet debonding areas.The core/facesheet debonding areas are shown in figure8, experimentally and numerically.Core/facesheet debonding areas are calculated by using ImageJ image processing software.The fracture toughness values of the sandwich composites which were obtained experimentally are given in table 5. LS-DYNA simulations were examined with LS-PrePost and obtained numerical core/facesheet debonding area values compared with experimental values are given in figure8.In this study 'S', '2 S', and '2Sec' sandwich composites debonding areas are about the diameter of the lower support at 70 J impact energy level.Because of

Table 5 .
Fracture toughness values of the specimens.