The viscoplastic model used was the Johnson- ... The approach developed by Hale was to evaluate wear rate brought about by a local collision of the slipper ...
Consideration of Wear at High Velocities Using a Hydrocode Anthony Palazotto1 and Stephen Meador2 Air Force Institute of Technology, WPAFB, OH 45433 The goal of this research is to study sliding contact wear of metals at high velocities. In particular, wear of test sled slippers at the Holloman High Speed Test Track at Holloman AFB, NM is being considered. Experimentation representative of the speeds seen at the test track is infeasible, so numerical studies with appropriate engineering approximations need to be performed. Previous studies have used finite element analysis techniques to characterize the wear phenomenon up to sliding velocities of 1,530 m/s. However, the aim of the test track is to reach sled speeds in excess of 3,000 m/s, and performing analysis at these sliding speeds is beyond the capability of the Lagrangian finite element technique. The drawbacks of the Lagrangian technique were overcome by using an EulerianLagrangian hydrocode, called CTH. The hydrocode is used to perform plane strain simulations of a test slipper colliding with a hemispherical asperity. Sensitivity studies have been performed regarding the initial conditions in CTH with respect to wear rate, and it has been found that the initial vertical velocity of the high speed slippers has little effect on the total wear rate. Results indicate that the model reasonably predicts the wear of a test slipper, though further experimental comparison would be beneficial.
I.
Introduction
The Holloman High Speed Test Track (HHSTT) performs a variety of tests at high velocities using a rocket sled system that rides on a set of rails. The sled is attached to the rail using slippers. Currently, the HHSTT constructs the slippers with VascoMax300, a maraging steel, and the rail is composed of 1080 steel. The objective of this research is to develop and evaluate numerical methods for quantifying wear rates of the slipper and rail materials in sliding contact at relative speeds ranging from 100 m/s to 1,500 m/s. These numerical methods are based on the viscoplastic behavior of the VascoMax300 material being considered.
II.
Holloman High Speed Test Track (HHSTT) Background
The HHSTT is a division of the Air Force Research Laboratory (AFRL) and is located at Holloman AFB in New Mexico. The test track is used for a variety of studies ranging from testing of aircraft munitions and egress systems to hypersonic aerodynamic effects. The use of the test track is more observable, and more efficient in terms of time and cost spent, than flight testing at the velocities seen by payloads at the track. The test track designers set a land speed record of 2,885 m/s (6,453 miles per hour) in April 2003, and customers are interested in performing tests in excess of 3,000 m/s. The HHSTT achieves these velocities using sleds that ride on a collection of rails laid over a length of approximately 10 miles. A typical setup for a configuration used to test munitions and impact phenomena is similar to a train connection. This particular configuration was used for a mission conducted in February 2008, which consisted of four rocket-powered Presented as Paper 2120 at the 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Material Conference, 4-7 April 2011. 1 2
Professor of Aerospace Engineering, Department of Aeronautics and Astronautics, AFIT, WPAFB, OH, Fellow Graduate Student, Department of Aeronautics and Astronautics, AFIT, WPAFB, OH 1
sleds. The sleds ride on two parallel rails and are ignited sequentially as they slide down the track. The first three sleds are aptly dubbed “pusher” sleds because they push the “forebody” sled down the track. The forebody sled contains the payload and instrumentation that is of interest to the team at the HHSTT. Figure 1 shows the test train layout with the pusher sleds. Figure 2 is a close up of the slipper. A slipper was recovered from the third stage sled of the February experiment; dissected, and metallurgically investigated.
Figure 1. Test Track Layout
Figure 2. Slipper- Rail Interface In 2009, Hale1,2,3 used the FEA technique to model mechanical wear rates for the third stage slippers. While wear is a three-dimensional phenomenon, the analysis was simplified using a plane strain modeling approach. This model simulated a collision between a semi-circular asperity having a radius of 6µm and the VascoMax300 test slipper. A material damage criterion, based on the viscoplastic behavior of the slipper material, was developed to determine if an element in the finite element analysis had “worn.” The viscoplastic model used was the JohnsonCook4 model. The total damage area accumulated during the simulation was divided by the distance slid during the simulation to calculate a plane strain wear rate.
III.
Wear Mechanisms
In order to properly analyze wear, a precise definition must be established to avoid ambiguity. The simplest definition is the removal of material volume through some mechanical process between two surfaces5. The material is progressively lost as the wear event occurs, and the mechanical process can take many forms. Sliding motion, the most severe process due to the tangential relative motion of the surfaces, is the process being considered in this research. Wear can also result from rolling of two surfaces, impact between materials, and from abrasive materials causing cutting, plastic deformation, and fracture. The approach developed by Hale was to evaluate wear rate brought about by a local collision of the slipper with an asperity. In actuality, the wear phenomenon is a collision of many asperities on the surface of the slipper with many asperities present on the surface of the rail. Hale carried out the numerical study of the slipper and dissected a recovered third stage slipper, studying its metallurgical characteristics very closely to find important features necessary to consider in a numerical model. The cut slipper base is shown in Figure 3. 2
Figure 3. Dissected Slipper The metallurgical investigation studied the following:: wear surface characterization, wear volume calculations, hardness testing, optical microscopy, and en energy dispersive x-ray ray spectroscopy (EDS). The result of the study was that wear can be represented by a viscoplastic constitutive relationship in a failure function, thermal distribution and melt. The worn slipper recovered from the run considered is sho shown wn in Figure 4. The total wear was determined to be 10,520 mm3 based on the nominal manufacturing thickness of the slipper. It should be recognized that the slipper was recovered from the field after it had been ejected from the rail after fulfilling its purpose of accelerating the main forebody sled. Thus, the resulting slipper specimen may include wear that has no means of precise evaluation due to the slipper intermittently contacting the ground during deceleration.. The end result is that exact comparison to the actual total wear is impossible. However, a generalized comparison can be made as will be seen subsequently; comparison was also carried out with other experimentations.
Figure 4. The Worn Slipper Specimen This research evaluates the asperity collision using an Eulerian Eulerian-Lagrangian Lagrangian hydrocode. In Lagrangian codes, the mesh is embedded within the material so the mesh grid and the material deform together. This technique can be desirable ble because the equations are conceptually straightforward and simple to solve. However, However issues can arise if the mesh becomes excessively distorted. Eulerian codes dif differ fer from Lagrangian codes in that an Eulerian mesh is fixed in space and the material flows ws through the mesh. The Lagrangian Lagrangian-Eulerian Eulerian code used for this research is called CTH and is developed by Sandia National Laboratories. The following two sections will explain the key elements of the code. More thorough descriptions of hydrocodes have be been en published by Sandia National Laboratories6,7 and by researchers in archived journals8. Additionally, Zukas9 published a book detailing the hydrocode simulation technique. The information presented here is taken from these sources.
IV.
Lagrangian Step and Eulerian Remap
CTH uses a two-step process to solve the conservation of mass, momentum, and energy equations. The first step is the Lagrangian step in which the equations are evaluated across the time step, and the mesh deforms with the material. Noo mass flow occurs across cell boundaries, so the cconservation ation of mass is satisfied trivially. The momentum and energy integrals are solved using their explicit finite volume representations. The stress deviators are then updated using the cell velocities, and the internal energy equation is used to update the cell pressure, density and temperature via a tabular equation of state.
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The constitutive equation is also implemented at this point, and this research utilizes the Johnson-Cook model discussed subsequently. Following the Lagrangian step is the Eulerian remap step, which maps the distorted cells back to the fixed mesh. The volume flux between the deformed and fixed mesh is calculated from geometry of the cell face due to motion, and an interface-tracking algorithm is used to track the location of material interfaces within mixed cells. The mass and internal energy of each material are then mapped to the fixed mesh. Finally, the interface tracking algorithm results are used to map the momentum and kinetic energies of the materials to the Eulerian mesh, and the equation of state is used to update the cell state variables.
Finite volume approximations are used to determine the conditions of each cell based on the conditions of the surrounding cell, but cells that are at a boundary of the mesh have at least one side without an adjacent cell. In order to solve the finite volume approximations, a boundary condition must be established to control mass, momentum, and energy fluxes across the boundary. CTH allows four possible boundary conditions: a symmetry boundary condition (type 0), a sound speed based absorbing boundary condition (type 1), an outflow boundary condition (type 2), and an extrapolation boundary condition (type 3). The type 0 boundary condition sets the values of all cell-centered parameters to the values of the adjacent cell in the mesh interior. The velocity between the boundary cell and the mesh interior is set to zero and any kinetic energy is converted to internal energy. Additionally, no mass flux is allowed across the boundary. The type 1 boundary condition allows mass to flow in and out of the mesh, and is used to approximate semi-infinite bodies. The type 2 boundary condition places an empty cell at the boundary and the boundary pressure is set to a user-specified void pressure. Mass is allowed to leave the mesh with the type 2 boundary condition, but it cannot enter the mesh. The type 3 boundary condition linearly extrapolates the boundary pressure from the interior mesh. This type of boundary condition allows mass to flow in and out of the mesh. The models used for this research utilized the type 1 boundary condition.
In 1983, Johnson and Cook developed a constitutive model for metals that are subjected to large strains, high strain rates, and high temperatures. The model is intended to be used for computations, so it is defined using variables that are common to most simulation codes. Test data for the model was obtained using torsion tests, with strain rates ranging from quasi-static to 400 s−1, and dynamic Hopkinson bar tensile tests over a range of temperatures. The elevated temperatures were obtained by surrounding the specimen with an oven for several minutes. The strains evaluated were limited by necking of the material, which complicated the analysis. Additionally, adiabatic heating resulting from high strains complicated the results because elevated temperatures showed a softening of the material strength. Based on the experimentation, Johnson and Cook proposed a flow stress, , of the form (1) where ε is the equivalent plastic strain, is the dimensionless plastic strain rate for , and is the homologous temperature. , , , , and are material constants. Homologous temperature is defined in Equation (2) where is the material temperature and is the ambient temperature. (2)
V.
Defining Material Failure
In order to determine wear, a criteria needs to be established to determine if a material has been damaged. This is done using the Johnson-Cook constitutive equation above. The method is carried out by evaluating the plastic strain at the maximum stress. Figure 5 indicates the Johnson-Cook stress-strain curves for VascoMax300 for various strain rates.
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Figure 5. Johnson- Cook Plastic Strain Rate Curves Though the main consideration was given to the slipper, the rail also had to be considered since it interacted in the wear environment. Thus, the Johnson- Cook equation for it was determined and coefficients of both VascoMax300 and 1080 steel are shown in Table 1. Table 1. VascoMax300 and 1080 Steel Johnson-Cook Coefficients Coefficient VascoMax300 1080 Steel A (GPa) 2.1 0.7 B (GPa) 0.124 3.6 C 0.03 0.17 M 0.8 0.25 n 0.3737 0.6 Before the wear results are shown, several other ideas are necessary to explain. The wear phenomenon is a three-dimensional feature and thus, in order to take this into account, two steps had to be taken. The first is to evaluate the wear per distance traveled in the collision with the 6 micron asperity extended into a spherical shape for each velocity considered, and second to extend the analysis to account for multiple asperity collisions by using the Archard representation1. A scaled factor accounts for the presence of multiple asperity collisions experienced by the slipper, and is derived by relating the wear rates to Archard’s wear rate model at lower velocities. Equation (3) shows the relationship between Archard’s wear, , and the single asperity wear rates. !" # $
%
'() &"
In this equation !" represents Archard’s wear coefficient, # is the loading, $ is the material hardness taken to be 2.0 GPa, &" is the plane strain single asperity wear rate, and % is the desired scaling factor. Rearranging the equation, the scaling factor can be defined as !" # '*) % &" $ Hale evaluated % for 10 m/s, incorporating a forcing function supplied by the HHSTT using a program called DADS (Dynamic Analysis of Designed Systems)10, and found that a good value was 11.77. The DADS program generated the actual velocity and force profile of the run that is being considered and is very valuable for this analysis. The details will not be shown but can be found in reference [1]. With the use of the scaling factors and the fact that the wear rate is a wear quantity per collision at various velocities, the total wear is found by integrating the 5
wear rate over the total distance of the run considered. The final analysis will be shown, but it should be pointed out that the sled bounces during a run. This was considered by following the profiles given by DADS, which indicated the slipper and rail were in contact for 30% of the entire run.
VI.
Results and Discussion
The analysis considered in this research has been carried out with the use of CTH, as previously indicated. Figure 6 and 7 indicate the model used for the analysis.
Figure 6. CTH Model
Figure 7. Mesh Used in CTH (1 micron x 1 micron cell with over 700,000 cells) 6
Before the actual results are shown it is valuable to indicate how the wear rate was found for each velocity considered: 1.
A CTH simulation is set up with tracer points initially placed in the center of each cell. The area associated with each tracer point is defined as the area of a cell. 2. The simulation is run, while outputting the plastic strain rate, plastic strain, and volume fraction of each tracer point. 3. This data is imported into Matlab. 4. A closed form function for critical plastic strain was determined as a function of the plastic strain rate using the Johnson-Cook viscoplasticity relationship. 5. A zero matrix is initialized in which the number of rows represents the number of time steps and the number of columns represents the number of tracer points (the time steps were determined by finding how much time it takes for the slipper to collide with the asperity after the slipper travels into the asperity 6micros. This time was then divided by 100). 6. The plastic stain of each tracer point (a point in the CTH that moves with the material through the simulation) for the first time step was compared to the critical plastic strain for each tracer point’s plastic strain rate at the first time step. If a tracer point is considered failed, then its spot in the matrix is changed to 1. 7. The remaining time steps are evaluated in the same manner, but if a given tracer point was tagged as failed in a previous time step then it is considered failed for the remaining time steps. 8. To account for mixed cells, each tracer point at each time step is multiplied by its volume fraction exported from CTH. This produces a matrix with values ranging from 0 to 1. 9. The total number of damaged cells for a given time step is determined by adding up all of the columns in each row. This number of cells is multiplied by the cell area to get the damage area at each time step. 10. The plane strain wear rate is then determined by dividing the total damage area at the last time step by the distance traveled during the simulation.
A coating of graphite epoxy is incorporated in the analysis which is typical for the actual environment considered. All of the analyses considered the accumulation of the temperature effect due to friction. This input is not shown but required friction, melt and a coefficient of fusion. The melt temperature of VascoMax300 is 1685 K. One of the main areas of research is the partitioning of heat between the slipper and the rail, and research in this area is being conducted concurrently. The results of this study can first be considered in a plot of wear rate volume. experimentation carried out by Wolfson11 and the finite element analysis are shown in Figure 8.
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Comparisons to
Mechanical Wear Rate, W sa [mm3/mm x 10-4]
Single Asperity Mechanical Wear Rate vs. Sliding Velocity
4 3.5 3 2.5 2 1.5 1 0.5 0
0
500
1000 Sliding Velocity [m/s]
1500
Finite Element Method Finite Volume Method (1 µm Coating) Wolfson (HHSTT 1960)
Figure 8. Wear Rate comparisons Wolfson carried out a set of experiments in 1960 that represent the only comparable data that has considered velocities in the range of interest for this research. Though the comparisons are not exactly the same, the authors feel confident that an understanding of the high velocity physics is represented fairly well. The results of the analysis considered a shock wave generated at a velocity of 600 m/s and is shown in Figure 9. One should notice that a Hugoniot Elastic Limit is indicated at the beginning of the asperity impact. Three rays were used to evaluate material pressure during an asperity collision; one along the 30 degree angle made between the impact and the horizontal rail and two others , one at 45 and the third at 60 degrees. This figure indicates the energy dissipation with respect to time and the effect the boundary conditions have on the stress wave.
Figure 9. Stress Wave at 600 m/sec 8
The total wear for the run is shown in Figure 10. To arrive at this result several steps were carried out. The recovered specimen was measured for the remaining volume and compared to the initial volume. The experimental wear, as previously indicated, was 10,520 mm3. The analysis required the integration over the run of the wear rate function and this led to a volume of wear equal to 4,816 mm3 which was approximately 46% of the total experimental wear. It should be realized that this only represents the mechanical wear of the event. Furthermore, as discussed earlier, the total wear in the slipper has been determined from a recovered specimen that has undergone many different forms of wear and not just slipper-rail interaction. When the melt wear is included (which is not being shown in this paper) an additional 2,200 mm3 is added to the mechanical wear which yields approximately 67% of the total wear. These results indicated that many of the characteristics of high velocity wear have been considered.
Comparison of Mechanical Wear Calculations with Experimental Wear
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Wear Volume Removed [mm3 × 1000]
2008 Third Stage Experimental Finite Element Method 10
10.52
Finite Volume Method (1 µm Coating)
8 4.82 6
4
2 4.30 0
0
1000
2000 3000 4000 Sliding Distance [m]
5000
Figure 10. Total Wear
VII.
Summary and Conclusions
Previous research in the wear field has produced models that are capable of evaluating the phenomenon at slow sliding speeds, and has provided a foundation for this research. Much of the past research studied the effects of mild sliding wear and friction, and the relationship between the coefficient of friction, the applied pressure, and the sliding velocity. These factors were critical for understanding the thermodynamics of the slipper as it slides against the rail. Temperature measurements taken of sliding bodies also illustrated the key mechanisms that result in melt wear. Previous research at AFIT laid the groundwork for modeling mechanical wear using a “single asperity” numerical solution. Metallurgy studies also have provided valuable insight regarding plasticity effects and the thermal environment of the HHSTT slipper. Based on this previous research, the wear model for the slipper was separated into mechanical wear and melt wear. The mechanical wear was modeled using an Eulerian-Lagrangian hydrocode to simulate the collision between the slipper and a hemispherical asperity. The simulations were two-dimensional plane strain in nature. Failure criteria were defined based on the viscoplastic behavior of the slipper material so that the mechanical wear rates from the plane strain simulations could be evaluated. The plane strain simulations provided an evaluation of the wear in a two-dimensional plane; however, the wear event is three-dimensional, so the results of the plane strain simulations were integrated across the width of the asperity to approximate the three9
dimensional effect. Sensitivity studies of the slipper initial vertical velocity and initial temperature were conducted. It was found that the vertical velocity did not have an effect on the wear rate because it makes a small contribution to the overall velocity vector, when considered in the context of the horizontal velocities seen by the HHSTT slippers. Conversely, the initial temperature did exhibit a significant effect on the wear rate. This is due to the nature of the viscoplasticity model used for this research. The wear rate sensitivity to initial temperature indicated that a thermal profile of the slipper needed to be generated, and this was accomplished by solving the heat conduction equation in one-dimension with two spatial boundary conditions: a flux boundary condition at the slipper-rail interface and a constant temperature boundary condition at the top edge of the slipper. The flux condition was defined using force data produced by the HHSTT to evaluate the frictional heating resulting from sliding. The possibility of defining a one-dimensional gradient as the initial temperature of the simulation was considered. However, due to the micro-level scope of the simulations, the temperature gradient was nearly constant. Rather than add unnecessary complexity to the model, the temperature at a depth of 400 microns into the slipper was chosen as the initial temperature. The 400 micron depth was based on hardness measurements taken by Hale of a used slipper indicating that the heat affected zone was approximately 400 microns deep. The wear rates, mechanical and melt, are expressed in terms of volume per distance slid. In order to evaluate the total wear removed, the wear rates needed to be integrated with respect to sliding distance. A simple integration of the single asperity wear rates would be an incomplete assessment, though. The nature of the single asperity simulation requires the assumption that the slipper is in contact with the rail during the entire collision event. However, it is well documented that the slipper does not remain in contact with the rail during a test mission, but actually bounces up and down. Therefore, a scaling factor accounting for the percentage of contact was introduced. An additional scaling factor needed to be introduced to account for multiple asperities on the rail. This was done by correlating wear rates with the model developed by Archard, which was based on experimentation and also accounts for the three-dimensional aspects of the wear phenomena. The results of this study are encouraging. Limited experimental wear data is currently available for the HHSTT slippers at high velocity. The experimental data that is available is generally in agreement with the results produced by this numerical modeling technique. The mechanical wear results were validated against the single available data point, and the results were within 46% of the experimental value. Additionally, the total wear volume of the slipper for the combined forebody and pusher sled data is approximately 4% of the slipper.
References 1 H a l e , C . S . “ C o n s i d e r a t i o n o f W e a r R a t e s a t H i g h V e l o c i t y ” , Ph.D. thesis, Air Force Institute of Technology, Wright-Patterson AFB, OH, 2009. 2
H a l e , C. S., A. N. Palazotto, and W. P. Baker. “Consideration of Wear at High Velocities.” Proceedings of the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. AIAA, Palm Springs, California, 4-7 May 2009. 3
H a l e , C. S., A. N. Palazotto, A. J. Chmiel, and G. J. Cameron. “Consideration of Wear at High Velocities.” Proceedings of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. AIAA, Schaumburg, Illinois, 7-10 April 2008. 4
Johnson, G. R. and W. H. Cook. “A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures”. Proceedings of the 7 th International Symposium on Ballistics, April 1983. 5
A r c h a r d , J. F. “The Temperature of Rubbing Surfaces”. Wear, 2(6):438–455, October 1959.
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Crawford, D. A. CTH Course Notes. Sandia National Laboratories, Albuquerque, New Mexico, 2225 May 2006. 10
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McGlaun, J. and Thompson S., “CTH: A Three Dimensional Shock Wave Physics Code “International Journal of Impact Engineering”, 1 0 ( 1 - 4 ) : 3 5 1 - 3 6 0 , 1 9 8 9 . 8
C. E. Anderson, Jr. “An Overview of the Theory of Hydrocodes”. International Journal of Impact Engineering, 5 : 3 3 – 5 9 , 1 9 8 7 . 9
Zukas, J. A. Introduction to Hydrocodes, volume 49. Elsevier, New York, 2004
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Hooser, M. D. “Simulation of a 10,000 Foot per Second Ground Vehicle”. Proceedings of the 21st AIAA Advanced Measurement Technology and Ground Testing Conference. AIAA, Denver, Colorado, 19-22 June 2000. 11
Wolfson, M., “Wear, Solid Lubrication and Bearing Material Investigation for High Speed Track Application ,Tech Report AFMDC- TR 607, March, 1960.
Acknowledgment The authors would like to thank Maj. Michelle Ewy of AFOSR for her financial support.
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