Erik P.Crton ,Bernt B.Johnsen ,Dennis-Bo Rhek ,Hns Broos ,Almr Snippe

a TNO,P.O.Box 45,NL-2280 AA Rijswijk,the Netherlands

b Norwegian Defence Research Establishment(FFI),P.O.Box 25,NO-2027 Kjeller,Norway

ABSTRACT The depth of penetration(DOP)method is a well-known ballistic test method for characterisation and ranking of ceramic armour materials.The ceramic tile is bonded to a backing material of semi-infinite thickness,and the penetration depth of the projectile gives a measure of the performance of the ceramic.There is,however,an inherent variability in the results from this test method.In this work,the accuracy and the variability of the DOP method has been investigated in a round robin exercise.Six ballistic test centres took part in the exercise.A test protocol was developed,in which the threat type(projectile and impact conditions)and a procedure on how to prepare the targets were specified.The targets consisted of alumina tiles of two different thicknesses that were bonded to polycarbonate backing cubes.Two different 7.62 mm armour piercing projectiles were employed;one with a hard steel core and one with a tungsten carbide core.The projectiles and the other materials all came from single material batches in order to avoid batch-to-batch variations in material properties. These materials were distributed between the ballistic test centres.The test results of the different ballistic test facilities were collected and compared.There was not a lot of variation between the average DOP values obtained at each laboratory,but the variation in penetration depth between shots was high.The consequence of this variation may be less confidence in the test results,and a statistical method was used to evaluate the required number of tests that are sufficient to obtain an average result with high confidence.In most cases,the required number of tests is much higher than what is practically feasible.This work was conducted as part of the European Defence Agency-project CERAMBALL.

Keywords:Ballistics Depth of penetration Test method Armour Ceramic Statistics

1. Introduction

Ceramics have been used for over forty years as a component in armour systems.Research on ceramic materials started in 1968 with the well-known work of Wilkins [1]. Ceramic materials combine attractive material properties like low density and high hardness.Especially against armour piercing(AP)bullets,ceramicbased armour can provide solutions that are more mass effective than armour systems based on steel.In ceramic-based armour,the ceramic is usually applied at the strike face and is supported by a backing layer.When the hardness of a ceramic material is high enough it can erode the AP core of an impacting bullet and spread the impact load over a wide surface of the backing material.Both these effects help the backing material to absorb the residual kinetic energy of the bullet.Wilkins used the now well-established ballistic limit orV50(projectile velocity at which the chance of perforation is 50%for a specified armour and a specified projectile)test on a range of ceramic materials that were backed by a constant thickness aluminium plate.TheV50is typically determined from a series of shots containing an equal number of minimum three nonperforations and minimum three perforations in a limited velocity range(e.g.40 m/s).

In the 1980's,Rosenberg[2]introduced a test set-up with a thick backing for the ranking of armour ceramic tiles.In this test a ceramic tile is assessed while it is attached to a thick,semi-infinite backing material.The thickness of the backing material is such that the residual projectile that perforates the ceramic strike face is stopped in the backing material without any deflection of the rear of the backing.The depth of penetration(DOP)of the projectile in the backing material is determined for each shot,and can then be compared to the penetration depth of the projectile in the backing without a ceramic strike face.Based on these two DOP values,several efficiency factors for a ceramic material can be determined.The thickness,Et,and mass,Em,efficiency factors are calculated using:

and

Here,Pis the penetration depth in the semi-infinite backing material,Tis the tile thickness and ρ is the density.Subscript‘ref’refers to the backing or reference material,and subscript‘cer’to the ceramic material.Sometimes the product of the thickness and mass efficiency factors is used as well.These efficiency values have been used to rank different ceramics in the projectile/target impact condition employed in the DOP test configuration.This test set-up,where the ceramic tile is perforated and the projectile penetrates into the backing material,has also been referred to as a residual depth of penetration(RDOP)test[3].However,in the literature the term DOP is commonly used[4,14,15,25],and this term will be used throughout this paper.

The semi-infinite backing materials in the DOP test are often metals,such as aluminium alloys for small calibre AP projectiles[3-9]or steel(RHA)for tungsten heavy alloy(WHA)long rods[10,15].However,in order to be able to measure the DOP these metals need to be X-rayed or cut open.Cutting a thick metal backing is laborious,especially considering that parts of the hard AP core remains inside.Moreover,the properties of the thick backing layer(e.g.bending stiffness,mass,sound velocity,hardness)may induce a different ceramic behaviour under impact,compared to what is obtained in more realistic and thinner backing layers.In some DOP test series with small calibre projectiles,polycarbonate(PC)cubes have been used as backing material[11].There are several reasons for this:(1)The PC bulk polymer material is easily purchased,(2)the PC is a ductile and optically transparent material,which helps to determine the penetration depth of the residual projectile(no need for X-ray analysis or to cut the thick backing material),even when the trajectory diverts from the original line-of-fire,and(3)the impedance(product of density and sound velocity)of the PC is much closer to that of realistic backing materials in body armour systems in their through-the-thickness direction.

Fig.1.Depth of penetration results for experiments using several types of alumina on aluminium alloy backing blocks[12].

Fig.1 shows a plot of individual DOP test results that were obtained by TNO for a range of alumina-based ceramic tiles[12].The tiles had a thickness of 8 mm and were glued onto an aluminium alloy backing.Similar comparisons of DOP data can be found in the literature[13-15].In Fig.1,the DOP results for a single ceramic are shown to vary up to 50%.Such a large variation in test results requires a large number of tests to get a statistically significant result.A small number of test results reduces the accuracy,and hence may prevent small differences in properties between ceramic materials to be determined.

This research was performed within the European Defence Agency (EDA)-project CERAMBALL. In the EDA-project, several European ballistic laboratories were working together with developers of ceramic materials to generate new and improved armour grade ceramics. During the early stages of ceramic development,a ballistic test method that could rank the candidate materials was needed.The differences in ballistic protection capability had to be distinguished using a minimal number of samples,as only a low number of relatively small-sized tiles were available for each material.The DOP method was considered as a candidate test method for new armour grade ceramic materials in this work.

The purpose of the work presented in this paper was to assess the variability of the DOP test method,given the specified test design and the experimental conditions,as well as to determine the number of test results required to demonstrate a certain(small)difference between two ceramic materials with a specified statistical confidence.To assess the variability of the DOP method,and to assess the variation between the different laboratories when conducting identical tests,a round robin was organised.In the round robin,all six laboratories that participated employed the same materials and followed the same test protocol.The testing was conducted employing a commercially available armour grade alumina and two types of 7.62 mm calibre AP bullets.Several different test designs are reported in the literature for DOP tests,for example designs where the ceramic tile is confined by a metal frame,or designs where the ceramic is clamped to the backing material.However,in this work a simple and cost-efficient test design,where the ceramic tiles where adhesively bonded to the PC backing,was specified.Furthermore,the DOP of the AP bullets into the backing material only(no ceramic)was not considered of relevance to this study.This meant that efficiency factors were not calculated.

2. Experimental

2.1. Materials

The ballistic laboratories that participated in the round robin test(ARWT,Austria;FFI,Norway;FOI,Sweden;Leonardo,Italy;TNO,the Netherlands;and VVU,Czech Republic)were supplied with the same materials;bullets,backing materials,ceramic tiles and adhesive.In order to minimize variations in material properties each of these materials were obtained out of a single batch from each of the suppliers.Alumina(Corbit 997,Industrie Bitossi SpA)was chosen as the armour grade ceramic material.The hexagonal tiles were from one batch and had a thickness of either 6 mm or 8 mm,and an edge-to-edge width of 63.5 mm.The tiles were checked for their flatness,then cleaned and degreased.When a tile showed a minor curvature its concave surface was used as strike face,as this would minimize the variation in the thickness of adhesive needed in the point of impact(in the centre of the tile).

A technical grade of polycarbonate(PC)was selected as backing material in order to allow for visual measurement of the depth of penetration directly after testing. PC cubes of 100 mm×100 mm×100 mm were cut from one large plate of 100 mm thickness.The original plate surface had a different texture compared to the cut surfaces of the cubes.In order to eliminate potential anisotropy effects due to the production method of the PC plate,the cubes were oriented such that the projectile trajectory was parallel with the normal of the original PC plate. A 2-component, room temperature curing epoxy (Permacol 2242)was used as adhesive.Before a tile was bonded to the PC cube a circle,with a diameter of 60 mm,or a cross were drawn in the middle of the PC cube surface.Then the tile was positioned centred on the circle or the cross.This eased the definition of the exact impact location of the projectile after the test,as at that stage all ceramic fragments and the cured epoxy bond line were shattered away from the cube.When bonding the tile to the PC cube,a sufficient amount of adhesive was first placed in the middle of the tile,and the tile was then manually pushed against the PC cube.Before the adhesive had set after a few minutes,it was made sure that the tile was positioned correctly and did not change position due to the flow of the adhesive.The resulting bond line thickness was quite uniform,with an average thickness of 0.20 mm;minimum and maximum thicknesses of 0.15 mm and 0.25 mm,respectively,were observed.Fig.2(a)shows a photograph of a PC cube with the bonded hexagonal alumina tile.

2.2. Ballistic testing

Two 7.62 mm armour piercing projectiles were used in the DOP tests in this round robin exercise;7.62 mm APM2(also known as 0.30-06 APM2)and 7.62 mm AP8.The two different projectiles were included in order to check the influence of the type of AP round.The 7.62 mm APM2 has a hardened steel core(φ 6.2 mm,5.2 g)with an ogive nose shape.The valid impact condition was specified as 800±10 m/s,with a maximal yaw of 5°,which was controlled by all laboratories.For the tests with this projectile,the 6 mm Corbit 997 alumina tiles were employed.The 7.62 mm AP8,on the other hand,has a tungsten carbide(WC/Co)core(φ 6.2 mm,5.2 g)with a conical nose.Here,the impact condition was specified as 900±10 m/s,also with a maximal yaw of 5°.Due to the higher density and hardness of the WC core,as well as its higher impact velocity,this AP round has a larger penetration capacity.Therefore,the thickness of the Corbit 997 alumina tile was increased to 8 mm in order to stop this round using a single PC cube as semi-infinite backing. For each projectile, the valid point of impact was maximal 10 mm from the centre of the tile,and any impacts outside 10 mm were considered invalid and not included in the analysis of the results.The majority of the impacts were within 5 mm from the centre of the tile.At least five valid shots were performed at each laboratory to determine the average DOP value for each projectile.

The penetration depth of the projectile into the PC cube was measured after the test.The distance from the cube surface to the furthest penetrating part of the projectile was measured.Fig.2(b)shows how a U-shaped metal plate was used to help in determining the DOP inside the PC cube after a test.Exactly how the DOP was measured was up to the individual lab,but painting some of the transparent epoxy adhesive on the side of the cube,in order to form a transparent film,or immersion of the cube in water aided in this measurement.Both methods reduce the light scattering originating from the roughness of the cut sides of the cube,thereby improving the visibility of the penetration path and the residual projectile inside the cube.

3. Results

3.1. Projectile impact and penetration

An example of a strike face on the PC cube after testing is shown in Fig.3(a).The ceramic tile was completely detached from the surface of the cube,and only parts of the adhesive bond line remained attached to the surface after the test.The contour of the ceramic tile,showing the original position of the tile on the PC surface,is visible.This helped in identifying the point of impact on the ceramic.As mentioned above,only impacts within 10 mm from the centre of the tile were considered valid and included in the analysis.A typical observation was that parts of the jacket of the bullet remained attached to the entrance of the channel where it had penetrated the PC backing.

When measuring the DOP,the distance from the cube surface to the furthest penetrating part of the projectile was determined.Hence, the actual path of the penetrating projectile was not measured.However,the trajectory of the penetrating fragments did in almost every case deviate very little from the original line-of-fire of the projectile,as can be seen in Fig.3(b).The difference between the two measurements would therefore be very small,and probably negligible.

3.2. DOP results for 7.62 mm APM2

Fig.2.(a)PC cube with an adhesively bonded hexagonal alumina tile before a shot,and(b)illustration of the DOP measurement after a shot.

In Table 1,the results from DOP testing of 6 mm alumina using the 7.62 mm APM2(at 800±10 m/s)are provided for each ballistic laboratory.Instead of calculating the mass and thickness efficiency factors,in this study we focus on the DOP values themselves.The main purpose of the work is to investigate the variation in the results,and this can be done from the DOP values.In Fig.4,the average DOP values are graphically shown per laboratory.The bars indicate the range of the obtained DOP values.The overall average DOP was calculated to be 39.4 mm,which is indicated in the figure as a dashed horizontal line.The average DOP for each individual laboratory is within the range 35.8 mm-42.2 mm,so it was never more than 3.6 mm(about 9%)from the overall average DOP.Hence,the DOP method initially shows to be relatively reproducible.However,the range bars are quite large relative to the average DOP values,which is also evident from the standard deviations and the 95%confidence intervals in Table 1.This can also be learned from Fig.5,in which all individual DOP values are plotted versus the impact velocity of the bullet.The measured DOP of the individual shots in the round robin were in the range from 22 mm to 60 mm.This means that the repeatability is rather low,and hence that the accuracy of the average DOP values,although they were obtained by at least five shots,is also expected to be low.

Fig.3.(a)Strike face on a PC cube after testing with 7.62 mm APM2.The original position of the adhesively bonded ceramic tile is clearly seen.(b)Side-view of 7.62 mm AP8 penetration into a PC cube.

Table 1Results from DOP testing of 6 mm alumina using 7.62 mm APM2(at 800 m/s)for all participating laboratories.Mean values and standard deviations(SD)are given.For the DOP results,the 95%confidence intervals(CI)are also presented(see Section 4.1).

Fig.4.Average DOP on 6 mm alumina obtained for each laboratory using 7.62 mm APM2(at 800±10 m/s).The bars show the range of values obtained with five to six shots.

Fig.5.All DOP values obtained in the round robin for the 6 mm alumina tested with 7.62 mm APM2(at 800±10 m/s)as a function of the impact velocity.

3.3. DOP results for 7.62 mm AP8

In Table 2,the results from DOP testing of 8 mm alumina using7.62 mm AP8(at 900±10 m/s)are provided for each ballistic laboratory.Fig.6 shows the average DOP results together with the range bars.The overall average DOP was calculated to be 41.3 mm,which is indicated in the figure as a dashed horizontal line.All laboratories are never more than 3.4 mm(about 8%)off compared to the overall average DOP.However,here also,the range bars are quite large compared to the average DOP values,and the standard deviations and the 95%confidence intervals in Table 2 are in some cases very large.This means that the accuracy of the average DOP values,although each was obtained with five to eight shots,again is low.The same can be concluded from Fig.7,which shows the DOP value for each individual shot in the round robin.The measured DOP was generally in the range from 25 mm to 57 mm,although one single shot for laboratory C gave a value as high as 76 mm.The standard deviation for laboratory C,see Table 2,merely reflects the influence of this outlier.Possible abnormal reasons to what could have caused the outlier,such as e.g.experimental errors,were investigated.However,no such reasons were identified.This outlier further underlines the expected variation in results when using the DOP method,at least when employing the current test design.

Table 2Results from DOP testing of 8 mm alumina using 7.62 mm AP8 at 900 m/s for all participating laboratories.Mean values and standard deviations(SD)are given.For the DOP results,the 95%confidence intervals(CI)are also presented(see Section 4.1).

Fig.6.Average DOP on 8 mm alumina obtained for each laboratory using 7.62 mm AP8(at 900±10 m/s).The bars show the range of values obtained with five to eight shots.

Fig.7.All DOP values obtained in the round robin for the 8 mm alumina tested with 7.62 mm AP8(at 900±10 m/s).

4. Statistical analysis

4.1. Evaluation of the DOP results

For both the 7.62 mm APM2 and the 7.62 mm AP8 projectile,it was observed that there was a large variation in the test results within each laboratory.This decreases the reliability of the test data from the DOP method.One method to evaluate how accurate the mean DOP value is determined,is by calculating the corresponding confidence interval(CI)[16,24].A commonly used level of confidence is 95%α=0.05.It is then expected that 95%of the estimated intervals of a given parameter does include the true value of said parameter.For a sample from a normal distribution with sample meanand sample standard deviation SD,the confidence interval is constructed as follows:

Here,tis a value based on the Student's t distribution corresponding to the confidence level(α/2)of the interval with(n-1)degrees of freedom,and wherenis the number of tests(in this case the number of valid shots).The values ofnand SD for each laboratory are given in Table 1 for 7.62 mm APM2 and Table 2 for 7.62 mm AP8.A confidence level of 95%was chosen for the analysis and the corresponding 95%confidence intervals are also given in the two tables.

4.1.1. 7.62 mm APM2

The 95% confidence intervals for the 7.62 mm APM2 projectile for the different laboratories are generally very broad,as shown in Table 1.The confidence intervals are in the range 38.9-45.3 mm for laboratory C(narrow),to 27.6-52.4 mm for laboratory B(broad).The results for laboratory B then implies that in 95%of the cases where the DOP is determined according to the same test procedure and with the same number of shots as employed here,the true mean DOP (with 95% confidence) is expected to be between 27.6 mm and 52.4 mm;this is a very wide range.When a difference in material performance is to be detected between two different ceramic materials,such large CI's means that very large and,in most cases,unrealistic differences in performance,and/or very large number of samples are required in order to distinguish between the two materials.

Assuming that the results from the six laboratories can be combined into one test series,thennis 34,the mean DOP is 39.4 mm,and the SD is 7.7 mm.This gives a 95%confidence interval of 36.7-42.1 mm.This more narrow CI is as expected,since a higher number of tests is likely to give a more accurate value of the mean DOP.

4.1.2. 7.62 mm AP8

For the 7.62 mm AP8 projectile,the calculated confidence intervals show similar large ranges as was observed for the 7.62 mm APM2 projectile(see Table 2).The smallest CI was 35.9-46.4 mm for laboratory F,and the largest CI was 30.4-56.3 mm for laboratory C.These ranges constitute as much as 26%and 60%,respectively,of the corresponding mean DOP values.Even when combining the tests from the six laboratories,which gives a total of 38 shots,a combined mean DOP of 41.3 mm,an SD of 9.5 mm and a CI of 38.2-44.4 mm,the CI width is still 15%of the mean.Once again,such large variations in results and confidence intervals would make a comparison of,or ranking between,ceramic materials difficult.The only way to lower the width of the confidence intervals is by performing a higher number of tests.

4.2. Estimation of detectable difference based on the number tests

4.2.1. Based on the DOP results for 7.62 mm APM2 and 7.62 mm AP8

It can be useful to obtain an estimate of the number of tests that are required to detect a difference in means in a study.In this case,this would be a measurable difference,δ,in the mean DOP between two ceramic materials.To do this a power test can be conducted[16].The power(1-β),which is in the range 0-1,is defined as the probability of rejecting a false null hypothesis,i.e.rejecting a hypothesis that two means are equal, while they in reality are different.A large power thus means that there is a high likelihood of detecting an effect,if indeed there is a real effect.In order to use the power test to estimate the number of required tests to detect a difference between two sample types,the standard deviation,SD,is needed together with the desired values of both α(probability of stating that the means are different when they are in fact equal)and(1-β)(probability of finding that the means are different when they are in fact different).In the following analysis,the commonly used values for α and(1-β)of 0.05 and 0.90,respectively,have been employed.The SD's found from combining the results from all six laboratories are used;the SD is then 7.7 mm for the 7.62 mm APM2 projectile and 9.5 mm for the 7.62 mm AP8 projectile.

The estimates from the power test of the required number of tests that are required to detect a difference in DOP are presented in Table 3.For both 7.62 mm APM2 and 7.62 mm AP8,a large number of tests are generally required.As an example,to detect a difference in mean DOP of 5 mm between two target types,an estimated number of 51 tests(of each target type)is required for 7.62 mm APM2,while the number is 78 tests for 7.62 mm AP8.For the teststhat were conducted here,with a mean DOP of approximately 40 mm,a difference of 5 mm corresponds to a difference of 12.5%relative to the mean.However,to perform 51 or 78 tests for each target type is in most cases unrealistic from an economical perspective.A more realistic number is five to ten tests of each target type.The numbers given in Table 3 indicate that this would require a detectable difference in DOP of 15 mm-20 mm,or larger,between the two materials.For tests with a mean DOP of around 40 mm,this requires a substantial improvement in performance of one target material relative to the other.

Table 3Required number of tests to detect a difference in mean DOP between two types of ceramic tiles.The estimates are based on the standard deviation found from combining the shots from all six labs into one series for each projectile type;SD=7.7 mm for the 7.62 mm APM2 projectile and 9.5 mm for the 7.62 mm AP8 projectile.The values for α and(1-β)are 0.05 and 0.90,respectively.

4.2.2. General method for evaluating the detectable difference

The estimates for the number of required tests in Table 3 are based on the SD from the tests that were performed in this study.However,a more general relationship between the number of tests and expected detectable differences between target types can also be elucidated.In this relationship,the influence of the size of the SD is a factor.The detectable difference ratio,δ/SD,is the relationship between the differences of two means,and,and the standard deviation for the data,SD[16].This ratio is also called the effect size index or Cohen'sd,henced=δ/SD=SD.In Fig.8,the estimated detectable difference ratio,δ/SD,is given as a function of tests performed at three different levels of power for α=0.05.Basically,the figure indicates the expected difference between two mean values for a given number of tests.For example,if ten tests are performed for each target type in a study,then the figure indicates that a difference in mean on the order of approximately 1.5×SD can be detected with a power of 0.90 and α=0.05.Hence,for small SD's,small differences in mean values can be detected,and vice versa for large SD's.This shows that in order for the DOP test method to be used as a reliable tool for ranking of the performance of different ceramic targets,without having to perform a very large number of tests,the standard deviation of the tests has to be low or the relative difference between the targets has to be large.This is common with other ballistic test methods,but may be of higher importance when employing the laborious DOP method.

5. Discussion

Fig.8.The estimated detectable difference ratio,δ/SD,as a function of the required number of tests at three different levels of power,and for α=0.05.The insert shows the region from 0 to 40 tests in more detail.

Many factors may have an influence on the results in a DOP test such as,for example,the material properties of the ceramic and the projectile,the impact velocity,the point of impact,thickness of the adhesive bond line,as well as the type of backing material.In this study,polycarbonate(PC)was chosen as backing material,for reasons explained above.The transparency of the PC material significantly reduces the time needed for measurement of the penetration depth, and hence improves the efficiency of the experimental work.Also,materials that are used as backing for ballistic inserts,or as semi-infinite backings in the DOP test,will be compressed in the through-the-thickness direction (at least initially),and for reflection of waves the through-the-thickness impedance is important.

Metals like aluminium alloy or steel are normally used as backing material for DOP tests.Their acoustic impedance,Z,is rather high due to their density of 2750 kg/m3and 7800 kg/m3,respectively,and sound velocity of abou t 5000 m/s,which giveZvalues of 14×106kg s/m2and 39×106kg s/m2,respectively.For a regular backing material for ballistic inserts,such as fibre composites of aramid or ultra-high molecular-weight polyethylene(UHMWPE),the impedance,Zfibrecomposite,in the through-thethickness direction is much lowerat 2×106-3×106kg s/m2(based on density 980-1400 kg/m3and a sound velocity in the through-the-thickness direction of about 2000 m /s[17]).For the PC material,the impeda nce,ZPC,is around 2.4×106kg s/m2(based on density 1200 kg/m3and a sound velocity of 2200 m/s).Hence,PC has a an impedance that is close to that of real-life body armour backing materials in the through-the-thickness direction,while metals have much higher impedance values.Therefore,with body armour applications in mind,PC can be considered as a better backing material in DOP tests compared to metals.

The point of impact of the projectile will have influence on the results if the impact is too close to the edge of the ceramic tile.In this study,the tiles were 63.5 mm in width and 6 mm or 8 mm in thickness,and the requirement was that the impact should be maximum 10 mm from the centre of the tile.Using a maximal semiapex angle of 60°[18]and a top radius of 4 mm for the truncated cone,the radius of the base plane of the cone fragment is 14.4 mm for a tile thickness of 6 mm,and 20 mm for a tile thickness of 8 mm.This demonstrates that the ceramic tiles were large enough to incorporate this truncated cone fragment even for a point of impact 10 mm away from the centre of the tile.(It should be noted that the majority of the impacts were within 5 mm from the centre of the tile.)The tile size should in this case therefore not have an influence on the results.Furthermore,some tests were discarded because the impact was outside the 10 mm requirement.The results from these tests,however,did not deviate in any way from the valid results.

The thickness of the adhesive layer between the ceramic and the backing can have an influence on the performance of ceramic armours.For ceramic/metal armours with a relatively thin metal backing,it has been argued that a thinner adhesive bond line will delay the shattering of the ceramic,and hence increase projectile erosion,while a thicker bond line will distribute the energy over a wider area,which is beneficial for the energy absorption in the backing[19,20].The fragmentation of the ceramic material is expected to be of greater importance,so the bond line thickness should be as small as possible.In the tests with the alumina/PC targets in this study,the bond line thickness was around 0.2 mm.This adhesive layer is relatively thin,and very close to the optimum thickness found in other studies[21,22](although it should be acknowledged that these studies were on targets with different designs and backing materials).However,in the DOP test,the aim is to rank different ceramics in an efficient way,and not to produce armours.Then,even an unfavourable bond thickness can to some extent be accepted,as long as it leads to reproducible results.

The statistical analysis showed that for a reliable ranking of ceramic armour materials when using the DOP test method,a large number of test results are required.This is due to the large variation in the results.DOP test results in the literature,using other projectiles and metallic backing materials,show a similar variation relative to the mean DOP in the test results[11-13,23].The small amount of tests that are normally applied prevents small differences between ceramic materials from being determined. An important reason for the wide spread in DOP test results seems to be connected to the test method itself.The impact of the hard and brittle armour piercing(AP)core of the projectile on the ceramic strike-face results in deformation and erosion of its originally ogive or conical nose.This process results in a unique nose shape of each residual projectile.Even for projectiles which have lost a similar amount of kinetic energy during the interaction with the ceramic strike face,i.e.the same residual kinetic energy is available for penetration of the backing material,the variations in nose shape will give different penetration behaviour.It is well known that the shape of the projectile nose has influence on the penetration of a rigid projectile in a ductile material;at equal mass and velocity a blunt projectile will penetrate less deep into the ductile target[26].This inevitably leads to variations in penetration depths.

Due to the high variation in the results in the DOP tests,this method was rejected as screening method for ceramic armour materials within the CERAMBALL project.Instead,other ballistic test methods,such as the residual energy method for both bare and(thin)polycarbonate supported ceramic tiles[12,23],andV50tests for ceramic tiles with a fibre-reinforced polymer(GFRP)backing,were applied.

6. Conclusions

The depth of penetration(DOP)method was applied in a round robin test in order to assess its reproducibility.In order to minimize material variations,all ballistic laboratories obtained the same projectiles(7.62 mm APM2 and 7.62 mm AP8),backing material(polycarbonate cubes),ceramic tiles(6 mm and 8 mm alumina,Corbit 997)and adhesive,of which each came from one production batch.Also,the impact conditions were according to clearly defined impact velocities,position and normal impact(yaw<5°).

For the 6 mm alumina tested using 7.62 mm APM2 at 800±10 m/s,the average DOP of the individual labs deviated no more than 3.6 mm from the overall average value of 39.4 mm.However,the variation in penetration depth for the tests within the individual laboratories was large.Although the average DOP was obtained using at least five valid shots,the width of the 95%confidence interval was as large as 24.8 mm(27.6-52.4 mm)for one laboratory,while it was 5.4 mm(36.7-42.1 mm)when all test were taken into account.For the 8 mm alumina tested using 7.62 mm AP8 at 900±10 m/s,there was a similar deviation from the overall average DOP value of 41.3 mm.In this case also,there were large variations in the penetration depth between shots,resulting in similarly large 95%confdience intervals.

A statistical reasoning was used to determine the required number of test results needed to measure differences in mean DOP for different samples types at a given confidence level.Based on the experiments conducted here,then 51 tests of each material for the 7.62 mm APM2 projectile,and 78 tests for the 7.62 mm AP8 projectile,would be required in order to detect a difference in DOP of 5 mm between two armour grade ceramic materials.The generation of such large numbers of test results is time-consuming and not cost-effective,and will in many cases be difficult to conduct in the early stages of a ceramic material development programme.

Acknowledgements

The authors would like to thank R.Haas(ARWT,Austria),P.Lundberg (FOI, Sweden), A. Bassano (Leonardo, previously Otomelara,Italy),and R.Mikulíkova(VVU,Czech Republic),for performing DOP tests and providing their test results.This work was conducted as part of the European Defence Agency-project CERAMBALL,contract number B 1091 GEM1 GP.