Numerical evaluation of an autofrettaged thick-walled cylinder under dynamically applied axially non-uniform internal service pressure distribution

Onur Güngör,Veli Çelik

aMKE Kurumu Mühimmat Fabrikası Ar-Ge Müdürlü˘gü,71100,Merkez,Kırıkkale,Turkey

bYıldırım Beyazıt Üniversitesi Do˘ga Bilimleri Fakültesi,06010,Keçiören,Ankara,Turkey

Keywords:Gun tube design Thick wall cylinder Residual stress Internal ballistics Service pressure Wall thickness Numerical modeling of internal ballistics

ABSTRACT A dynamical moving pressure structural numerical calculation model using the internal ballistics calculation pressure-time results was constituted and the vicinity of the internal ballistics and quasiinternal ballistics structural model was checked.The Von Mises stresses obtained by the dynamical structural numerical model calculations and the Von Mises stresses calculated from the shot test strain measurements were compared.The difference for the worse case was 20%and for the best case was 0.1%.Furthermore,the model gave better agreement for the higher charge masses.The numerical structural quasi-internal ballistics computation model created was verified for the top charge mass which represents the highest stress condition and used in a gun barrel design.

1.Introduction

Inspection of the effects of the pressure in a gun barrel which is the result of the ignition of the propellant in order to propel the projectile along the barrel and which creates different loading conditions at different points of the barrel,has been the subject of various studies.Rabern and Lewis[1]performed two and threedimensional simulations to study the effect of this pressure front and its influence on projectile gun tube interaction and lateral movement of the projectile in the gun tube caused by variation of the gun centerline during projectile launch and recoil.Tzeng and Hopkins[2]studied the dynamic effects of moving internal pressure througha composite barrel by using finiteelement method.Qu et al.[3]studied the influence of the autofrettage levels on the residual stress distribution of the rapid- firing gun barrel after autofrettage and 50 consecutive shots were investigated by using the thermal-structure direct coupling method.

In the former study[4],residual stresses inherited by the autofrettage process and changes in the residual stresses in the inner and outer diameters where material removed from the barrel by machining after autofrettage process were incorporated into the numerical calculations by using Abaqus finite element software[5].The efforts given to understand the autofrettage and postautofrettage processes,were not included in this work.

2.Materials and methods

The autofrettage operation was verified by comparing numerical calculation results and permanent expansion measurements,after autofrettage process.The sections removed by machining were also removed from the numerical model by using proper subtraction technique explained in the Abaqus user's manual[5]to obtain the residual stress state of the gun barrel at the onset.Internal ballistics calculations were done using BALLISTICeda software MKEK release that MKE Corp. financed EDA Engineering Design&Analysis Co.to develop.Inside the barrel,the one-dimensionalmotion of projectile with spin was simulated by using the software[6].After this step,a separate finite element model was created to affect the load on the barrel during the movement of the projectile in the barrel,which changes according to the axis and the projectile motion.For this,a disc with a mass equal to the mass of the projectile was included in the model.The internal gas pressure vs.time profile from the ballistics calculation was applied to the bottom side of the projectile.Since the projectile was mobile,it was necessary to write a subroutine within Abaqus[4]to apply the pressure-time curve to the inner wall of the barrel behind the projectile.The subroutine applies pressure values corresponding to the time of the pressure time curve to the inner wall of the barrel according to the new position,which occurs with the pressure applied behind the projectile for each millisecond of time.In this way,the load forces in the gun barrel due to the gas pressure could be calculated.The load that the projectile applies to the gun barrel due to friction was defined using friction coefficient of 0.15,which was the highest value that would define the friction surface at the projectile-barrel interface and it would not increase the calculation burden.The most important reason for choosing the highest value of friction coefficient here was to be able to include in the calculations the resistance forces that would occur during the engraving process,due to the rifling of the barrel,in the basic model.Because,one of the effects that delay the movement of the projectile in the gun barrel is actually the engraving of the driving band.The commencement of rifling region is the region where the highest frictional forces occur between the gun barrel and the projectile during the engraving process.The details of the model are described in Fig.1.Preliminary trial calculations were conducted to make the subroutine work correctly.The consistency of the results was checked and the confirmed the pressure was loaded correctly onto the barrel and behind the projectile.

The projectile starts to move with the effect of pressure applied(forward and spin motion).In this calculation,the internal ballistics simulation was dynamically handled with the structural behavior of the materials in the structural simulation program.The structural analysis and the internal ballistics calculation were interconnected in a sense.In Abaqus,angular velocity vs.time values from internal ballistics calculations could be applied on the projectile as boundary conditions to simulate the spinning motion that results in circumferential frictional forces at the barrel-projectile interface in addition to the axial ones.Unfortunately,spin could not be applied because of subroutine did not let to do so.So that,frictional forces because of axial motion of the projectile could be included in the model but frictional forces because of rotational motion could not.In the above-mentioned model frame, first of all,autofrettage was applied to the original dimensions of the gun barrel by displacing the inner radius as much the autofrettage ratio then the machined inner and outer parts of the gun barrel were numerically removed from the model and the pre-stressed barrel was obtained.

Using pressure-time profiles calculated from internal ballistics calculations,together with the structural simulation model described above,then the loading profile could be extracted along the axis of the gun barrel for different combinations of ammunition and propellant masses.Obtained findings were compared for different ammunition models with different charge masses to stress values obtained in shot tests with the gun barrel having the same dimension as with the model.Loading conditions differ for different types of ammunition and propellant charge in the barrel in each case.The maximum loading for this gun barrel is for the long-range ammunition which is the situation when trying to send the ammunition to its longest range.

In Fig.2,the upper part of the figure shows that the projectile is in the start position to move and the gun barrel having the stresses left on after autofrettage and chip removal processes respectively.In the lower part,the stress distribution of the gun barrel and the highest Von Mises stress are shown where the pressure is highest.For different combinations of ammunition and propellant masses,the place where the highest stress occurs and the amount of stress varies.The figure below shows the load case that can occur at the highest working pressure.

3.Results and discussion

A series of tests were held in Ministry of Defense firing range in Konya.One dimensional rosette type strain gauges were used.For the measurements,the total of six strain gauges was bonded on the gun barrel at three different angles(-45o,0oand+45oto the barrel bore axis)and two different positions(470 mm and 670 mm off from the breech)(Fig.3).

3.1.Ballistics and numerical dynamic model calculation findings

The pressure time obtained by the ballistics calculation was applied in the structural numerical model.Travel time and velocity time curves calculated by both models of the projectile in the barrel are compared below(Fig.4 and Fig.5).In this way,it was desired to demonstrate that the loading case is accurately represented in the structural model by showing the internal ballistics harmony.

Compared to the ballistics calculations,it was determined that the projectile moves faster in the barrel in finite element model calculation(Fig.4 and Fig.5).The projectile leaves the barrel approximately 2.5 ms early in Abaqus calculation.The early departure of the projectile from the barrel was an indication that it begins to accelerate earlier and it was considered that the delay of the projectile during the engraving process was not fully represented in the model.Furthermore,the complexity of applying the changing friction coefficient in terms of time and disabled rotational friction effects because of the subroutine in Abaqus might have led that kind of result.

From Figs.5 and 6,it can be seen that the highest pressure point in the barrel compared to the internal ballistics calculation is normally a little further ahead than expected due to the faster advancing movement of the projectile.This means that the critical section where the stresses are highest is displaced a bit forward in structural quasi-internal ballistics model compared to internal ballistics model.This might represent an unexpected increase of the pressure in reality so that by using the calculated stress results of the quasi-structural internal ballistics model might end up with a safer design of a gun barrel.Considering these possibilities that,critical section where the loading occurs most is the first 15%of the gun barrel throughout the length.The muzzle velocities are also similar to each other,but there is a bias in velocity and time(Fig.5).

3.2.Comparison of measurement and calculation results and determination of model accuracy

When the stresses on the normal and the shear stresses occurring on the surface of a plane are measured according to the coordinate system,the principal stresses(Fig.7)of the unit element can be found by rotating the coordinate system at an angle where shear stresses to be zero and the highest normal and shear stresses can be expressed in terms of each other.Thus,the safety condition of the material is evaluated by calculating Von Mises Stress with the help of the principal stresses found.Von Mises stresses were calculated by using normal and shear stresses obtained by measurements which were used to calculate principal stresses.

Similar to the strain gage measurements,Von Mises stresses were obtained in the calculations by placing artificial probes on the barrel construction elements 470mm and 670mm from the barrel breech.Internal ballistics curves obtained by ballistics calculation and used in structural numerical calculations were calibrated with measured barrel exit velocities.The values obtained from numerical calculations performed with different charge masses weresummarized below and compared to the measurements(Tables 1 and 2).

Table 1 Measurement and calculation results.

Table 2 Corrected measurement and calculation results.

At first glance,it can be seen that there are serious differences between measurement and calculation values(Table 1),but it should be noted that the diameter expansion of the barrel exposed to loading with pre-tension is less than without pre-tension one.The working logic of strain gauges is to detect the shape change and to pass the strain values in the frame of the material properties of materials.For this reason,a material with less deformation will cause a less calculated stress value to be assessed.That's why the residual Von Mises stresses calculated must be added to the measured Von Mises values.The residual Von Mises stress on the element at the position where the N-R01 strain gauge was placed at is 365.89MPa and the element at the position of the N-R02 strain gauge is 343.49 MPa.The following table appears when these values are added to the measured values(Table 2).

CM1 represents the minimum,CM2 the medium and CM3 the maximum charge mass.Fig.8 shows that while increasing the charge mass,calculated(NR#-C)and measured(NR#-M)values of Von Misses stresses were getting closer.The difference for the minimum charge mass(CM1)between the calculated and measured stresses was up to 20%,for the medium charge mass(CM2),it was up to 9%and for the maximum charge mass(CM3),it was up to 0.6%.For the best case,the difference was 0.1%.It was determined that the calculation models have very close results for the highest charge mass compared to the lower charge masses.To calibrate internal ballistics models,the Doppler radar measured muzzle velocity and copper crusher measured maximum pressure and those values were utilized.In similar closed volume systems,for the lower propellant charge masses,the volume between projectile and propellant is more than the one for the higher charge masses.This results in the changing of internal ballistics hence the standard deviation increase of muzzle velocities.Therefore,it's harder to calibrate the highest volume(lowest charge mass)state.If piezoelectric pressure transducer could have been utilized,there could have been the better ballistic match for each circumstance.

As a result,the numerical structural quasi-internal ballistics computation model created was verified for the top charge mass which represents the highest stress condition and used in a gun barrel design.It is also concluded that results of strain measurement should be carefully examined.

Acknowledge

The author would like to thank Ministry of Science,Industry,and Technology which supported this project under the Industrial Thesis Support Program,to Ankara Yıldırım Beyazıt University and MKE Corporation and to everyone who contributed to the Project.