Plane Thermoelastic Waves in Infinite Half-Space Caused FACTA UNIVERSITATIS Series: Mechanical Engineering https://doi.org/10.22190/FUME220903003A © 2020 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper EXPERIMENTAL AND NUMERICAL INVESTIGATION ON THE PERFORMANCES OF A SMALL WEAPON BARREL DURING ITS LIFECYCLE Walid Boukera Abaci1, Nebojsa Hristov1, Igor Radisavljevic2, Lazar Stojnic1, Aleksa Anicic3 1University of Defense in Belgrade, Military Academy, Belgrade, Serbia 2Military Technical Institute, Belgrade, Serbia 3Proof House for Experimental Testing, Kragujevac, Serbia Abstract. The paper presents experimental and numerical investigations on the performances of a small caliber rifle barrel during its lifecycle. Two 7.62 mm rifle barrels were used, the first was considered as a standard barrel, the second barrel was subjected to an accelerated life cycle test. Measurements of the muzzle velocity, the rate of fire and the firearm accuracy and precision were carried out. The paper presents the correlation between the measured parameters and the total number of shots fired. After the durability tests, longitudinal cross sections were made by cutting the tested and the standard barrels. 3D scanning was employed to perform a comparison between the tested and the standard bore surfaces. ANSYS Explicit dynamic analyses were performed based on the obtained surface scans. The numerical analyses results of the tested and the standard barrels showed good agreement with the experimental and the numerical internal ballistic model results. Key words: Accelerated lifecycle tests, Muzzle velocity, Rate of firing, Accuracy, Precision, Bore damage, 3D scanning, Explicit dynamic analysis 1. INTRODUCTION The performance of weapon barrels decreases significantly during their usage. During the firing, the barrel is subjected to high thermo-mechanical stresses caused by the highly pressurized combustion gases and the interaction with the accelerated projectile. For the brief time that the firing process takes the barrel will be affected by the chemically reactive gases at elevated pressures and temperatures. Inevitable damage will occur to the internal surfaces that progress with repetitive usage of the barrel. Those damages are known as the Received: September 03, 2022 / Accepted: January 15, 2023 Corresponding author: Nebojsa Hristov University of Defence Belgrade, Military Academy Belgrade, Veljka Lukića Kurjaka 33, 11042 Belgrade E-mail: (nebojsahristov@gmail.com) 2 W. BOUKERA ABACI, N. HRISTOV, I. RADISAVLJEVIC, L. STOJNIC, A. ANICIC wear and erosion of the barrels. Unwanted phenomena that lead to the degradation of the barrel performances. The exterior ballistic process highly depends on the initial directional and rotational muzzle velocities. Internal surface damage will affect the projectile surface topography and the initial velocities which will affect the bullet’s aerodynamic parameters and induce a significant loss in the accuracy and precision of the rifle. Much research has been established to study and predict the wear and erosion of the barrels experimentally and numerically [1-7]. Jaramaz et al. [8] have developed a laboratory apparatus and a method for determining the erosion coefficient of gunpowder both experimentally and theoretically. Abhilash et al. [9] and Johnston [10] summarized in their reviews the various studies on erosion taking place in the weapon barrel and gave a list of various methods developed over the years to calculate and mitigate the barrel wear. New research has been conducted to study the bore damage of the barrel with the use of the new numerical advanced analysis tools to accurately predict its effect. Shen et al. [11] studied the influences of bore damage on the bullet-barrel interaction process and the end of a 12.7 mm machine gun barrel's service life. Based on the damage data obtained through barrel life tests they developed a novel finite element mesh generation method for the damaged barrel and a new transient coupled thermo-mechanical finite element (FE) model. Based on the barrel's accelerated life test, and using numerical simulation technology and the ballistic performance change at each shooting stage, Li et al. [12] reproduced the whole process of projectile shooting and established a relation between the angle of attack of the projectile and the wear of the barrel. They showed that the projectile muzzle spin rate decreases 57.5% than that of a barrel without wear. Xiaolong et al. [13] also analyzed wear mechanism at different positions in the bore and established a three-dimensional barrel-wear finite element model using a parametric modeling method and concluded that the fundamental reason for interior ballistic performance degradation was wear on the initial position of the rifling. Ding et al. [14] provided a new finite element meshing strategy for the worn barrel and a new parametric geometric modeling method for gun barrel using Python code and ABAQUS software. By considering the gases propelling force and the changing friction stress effect, the user subroutine VUAMP and VFRICTION were implemented to develop a transient coupled thermo-mechanical FE model to compute the plastic deformation of the rotating band and the performance of interior ballistics. In order to investigate the small caliber rifle performances during the course of its lifecycle, durability tests were conducted to accelerate the barrel lifespan, measures of the initial velocity, the rate of firing and the firing accuracy and precision were taken regularly. The internal surfaces of the used and standard barrels were obtained using 3D scanning. The obtained results were used to perform explicit dynamic analyses using ANSYS software. 2. EXPERIMENTS Two 7.62 mm automatic rifle barrels were used. The first one is a new barrel and is considered as a standard barrel. The second one is a used barrel. It was used for 8000 rounds before performing a durability test. The durability test consisted of firing a large number of shots in different regimes using a standard nitrocellulose propellant. The experiments were performed with the standard atmospheric conditions. After every 1000 shots, a series of performance measurements were made: Experimental and Numerical Investigation on the Performances of a Small Weapon Barrel... 3 - The initial velocity of the V0 on a group of 10 shots (3 x 10 Shots) - The rate of firing on a group of 60 shots (2 x 30 shots) - Accuracy and precision tests on 3 targets in a group of 10 shots per target at a distance of 100 m. During the durability test, 13,860 rounds were fired (a total of 21,900 rounds were fired from the used rifle) of ammunition 7.62 × 39 mm. The velocity V0 was measured using a ballistic chronograph placed 2.5 m from the muzzle. The rate of fire was determined using a measuring system based on optical and sound sensors to register the cadence. The device is an integral part of the laboratory equipment for testing ballistic characteristics in the Zastava Arms test center. The system is equipped with sound and light sensors to be able to detect the sound produced by the shot, as well as the flash from the muzzle of the weapon when fired. The time between two firing was measured with an accuracy of 1 μs. The measurement results were collected using a specific acquisition system. The accuracy and precision of the barrels of the rifle are tested under favorable atmospheric conditions in a covered area of the shooting range protected from the wind and outside influences. Before the start of the test, parts that could affect shooting accuracy were replaced and the weapon was cleaned and then inspected. Precision and accuracy were tested by shooting 10 bullets of the same series and original packaging for each of the three targets. Targets were placed at a distance of 100 m with sight. The shooting was performed by an excellent sitting down shooter using a tactical riflescope. The aiming point was the center of the black disk of the target that should be on the weapon horizon. After shooting, the target (Fig. 1) was inspected and the coordinates of the scatter were collected. Fig. 1 One of the three targets after shooting 10 shots at 17000 rounds 3. RESULTS OF THE EXPERIMENTS The durability test results are summarized in Table 1. 4 W. BOUKERA ABACI, N. HRISTOV, I. RADISAVLJEVIC, L. STOJNIC, A. ANICIC Table 1 Durability test results N x 103 0 8 9 10 11 12 13 14 V0 [m/s] 720.21 690.83 692.02 691.18 687.61 692.58 688.40 681.84 Rate of firing [shot/min] 620 622 627 627 635.5 629 631 635.5 N x 103 15 16 17 18 19 20 21 V0 [m/s] 685.59 675.38 677.49 673.64 667.01 669.89 664.81 Rate of firing [shot/min] 638 633.5 635 641 640.5 641 642 Figures 2 and 3 represent the initial muzzle velocity and the rate of firing as a function of the fired round number. Fig. 2 Muzzle velocity vs. Number of rounds Fig. 3 Rate of fire vs. Number of rounds The muzzle velocity experienced a decrease of 7.69% while the rate of fire experienced an increase of 3.55% between the results of the standard barrel and the results of the tested barrel after 21,800 rounds were fired. Experimental and Numerical Investigation on the Performances of a Small Weapon Barrel... 5 The XY coordinates of the shots on the targets were collected and treated to obtain the coordinate of the center of shots, and the XY standard deviations of the shots as a function of the number of rounds (Figs. 4 and 5). Fig. 4 Position of the center of shots vs. Number of rounds Fig. 5 Standard deviations vs. Number of rounds The Circular Error Probable (CEP) is the radius of a circle that has a 50% probability of containing the target. The CEP of each of the measures was calculated approximately using Eq. (1), [15], the obtained results were presented in Fig. 6. 2 max( , ) (0.67 0.8 ) where if 0 0.5 if 0 max( , ) 0.5 . 19 (1 ) 5 / L x y L S x y L S L w CEP w ww w                            (1) The accuracy of a rifle refers to how close the measurements are to the aiming point. The precision of the rifle refers to how close the measurements are to each other. The coordinate of the center of shots presented in Fig. 4, showed that the accuracy of the tested barrel was independent of the number of the total round fired. However, the precision was 6 W. BOUKERA ABACI, N. HRISTOV, I. RADISAVLJEVIC, L. STOJNIC, A. ANICIC affected as it is shown in Figs. 5 and 6. The standard deviation of the results and the CEP increased with the total round fired. Fig. 6 CEP vs. Number of rounds After the tests, longitudinal sections were made from the tested and the standard barrels using the wire-cut electrical discharge machining (EDM) process. The EDM process is a technique using sparks produced by electrical discharge to manufacture work-pieces in accurate dimensions and shape [16,17]. Figures 7 and 8 show the longitudinal sections of the standard barrel and the used barrel, respectively. Accurate views of the origin of rifling were obtained using an optical microscope as it can be seen in the Figs. 7 and 8. Fig. 7 Longitudinal section of the standard barrel Fig. 8 Longitudinal section of the tested barrel 4. LASER SCANNING OF THE INTERIOR SURFACES For the purposes of measuring the interior surfaces and creating a 3D model, a 3D scanner Hexagon RS5 was used, with a stabilized Absolute arm platform 8525-7, shown Experimental and Numerical Investigation on the Performances of a Small Weapon Barrel... 7 in Fig. 9. With a precision of 0.048 mm, this system enables the reliable determination of 3D point clouds of the inner surface for the longitudinal cross-sections of the tested and the standard barrels. The technical characteristics of the laser scanner and the stabilization platform can be found in the Hexagon brochure [18]. The RS5 laser scanner scans results of the used and the standard barrels were introduced to the POLYWORKS software where preliminary preparations were made like setting the geometries approximately in the Cartesian reference and deleting the majority of the unwanted scanned surfaces and points (Fig. 10). The initial results were imported to Matlab developed code as STL files, in order to extract the Cartesian coordinates of the 3D scatter plot points. Points that do not belong to the barrel bore surface were removed. The XYZ coordinates of the center of two distant sections were determined using the average value of all the XYZ specific section points. The rotation and translation matrix were calculated using the resulting vector between the two sections centers. Using those rotation and translation matrixes the geometries were installed in the Cartesian coordinate system. The average distance of the lands and grooves from the barrels axes were calculated following a cylindrical helix curve. The obtained results are presented in Fig. 11. Fig. 9 3D scanner Hexagon RS5 with a stabilized Absolute arm platform 8525-7 Fig. 10 3D scans of the standard (left) and tested (right) barrels The origin of rifling was the most damaged area of the bore where the total land material was removed. This will increase the free travel distance of the projectile and delay the 8 W. BOUKERA ABACI, N. HRISTOV, I. RADISAVLJEVIC, L. STOJNIC, A. ANICIC proper engraving of the bullet jacket. Increasing the free travel distance will decrease the total time of the firing process, which can explain the rise in the rate of fire. The thickness of the lands decreases unevenly with a maximum loss in the average land radius value of 0.17 mm at the axial position 76 mm from the bottom of the barrel. Fig. 11 Average radius of the internal surfaces (Lands and Grooves) of the used (UB) and the standard barrels (SB) as a function of the axial position 5. EXPLICIT DYNAMICS ANALYSES Based on the 3D laser scanning data two CAD models (Fig. 12) for the standard and tasted barrels were created and used in an explicit dynamic analyses to simulate the interior ballistics process of a coupled projectile-barrel system. The explicit dynamic analysis is used to provide a firing process model considering its short-duration and high-pressure loadings. Such a complex phenomenon requires advanced analyses tools to accurately predict its effect on the rifle and the bullet design. Creating a high-quality mesh is one of the critical factors that must be considered to ensure simulation accuracy. A high-quality mesh means that there is an optimal balance between the computational cost and the level of fineness achieved. The meshing was made in a helicoidally way for both the barrels and the bullet to match the shape of deformations. Fig. 12 CAD Models for the standard (left) and the tested (right) barrels Experimental and Numerical Investigation on the Performances of a Small Weapon Barrel... 9 The three-dimensional refinement was made manually by retaining the element types and attempting to convert the elements in the regions where the interactions accrue between the barrel and the bullet into smaller elements of the same type as the original elements. This refinement effectively decreases the cell size of only the target area but does not increase the computational cost dramatically. In order to refine the mesh in the radial, axial and azimuthal directions special transitional mesh elements (Fig. 13, left) were needed to increase the number of cells in the desired direction. More developed mesh elements (Fig. 13, right) were needed to increase the number of cells in two directions simultaneously. The whole model was used for the analyses. Fig. 13 Transitional mesh elements in one (left) and two (right) directions Fig. 14 represents the HEX8 elements (8 Nodes hexahedron) mesh of only a quarter of the projectile and the barrel to show the mesh refinement in all three (XYZ) directions. Fig. 14 Helicoidal mesh of a quarter of the (left) projectile and the (right) barrel The number of nodes, elements and the type of elements are presented in the Table 2. Table 2 Type and number of finite elements Geometries Barrels Bullet Number of nodes 517,932 159,435 Number of elements 446,812 143,504 Type of elements HEX8 HEX8 The projectile core and the barrels are made of the same material (steel), which is assumed to have a linear elastic behavior. The steel mechanical and thermal properties are presented in Table 3. The projectile jacket material (brass) has a homogeneous, isotropic, elastic-plastic behavior with Johnson-Cook plastic deformation and failure models. The brass mechanical and thermal properties are summarized in Table 4. The contact between the barrel and the projectile is a frictional contact with penalties. 10 W. BOUKERA ABACI, N. HRISTOV, I. RADISAVLJEVIC, L. STOJNIC, A. ANICIC Table 3 Steel mechanical and thermal properties [13-14] Parameters E [GPa] Poisson ratio Density [kg/m3] Yield Stress [MPa] Specific heat cp [J/kg K] Thermal conductivity [W/m K] Value 206 0.31 7850 933 483 30 Table 4 Brass jacket material mechanical and thermal parameters [11] Elastic and thermal parameters E [GPa] Poisson ratio Density [kg/m3] Specific heat [J/kg K] Thermal conductivity [W/m K] Value 115 0.31 8800 375 110 Plastic Parameters A [MPa] B [MPa] C n m Tm [K] ε̇0 [s-1] Value 206 505 0.01 0.42 1.68 1189 5x10-4 Damage and fracture parameters D1 D2 D3 D4 D5 Value 0.54 4.89 -3.03 0.014 1.12 The stresses in the barrel caused by the firing are the results of different loads. The main loads are the mechanical and thermal loads generated by the combustion of the propellant. For reasons of simplification in this study, all the loads are neglected except the stresses caused by the generated pressure of the propellant combustion and the interaction between the barrel and the bullet. Fixed support boundary condition was applied on the rear surface of the barrel. Moreover, the whole model was used, i.e. no symmetry conditions were applied. The loads introduced to the analyses are time-space dependent loads (Fig. 15). They are applied as tabular data in a way that for each time step we introduced a pressure load applied on the interior walls of the barrel and the back of the projectile. The loads were calculated using the two-phase flow internal ballistic model presented in [19]. The two- phase flow model considers both the solid (gunpowder grains) and the combustion gaseous component during the firing process and at a given time compute different pressure values along the barrel. Fig. 15 Time-space dependent loads on the barrel and the projectile Experimental and Numerical Investigation on the Performances of a Small Weapon Barrel... 11 6. EXPLICIT DYNAMIC ANALYSES RESULTS DISCUSSION For a reasonable comparison between the analytical and the numerical analyses, both must have the same input parameters. For that reason, the bullet was suppressed in a preliminary simulation to neglect the effect of the bullet acceleration on the barrel. The total equivalent stresses obtained by the dynamic explicit analyses are compared with the analytical stress. The analytical equivalent stress is calculated by the von Mises formula, 2 2 21 (( ) ( ) ( ) ) 2 e r t r z t z             (2) where r is radial stress, z is axial stress and t is tangential stress [20]. Figure 16 represents the analytical and numerical equivalent total stresses as a function of the barrel radius (R) obtained in simulations with and without projectile for section 60 mm at 0.34 ms (Fig. 16, left) and section 120 mm at 0.38 ms (Fig. 16, right) from the bottom of the barrel. The equivalent stresses obtained by the simulations have the same trend as the analytical equivalent stresses for values of radii greater than 5 mm. The graphs of the simulations equivalent stresses show fluctuations for radii smaller than 5 mm, which is the region of the grooves and lands. Those fluctuations could be explained by the creation of stress concentrations created in that region [21]. The equivalent stresses obtained by the simulation without projectile showed a good match with the analytical stresses, whereas the equivalent stresses obtained by the simulation with projectile were higher than the analytical stresses due to the presence of the projectile. The rotation and translation of the projectile generate other types of stresses on the barrel, such as the axial stress and torsional stress. Fig. 16 Analytical and numerical equivalent total stresses for section 60 mm at 0.34 ms (left) and 120 mm at 0.38 ms (right) from the bottom of the barrel The second and third comparisons were made between the position and the velocity of the projectile results calculated by the numerical model two-phase flow [19] and the results obtained by the explicit analysis of the standard barrel, as it is shown in Fig. 17. The projectile position and velocity results obtained by the simulation showed good match with the results obtained by the internal ballistic model. 12 W. BOUKERA ABACI, N. HRISTOV, I. RADISAVLJEVIC, L. STOJNIC, A. ANICIC Fig. 17 Position (left) and velocity (right) of the projectile obtained by the numerical simulations and the internal ballistic model Fig. 18 shows the position of the projectile at the end time where the projectile reaches the muzzle. Fig. 18 Position of the bullet at the end of the simulation Figures 19 and 20 show a comparison between the equivalent total plastic strain obtained by the simulations and the deformations of the projectiles fired by the standard and the tasted barrels after the durability test. Fig. 19 Equivalent total plastic strain of the bullet fired by the standard barrel at the end of the simulation (left), experimental plastic deformations of the projectile (right) Fig. 20 Equivalent total plastic strain of the bullet fired by the used barrel at the end of the simulation (left), experimental plastic deformations of the projectile (right) Experimental and Numerical Investigation on the Performances of a Small Weapon Barrel... 13 Figures 19 and 20 show apparent similarity in the shape of the plastic deformation obtained by the experiments and the explicit dynamic analyses for both tested and standard barrels. At the beginning of the barrel lifespan, the engraving of the projectile outer surface is done at small accelerations. The uniform lands thickness is sufficient to allow the projectile to gain rotational velocity without further bullet-jacket deformation. The initial depth of the deformation will stabilize the smooth movement of the projectile on lands. However, with the continued use of the weapon, the interior surface will be deteriorated, and the thickness of the lands will decrease unevenly, the engraving of the projectile outer surface will be done far from the origin of refiling at significant accelerations. The bullet will no longer have a smooth movement on lands behavior and more azimuthal bullet-jacket deformation will occur, which will generate more vibration, more friction and material deformation energy loss, less rotational and directional velocities and a displacement from the initial spin axis. Figure 21, left, shows the velocities of the projectiles as a function of time determined by the simulations. The projectiles velocities reached are 717.29 m/s and 669.95 m/s for the standard and tested barrel, respectively. Fig. 21, right, shows the angular velocities of the projectiles as a function of time determined by the same simulations. The projectiles angular velocities reached are 171,824 RPM and 135,786 RPM for the standard and tested barrel, respectively. Fig. 21 (left) Projectile velocities and (right) angular velocities of the standard and tested barrels as a function of time From the simulations results, the projectiles initial axial directional velocities drops by 6.59% and 20.97% in the projectile initial angular velocities between the standard and tasted barrels. The initial angular velocity of the projectile is crucial in the projectile flight stability and affects the rifle precision. A reduction of 20% would affect the projectile flight stability and result in a sharp decline in the firing range and precision. Table 5 shows the initial velocities comparison between the experimental and the simulation results for both the standard and used barrels. The percentage of the difference between the experimental and the simulation velocities were less than 1% for both the standard and used barrels. The satisfactory agreements between the presented results increase the credibility of this work. 14 W. BOUKERA ABACI, N. HRISTOV, I. RADISAVLJEVIC, L. STOJNIC, A. ANICIC Table 5 Initial velocities comparison Standard barrel [m/s] Used barrel [m/s] Experimental results 720.21 664.82 Simulation results 717.29 669.95 Percentage of the difference Experimental vs. Simulation 0.41% 0.77% 7. CONCLUSION The paper presented experimental and numerical investigations on the performances of a small caliber rifle barrel during its lifecycle. Durability test experimentations were conducted on a 7.62 mm automatic rifle. Appropriate measurements were made to track the rifle performances during the stages of its lifecycle. After the durability testes, the used and the standard barrels were cut longitudinally using the wire-cut EDM process to enable the detection of the rifle’s internal surfaces damage using 3D scanning. Based on the 3D scans, ANSYS explicit dynamic analyses were conducted to investigate the behavior of the tested and the standard barrels. Special transitional mesh elements were used to be able to refine the regions where the interactions accrue between the barrel and the projectile. The following conclusions can be extracted from the experimental and simulation results:  The tests showed correlations between the performances of the rifle and the total number of shots fired. The muzzle velocity experienced a drop of 7.66% at the end of the tests while the rate of firing experienced an increase of 3.55%. The accuracy of the firing was independent of the total round fired number. According to the standard deviation of the shots and the CEP tests the precision of the rifle decreases with the repetitive use of the weapon.  The optical microscope images showed the degradation of the bore internal surface in the region of the origin of rifling. Moreover, according to the calculation of the average distance of the lands and grooves from the barrels axes the origin of rifling experienced the severest damage with total removal of the land material.  The numerical analyses showed satisfactory agreements with the experimental and the internal ballistic model results. The equivalent stresses obtained by the simulation without projectile showed good agreement with the analytical stresses. The projectile position and velocity results achieved by the simulation were similar to the internal ballistic model results. Furthermore, visible similarities in the projectile surface plastic deformation were captured between the experiments and the numerical analyses. On the top of that, the differences between the experimental and the simulation velocities were less than 1% for both the standard and used barrels.  According to the simulation results, the projectile experienced a drop of 6.59% and 20.97% in the initial and rotational velocities respectively between the standard and tasted barrels. Which also indicates the diminution of the rifle barrel performances. The explicit dynamic analyses were employed to provide a model of the short duration firing process for the standard and tested barrels. Since it is too expensive to perform physical testing, success in modeling this process can help in the improvement of the rifle’s Experimental and Numerical Investigation on the Performances of a Small Weapon Barrel... 15 design. A reliable explicit dynamic analysis can accurately predict complex responses, such as large material deformations and failure and interactions between the barrel and the projectile. 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