Simulation and experimental study on the surface morphology and energy lost of the target material under non-overlapping impact of angular particles

College of Pipeline and Civil Engineering,China University of Petroleum(East China),No.66,West Changjiang Road,Huangdao District,Qingdao 266580,China

Keywords:Multi-impact experiment Angular particle Surface morphology Energy lost ABAQUS/CAE simulation

ABSTRACT In order to further understand the effect of solid impurities on pipeline wall during erosion,the particle impact process without fluid was extracted for specific study.The effect of multi-impact particles on the wall of pipeline was studied experimentally and simulated.In this experiment,an improved ejection apparatus was implemented to carry out multi-impacts non-overlapping impingement by rhombic particles made of high speed steel(W18Cr4V)on the AA6061 aluminum alloy plate through changing particle angle,incident angle,orientation angle and impact velocity.As a result,each particle's penetration depth was investigated and particles'rebound trajectory can be described through this experiment as well as surface morphology of the target material after impingement.The ductile damage criterion,shear damage criterion and MSFLD damage criterion were jointly implemented in ABAQUS/CAE software to simulate the whole process of collision which proved to be effective by getting consistent result compared with experimental data.It is found that under the condition of continuous non-overlapping impact,the target material produces a small work hardening effect in the impact area by converting kinetic energy of moving particles into internal energy of plate so as to reduce the penetration depth of each impact particle.

1.Introduction

Mostly in the procedure of oil and gas transportation are complicated two-phase [1]or three-phase stream [2,3].The solid particles existed in oil and gas production and the mechanical impurities in the pipeline impinge on the wall with fluid movement,resulting in erosion[4]and wear of the inner wall of the pipe which can cause huge economic loss and safety accidents,especially in the component with a sudden change in flow direction like bend pipe[5,6],tee[7,8]and reducer[9,10].Relatively mature theories have formed in the macroscopic study of pipeline erosion failure,such as DNV erosion model [11],Zhang et al.erosion model[12],Ahlert erosion model[13],Oka et al.erosion model[14]which are usually applied in CFD flow simulation[15]software to predict the impact sites and erosion rate of complex sandbearing two-phase or multi-phase flow happened in straight pipe[16],bend pipe,Tee and reducer.The pipeline is improved based on the simulation results to thicken the erosive sites or to create a buffer space by changing the original structure of pipeline to reduce the impact momentum of particles to lower impingement effects.

The macroscopic study in the prediction of erosive area[17]in pipeline is remarkable.However,the research can only provide consultative suggestions for the prevention of pipeline erosion while cannot get a further understanding of erosive theory for lacking mechanical property and energy lost analysis after impingement of particles.As a result,the erosion study should start from micro level.There are several classical erosion theories in earlier times include the micro-cutting theory of Finnie[4],the deformation wear theory of Bitter[18],the platelet theory of Levy[19]and the rigid-plastic theory of Hutchings[20].These models have their own pertinence.But also have shortcomings.Micro-cutting theory was the first complete theory to quantitatively describe the impact of rigid particles on plastic metals,but it mainly explained the erosion behavior at low impact angle.The prediction of impact behavior under high impact angle and brittle material erosion was not acceptable due to the high deviation.The theory of deformation wear has been verified on a single particle erosion wear tester,however it lacks physical model to support.The platelet theory was proposed based on the statistics of a large number of experiments.Hutching's theory mainly studied the normal impact of spherical particles,which has certain usage limitations.

On the basis of the above theories,the later research was carried out on the combinations of different impact particles and target material.R.Sahooh et al.[21]employed a statistic approach to evaluate the effect of microstructural degradation on solid particle erosion behavior of 2.25Cr-1Mo steel in sand blast experiment.The static influence of four control factors on steel are given respectively.E.Avcu et al.[22]used various analysis and models of scanning electron microscope to investigate the effect of Al2O3erodent particle impact on Ti6Al4V alloy.In these studies,sand-blast experiment was conducted to obtain the statistic result of erosion behavior by employing a great bunch of particles whose specific characteristic was neglected.In the study of one or several impact particles,sphere particles were taken as the research object on some occasion to simplify the operation complexity of experiment and simulation.Tirupataiah et al.[23]implemented 10 target test materials to characterize the nature of elastic rebound of a tungsten carbide ball and the function relationship was explained on the basis of simple theoretical models.Papini and Spelt [24]analyzed the erosion behavior of a thin coating on a steel substrate under the impact of individual steel spheres.Particles were set in rhombus for a more precise and accurate result.Hutchings and co-workers [20,25,26]developed the rigid-plastic theory and predicted the collision kinematics and crater dimensions for square and spherical particles.Papini and Dhar described an improved rigid-plastic model[27–29]and verified it through a wide range of experiments of single angular particles [30].However the research of angular particles are still rare.

FEM(finite element analysis method)[31]was widely used in particle impact simulation.Shimizu et al.[32]simulated and analyzed the plastic deformation of alloy surface due to the impact of single particle in different angles.Azimian et al.[33]created a 3D FEM model in Lagrange reference frame to simulate the erosion behavior due to single multi-particle impacts.Recently a new SPH(smoothed particle hydrodynamics) [34]method originally applied in aerodynamic analysis gradually appeared in impact wear simulation.Dong et al.[35,36]analyzed the erosion behavior include rebound behavior and rotating behavior by implementing SPH method and proved the effectiveness of this method by obtaining good agreements with experiment.However further exploration is still needed to determine whether the simulation of other collision parameters are valid.The ductile[37],shear[38,39]and Müschenborn–Sonne Forming Limit Diagram(MSFLD)damage initiation criteria[40]exhibit great effectiveness in the simulation of material damage and removal.This paper creatively applied this method to simulate the material removal and chip separation procedure which showed great agreement with experiment data.

In this paper,the accurate penetration depth histogram of particle under multiple non-overlapping impacts was measured on the surface of target material.Combined with the analysis of stress distribution and energy absorption resulting from ABAQUS/CAE simulation to make a further understanding on the non-linear variation regulation of crater volume.In the same time,the collision crater shape varied with incident parameters were also obtained.

2.Experimental

2.1.Experimental device

The experimental device employed in this paper was designed and built according to Dhar's catapult apparatus [29]in 2005.It implemented a whole rectangular stainless steel plate with a huge mass as the base to reduce mechanical vibration during impact.The catapult was loaded manually by pushing down the launching end of the arm until it was locked into the release mechanism.A hard robber block attached on the apparatus was employed to stop the arm once it was launched.The elastic potential energy of the spring was converted into the kinetic energy of the particle which was held by a holder attached at the end of the arm through this progress.The arm was clamped by the bearings besides to ensure the particles being impacted at the same position.The soft plastic protective cover in rectangular shape was built,which effectively prevented the particles from flying away after hitting the target material.By changing the spring(parameters in Table 1)with different elastic coefficients to get different ejection velocities,spring elastic coefficient can be calculated by Eq.(1):

where,d is wire diameter,Dmis mean coil diameter,equal to O.D.(outside diameter)minus wire diameter.Ncis active coil number,equal to total number of coils minus 2.

Table 1 The parameters of spring

2.2.Experimental material

The target material used in the experiment is AA6061 aluminum alloy which has a low value of hardness and an excellent plastic deformation property.Crater is able to be easily generated after impingement.In the process of experiment,the enlarged particles are adopted for that it is not easy to carry out the experiment with tiny particles.High speed steel(W18Cr4V)is chosen for particle material with hardness value HRC65,which is much larger than aluminum alloy target plate(hardness value is HB30).This property can ensure that particles'deformation can be neglected.The particles are three-dimensional in rhombic shape.They are all in same mass quality.The width of the particle is constant.The front edge line of particles can create craters when impinges on the surface,and the target material is polished to make the surface smooth before experiment(Fig.1).

Fig.1.Targets and particles used in experiment.

2.3.Data and image acquisition device

There are four related variables in this experiment,each time to change a parameter will conduct three parallel experiments.5 particles impact continuously on the target in an experiment.The crater depth is measured by a 3D confocal laser scanning microscope in Fig.2.The mean value of three measurements is taken as the final result.High speed camera from Japan company(version MEMRECAM HXLink HX-7S)is adopted which can reach to 5 megapixel at 800 fps.The highest shooting speed can reach to 210000fps.Cold light lamp is employed to meet the light demand.Friction occurs when the ejection arm rotates on the bearing,some of the energy is consumed in the form of heat.As a result,the real impact velocity of particles is determined by high speed camera[41].

Fig.2.3D scanning picture of crater.

3.Simulation Methods

3.1.Material model

The density of the particle is ρ=14,850 kg·m?3,Poisson's ratio is υ=0.22,young's module is E=640GPa.Target material is AA6061 aluminum,density is ρ=2700 kg·m?3,young's module is E=70GPa,Poisson's ratio is υ=0.33,yield stress is σ0=130 MPa.After the target material reaches the yield point,the plastic deformation occurs and chip separation happened.Plastic stress–strain relationship is obtained by Ramberg-Osgood equation.

where,the value of B and H is B=7GPa,H=3.0,the elastic–plastic property data is made in a table to input into the Material Model in ABAQUS/CAE.A maximum plastic strain of 20%criterion is used to capture material failure before maximum strain is reached.The particles and target material used in the experiment are depicted in Fig.3.The two-dimensional definition diagram of particle parameters is demonstrated in Fig.3.viis the impact velocity,αiis the initial incident angle between the velocity direction and the horizontal line of the target surface.θiis the initial orientation angle between the diagonal of the particle and the vertical line of the target material.vr,αr,θrare defined as rebound velocity,rebound angle and rebound orientation angle.A is the particle angle penetrate into the target surface.H is the side length of the particle,W is the depth of the particle.(The unit of velocity is m·s?1,the unit of length is mm,the unit of angle is(°)).

3.2.Ductile damage criterion

For ductile material,the deformation of the target plate is unavoidable for the impact object whose hardness is far higher than the target material.Three main process of ductile failure can be described as void nucleation,void growth and void coalescence.The ductility criterion used in the model assumes that the equivalent plastic strain at the beginning of damage is a function of the triaxial stress and strain rateHere the η=?p/q is the triaxial stress,p is pressure stress,q is the equivalent stress,is the equivalent plastic strain rate.

The ductile failure initiation criterion expressed by equivalent plastic strain rate is

Fig.3.The definition of angle and velocity of the particle.

3.3.Shear damage criterion

Shear failure is caused by shear band localization.For shear failure,it is assumed that the equivalent strain at fractureis a function of the shear stress ratio,θS,given by

where,ksis a material parameter and the value of it in this paper is 0.3,φ is the ratio of the maximum shear strain to the equivalent strain(Von Mises),given by:

The shear failure initiation criterion that is represented by a correlation to the equivalent plastic strain is given by

4.Results and Discussion

4.1.Model verification

We should know that the hourglass phenomenon in ABAQUS/CAE software is a numerical problem existed with unit itself which is unavoidable in simulation.In order to control it,energy balance should be calculated to prove the model's effectiveness.The equation can be described as:

The energy definition can be found at[40].To avoid excessive artificial or spurious strain energy(hourglass effect),ECD(artificial strain energy) should be a small fraction of internal energy (1%–2%).This condition is verified to compare the artificial strain energy (ALLAE)with the total strain energy(ALLIE)in Fig.4.Energies with a value of zero were not plotted.

Fig.4.Comparison of energy vs.time.

The experimental results under the conditions of particle angle of 45°,impact angle of 71.2°,orientation angle of 5.5° and velocity of 15.6 m·s?1are compared and analyzed with the simulation results.The polyline chart of impact crater depth was obtained as shown in Fig.5.The maximum crater depth difference between the simulated value and experimental value is about 10.0 μm,less than 10%of experimental value,which is acceptable.

Fig.5.Polyline chart of experimental and simulated penetration depth.

4.2.Particle velocity

In the parameter study of particle velocity,the other parameters such as the particle angle,impact angle and orientation angle of the experiment are set as 45°,71.2° and 5.5° respectively.The velocity calculated through paragraphs shoot from high speed camera can reach to 13.5 m·s?1,15.6 m·s?1,17.2 m·s?1.The relative measurement error is about±0.5 m·s?1the particle's kinetic energy is related to particles' velocity.Higher velocity can cause more sever destruction to pipelines.Fig.6 shows that the residual stress on target surface changes with incident times.The surface area on the target contacted with particle's penetration anger is the location where generates maximum residual stress for its high impact force acts on a small area.The kinetic energy remains to be small after impingement process due to energy dissipation as well as energy conversion from kinetic energy whose transform rate shows to reach to 74.16%,76.72%,75.64%in Fig.7.It is noted that most of the kinetic energy form of particle is stored in the target material.Penetration depth under each impact was demonstrated in Fig.8.The decrease of depth under each time of collision proved the protection of surface residual stress.

Fig.7.Kinetic energy loss of particles and internal energy increment of target material.

Fig.6.Distribution of Mises stress near crater vs.impact times.

Fig.8.Penetration depth vs.velocity(vi ).

4.3.Particle angle

Here particle incident angle is set as 15.6 m·s?1,impact angle is 90°±2°,orientation angle is 5.5°±2°.Pictures are shot for the first impact procedure of particles whose angles are set as 45°,60°,90°,120°,135°.Particles with higher impact angle are more prone to rotate around the adjacent angle once it hit to the target surface in Fig.9.While in simulation we enlarge the range of particle angles of which are set as 30°,45°,60°,90°,120°,135°,150°respectively.Internal energy graph is obtained in Fig.10 and shows a tendency to increase first and then decrease with the maximum energy absorb value happened in 120°.While the running speed of model keeps declining with the increase of particle angle.Damage dissipation energy can be the highest when the particle angle is 45°and then decrease with angles become larger as is depicted in Fig.11.Graph of Penetration depth of particle verses particle angle is shown in Fig.12.

4.4.Incident angle

Fig.10.Internal energy vs.time under different particle angles(A).

Fig.11.Damage Dissipation Energy vs.time under different particle angles(A).

Fig.9.The experimental graphs of impact under different particle angles(A).

Fig.12.Penetration depth vs.time under different particle angles(A).

Fig.13.Surface morphology under different incident angles(αi ).(a)Incident angle 65°(b)Incident angle 45°(c)Incident angle 35°.

Fig.14.The distribution of surface stress and the two-dimensional morphology of target material after fifth impact under different incident angles(αi ).

Incident angle varied by rotating target plate.Particles with A=45°are adopted in the experiment,and velocity is 15 m·s?1.Fig.13 shows the crater topography of target material corresponding to the single impact of the experimental particles at the incident angles of 65°,45°and 25°.It shows that Material accumulates in front of the surface crater when particles impact at a high incident angle.However,particles only scratch from target material surface or even cause a chip separation from it in a low incident angle.With incident angle decrease,the width of impact crater increase and demonstrate a smooth crater surface as is depicted in Fig.13c.Incident angles were set as 25°,35°,45°,55°,65°,75°,85°respectively in computational simulation process.Orientation angel was equal to incident angle in order to make diagonal of particles in the same line with incident direction.Fig.14 demonstrates twodimensional morphology of crater after 5 particles'collision under the change of incident angle.It obviously shows the formation of cutting chip on target material and the deformation of plate surface under different conditions.Three different impact influence can be seen in Fig.14.From left to right to see the effect on the surface of the target were crash,cutting and plow respectively.Chip separation occurs under oblique cuts condition.As is depicted in Fig.15,energy absorption of collision plates tend to be the same except for the condition of incident angle as 25°.Impact particles plow the particle surface in this special case to produce small damage to target material which can also be proved in Fig.16.Damage dissipation energy decrease as incident angle increase from 35°(Fig.17).

Fig.15.Internal energy vs.time under different incident angles(αi ).

4.5.Orientation angle

Fig.18 shows the computational graph of rotation of single particles when orientation angle is 0°,5°,10°,15°,20°,25°,30°,35°,40°respectively.In this group of experiment,particle angle is set as 45°,incident angle is set as 70°.In Fig.18,rhombic particles with mesh are particles in incident direction.Rhombic particles in gray are particles after collision.It is found that particles rebound nearly along the incident direction when the sum of orientation angle and incident angle is 90°andno rotation phenomenon occurs.The movement of particle changes from linear motion to rotational motion after impinging on the target material.It spins around the impact spot and then fly away.As is depicted in Fig.19,the velocity vican be decomposed into v1in the diagonal direction of the two-dimensional plane of the particle and v2in the direction perpendicular to the diagonal.v1plays an role to deepen the crater while v2makes the particle rebound rotationally.As is shown in single particle rebound graph Fig.18,there is a critical orientational angle θcriin a fixed incident angle αi,The research shows that|αi|+|θcri|≈90°.For orientational angle less than θcri,particles rotate forward after impact,for values higher than θcri,particles rotate backward.It is noticed that the greater the value of|90°-αi-θi|,the larger the angular velocity of the particle.From the internal energy of the plate shows in Fig.20,internal energy reach to maximum value when the orientation angle is 15°which indicates that the particle impacts most strongest to the target plate.

Fig.16.Damage dissipation energy vs.time under different incident angles(αi ).

Fig.17.Penetration depth vs.time under different incident angles(αi ).

5.Conclusions

1.The coupling numerical model of rhombic particles impact on the AA6061 aluminum alloy plate is established by using ductile damage criterion,shear damage criterion and MSFLD damage criterion.The accuracy of the model is verified by comparing the simulation result with experimental result.The diagram of energy under different parameters obtained through simulation shows that the maximum stress area on the surface after impact is the area corresponding to the sharp angle penetration.

2.As is showed from particle penetration graphs,a small phenomenon of work hardening created in the surface of the target after being impinged by rhombic particles which can give protection to the target material from being impact of later particles.The penetration depth of the particle decreases with impact times and gradually comes to a stable level.Therefore,in any multiparticle impact model,strain hardening should be used as a reference criterion for further research

3.The above analysis showed that the main factor that affects the particle rotation and causes multiple impacts is that the velocity direction is not on the same line as the diagonal of two-dimensional plane of the particle.That is,the sum of incident angle and orientation angle in an experiment is not 90°which causes rotation after collision of particles.For a fixed incident angle αi,there is a critical orientation angle θcrithat is close to the complementary to it.Particles rebound and rotate forwards when initial orientation angle less than θcriwhile particles rotate backwards when initial orientation angle greater than θcri.

Fig.18.Single particle rotates under different orientation angles(θi ).

Fig.19.Particle velocity decomposition diagram.

Fig.20.Internal energy vs.time under different orientation angles(θi ).

4.The internal energy of the target material increases first and then decreases with the increase of particle angle.When the particle angle is 120°,the energy absorbed by the target reaches the maximum value.When the particle angle is greater than 45°,the damage energy consumption decreases with the increase of particle angle.Under the incident angle of 25°,the surface of the target material is plowed,and only a small amount of material chip is separated which lead to a minimal energy absorption as well as damage energy consumption which decrease as incident angle increase from 35°.

Declaration of competing interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work,there is no professional or other personal interest of any nature or kind in any product,service and/or company that could be construed as influencing the position presented in,or the review of,the manuscript entitled,“Simulation and experimental study on the surface morphology and energy lost of the target material under nonoverlapping impact of angular particles”.

Acknowledgements

The authors acknowledge the financial support from the National Natural Science Foundation of China(China,Grant No.51874340),the Natural Science Foundation of Shandong Province (China,Grant No.ZR2018MEE004).