Fretting wear and the hardness differential

At the Wear of Materials Conference Ken Budinski of Bud Labs presented a paper on the effect of hardness on fretting wear between steel surfaces.  A series of tests were carried out between a 60 HRC steel surface and a steel counterface of the same or lower hardness.  Some tests were lubricated while other tests were unlubricated.

Some of the most interesting data in the paper is shown in the figure above.  The difference in hardness had little effect on the tests carried out in air except at the largest separation (60 HRC vs. 27 HRC performed worst).  However, with mineral oil the hardness differential had a large effect.  The big change took place between a hardness separated by 10 HRC and 21 HRC.  

As the difference in hardness increased more adhesive wear and pitting occurred.  Even though the counterface with a 50 HRC had less wear than a 60 HRC counterface it had a deeper pit depth.  The author thought that a hardness differential of less than 10 may be ideal.  He hypothesized that a differential of 5 HRC might be best, but more testing would be required to determine the optimal value.  

The reason for the superior performance of the lubricated contacts is that abrasive wear was eliminated from the contact.  Once abrasion was removed, adhesion became the dominant form of damage.  This points to eliminating oxidation as being one of the primary ways to reduce fretting damage between any couple.  

Another interesting characteristic of adhesive wear becoming the dominant wear mechanism is that the shape of the wear profile changed.  It caused pits and “up-features” in the wear scar instead of the smoother surface typical of abrasion.  

The findings of this study go into more depth than previous investigations, but Budinski mentioned several studies carried out by Waterhouse with various co-investigators who made similar observations with regard to wear volumes, wear profile shape, and hardness effects.

• K.G. Budinski, Effect of hardness differential on metal-to-metal fretting damage, Wear (2013), http://dx.doi. org/10.1016/j.wear.2013.01.003

Numerical modeling of different geometries under fretting fatigue

I recently read an interesting article by Hojjati-Talemi et al. at Ghent University published this year.  They investigated the effects of contact geometry on fretting fatigue life both experimentally and analytically.  Their geometrical investigation studied the effect of both the width of the pad and its shape (cylinder or flat).  

In the numerical part of their investigation they made use of two different software packages.  The first was Abaqus which they used to model the stress in the contacts.  Once they had gained an understanding of their initial stress fields, they modeled fatigue in a specialized software called FRANC2D/L which is a product of Cornell.  In Franc2D/L they modeled the geometry and matched the Abaqus stress patterns and then began using that software to analyze fatigue crack growth. (It is possible to do the whole process in ABAQUS, but you need to write your own fatigue subroutine.)

The experimental test rig Hojjati-Talemi et al. used is shown in Figure 1 and their finite element model is shown in Figure 2.  They modeled only a quarter of the system based upon two symmetry assumptions.  The tips of the pad were either flat or cylindrical.  The width of the pad contact sections was varied which meant that the contact radius changed for the cylindrical specimen (width = 2 x radius).  

The study found that fatigue life was longer in the flat on flat configuration than the Hertzian line configuration due to lower maximum stresses.  Similarly, the fatigue life dropped as the pad became narrower because this also increased the stress.  The fatigue cracks always initiated at the trailing edges of the contact.  The experimental lives were about 18% lower than the numerical model which is not ideal because it is better for a model to be conservative.  

It was an interesting article especially in that it demonstrated another finite element fatigue software under fretting conditions and gave us a better understanding of how contact geometry influences fretting fatigue life.  

• Hojjati-Talemi, R., Wahab, M. A., De Baets, P., 2012, “Numerical Investigation into the Effect of Contact Geometry on Fretting Fatigue Crack Propagation Lifetime,” Tribology Transactions, Vol. 55, pp. 365-375.  

The role of oxide particles in the fretting wear of mild steel

Iwabuchi carried out a study some time ago to determine the effect of iron oxide particles on fretting wear.  One of the reasons for this study was that there are three far different impacts third body particles have been observed to cause in fretting contacts:

1. Abrasive action which increases wear
2. Protective action from a compacted oxide layer
3. No significant effect

Iwabuchi investigated whether changing the normal load and displacement amplitude was beneficial or detrimental to the wear rate.  He studied this by adding oxide particles to the contact additional to any which occurred naturally.  The tests were carried out using a cylinder-flat geometry which has a Hertzian line contact.

One of the most interesting parts of his paper was a map illustrating when the particles were beneficial and when they were harmful.  This is shown in the figure below (o indicated helpful, x indicated detrimental).  Observe that in general the particles are more beneficial at lower displacement amplitudes.  Different regions where the third body helps surround a connected region where the particles are detrimental.

From his tests Iwabuchi found that both the beneficial and negative effects are present at the same time in fretting contacts; however, their relative importance depends on the values of normal force and slip amplitude.  The reduce wear the ideal is to have the particles form a compact layer in which they will alleviate wear.  However, if they are loose and separated they become abrasive and cause more wear.  Generally increasing the displacement amplitude or normal force will increase the removal of these particles and cause the breakup of the compacted masses.  At the highest load for some undiscovered reason the normal force tended to hold together rather than break up the third body mass.

• Iwabuchi, A., 1991, “The role of oxide particles in the fretting wear of mild steel,” Wear, Vol. 151, pp. 301-311.

Laser dimpling to reduce fretting wear in conformal fretting contacts

Varenberg, Halperin, and Etsion have carried out a study investigating the use of laser dimpling to reduce fretting wear in conformal contacts.  Conformal contacts are where we would expect to see the largest reduction in fretting damage because laser dimples work well at reducing wear in hydrodynamically lubricated contacts (generally low pressure conformal contacts) but it is more difficult for them to yield improvements under elastohydrodynamically lubricated conditions (non-conformation and high pressure situations).  

Varenberg et al. found that when adhesive wear was dominant the wear particles acted like a solid lubricant and reduced wear.  On the contrary, when abrasive wear was predominant, the third body particles had the opposite effect and having more wear particles increased wear loss.  Surface pores allowed wear particles to be removed from the contact (into the pore) and so increased wear under adhesive conditions and reduced it when abrasive wear was dominant.  At low normal loads the surfaces without pores had a lower wear while at higher loads the surfaces with pores had a higher wear.

Varenberg were able to determine the amount of fretting wear particles separating the first bodies by measuring the electrical contact resistance.  The oxide particles had a high electrical resistance so that when they left the contact interface more direct first body contact occured and the electrical resistance was reduced.  

Actual wear volume measurements were not take to prove this relationship but the energy dissipation rate and coefficient of friction were recorded during a number of test conditions.  The energy dissipation rate should linearly correspond with the wear rate according to the dissipated energy wear law.  

It is also interesting to see how the dimples are believed to fill up.  The pores filled from their upper corners.  The wear particles did not always work their way to the bottom.  The particles tend to agglomerate together and so started off near the top and pushed their way across the opening.  Following testing a pore which had been filled up could be pushed on and the contents would move downward.  From this description it seems like it is also possible that there is a very loose mixture of particles in the pore which could be easily compacted.

• Varenberg, M., Halperin, G., Etsion, I., 2002, “Different Aspects of the Role of Wear Debris in Fretting Wear,” Wear, Vol. 252, pp. 902-910.

 

Plastic shakedown and fretting wear in the gross slip regime

Fouvry wrote an interesting article on the effect of plasticity on fretting wear in 2001.  This investigation combined analytical and experimental work.  The experimental part of the test was a fretting wear study performed in the gross slip regime; the analytical part was based on plasticity theories and equations.

Two different wear rates were observed at the different normal loads tested.  It is a little difficult to tell for sure about the lower normal force because it is so small on the figures.  With the test at a higher normal force the early part of the test had a higher wear rate than the later part of the test.  

Fouvry connected this reduction in wear rate to the mean pressure of the contact dropping below 150 MPa.  The tests were carried out with a Hertzian line contact, so the maximum and mean pressure drop throughout the test as the contact becomes wider.  Once the mean contact pressure dropped below 225 MPa, the wear rate began to get smaller and it reached a fairly consistent low value by 150 MPa.  

The cut off level for the wear rate was related to the plastic deformation of the surface.  It was hypothesized that the transition pressure between high and low wear rates is related to the shakedown pressure.  However, the shakedown pressure did not correspond well to the measured transition pressure.  When assuming a smooth surface, the transition pressure was too low.  When considering asperities, the transition pressure was too high.  Fouvry felt that more effects need to be included to come up with an explanation of the transition criterion.  Possibly the missing variable is related to the third body.  

Another scientists named Kapoor had done similar work before and demonstrated that under lubricated sliding conditions plastic deformation determined a transition in the wear rate.  However, using a parallel analysis under fretting conditions did not prove fruitful because of the high coefficient of friction characteristic of fretting.  In this study the coefficient of friction was between 1.0 and 0.6 for all tests which is typical of fretting.

• Fouvry, S., 2001, “Shakedown analysis and fretting wear response under gross slip conditions,” Wear, Vol. 251, pp. 1320-1331.  

3-D Fretting wear analysis of a multi-component electrical contact

As I have written before, electrical contacts are one of the major technologies affected by fretting wear and fretting corrosion.  Hsu and Liao wrote a paper in 2012 in which they conducted a three-dimensional fretting wear analysis of an audio-jack electronic connector.  While most analyses of electronic contacts looked at their ability to continue carrying an electronic signal, this study checked for mechanical failure of the component.  Consequently, it is closer to a traditional fretting wear analysis.  Both a numerical and experimental set of tests were carried out in this study.

The audio-jack was modeled using five terminals and a rigid male terminal was inserted into the model.  The ABAQUS finite element software was used for the numerical calculations.  The force was measured during insertion of the male terminal and corresponded with my expectations:  the force increased for the first half of the halfway process and then dropped as the rigid terminal clicked into place.

The wear model was programmed similarly to the previous models I am studied as was illustrated by a flow chart.  First, a single fretting cycle was modeled.  The contact data from this cycle was used to calculate the wear rate at each node.  The wear rate was assumed to remain constant over an increment of cycles which were modeled as a single block.  The finite element geometry was updated to reflect the new worn geometry and another cycle was run.  This process was repeated until the simulation was complete.  

Both the experimental and numerical results demonstrated that the insertion and withdrawal forces declined throughout the tests.  The greatest reduction in force occurred during the first 4000 cycles.  The model was better at predicting withdrawal forces than input forces which it consistently under predicted.  

The wear scars calculated are shown in the illustration below.  Notice that the wear scar depth is significant with regard to part thickness and dimensions.  No wear scar profiles were taken to show a comparison of the shape of wear scars from the field data or experiments with the numerical model.  However, this is listed as future work by the authors.  

The parts were tested for 20,000 cycles until long past fatigue failure (failure was defined as either the insertion force or withdrawal force going outside of design specifications).  In the experimental study and numerical analysis failure occurred at 7,000 and 9,000 cycles respectively.  This difference corresponds to differences in strength of about 3%.  

Overall this was an interesting study and it demonstrated that fretting wear analyses can be carried out on a complex multi-part geometries.  Before most analyses have been 2-D and simple geometries although there have been a few with tougher 3-D geometries.

• Hsu, S., Liao, K., 2012, “Wear analysis and verification of metallic terminals for electronic connectors,” Engineering Failure Analysis, Vol. 25, pp. 71-80.

Simulation for fretting corrosion of electrical contacts

Lee, Jeong, Joo, and Park from South Korea have published an experimental and numerical analysis of fretting corrosion in electrical coatings.  This was an interesting study dealing with the effect of wear and corrosion on electrical resistance instead of most papers which I read which try to analyze wear loss or fatigue life.  

The contacts studied were made of copper with a tin coating.  The coating wore away quickly and after that the copper substrate began oxidizing and eventually its entire surface was oxidized.  The percentage of surface covered with copper oxide had a large effect on contact resistance as seen in the figure they published.  It appears not to have too detrimental of an effect until the oxidation covers 90 percent of the contact surface.  However, as seen from the modeling results below this happens around 12,000 cycles into the simulation.  

The contact evolution had three stages: first the tin coating is removed.  Second, the copper substrate is exposed.  Third, the contact becomes covered in copper-oxide.  The second two were the primary focus of the Abaqus model.

From the experimental tests the researchers found fretting wear was predominant during the first 8000 cycles when the coating is being removed.  The wear mechanisms were primarily adhesive and abrasive wear.  The fretted area expanded during this time due to the changing contact geometry.  After the coating has worn through fretting corrosion became the primary damage process.  

The fretting corrosion process was modeled using Abaqus in a three-dimensional simulation.  However, not many details of the simulation were given in the paper.  The copper oxide properties were assigned at random locations along the surface using a fortran program.  

• Lee, K.Y., Jeong, D.K., Joo, H.G., Park, Y.W., 2011, “Simulation for fretting corrosion of tin-coated copper contacts,” Materials and Corrosion, Vol. 62, pp. 352-356.

Finite element analysis of fretting wear of steel ropes

Cruzado, Uchegui, and Gomez have written an interesting paper numerically analyzing fretting wear occurring in bundles of steel wires.  Some of the keys aspects of this study are that the modeling was three-dimensional and that the effects of different finite element modeling parameters on simulation accuracy and speed were investigated.  The modeling was carried out on the crossed cylinder geometry which is simple enough geometry to be easily meshed, for parameters to be analyzed, and for results to be interpreted.  

The Abaqus finite element program was used for this study along with the UMESHMOTION subroutine.  The authors cited the work by other scientists in England and France as the inspiration and building blocks for their study.  Those analyses were also carried out with Abaqus.  

A partitional meshing strategy was used for the two cylinders and its results can be seen in the picture below.  The cubic shape of the elements is better for uniform numerical analysis than the tetrahedral elements.  Three-dimensional eight node linear brick element were used in the study.  Partitional meshing is a relatively simple way of having a highly organized mesh and refining it along in three dimensions although it is different from the strategies which I have seen used in two dimensional studies.  

For the crossed cylinder geometry it was important to model wear on both surfaces not only the upper or lower body.  However, the contact was solved using a master-slave algorithm.  This makes it difficult to determine the pressure and slip on the master surface.  The pressures and slips need to be interpolated onto the opposing surface.  Cruzado et al. tried three strategies for interpolating between the surfaces:  

• Bivariate interpolation
• Triangle-based linear interpolation
• Nearest interpolation

The effect of mesh size was investigated.  Mesh refinement was not found to have a large effect on the surface dimensions of the wear scar, but it did affect the wear depth.  A coarse mesh led to a trapezoidal profile for the wear scar.  The authors decided that the optimal size was 3% to 4% of the final wear scar width.  

The authors also studied the number of steps needed to carry out each cycle and found that a specific value was optimal.  The value in and of itself is not critical because it will probably vary with different simulation loadings and geometries.  If fewer than the critical number of increments was used convergence problems appeared.  The cycle jump or number of real life cycles each computational fretting cycle represented was also found to be extremely important.  The authors gave their solutions which would be a good starting point for anyone carrying out similar studies.  

• Cruzado, A., Urchegui, M., Gomez, X., 2012, “Finite element modeling and experimental validation of fretting wear in thin steel wires,” Wear, Vol. 289, pp. 26-38.  

The effect of size on fretting fatigue

In ASTM STP 1367 entitled “Fretting Fatigue:  Current Technology and Practices,” Nowell, Hills, and Moobola described what effect the size of different features has on fretting fatigue.  They stated that the large number of these factors is one reason why it has been so difficult to predict fretting fatigue crack initiation.  Here are a the most important factors:

1. Material grain size
   Cracks tend to nucleate on grain boundaries.  Consequently smaller grains tend to reduce fatigue life because there are more sites for initation.  
2. Characteristic persistent slip band length
   Persistent slip bands are formed by dislocations moving on glide planes.  These are the first step in crack nucleation.  
3. Overall size of the contact
   Cracks usually form in the slip zone of the contact.  The larger a contact is the more potentially weak regions are open to crack formation.  
4. Typical asperity contact size
   All loads are transmitted through individual asperity contacts.  This means that the stress is dependent on the number and geometries of the asperities.  The stresses surrounding an asperity contact will be higher than predicted by the overall contact pressure.
5. Characteristic asperity spacing
   The spacing of asperities will affect the load carried by each asperity and the local stress that drives dislocation movement.
6. Slip amplitude
   Depending on the slip amplitude each asperity will undergo a different number of loadings during each cycle.  
7. Transition crack size for long crack growth
   The threshold stress intensity factor is lower for short than for long cracks.  This value is important for fretting fatigue because small cracks are initiating and growing from the slip zones.

There are several more important relationships.

• The relative sizes of grain size and contact size govern the number of grains exposed to the most severe loading conditions.  
• When the third body effect is important the authors suggest two parameters will become more important: overall contact size and the characteristic third body size.  Additionally the ratio of the two values will be important.  
• The ratio of asperity to grain size is important variable because it determines whether the contact can be assumed to have a smooth surface or whether roughness must be included to the analysis.  

Refence

• Nowell, D., Hills, D.A., Moobola, R., 2003, “Length Scale Considerations in Fretting Fatigue,” ASTM STP 1367.  

Finite element fretting wear modeling of a three-dimensional spline coupling

In most studies finite element fretting models have been used to analyze two-dimensional contacts.  However, as processing power becomes less expensive, we can expect that three-dimensional models will become the norm.  The finite element method has already been used for three dimensional fretting wear analysis with Abaqus.

One reason for using three dimensional analysis is that many “real world” components and interactions are too complex to be closely approximated in two dimensions.  One such application is the spline-coupling which appears in the gas turbines used to power airplanes.  These couplings experience varying torques, axial loads, and bending moments during each flight.  A schematic of the coupling is shown in the following figure.  Expand the image for a better view.

The authors give a list of six tools which are required in order to perform this analysis:

1. A detailed geometrical model of the coupling; (ii) knowledge of how the coefficient of friction changes with distance slid;
2. (iii) a solver to calculate the contact pressure, traction and sub- surface stresses, and slip distributions at preset increments during the application of each loading cycle;
3. (iv) a mesh of sufficient detail to permit adequate resolution of the parameters listed in (iii);
4. (v) an algorithm to calculate the wear, and its direction, at each contact node after a prescribed number of simulated loading cycles;
5. (vi) a routine to re-mesh the contact elements according to the computed contact node wear values and directions.

A great deal of complexity has been included in modeling the spline coupling.  For example see the loading cycle which was matched to the operational conditions.  Here a major cycle was considered to be a flight while minor fluctuations were the change in loading during a flight.  

Interestingly, a non-linear wear rate was observed.  At the beginning of the test the wear rate was very high and it decreased to a roughly constant value by 4,000 cycles.  This took place at many  locations across the spline-coupling.  

Two different approximate geometries were modeled in this study: an cyclic-symmetric model with one tooth and a full model with all 18 teeth.  However, the simplified model did not work well because it could only model axially symmetric torque and axial loads.

• Ding, J., McColl, I., Leen, S., 2007, “The application of fretting wear modelling to a spline coupling,” Wear, Vol. 262, pp. 1205-1216.