Aus Wissenschaft und Forschung 21 Tribologie + Schmierungstechnik · 65. Jahrgang · 5/ 2018 A contact model for the efficient simulation of abrasive wear of multiphase friction materials G. Vorlaufer, F. Heindl, U. Cihak-Bayr, P. O. B. Velazquez, Z. Rózsavölgyi* Es wird ein Programm zur Vorhersage des Verschleißverhaltens von mehrphasigen Werkstoffen, wie sie üblicherweise in Bremsanwendungen eingesetzt werden, vorgestellt. Die Materialauswahl von Verschleißmaterialien muss zahlreiche Einflussfaktoren berücksichtigen, welche sich teilweise durch eine starke gegenseitige Abhängigkeit zueinander auszeichnen. Eine Erhöhung der Lebensdauer kann somit nicht nur mehr auf den Erfahrungswerten von klassischer Ingenieursarbeit basieren. Um die Zeit von Entwicklungszyklen und damit einhergehend die Kosten zu reduzieren, wird eine Entwicklungsreihe aufgebaut, die eine Vorauswahl von Materialien auf Basis numerischer Simulationen und kosteneffizienter Modellversuche ermöglicht, um die Anzahl von Prototypen zu reduzieren. Der Verschleiß von Komponenten wird durch die reale Kontaktfläche bestimmt, eine Modellierung des Kontaktes auf der Ebene der Mikroskala ist somit unerlässlich. Ein statistisches numerisches Modell basierend auf der Kontaktmechanik von Greenwood- Williamson wird für mechanisch heterogene Kontakte in inhomogenen Materialien vorgestellt. Die Rauheit der Oberfläche ist einer bestimmten Materialphase zugeordnet, deren mechanische Reaktion auf externe Kräfte durch Nanoindenter-Messungen bestimmt wurde. Äußere Einflüsse beim Bremsvorgang wie z .B. Sandteilchen werden durch Anpassung des Kontaktmechanikmodells und Modifikation der Kontaktfläche und der daraus resultierenden statistischen Druckverteilung berücksichtigt. Diese Druckverteilungen werden auf einen FEM-Code übertragen, der den Verschleiß des Materials unter verschiedenen Umgebungsbedingungen numerisch berechnen kann, indem er die in einem Modellversuch für verschiedene Werkstoffe ermittelten Verschleißraten verwendet. Schlüsselwörter Verschleißmaterial, Verschleißrate, Mikrokontaktmodell, Simulationsmodell, Greenwood-Williamson In this paper we present a routine to predict wear behaviour of multiphase materials commonly used in brake applications. The material selection for friction materials have to take into account numerous influencing factors, partially with strong mutual dependencies. Thus, increasing the life-time based solely on traditional engineering experience is no longer feasible. In order to reduce development cycles in time and cost, a chain of development tools is built, which enables material preselection based on numerical simulations and cost-efficient model tests to reduce the number of prototypes. The wear of the friction materials is determined by its real contact area and thus modelling the contact on the microscale is essential. A statistical numerical model based on the contact mechanics of Greenwood- Williamson is set up for mechanically heterogeneous contacts occurring in inhomogeneous materials. The asperities are assigned to specific material phases whose mechanical response was determined by nanoindentation measurements. External brake conditions like sand particles are incorporated by adapting the contact mechanics model and modifying the contact area and the resulting statistical pressure distribution. These pressure distributions are transferred to a FEM code, which can numerically calculate the wear of the component under various environmental conditions by using wear rates determined for different materials in a model test. Keywords Friction material, wear rate, micro contact model, simulation model, Greenwood-Williamson Kurzfassung Abstract * Dipl.-Ing. Dr. Georg Vorlaufer Dipl.-Ing. Franz Heindl Dipl.-Ing. Dr. Ulrike Cihak-Bayr Dipl.-Ing. Dr. Pedro Osvaldo Bedolla Velazquez AC 2 T research GmbH, 2700 Wiener Neustadt, A MSc. Zsolt Rózsavölgyi Knorr-Bremse GmbH, 2340 Mödling, A T+S_5_18.qxp_T+S_2018 28.08.18 13: 50 Seite 21 Following the main line of arguments of Greenwood and Williamson, the following simplifications and assumptions are made concerning the microscopic contact: • The real contact area is much smaller than the apparent one. • Contact takes place between individual asperities. • On average, contacting asperities are separated far enough of each other such that mechanical interaction between them can be neglected. • Asperities have a characteristic radius of curvature r and the nominal asperity density is proportional to 1/ r 2 with the constant of proportionality being in the order of 1. • The probability density function of the height distribution of asperities is known. In addition, the following simplifications are made for the sand grains: • Sand grains have a spherical shape • The typical radius of a sand grain R is much larger than r • Compared to the materials of the rubbing bodies, sand grains are considered rigid • There is a single layer of sand grains between the rubbing bodies • Within this layer, sand grains are densely packed In a first step a typical length scale s is defined in order to separate the microand macro-scale. As shown in figure 2, on the macro-scale, i. e. at a level of observation with length scales much larger than s, materials are considered homogeneous with smooth surfaces, whereas on the micro-scale, i. e. at a level of observation with length Aus Wissenschaft und Forschung 22 Tribologie + Schmierungstechnik · 65. Jahrgang · 5/ 2018 1 Introduction Friction materials need to meet a range of requirements necessary to achieve optimal performance in use. One of the critical requirements the friction materials must fulfil is wear resistance against abrasion. Abrasion is recognized as a dominant wear mechanism in such applications, due to the presence of dust, sand and wear particles in the contact. In order to obtain a reasonable wear resistance and constant friction properties, modern friction materials are typically made out of metal matrix composites, i. e. multiphase materials consisting of hard ceramic particles embedded in a softer metal matrix. Although the amount of research performed on such friction materials is vast, the materials and their composition still have to be determined by trial-and-error methods. The overall aim of the present research activity is to establish a routine to predict wear behaviour of friction materials in field applications using a lab-to-field approach. In combination with modelling and numerical simulation, detailed knowledge about tribologically relevant quantities, such as contact pressure and temperature, sliding velocity and dissipated frictional energy, is obtained. Comparison of these quantities in the lab to those in the field allows a transfer of experimental findings to the field and predict wear rate [1]. 2 Modelling approach Within the present approach, a standard dry sand abrasion test modified by AC2T is used to quantify wear rates of different materials under abrasive conditions. In this test, the usual rubber wheel is replaced by a steel wheel and operating temperatures may be adjusted from room temperature up to several hundred degrees centigrade [2]. Apart from macroscopic parameters, like the nominal load, sliding velocity or environmental conditions, the wear rate of friction material is determined by the contact situation on the microscale. Thus, detailed analysis of the static contact situation is performed using a two-scale modelling approach where classical finite element analysis is used to determine the overall (macroscopic) contact pressure distribution [3] and wear rate. Small-scale features, such as the heterogeneity of the material and surface roughness (see figure 1) are incorporated into the analysis in form of a statistical approach similar to the pioneering work of Greenwood and Williamson [4]. Additionally, the abrasive effect of sand or dust in the field is experimentally simulated by Ottawa sand and numerically by including a statistic distribution of third particles. Figure 1: Surface topography and microstructure of a typical friction material [5] T+S_5_18.qxp_T+S_2018 28.08.18 13: 50 Seite 22 scales much smaller than s, material structure and surface roughness is taken into account. 2.1 Statistical description of surface roughness By means of s, a unique decomposition of the surface topography into a macroscopic profile (mean profile) and microscopic roughness may be obtained, e. g. using Fourier transform based low-/ high-pass filter techniques. As shown in figure 3, the true (real) profile x (i) (i = 1 and i = 2 denote base and counter body, respectively) is decomposed according to (1) where x- (i) denotes the mean profile and ζ (i) the microscopic elevation measured in direction of the outward directed mean surface normal n- (i) . The true gap g may then be approximated by (2) where g- denotes the macroscopic gap and δ = ζ (1) + ζ (2) the combined microscopic approach of base and counter body. In terms of statistics, surface roughness may be described via its probability density function φ(ζ), where φ(ζ) dζ denotes the probability of a point on the surface having a microscopic elevation between ζ and ζ + d ζ. Having a measured surface topography at hand, φ(ζ) may be obtained numerically. In case that the topographic features of the individual material components can be identified, as, for example, shown in figure 1, it is possible to assign different probability density functions to each if these components. Figure 4 shows the probability density functions for the metal matrix, hard phase and the overall surface topography of the data presented in figure 1. 2.2 Modelling of specific materials - Mechanical response of individual asperities The following considerations refer to the respective characteristics, given by the roughness of the surface, of materials. Modelling of materials, depending on the intended use, is possible by changing the boundary conditions, e. g. hardness response. Aus Wissenschaft und Forschung 23 Tribologie + Schmierungstechnik · 65. Jahrgang · 5/ 2018 Figure 3: Decomposition of the surface topography into mean profile and roughness Figure 2: Scale separation of material structure (left) and roughness (right) according to a typical length scale s ! "# % & ! "# ' ( ! "# )& ! "# * + ,& ! -# . & ! / # 0 3 )& ! / # . ,( ! / # ' ( ! -# 0 % *4 . 5 ! Figure 4: Probability density function of surface roughness calculated from the topography shown in figure 1 T+S_5_18.qxp_T+S_2018 28.08.18 13: 50 Seite 23 ! "# &$' % 4 ( ) * +) 3 ,$(- .) limit of the assumption stated earlier, the force acting on a sand grain may be approximated as (4) where N asp is the nominal asperity density. A sand grain clamped between the two surfaces of base and counter body will adjust itself such that the forces exerted to both bodies are equal, i. e. (5) where g- denotes the macroscopic gap between base and counter body, F eq and d eq the equilibrium force and displacement, respectively, of a sand grain with Aus Wissenschaft und Forschung 24 Tribologie + Schmierungstechnik · 65. Jahrgang · 5/ 2018 When an individual asperity of the base or counter body is brought into contact with a sand grain, it deforms in such a way that no geometric overlap exists. As a consequence, a reaction force is built up. In general, the reaction force F asp is a function of the displacement d, i. e. F asp = F asp (d), and depends on the elasto-plastic material properties. For simple elastic solids it may be obtained within the framework of Hertzian contact mechanics as (3) with E * being the reduced Youngs modulus (contact modulus), see [6]. Clearly, above relation only applies until the onset of plastic deformation. In general, the mechanical response of individual asperities may be simulated numerically or experimentally, e. g. using suitable indentation experiments. Here, the load-versus-indentation behaviour was obtained via nanoindentation experiments using a commercial grade nano-indenter (Hysitron Triboindenter TI 900, see for example [7]) equipped with a conical diamond tip with a tip radius of 1 µm which corresponds to a typical radius of asperity curvature. The measurement results are depicted in figure 5. 2.3 Contact mechanics of single sand grains As mentioned above, sand grains are considered rigid spheres with radii R >> r. Therefore, an individual sand grain will usually contact several asperities. Within the ! "#$% &', () * 2+ - #./ 0 1 (1 3 4 0 (5 = >= #./ 6( 7 ' 8 9' : 7 1 : 8 5; <&5) * ! "#$% &: ) E', 2' 7 BC 7 ( @A F Figure 5: Nano-indentation measurements for the different components (nine single measurements for the matrix and hard phase) of the example material shown in figure 1 @A &', BC ) * ! "#$% &D) E', ( @A F Figure 6: Equilibrium force as a function of gap for a sand grain diameter of 100 µm T+S_5_18.qxp_T+S_2018 28.08.18 13: 50 Seite 24 radius R. In figure 6, the values of F eq are plotted as a function of g- for a grain diameter of 100 µm (R = 50 µm). Due to the different asperity height distributions (see figure 4) and different mechanical responses (see figure 5) of hard phase and matrix, two separate curves are obtained. 2.4 Numerical modelling of sand grains as third particles Sand grains used in the abrasion test are not uniform in size. Hence, to describe the total effect of sand in the contact between the sample and the wheel, a size distribution of sand grains is needed. This distribution is obtained by sieving the sand collected after an abrasion test. The sieving results are summarized in table 1. The probability distribution for the sand grain radius, ψ(R), is then obtained by fitting a piecewise constant probability density function to these mass fractions. Results are shown in figure 7. 2.5 The microscopic contact model Combining all previous steps, the microscopic contact model manifests itself as a functional dependence between a macroscopic expected value of the contact pressure and a macroscopic gap. By means of the statistical sand grain distribution the contact model can be expressed as (6) with N grain = 1/ (4 R- 2 ) being the nominal grain area density calculated via the mean grain radius R-. The result is shown in figure 8. Knowing the area fraction of hard phase and matrix, which in case of the material at hand corresponds to a hardphase = 0.02 and a matrix = 0.98, respectively (see figure 1), the total effective contact pressure is given by (7) 3 Simulation of the abrasion test 3.1 Simulation setup The macroscopic simulation of the abrasion test is realised by means of a 2D finite element (FE) model using commercial grade simulation software COMSOL Multiphysics. The model applies structural mechanics equations using large deformations and plane strain approximation. The FE mesh is depicted in figure 9. The rotation axis of the wheel is held fixed at the coordinate origin, while the sample (represented by the rectangular mesh on the left side of figure 9) is allowed to move freely in horizontal direction. An external load corresponding to the expe- Aus Wissenschaft und Forschung 25 Tribologie + Schmierungstechnik · 65. Jahrgang · 5/ 2018 Figure 8: The microscopic contact model Figure 7: probability density function of sand grain radius Table 1: Sieving results Sieving fraction in µm Mass fraction in % 250 - 300 7,5 200 - 250 77,3 100 - 200 6,3 45 - 100 5,8 0 - 45 2,3 Total 99,2 ! "#$% & ' ( )*+,- . / #0& 1 23 #04 $% & 50 6 7 ! " GKG+L #$% & ' > ? +*@A? +B2 ! " ? +*@A? +B2 # #$% & M > F+G*,H ! " F+G*,H #$% & T+S_5_18.qxp_T+S_2018 28.08.18 13: 50 Seite 25 Figure 10 shows the progressive change in surface profile, whereas the von Mises stress field at the beginning and the end of the simulation is shown in figure 11. Aus Wissenschaft und Forschung 26 Tribologie + Schmierungstechnik · 65. Jahrgang · 5/ 2018 rimental one is applied to the sample in positive horizontal direction. Mechanical contact is established between the sample and the wheel by means of a penalty contact formulation. A custom penalty function is implemented which exactly represents the pressure - gap relationship p total (g-) from equation 7. Thus, the macroscopic contact pressure and gap distribution is a result of the FE simulation and depends not only on the macroscopic contact geometry and external load conditions, but also on the specific form of the statistical micro contact model. 3.2 Wear progress According to Archard [8], the worn volume in a sliding contact is proportional to the applied load and the sliding distance. Applying this relation in a time and space resolved notation [9], the linear wear rate h ̇ at a given point of the contact zone is given by (8) where k is a dimensional wear constant, p the contact pressure and v the sliding velocity. Wear progress is realised in the FE simulation by an iterative procedure, where at each iteration step the macroscopic sample geometry is updated according to the wear height accumulated in the previous iteration step. Subsequently, the contact pressure distribution is updated using the new contact geometry. The iterative procedure is terminated when a total amount of sliding distance corresponding to that of the abrasion test (≈ 718 m) has been reached. 3.3 Simulation results By means of the FE simulation the usual macroscopic quantities such as contact pressure distribution, stresses and strains can be calculated. In addition, due to the iterative wear simulation procedure, a progressive change of the macroscopic contact surface may be observed which in turn results in a transient behaviour of all other mechanical quantities. Figure 9: Mesh for the finite element simulation model of the abrasion test +, '-. / . 0* 1 2 ! '-. / . 0* 3 Figure 10: Progressive change of the macroscopic surface profile due to wear Figure 11: Von Mises stress distribution at the beginning (left) and end (right) of the wear simulation T+S_5_18.qxp_T+S_2018 28.08.18 13: 50 Seite 26 4 Conclusion The numeric modelling of the wear process is an essential tool to better understand the interaction of materials in a wear process. The presented model is based on a statistical approach in contact mechanics and can incorporate third particles, such as sand, statistically too. The real contact pressure was shown to be calculated for specific and inhomogeneous materials by using elastic properties extracted from nanoindentation measurements. Thus, the effect of different phase contents can also be determined. Linking the contact mechanics model to a conventional FEM code and incorporating experimentally determined wear rates enables simulation of the material-specific wear rates of all friction components. The environmental conditions of different braking situations are taken into account - not only by using different pv values, but also by including the modelled sand particles. With the aim of simulation and various material tests, the characterisation and qualification of the newly developed friction materials can be carried out under exactly defined conditions. Laboratory materials tests give the input data for the calculation. The laboratory wear test validates the results of the simulation. This could eliminate the necessity of the longterm and expensive field tests carried out with various material combinations. The presented simulation method speeds up the development and leads to optimized friction materials that fit the purpose. 5 Acknowledgments The presented research was funded by the Austrian COMET program (Project XTribology, No. 849109), and the work was carried out at the “Excellence Centre of Tribology” (AC 2 T research GmbH) in cooperation with Knorr-Bremse GmbH. 6 References [1] Bedolla P. O., Bianchi D., Vorlaufer G., Polak R., Rechberger C., Pauschitz A.: Combined experimental and numerical simulation of abrasive wear and its application to a tillage machine component, submitted to Tribol Int [2] Rojacz H., Pahr H., Baumgartner S., and Varga M.: High temperature abrasion resistance of differently welded structural steels, Tribol Int 113, 487-499 (2017) [3] Ilincic S., Tungkunagorn N., Vernes A., Vorlaufer G., Fotiu P. A. and Franek F.: Finite and boundary element method contact mechanics on rough, artificial hip joints, P I Mech Eng J-J Eng 225 (11), 1081-1091 (2011) [4] Greenwood J. A., Williamson J. B. P.: Contact of nominally flat surfaces, Proc Roy Soc Lond 295 (1442), 300- 319 (1966) [5] Vorlaufer G., Vernes A., Pauschitz A. and Franek F.: A two-scale elasto-plastic model of rough heterogeneous surfaces in dry contact, 43rd Leeds -Lyon Symposium on Tribology, 6th-9th September 2016, Leeds, UK [6] Johnson, J. L. Contact mechanics, 1985 (Cambridge University Press, Cambridge) [7] Rodríguez Ripoll M., Ojala N., Katsich C., Totolin V., Tomastik C. and Hradil K.: The role of niobium in improving toughness and corrosion resistance of high speed steel laser hardfacings, Mater Design 99, 509-520 (2016) [8] Archard J. F. and Hirst W.: The wear of metals under unlubricated conditions, R Soc Lond Proc Ser A 236, 397- 410 (1956) [9] lincic S., Vernes A., Vorlaufer G., Hunger H., Dörr N. and Franek F.: Numerical estimation of wear in reciprocating tribological experiments, P I Mech Eng J-J Eng 227 (5), 510-519 (2013) Aus Wissenschaft und Forschung 27 Tribologie + Schmierungstechnik · 65. Jahrgang · 5/ 2018 Umzug oder Adressenänderung? Bitte T+S nicht vergessen! Wenn Sie umziehen oder Ihre Adresse sich aus sonstigen Gründen ändert, benachrichtigen Sie bitte auch den expert verlag. expert@expertverlag.de. | Tel: (07159) 9265-0 | Fax (07159) 9265-20 T+S erreicht Sie dann ohne Verzögerung und ohne unnötigen Aufwand. Danke, dass Sie daran denken. T+S_5_18.qxp_T+S_2018 28.08.18 13: 50 Seite 27