An interface shear damage model of chromium coating/steel substrate under thermal erosion load

Xio-long Li ,Yong Zng ,*,Yong Lin ,Min-yu M ,Lei Mu ,Qin Qin

a School of Mechanical Engineering,University of Science and Technology Beijing,Beijing,100083,China

b Institute for Advanced Materials and Technology,University of Science and Technology Beijing,Beijing,100083,China

c Beijing Key Laboratory for Corrosion,Erosion and Surface Technology,Beijing,100083,China

Keywords:Cr coating/steel substrate Thermal erosion Finite element simulation Ultimate shear strength Interface shear damage model

ABSTRACT The Cr-plated coating inside a gun barrel can effectively improve the barrel’s erosion resistance and thus increase the service life.However,due to the cyclic thermal load caused by high-temperature gunpowder,micro-element damage tends to occur within the Cr coating/steel substrate interface,leading to a gradual deterioration in macro-mechanical properties for the material in the related region.In order to mimic this cyclic thermal load and,thereby,study the thermal erosion behavior of the Cr coating on the barrel’s inner wall,a laser emitter is utilized in the current study.With the help of in-situ tensile test and finite element simulation results,a shear stress distribution law of the Cr coating/steel substrate and a change law of the interface ultimate shear strength are identified.Studies have shown that the Cr coating/steel substrate interface’s ultimate shear strength has a significant weakening effect due to increasing temperature.In this study,the interfacial ultimate shear strength decreases from 2.57 GPa(no erosion)to 1.02 GPa(laser power is 160 W).The data from this experiment is employed to establish a Cr coating/steel substrate interface shear damage model.And this model is used to predict the flaking process of Cr coating by finite element method.The simulation results show that the increase of coating crack spacing and coating thickness will increase the service life of gun barrel.?2020 The Authors.Production and hosting by Elsevier B.V.on behalf of China Ordnance Society.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1.Introduction

The life of modern barrel weapons is normally limited by erosion of the bore as opposed to fatigue[1].The thermal shock of high-temperature gunpowder gas is the main cause of barrel erosion[2-6],although barrel erosion involves a complicated mechanism[7,8].Various new intrinsic surface treatment technologies have been proposed to delay erosion of the barrel’s inner wall,including plasma spraying,magnetron sputtering,and chemical deposition.However,these new intrinsic surface treatment technologies are constrained by factors such as manufacturing cost,processing efficiency,and performance.Thus,these processes require substantial modification before they can be feasibly applied to the barrel.Cr has the advantages of being antierosion,wear-resistant,and low-cost to manufacture.For the last several decades,electroplating Cr has been used to protect the barrel’s inner surface,and is still the main means of extending its service life[9-13].

Because the Cr coating’s thermal expansion coefficient and that of the steel substrate are not matched,the Cr-plating coating often cracks under cyclic thermal stress due to insufficient toughness.On the one hand,the generation of Cr coating cracks provides a channel for the substrate erosion by the high temperature gunpowder gas.On the other hand,it causes the Cr coating/steel substrate interface’s damage degradation behavior.Finally,the supporting effect of the substrate on the Cr coating is weakened,and the crack spreads along the interface between the coating and the substrate,causing the Cr coating to peel off under the action of projectile impact and gas flushing.Underwood et al.[14-16]considered the influence of gunpowder heat on the interface stress,and proposed a shear failure criterion for the barrel coating material.Harris et al.[17,18]analyzed the interface damage evolution tendency of interfaces under transient thermal stress and pressure.

Researchers have designed a variety of simulation test methods to evaluate the material’s erosion effect and the interface damage in a barrel.Among these methods,laser heating technique has been well established to simulate the thermal shock and temperature rise on the internal surface of a barrel during a projectile launch process.For example,PJ Cote et al.[19-21]studied the formation of Cr-plated cracks of the barrel material under various atmospheres,the heat-affected zone in the base steel,and the interface degradation by using laser pulse heating technology.Underwood et al.[22]used laser heating to simulate the thermal damage process of different coating materials on the gun’s steel substrate.Warrender et al.[23]found that the coating’s fracture toughness changes as the laser pulse energy changes.Therefore,the laser heating method is an efficient,convenient,and energy controllable method for studying the thermal effect of high temperature on the barrel material.

The current study has been thus proposed to shed light on how thermal erosion affects the interfacial ultimate shear strength by conducting a series of coating cracking experiments.To this end,a laser emitter is used to apply thermal shock loading to each sample,thereby simulating the thermal erosion process.Meanwhile,in-situ tensile test and finite element simulation are performed for a better understanding towards a reasonable correlation between thermal erosion and interfacial limit shear strength.To describe the Cr coating/steel substrate interface shear damage process,we employ a cohesive zone model(CZM)based on elastoplastic mechanics,since the cohesive zone model has been widely used for cracking and failure of coating materials known for crack paths[24-29].Therefore,this study establishes a modified CZM of Cr coating/steel substrate interface shear damage considering thermal erosion factors,and the interface damage and coating flaking process are analyzed by finite element method.

2.Experimental procedures

2.1.Preparation of specimens

The tested material is selected from the 25Cr3Mo3NiNb barrel steel,annealed at 905°C.The chemical composition of the tested material is depicted in Table 1.The specimen is cut into a sheet-like tensile specimen as shown in Fig.1.The processed specimen is then double-sided polished to facilitate subsequent Cr plating.The Cr coating structure can be controlled by the current density,temperature,and energization mode during the electroplating process.In this study,a single coating of hard Cr is used.The specific process parameters are:220 g/L CrO3,2.6 g/L H2SO4,63-67°C solution temperature,30 A/dm2current density,and 1 h of plating time.

Table 1Chemical composition of the barrel steel.

Fig.1.Dimensions of the tensile specimen.

2.2.Laser thermal erosion test

The energy distribution of a circular laser spot can be expressed as:

where r0is the characteristic radius of the heat flow distribution and Q is the laser power(LP).

The transient temperature field in the specimen surface laser action area is[30]:

where k stands for thermal conductivity of the surface material,η the laser absorption rate of the surface material,a concentration coefficient of the heat flow,and x0the center of the laser spot.

The laser spot moves uniformly along the lengthwise direction of the specimen(x-axis).According to the heat conduction theory,the relationship between the specimen’s temperature change and the heat transfer is[31]:

whereρis the material density,c the material’s specific heat capacity,T the transient temperature field induced by the laser irradiation on the specimen surface,t the time,and I the heat generation.

During the firing process,the inner surface maximum temperature has been reported to range from 600°C to 780°C for a 7.62 mm caliber rifle[32,33],and from 700°C to 830°C for a 155 mm caliber gun[34,35].According to these references,a reasonable specimen surface temperature is obtained by setting the laser emission power appropriately.The identified relation between LP and maximum temperature on the coating surface during the erosion test is shown in Table 2.A laser beam(generated by a laser emitter)is perpendicularly projected to the specimen surface to mimic the thermal erosion process,as shown in Fig.2a.The circular laser spot has a 2 mm radius and moves at a speed of 500 mm/min with its to-and-fro movement pattern shown in Fig.3.In each test,the to-and-fro movement within the targeted thermal erosion zone is run 10 times,meanwhile a high temperature infrared thermometer(Raytek RAYR3I2ML3+,Fluke Process Instruments,United States)is used to measure and record sample surface temperature as shown in Fig.2b.

Table 2Surface maximum temperature of the Cr coating under different power of laser beam.

3.Interface ultimate shear strength

3.1.Principle of tensile test

Since the Cr coating/steel substrate is a composite material and the surface coating is very thin,conventional mechanical experiments are not feasible when determining the interfacial ultimate shear strength.Agrawal and Raj[36,37]proposed a tensile test for the ultimate shear strength measurement of brittle material with a tough substrate structure,as shown in Fig.4.The method works based on the principle that the Cr coating and the substrate simultaneously undergo elastic deformation under tensile load action.As the specimen is continuously stretched,the Cr coating’s tensile stress is transmitted by the interface.Since the Cr coating is a brittle material,it will first crack perpendicular along the direction to the stretching direction.When the number of cracks reaches at saturation,the coating’s tensile stress and the coating/substrate interface’s shear stressτreach equilibrium.The corresponding stress balance can be expressed as:

Fig.2.Test device of laser thermal erosion:(a)Laser emitter;(b)High temperature infrared thermometer.

Fig.3.The trajectory of laser spot.

Fig.4.Diagram of determining the interfacial ultimate shear strength by tensile test:(a)Initial state;(b)Crack saturation.

whereσbis the breaking strength of the coating layer,h the coating thickness,and L the spacing between two adjacent coating cracks.It is assumed thatσbis uniform over the longitudinal cross section of the coating layer.

3.2.Estimation of the interfacial ultimate shear strength

Displacement control is applied to the in-situ tensile testing machine at a speed of 0.1 mm/min.When an initial crack occurs on the surface of the coating,the corresponding strainεis recorded,as shown in Fig.5.Then the corresponding fracture stress is determined by multiplying the elastic modulus(280 GPa[38])of Cr and the measured fracture strain.The surface topography of Cr coating at the moment of crack saturation is characterized by scanning electron microscopy,as shown in Fig.6.The maximum crack spacing of the uneroded Cr coating is 25.36μm,and the Cr coating’s crack spacing increases significantly as the degree of thermal erosion increased.When LP is 160 W,the Cr coating’s maximum crack spacing expanded to 50.18μm.

Fig.5.Stress-strain curve of the thermal erosion specimens.

Based on the interfacial ultimate shear strength test results,the finite element models of the cases having L values of 25.36μm and 50.18μm are established by using ABAQUS/Standard.The parameters of the materials are shown in Table 3.The vertical displacement of the model is restricted,and transverse tensile load are applied at both ends of the specimen.The corresponding shear stress and tensile stress distributions under different crack spacing are obtained by simulating the stretching process,as shown in Figs.7 and 8.The stress contours demonstrate that the coating’s shear stress is concentrated at both ends of the crack,and the tensile stress is maximized in the middle of the crack.Furthermore,the stress distribution trends of the two different crack spacing samples are basically the same,and the shear stress shows an elliptical distribution trend[39].Therefore,in this study,the shear stress distribution of Cr coating/steel substrate interface can be expressed by an elliptic function:

Fig.6.Maximum crack spacing of Cr coating at saturation:(a)No erosion;(b)LP of 40 W;(c)LP of 80 W;(d)LP of 120 W;(e)LP of 160 W.

Table 3Parameters of the materials.

According to equation(4),the fracture strengthσbexpression of the coating can be obtained as follows:

where a=Lmax/2 and b=τuss.Thus,the interfacial ultimate shear strengthτusscan be formulized as follows:

Based on the above analysis,we calculate the interfacial ultimate shear strength change of the chrome-plated steel substrate with the degree of thermal erosion.As shown in Table 4,the Cr coating/steel substrate’s interfacial ultimate shear strength reduces from 2.57(LP=0 W)GPa to 1.02 GPa(LP=160 W),which shows a significant weakening effect due to increasing temperature.

Fig.7.Distributions of the interfacial shear stress and coating tensile stress with a crack spacing of 25.36μm.

Fig.8.Distributions of the interfacial shear stress and coating tensile stress with a crack spacing of 50.18μm.

Table 4Interfacial ultimate shear strength of Cr coating/steel substrate of different thermal erosion specimens.

4.Cr coating/steel substrate interface shear damage model

4.1.Interface cohesion zone

According to the principle of tensile test,after the surface crack is formed,the substrate continues to stretch the Cr coating,and the stress of the Cr coating is transmitted by the interface,so that the Cr coating and the steel substrate have higher stress near the end of the interface.Fig.9 shows the cross-sectional microscopic morphology of the specimen perpendicular to the tensile direction.Due to the shearing force,voids nucleation occurs and gradually grows to form incipient micro-cracks.The cohesive fracture-based CZM proposed by Dugdale[40]indicated that there is a fracture process zone at the crack tip.The constitutive relationship between cohesion and open displacement was established in this region,which could effectively describe the crack change process.Therefore,this study establishes a specialized CZM that evolves from the nucleation process,as shown in Fig.10.

Typical cohesion zone models include bilinear,trapezoidal,polynomial,and exponential forms.The first two models belong to a linear discontinuous model,while the tension-separation relationship in polynomial and exponential models is nonlinear and continuous,more in line with the actual case.The exponential cohesion model shows a better predictive performance,particularly for the crack initiation and cracking of the thin film coating on the tough substrate.The fracture energy control equation of the CZM under case of the two-dimensional plane stress state is[41-44]:

whereΔnandΔtare the normal and tangential displacement values at the interface,φnthe normal fracture energy,andδnandδtthe characteristic displacements(the displacement value corresponding to the stress maximum point)of the normal and tangential interface cracking,respectively.The expression of q and r is as shown in Eq.(9):

whereφtis the interfacial fracture energy required to form a complete interface crack under pure shear state.Δn*is the normal displacement value when the normal stress is zero and the tangential direction is completely cracked.The stress expression on the interface is:

Fig.9.Cross-sectional micromorphology of the specimen perpendicular to tensile direction.

Fig.10.Schematic diagram of the CZM of the Cr coating/steel substrate interface:(a)Void nucleation;(b)Damage initiation.

The exponential cohesion’s normal strength and tangential strength(stress maximum)areσmaxandτmax,respectively,and the relationship between these parameters in the exponential cohesion model is:

Since the Cr coating/steel substrate interface cracking process in a gun barrel is only related to the shear stress and belongs to the slip-open type(type II)cracking,the normal displacement isΔn=0.Then,the relationship between the fracture energy control equation and the tension displacement in the shear direction is as follows:

According to Eq.(14),in order to describe the tangential traction-separation curves for the exponential CZM,it is also necessary to determine the tangential interface characteristic length,δt.d describes the relative displacement between the initial crack(Fig.11a)on the Cr coating’s surface to the moment of reaching the saturated crack(Fig.11b).At this time,the shear stress in the cohesive zone reaches the maximum value,and the interface damage begins to occur.Since the Cr coating’s deformation force in the process is generated by the interface,the tangential interface’s characteristic lengthδtcan be expressed as:

4.2.Modified tangential damage CZM

The Cr-coated steel substrate’s bonding interface is affected by the high temperature cyclic load and the interface is damaged.For the temperature load,the cohesive energy damage factorλs(0<λ≤1)and the interface characteristic length damage factorλδare introduced,and the fracture energy control equation model is modified to obtain the shear state fracture energy control equation considering the damage:

Thus,the tangential tension-displacement relationship is determined as:

Fig.12 shows the crack width at the maximum crack spacing for saturated cracks.The Cr coating’s crack width increases with the degree of erosion.The average crack width increases from 0.714μm(no erosion)to 0.9μm(LP=160 W),which is related to the reduction of the Cr coating fracture stress.The value ofλδfor the specimen without any erosion is set to be 1.0,and the characteristic length factor of the corresponding different erosion states is determined.At the same time,the value ofλsis determined in combination with the interfacial shear strengthτmaxobtained by derivation.

Fig.12.Saturation crack width of Cr coating:(a)No erosion;(b)LP of 40 W;(c)LP of 80 W;(d)LP of 120 W;(e)LP of 160 W.

Fig.13 shows the relationship betweenλδand the Cr coating surface temperature changeΔT,which is defined by whereΔT=T2-T1,where T2is the coating surface erosion temperature and T1the specimen’s initial temperature.The results indicate a good linear relationship between these two variables.Fig.14 shows thatλsdecreases linearly with an increasing ofΔT.Therefore,the expression ofλδwith respect toΔT is established as follows:

Fig.13.Fitting curve of coating surface temperature variation andλδ.

Fig.14.Fitting curve of coating surface temperature variation andλs.

Likewise,λsis expressed as:

where k1=0.001/°C,l1=0.47,k2=-0.0029/°C,and l2=2.52.Thus,it can be inferred that interface begins to exhibit tangential damage when the Cr coating’s surface temperature reaches 550°C.The Cr coating thickness in a real barrel is greater than that of the test specimen,and thus the initial surface erosion temperature related to the interface tangential damage could be even higher.

The tangential fracture energy curves and the tangential traction-separation curves with different thermal erosion damage degrees are obtained based on the modified shear damage model,as shown in Fig.15 and Fig.16,respectively.Bothλsandλδtogether control the trend of fracture energy.Since the change in interface characteristic length change is not significant,the interface damage shows a stronger dependence onλsthanλδ.Moreover,the interface damage gradually increases with a decreasingλs.The critical maximum tangential fracture energy decreased from 1514 J/m2to 756 J/m2as the LP increased to 160 W.For the traction-separation curve of interface damage,the shear strength decreases obviously with increasing of thermal damage.Therefore,by introducing damage factors,the modified shear damage model can characterize the interface’s decreasing trend bearing capacity due to the accumulation of damage.

Fig.15.Interface tangential damage fracture energy.

Fig.16.Interface tangential damage traction-separation curve.

5.Failure analysis of steel substrate/Cr coating interface

5.1.Establishment and simulation of finite element model

A two-dimensional Cr coating/steel substrate model is established and a cohesive zone in nearly zero thicknesses[45]is located at the interface between the coating and the substrate by using ABAQUS/Standard.Cohesive zone parameters are determined based on the discussion in Section 4.The initial criterion of material damage in the cohesive zone is the maximum stress criterion,and the damage evolution is simulated using the energy control method under the independent mode(Mode-Independent).The bottom of the substrate is completely constrained,and a tangential load is applied to the upper surface of the coating to simulate the process of the projectile rubbing the Cr coating,as shown in Fig.17(a).The coating and the substrate mesh are of the Standard type(CPS4R),and the mesh type for cohesive area is Cohesive(COH2D4)[46].In addition,mesh refinement has been used in the transition area of the coating and the substrate,as shown in Fig.17(b).The steel substrate/Cr coating interface failure process without considering the effects of temperature can be seen from Fig.18.Under the influence of the tangential load,the interface begins to appear damaged.When the critical maximum tangential fracture energy is reached,the interface completely fails and the coating eventually separates.

5.2.Effect of coating crack spacing

The coating crack spacing L is set from 10μm to 50μm,and the surface shear stress-displacement curve is extracted,as shown in Fig.19(a).It is found that the surface shear stress of the Cr coating increased from 538 MPa with L of 10μm-841 MPa with L of 50μm.The compressive stress of the Cr coating gradually decreases with the increasing of the coating crack spacing.The internal compressive stress of the Cr coating with L of 50μm is only one fourth of which with crack spacing of L=10μm,as shown in Fig.19(b).It indicates that an increase in L leads to a higher friction force(between the projectile and the bore inner surface)to cause the interface damage and the coating fall off.And an increase in L can also effectively reduce the degree of extrusion load inside the Cr coating.According to the shear stress-displacement curve at the interface during the separation process,as shown in Fig.19(c),the spacing of the Cr coating does not affect the shear strength of the interface.

Fig.17.Two-dimensional Cr coating/steel substrate model:(a)boundary constraint;(b)mesh generation.

Fig.18.Steel substrate/Cr coating interface damage and failure process:(a)load application;(b)interface damage;(c)interface failure;(d)coating separation.

5.3.Effect of coating thickness

Taking the Cr coating thickness H as a variable,the surface shear stress-displacement curve of the coating with different H and the internal compressive stress-displacement curve of the coating are obtained,as shown in Fig.20(a)and Fig.20(b),respectively.The data shows that with the increase in H,the shear stress of the coating surface increases from 710 MPa with a H of 5μmto 892 MPa when H=9μm.Meanwhile,the compressive stress of the Cr coating decrease from 818 MPa to 415 MPa.Therefore,an increasing in the thickness of the Cr coating could increase the threshold at which the contact friction of the projectile causes the coating to flake off,and reduce the degree of extrusion load inside the Cr coating.The change in the thickness of the Cr coating does not affect the shear strength of the interface,as shown in Fig.20(c),which is consistent with the conclusion of the effect of the coating crack spacing.

Fig.19.Stress-displacement curves of coating and interface under different coating crack spacing:(a)coating surface shear stress;(b)coating compressive stress;(c)interfacial shear stress.

Fig.20.Stress-displacement curves of coating and interface under different coating thickness:(a)coating surface shear stress;(b)coating compressive stress;(c)interfacial shear stress.

6.Conclusions

(1)The thermal erosion simulation of the barrel bore can be realized by using the laser emitter.Through a combination of the in-situ tensile test and finite element method,we obtain the elliptical distribution law of interface shear stress for the Cr coating/steel substrate.In this study,the initial surface erosion temperature of interface shear damage,which is 550°C,is obtained by introducing the damage factor into the exponential cohesive zone model,and the relationship between Cr coating surface temperature and interface shear damage is established.

(2)The finite element simulation analysis of interface shear separation process shows that the increase of coating crack spacing and thickness is conducive to reduce the extrusion stress of coating,and increase the tangential stress of coating falling off caused by bullet friction.It should be noted that the change of coating crack spacing and thickness does not affect the shear strength of the interface.Therefore,by improving the preparation process to increase the crack spacing of Cr coating in use,and appropriately increasing the coating thickness,the service life of gun barrels can be extended.

Declaration of competing interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.