abstracts - tu berlin...increases the true contact area, and (ii) tangentially to the surface,...

Adhesion and Friction: Simulation, Experiment, Applications Berlin, Germany,

November 13-16, 2017

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Abstracts

Interplay between scales in simulations of friction using hierarchical, multiscale adhesive nano-asperity blocks

F.M. Borodich1, N. Almuramady 1,2, A. Pepelyshev3 and O. Savencu4

1School of Engineering, Cardiff University, UK 2College of Engineering, Al-Qadisiyah University, Al-Qadisiyah, Iraq,

3School of Mathematics, Cardiff University, UK 4Romania

Friction is defined as the force resisting the relative motion of bodies in contact. Friction between non-lubricated solids is a longstanding problem. The importance of the problem increased due to development of nanotechnology and introduction of micro-devices working in clean and vacuum environment. Here the apparent friction has calculated using the total energy dissipated over the sliding distance through different physical and chemical mechanisms. It has been proposed to simulate friction between rough surfaces using a nominally flat slider represented as a multiscale, hierarchical system of connected deformable components. This representation reflects the physical mechanisms which are most relevant to dry friction in vacuum environment at the specific length scales: the chemical interactions at the atomic scale, the molecular adhesion at the nanoscale, the mechanical interlocking of asperities at the microscale and the coupling of all lower scale asperities at micro and macro-scales. It describes also the transfer of the deformations between scales of the hierarchical structure and the vertical degree of freedom of the asperities. In addition, the Polonsky-Keer effect has been taken into account, i.e. the nano-blocks that represent the atomic scale and the nano-scale asperities of crystalline materials, do not have plastic deformations even under very high pressure. The experimental data on roughness at micro and nano-scales has been obtained by a profilometer and an AFM respectively. Using statistical methods, one can utilise the concept of Representative Elementary Pattern of Roughness (REPR) that has been introduced by senior authors. The geometry of microscale roughness and the nano-blocks has been defined using statistics of both nano and micro-scale asperities. For simulations of friction between nominally flat surfaces, two models were used: (i) the fixed gap and (ii) the fixed load models. Although the models include some known concepts, the nanotribological interpretation of the features is novel. The fixed load model was used for simulations of friction not only between nominally flat surfaces but also between the teeth of microgear MEMS when a tooth is described as a smooth curved surface covered by adhesive nano-asperity blocks (the microgear MEMS tooth surface does not have any microscale roughness). The influence of the molecular adhesion is twofold: (i) normally to the surface, adhesion increases the true contact area, and (ii) tangentially to the surface, adhesion opposes the relative sliding, hence it dissipates energy. Numerical simulations show that the force of friction is not constant; it dependents on the local features of the roughness profile of the substrate. However, in general the Amontons law is confirmed. It has been also shown that clean silicon surfaces of MEMS are prone to stiction, hence functionalized coatings have to be used.

Asymptotic modelling of bioinspired fibrillar adhesives

Ivan Argatov

Department of Materials Science and Applied Mathematics, Faculty of Technology and Society, Malmö University, SE-205 06 Malmö, Sweden, [email protected]

In recent years, a significant amount of research attention has been paid to adhesion of biological systems [1–3]. For the so-called dry adhesive biological systems, like those of gecko lizards, the explanation of the adhesion mechanism was given [4,5] in the framework of the classical JKR (Johnson–Kendall–Roberts) theory [6], originally derived for single spherical contacts. These recent biological studies [3,5] have inspired the future development of fibrillar and patterned surfaces of polymeric materials, which possess superior adhesive properties compared to the adhesion characteristics of the same materials with the smooth adhering surfaces, which are fabricated without any patterns or fibrils. One of the most interesting aspects of the adhesion mechanism of fibrillar adhesives is formulated as the principle of contact splitting [5], which states that the adhesion force for a given apparent contact area increases as the total contact is split up into ever-finer contact elements. This theoretical result, which follows from the dimensional reasons inherent in the JKR analysis, was obtained under the simplifying assumption of non-interacting micro-contacts. However, as it was observed a recent review [3], the majority of analytical models developed up to date inherently assume that neighbouring pillars deform independently, thereby still utilizing the non-interaction approximation. In the present research, the problem of multiple adhesive contact for a system of interacting micro-contacts is re-examined using the multi-scale asymptotic modelling approach [7]. A special attention is paid to estimating the adhesive strength when the real density of contacting regions approaches the saturation limit. Acknowledgments The research has been carried out with the support of the Deutsche Forschungsgemeinschaft, PO 812/52-1, “Multi-scale adhesive contact for layered media: Asymptotic modelling, BEM simulation, and MDR extension”. References [1] Gorb, S.N., Popov, V.L., 2002. Probabilistic fasteners with parabolic elements: biological system, artificial model and theoretical considerations. Phil. Trans. R. Soc. A, 360, 211–225. [2] Spolenak, R., Gorb, S., Gao, H., Arzt, E., 2005. Effects of contact shape on the scaling of biological attachments. Proc. R. Soc. A, 461, 305–319. [3] O’Rorke, R.D., Steele, T.W.J., Taylor, H.K., 2016. Bioinspired fibrillar adhesives: a review of analytical models and experimental evidence for adhesion enhancement by surface patterns. J. Adhes. Sci. Technol., 30, 362–391. [4] Sitti, M., Fearing, R.S., 2002. Nanomolding based fabrication of synthetic gecko foot-hairs. In Proc. 2nd IEEE Conf. on Nanotechnology, Piscataway, NJ, USA, pp. 137–140. Piscataway, NJ: IEEE Press. [5] Arzt, E., Gorb, S., Spolenak, R., 2003. From micro to nano contacts in biological attachment devices. Proc. Natl. Acad. Sci. USA, 100, 603–606. [6] Johnson, K.L., Kendall. K., Roberts, A.D., 1971. Surface energy and the contact of elastic solids. Proc. R. Soc. London A, 324, 301–313. [7] Argatov, I.I., 2011. Electrical contact resistance, thermal contact conductance and elastic incremental stiffness for a cluster of microcontacts: Asymptotic modelling. Quart. J. Mech. Appl. Math., 64, 1–24.



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A very simple estimate of adhesion of hard solids with rough surfaces based on a bearing area model

M. Ciavarella

Politecnico di BARI. Center of Excellence in Computational Mechanics. Viale Gentile 182, 70126 Bari. [email protected]

In a recent note [1], we suggested a single-line equation estimate for adhesion between elastic (hard) rough solids with Gaussian multiple scales of roughness. It starts from the new observation that the entire DMT solution for "hard" spheres (Tabor parameter tending to zero) with the Maugis law of attraction can be obtained using the Hertzian relationship load-indentation and estimating the area of attraction as the increase of the bearing area geometrical intersection when the indentation is increased by the Maugis range of attraction. The bearing area model in fact results in a simpler and even more accurate solution than DMT for intermediate Tabor parameters, although it retains one of the assumptions of DMT, that elastic deformations are not a¤ected by attractive forces. Therefore, a solution is obtained for random rough surfaces combining Persson’s adhesiveless asymptotic simple form solution with the bearing area model, which is trivially computed for a Gaussian. A comparison with recent data from extensive numerical computations involving roughness with wavelength from nano to micrometer scale of Pastewka and Robbins [2] shows that the approximation is extremely good for the pull-o¤ in the simulations, and it remarks the primary importance in this regime of a single parameter, the macroscopic well-defined quantity (rms) amplitude of roughness, and small sensitiveness to rms slopes and curvatures. The model is much simpler than that of Scaraggi and Persson [3], which has similarities being a DMT model which convolutes the distribution of separations obtained with approximate solution of the adhesionless model of Persson.

Keywords: Roughness, Adhesion, DMT model, Persson’s theory

References [1] Ciavarella, M. (2017) A very simple estimate of adhesion of hard solids with rough surfaces based on a bearing area model, Meccanica, May 2017, DOI: 10.1007/s11012-017-0701-6 [2] Pastewka, L., & Robbins, M. O. (2014). Contact between rough surfaces and a criterion for macroscopic adhesion. Proceedings of the National Academy of Sciences, 111(9), 3298-3303. [3] Scaraggi, M., & Persson, B. N. J. (2015). Friction and universal contact area law for randomly rough viscoelastic contacts. Journal of Physics: Condensed Matter, 27(10), 105102 1

A bioinspired strain-stiffening Polymer with advanced properties for tissue engineerings

M. Timmermann, C. Selhuber-Unkel

Kiel University, Germany When designing materials for tissue engineering, a typical strategy is to mimic the in vivo environment of cells. A drastically underestimated property is the non-linear mechanical behavior of body tissues. In fibrin and collagen type I gels, the elastic modulus increases by orders of magnitude in response to applied strain [1,2]. Studies have shown that NIH 3T3 fibroblasts and hMCSs react to this strain stiffening not only with advanced spreading but also with an increased communication distance, which might be a key to pattern formation during tissue development [3].

Materials that mimic this behavior for tissue engineering are mostly limited to soft hydrogels. Instead, we use a cell-inspired approach to make the strain-stiffening effect applicable to elastic materials regardless of their initial stiffness. This could open the field for a whole variety of artificially grown body tissues.

Cells react to external forces by reversibly cross-linking cytoskeletal fibers and therefore increasing their stiffness. The material we are developing mimics this behavior. Our material has a specially designed microstructure so that deformation leads to a reversible interconnection of internal surfaces and, due to higher friction between these surfaces, to a stiffening of the material as a whole. Exactly this friction is a key factor for the material´s working principle. It can either arise from the material´s tack [4] or can be increased by reversible biological binding-systems. FEM analysis has been used to optimize the sample shape and will be used to model a realistic friction behavior to help us find the optimal surface coating for a maximum strain-stiffening effect in real samples.

A successful implementation of this approach could revolutionize the field of strain-stiffening materials and might find applications not only in biomaterials for tissue engineering, but also in classical engineering as special macroscopic shock absorbing structures.

[1] Storm C et al. (2005) Nonlinear elasticity in biological gels. Nature 435: 191–194. [2] Janmey PA et al. (2007) Negative normal stress in semiflexible biopolymer gels. Nat Mater 6: 48–51. [3] Winer JP et al. (2009) Non-Linear Elasticity of Extracellular Matrices Enables Contractile Cells to Communicate Local Position and Orientation. PLoS ONE 4(7): e6382. [4] Mikrut, M. (2007). Low surface energy rubber materials : relationship between network architecture and tack of silicone rubbers. Enschede



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Effect of pressurized synovial fluid on cartilage contact mechanics

Gennaro Vitucci* and Gennady Mishuris

Department of Mathematics, IMPACS, Aberystwyth University, UK

Degenerative pathologies of the diathrodial joints, e.g. osteoarthritis, affect tens of millions people worldwide. Population aging is prospected to worsen such a scenario even further in the next decades. Various physical factors and scales are known to contribute to the evolution of the diseased joint from a light inflammatorystate up to cartilage disintegration. Nevertheless safe and efficient prevention and cures are not available yet.

In mechanics, a thorough attention has been dedicated to the modelling of the cartilage layers covering the bones in the contacting zone. Elastic, viscoelastic, multi-phasic constitutive models have been implemented in an attempt to predict the solicitations which can cause damage and allow it to progress.

Very little consideration has been given in the past to the mechanical role of the synovial membrane in constraining the lubricating fluid in the joint capsule. The reason lies in the common belief that no main mechanical function is provided by it, though no quantitative estimation has ever made available in literature.

In order to address this concern for the first time, we study the two-dimensional problem whose geometry is described in Fig. 1. A biphasic thin layer of cartilage is attached at a rigid bone extremity and shaped as a parabola. An incompressible fluid fills the bursa and is prevented to escape by a linear elastic membrane. The unilateral contact is analysed together with the hypotheses of absence of friction and homogeneous pressure of the fluid. Since the membrane elasticity is generally affected by inflammatory states, the preliminary results of such nonlinear problem are aimed to investigate the effects of the membrane stiffness on the contact development.

Further work will be done in order to state the lubrication equations close to the point A in Fig. 1, for which the oversimplified assumption of homogeneous fluid pressure will be removed. Acknowledgments

The authors feel to acknowledge the EU project FP7-MC-ITN-2013-606878-CERMAT2 for the support to the present research.

Influence of small-scale roughness on flat-stamp adhesion – A numerical study

Roman Pohrt

Technische Universität Berlin, Germany When in a recent study, the adhesion of flat stamps was investigated in the frame of JKR theory, one of the key findings was the importance of a filling factor. According to this result, a flat stap indenter which has considerable faults preventing full contact will see its adhesive capacity reduced. The degree of reduction depends mostly on the percentage of surface in contact, not on the particular fault shape. In the current work, we follow a similar approach. A flat stamp indenter is superposed with a small scale roughness which does not notably alter the non-adhesive indentation behavior. However, when pulled off, this roughness does indeed reduce the attracting force considerably. We use a parametric sinusoidal roughness type to display the effects separately and deduce general conclusions.



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Adhesion of surfaces with wavy roughness and a shallow depression

A. Papangelo1, M. Ciavarella2

1 Department of Mechanical Engineering, Hamburg University of Technology, Am Schwarzenberg-Campus 1, 21073 Hamburg, Germany

E-mail: [email protected] 2 Politecnico di BARI. Center of Excellence in Computational Mechanics. Viale Gentile 182,

70126 Bari E-mail: [email protected]

Keywords: adhesion, rough dimple Recently, a simple and elegant ”dimple” model was introduced by McMeeking et al. (2010) [1] to show a mechanism for a bistable adhesive system involving a surface with a shallow depression. Under the assumption of JKR regime of adhesion, the system shows a bistable behavior: i) a ”strong adhesive” regime if squeezed in full contact, ii) a “weak adhesive” regime when pull-off happens in partial contact [2]. This is similar to the contact of surfaces with a single scale of periodical waviness. We have solved the adhesive problem under the more general assumptuion of a Maugis-Dugdale cohesive model showing that the system behavior depend on a ‘generalized Tabor parameter’ given by the ratio of theoretical strength to elastic modulus, multiplied by the ratio of dimple width to depth. It is shown that bistability disappears for generalized Tabor parameter less than about 2. Introduction of the theoretical strength is needed to have significant results when the system has gone in full contact. We add to this model the effect of roughness, in the simple form of axisymmetric single scale of waviness, permitting a very detailed study, and we show that this induces a resistance to jumping into full contact on one hand (limiting the ”strong adhesion” regime), and an enhancement of pull-off and of hysteresis starting from the partial contact state on the other (enhancing the ”weak adhesion” regime). The system becomes pressure-sensitive also in the intermediate states, as it is observed in real adhesive rough systems. The model obviously is specular to the Guduru model of rough spheres (Guduru,[3]), with which it shares the limitations of the analysis assuming a connected contact (crack) area, and serves also the purpose of showing the effect of a depression into an otherwise periodic rough contact, towards the understanding of adhesion with multiple scales of roughness.

References [1] McMeeking, R. M., Ma, L., and Arzt, E. (2010). Bi-Stable Adhesion of a Surface with a Dimple. Advanced Engineering Materials, 12(5), 389-397.

[2] Papangelo A, Ciavarella M. (2017) A Maugis-Dugdale cohesive solution for adhesion of a surface with a dimple. J. R. Soc. Interface 14: 20160996. http://dx.doi.org/10.1098/rsif.2016.0996

[3] Guduru, P.R. (2007). Detachment of a rigid solid from an elastic wavy surface: theory J. Mech.Phys. Solids, 55, 473–488

Structural Ordering of Molybdenum Disulfide under Extreme Conditions studied via

Reactive Molecular Dynamics Simulations

P. Nicolini1, R. Capozza2, T. Polcar1,3

1 Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo náměstí 13, 12135, Prague 2, Czech Republic 2 Italian Institute of Technology-IIT, via Morego 30, 16163, Genova, Italy

3 Engineering Materials, Faculty of Engineering and Environment, University of Southampton, Southampton SO17 1BJ, United Kingdom

Molybdenum disulfide, the most studied member of the transition metal dichalcogenides family, has been used as solid lubricant for several decades, showing extremely low friction coefficients [1] and stability to high temperature. Its lubricating properties are ascribed to the weak van der Waals interactions between sulfur atoms in the crystalline layered structure. Moreover MoS2, even when prepared in the amorphous state or made of randomly oriented domains, can undergo shear induced structural transitions to the more ordered layered state affecting its tribological properties[2]. Exploiting a recently developed classical force field[3] able to treat explicitly formation and breaking of bonds, we investigate by molecular dynamics simulations, the shear induced structural changes and possible layer formation in the amorphous molybdenum disulfide. The ordering process is studied in details, with particular regard to the estimation of the thermodynamic properties that govern the process itself. A connection with crystallization theories is finally found, conferring a predictive power to the achieved results. Overall, this study aims at gaining an atomic level understanding of the dynamics of layer formation process in MoS2, thus controlling and possibly improving its tribological properties. [1] J.M. Martin et al., Phys. Rev. B, 48, 10583(R) (1993). [2] J. Moser, F. Lévy, Thin Solid Films, 228, 257 (1993). [3] T. Liang et al., Phys. Rev. B, 79, 245110 (2009).



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The Prandtl-Tomlinson Model with Time-Varying Interaction Potential: Analytical Predictions and Experimental Results

Enrico Gnecco(1), Andre Schirmeisen(2), and Juan J. Mazo(3)

(1) Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Germany (2) Institute of Applied Physics, Justus Liebig University Giessen, Germany

(3) Dpto. Física de la Materia Condensada and Instituto de Ciencia de Materiales de Aragón, Spain

The nonlinear Prandtl-Tomlinson (PT) model is possibly the simplest mechanism explaining the stick-slip motion of a sharp tip elastically pulled on a crystal surface [1]. In its basic version the PT model assumes constant tip-surface interaction. Here we will assume that this is not the case and discuss the influence of contact oscillations and of a monotonic increase of interaction due to “contact ageing” on the model results. In the former case the friction force is expected to decrease almost linearly with the oscillation amplitude until the stick-slip is replaced by steady sliding [2,3]. In the latter contact ageing results in a characteristic velocity weakening of friction which, in specific parameter ranges, can supersede the velocity strengthening caused by thermally activated stick-slip [4]. Interestingly, a similar approach can be used to reproduce the patterning process of compliant amorphous surfaces indented by a tip sliding on them [5]. In all cases, the main predictions of the extended PT models have been supported by experimental results. [1] V.L. Popov and J.A.T. Gray. Prandtl-Tomlinson model: History and applications in friction, plasticity, and nanotechnologies. ZAMM-J. of Applied Math. and Mech. 92, 683 (2012).

[2] R. Roth, O. Y. Fajardo, J.J. Mazo, E. Meyer, and E. Gnecco. Lateral vibration effects in atomic-scale friction. App. Phys. Lett. 104, 083103 (2014).

[3] O. Y. Fajardo, E. Gnecco, and J.J. Mazo. Out-of-plane and in-plane actuation effects on atomic-scale friction. Phys. Rev. B 89, 075423 (2014).

[4] J.J. Mazo, D. Dietzel, A. Schirmeisen, J.G. Vilhena, and E. Gnecco. Time strengthening of crystal nanocontacts. Phys. Rev. Lett. 118, 246101 (2017).

[5] E. Gnecco, P. Pedraz, P. Nita. F. Dinelli, S. Napolitano, and P. Pingue. Surface rippling induced by periodic instabilities on a polymer surface. New J. Phys. 17, 032001 (2015).

Dynamic ratchets and actuators

Mikhail Popov1,2,3,*, Qiang Li1

1Technische Universität Berlin, 10623 Berlin, Germany 2National Research Tomsk Polytechnic University, 634050 Tomsk, Russia

3National Research Tomsk State University, 634050 Tomsk Russia * [email protected]

Reduction of friction by ultrasonic oscillation and frictional drives are closely related phenomena [1][2], which are studied here within a macroscopic, contact-mechanical framework. Both normal and tangential (in-plane) oscillations have the capacity to reduce the static and sliding coefficients of friction. When applied at the same time, they can be used to realize vibrational actuators and drives. In the present work we analyze the dynamics of a frictional contact with load-independent normal and tangential stiffness under the action of superimposed normal and tangential oscillation with different phase shifts. Depending on the relative amplitudes (and their relation to the sliding velocity) and the phase difference, we find a continuum of operating modes ranging from symmetric reduction of the coefficient of friction, over states with increasingly asymmetric reduction (which we term “dynamic ratchets”) to the production of directed force and motion (frictional drives and actuators). As in previous works utilizing our contact-mechanical model [3], it is possible to derive the critical velocity of controllability, which marks the disappearance of stick-slip in the contact and therefore the region of active influence:

( ) ( ) ( )( )220 0 02 / sgn( ) cos /c x z x x z z x zv u k k u u v k k uω µ ϕ µ= ∆ + ∆ ∆ ⋅ + ∆ , (1)

where ω and ϕ are the frequency and phase difference of the oscillations, xu∆ and zu∆

are the tangential and normal amplitudes, xk and zk the tangential and normal contact

stiffness, 0µ is the local coefficient of friction and 0v the sliding velocity. The static coefficient of friction, another important parameter, can be approximately determined as

2 2

20 ,0 0 ,0 0 ,0

21 coss z x z x x x

z z z z z

u k u u k uu k u k u

µ ϕµ µ µ

∆ ∆ ∆ ∆= − + ⋅ +

. (2)

While a complete analytical description of the macroscopic force of friction in the studied system is not possible, the above quantities represent important “corner stones” of the numerically obtained dependences, and allow easier parameterization and interpretation of the results. References [1] Storck, H., Littmann, W., Wallaschek, J., and Mracek, M., The effect of friction reduction in presence of ultrasonic vibrations and its relevance to travelling wave ultrasonic motors, Ultrasonics, 2002, vol. 40, no. 1-8, pp. 379-383. [2] Teidelt, E., Oscillating contacts: friction induced motion and control of friction, PhD thesis. Technische Universität Berlin, 2015. [3] Popov, M., Popov, V. L., Popov, N.V., Reduction of friction by normal oscillations. I. Influence of contact stiffness, Friction, 2017, vol. 5, no. 1, pp. 45–55.



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Dynamic stimulation of cell adhesion by light: From functional molecules to mechanosensin

Christine Selhuber-Unkel

Kiel University, Germany

Cells are extremely dynamic and active systems that interact with their environment through a variety of mechanisms. They are not only influenced by the structure of their environment, but also by chemical and physical stimuli. Dynamic photoresponsive interfaces that mimic the extracellular space are highly promising for controlling cell adhesion in a well-defined manner. Our interfaces are based on azobenzene molecules that contain adhesion ligands (RGD peptides) as headgroups. They are not only able to switch cell adhesion, but also to control cellular mechanosensing with molecular precision, if push-pull substituted azobenzenes are used. We have shown using atomic force microscopy (AFM) that cell adhesion is enhanced by the high-frequency oscillation of such push-pull-azobenzenes and that even gene expression in cells is influenced. In the future such interfaces should enable us to control cellular properties and particularly mechanosensing in biomedical applications, where the local stimulation of cell adhesion is envisaged. Reference: L. F. Kadem, K. G. Suana, M. Holz, W. Wang, H. Westerhaus, R. Herges, C. Selhuber-Unkel (2017): High Frequency Mechanostimulation of Cell Adhesion. Angewandte Chemie International Edition, 56: 225-229.

Simulations of the peeling behaviour of membranes

D. Liprandi1, L. Brely1, G. Costagliola1, F. Bosia1, N. Pugno2,3,4

1Department of Physics and “Nanostructured Interfaces and Surfaces” Centre, Università di Torino, via P. Giuria 1, 10125 Turin, Italy

2Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, Università di Trento, via Mesiano, 77, 38123 Trento, Italy

3School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, E14NS London, UK

4Ket Lab, Edoardo Amaldi Foundation, Italian Space Agency, Via del Politecnico snc, Rome 00133, Italy

Biological attachment structures are usually studied using single or multiple peeling models, which involve one-dimensional tapes or contacts [1]. This approach is oversimplified for many practical problems, since the adhesive behaviour of a large number of complex two-dimensional structures (e.g. spider web anchorages) is still poorly explained. Here, we develop a model to simulate the detachment of a membrane attached to a surface. To do so, we use a 3D numerical model based on two-dimensional contacts coupled with the substrate using a cohesive law. Our goal is to better understand the mechanical behaviour of the biological adhesives with complex geometries or material anisotropies by analysing the interaction between the stress distributions at the interface and in the membrane itself. Results show how parameters can be adjusted to optimize or tune the pull-off force for different loading scenarios. Preliminary results are also presented relative to coupled adhesion-friction simulations using the same numerical approach, showing the influence of patterned surfaces [2].

Figure 1 Example of a membrane being pulled from a central point at an angle of 60°

References: [1] Lucas Brely, Daniele Liprandi, Federico Bosia, Nicola M. Pugno. “Optimal Adhesion Control via Cooperative Hierarchy, Grading, Geometries and Non-linearity of Anchorages and Adhesive Pads” in Bio-inspired Structured Adhesives. Springer, Berlin, p. 81-93 (2017). [2] Gianluca Costagliola, Federico Bosia, and Nicola M. Pugno, Static and dynamic friction of hierarchical surfaces. Phys. Rev. E 94, 063003 (2016)



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Capillary force model at a rough interface in presence of a thin water film

M. Bazrafshan1,2*, M.B. de Rooij2, D.J. Schipper2

1 Material innovation institute (M2i), Elektronicaweg 25, 2628 XG , Delft, Netherlands 2 Laboratory for Surface Technology and Tribology, Department of Engineering Technology,

University of Twente, P.O. box 217, 7500AE, Enschede, Netherlands A Boundary Element Model (BEM) for the formation of menisci at the rough interface of two contacting bodies is proposed, where a thin water film is adsorbed on the surfaces due to the condensation from the humid environment. Rather than a film with uniform thickness, the true distribution of the water films over the surfaces is considered. The model is first verified through the well-known capillary force model at the smooth contact of a rigid ball-on-flat configuration for different values of the Relative Humidity (RH) of the environment. Then, the adhesive contact at a rough interface is considered. It is found that the capillary force first increases with the RH as long as the non-contacting part of the interface is not completely wetted by meniscus. From this point on, the capillary force decreases rapidly with RH as a result of decreasing the capillary pressure. Furthermore, it is confirmed that employing a water film with uniform thickness overestimates the capillary force compared to the one resulting from the true distribution of this film. Keywords: Capillary, Thin Water Film, Boundary Element Method

MD Sliding Simulations of Amorphous Silica Tribofilm. The Impact of Some Factors.

A.I. Dmitriev, A.Y. Nikonov and W. Österle

Institute of Strength Physics and Material Science, Russian Academy of Sciences Tomsk, Russia

In the paper the sliding behavior of simplified amorphous SiO2 tribofilms were simulated by molecular dynamics modeling. The objective was to identify mechanisms explaining the experimentally observed lubricating properties. The impacts of layer thickness, normal pressure, temperature and interatomic potential were studied systematically. While the layer thickness was not critical, all the other parameters showed special effects under certain conditions. For instance towards the end of a simulation we sometimes observed cross-sections showing features with almost circular shape. From other hand the rise of normal pressure can prevent the void formation and could even eliminate voids if applied at high temperature. At this stick-slip sliding was changed to smooth relative motion at high temperature due to void healing. Two potentials (Tersoff and ReaxFF) were applied for simulating uniaxial tensile tests and sliding within a thin film formed from silica nano-particles. The simulations were also performed at two temperatures corresponding to moderate and severe tribological stressing conditions. Simulations with two different potentials revealed the need of considering different temperatures in order to obtain a sound interpretation of experimental findings.



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Interplay between adhesion and friction

M. Khajeh Salehani*1, N. Irani1 and L. Nicola1;2

1Department of Materials Science and Engineering, Delft University of Technology, 2628 CD Delft, The Netherlands

2Department of Industrial Engineering, University of Padova, 35131 Padua, Italy

e-mail: * [email protected]

In this study, consequences of the interplay between adhesion and friction in the contact response of elastic solids is investigated using Green’s function molecular dynamics [1]. First, the technique is extended to explicitly describe both solids in contact and their interactions through a mixed-mode coupled cohesive zone model [2]. While the presented formulation is applicable to elastic solids with arbitrary material properties and generic surface roughness obeying the small slope approximation, the focus of our analysis is on the indentation of a two-dimensional periodic array of circular rigid punches into a flat elastic solid. Simulations are carried out to evaluate the dependency of contact size, load-displacement curve and pull-off load on the interface properties. This dependency is examined for bodies with various Poisson’s ratio, height and for various spacing between punches. Our results show that coupling adhesion and friction results in an increase in the contact size and a decrease in load for a given applied displacement. Consequently, a significant decrease is observed in the predicted pull-off load. Nevertheless, due to the interplay of adhesion and friction, the pull-off load is found to increase with friction. The results are compared with JKR and DMT theories. REFERENCES

[1] S. P. Venugopalan, L. Nicola, and M. H. M¨user, “Green’s function molecular dynamics: including finite heights, shear, and body fields,” Modelling Simul. Mater. Sci. Eng., 25(3), 034001 (2017).

[2] J. P. McGarry, E. O. Mairtın, G. Parry and G. E. Beltz, “Potential-based and non-potentialbased cohesive zone formulations under mixed-mode separation and over-closure. Part I: Theoretical analysis”, J. Mech. Phys. Solids, 63, 336-362 (2014).

Study of the correlation between nanoscale adhesion and friction using nanopatterned surfaces

Prashant Pendyala1, Hong Nam Kim1,2, Harpreet S Grewal4, Il-Joo Cho1,2, Eui-Sung Yoon1,3,*

1Center for BioMicrosystems, Korea Institute of Science and Technology, Seoul, South Korea. 2Division of Bio-Medical Science and Technology, University of Science and Technology, KIST

School, Seoul, South Korea 3Division of Nano & Information Technology, University of Science and Technology, KIST

School, Seoul, South Korea 4Department of Mechanical Engineering, Shiv Nadar University, Uttar Pradesh, India.

*Corresponding Author, Email: [email protected]

Adhesion in relation to friction was assumed as an effective additional normal load. Such an assumption is valid at macro scale friction experiments where scale of interaction geometry is large compared to range of intermolecular and surface forces. In the case of tribological interactions, adhesion is highly dependent on the complex evolution of interaction volume and the deviations in geometry resulting from deformation. We study the correlation between adhesion and friction characteristics of nanoscale tribological interactions using nanopatterned surfaces under varied physico-chemical characteristics. Capillary force lithography in combination with nano-drawing procedures were employed to generated nanoscale cylindrical, mushroom-shaped and hierarchical patterns with varying curvature, surface energy and distribution. Parameters that control the real contact area between the indenter the patterns such as curvature, surface energy and density of the patterns predominantly influenced the adhesion. Effective lateral contact stiffness dominated the friction. Interestingly, in contrast to previous studies, cylindrical and mushroom-shaped pillars showed similar adhesion characteristics but different frictional characteristics. We showed that this phenomenon is due to a larger ratio of the mushroom flange thickness to the radius of the pillar stem. Importantly, we observed master curves in the log plot of adhesion versus friction that correlate the tribological behavior to physico-chemical aspects of the individual interactions. Predominantly, the slope of the master curves was related to the effective lateral stiffness of the contact. These results will aid the identification of simple pattern parameters that can be scaled to tune adhesion and friction and will help broaden the understanding of nanoscale topographical interactions.



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Loss of an adhesive contact at normal and tangential loading

Iakov A. Lyashenko1,2,*, Valentin L. Popov2, Alexander E. Filippov2

1Sumy State University, 40007 Sumy, Ukraine 2Institut für Mechanik, Technische Universität Berlin, 10623 Berlin, Germany

*E-mail: [email protected] We consider the adhesive contact between rigid parabolic indenter and an elastic halfspace. In the case of adhesive contact, according to JKR theory, at normal motion this situation can be described by Heß rule [1] within the method of dimensionality reduction. According to the Heß rule which defines the maximum tensions of the individual springs maxl∆ in discreet contact,

that are located along the edges of contact:

max *

2 alEπ γ∆

∆ = ,

where a is the radius of the contact, *E is the effective elastic modulus, and γ∆ is the surface energy (work of adhesion). However, mentioned rule is correct only in the case of normal motion. In [2] we considered simultaneous normal and tangential motion of the indenter. In this situation we used the Heß rule, taking into account that tension of the spring can occur in both normal and tangential direction. Thus the destruction of the adhesive contact can appear only at tangential motion. We assume that adhesive bonds did not recover after destruction and springs are sliding without friction and did not affect the tangential force. This assumption allows us to obtain the ratio between normal and tangential forces, at which the destruction of the contact is observed. We also consider and describe two cases of motion: with controlled load and controlled displacement. Obtained analytical results are confirmed by numerical simulations within the framework of method of dimension reduction. We also generalize obtained results for the case, where the work of adhesion forces depends on the direction of the motion. This situation described in [3], where we introduced parameter λ , to describe the contribution from both normal and tangential motion. We also obtained dependencies for the critical forces, at which the destruction of adhesive contact for different values of parameter λ varying in the range from 0 to 1. Case 1λ = is corresponded to situation when the work of adhesive forces does not dependent on the direction of motion. It is worth to mention that developed approach can be generalized only in the case when destruction of the contact observed at positive distance between the indenter and halfspace. In this case adhesive forces did not recover as the indenter is always located over the surface of halfspace.

*This work was partially supported by the Ministry of Education and Science of Ukraine under the project “Thermodynamic theory of the phase transitions between structural states of the boundary lubricant with spatial inhomogeneity” 0116U006818 [1] V. L. Popov, M. Heß. Method of dimensionality reduction in contact mechanics and friction. 2015. Berlin, Germany: Springer. [2] V. L. Popov, I. A. Lyashenko, A. E. Filippov, Influence of tangential displacement on the adhesion strength of a contact between a parabolic profile and an elastic half-space // Royal Society Open Science. – 2017. – Vol.4. – P. 161010. [3] J. F. Waters, P. R. Guduru, Mode-mixity-dependent adhesive contact of a sphere on a plane surface / Proc. Royal Soc. A. – 2010. – Vol. 466(2117). – P. 1303-1325.

Competition of adhesion and plasticity and the laws of adhesive wear

V.L. Popov

Technische Universität Berlin

In 1953, Archard published a paper [1] devoted to contact and rubbing of rough surfaces, which contained most important ideas of the contact mechanics of rough surfaces, including the main ideas of the theory of adhesive wear. In particular, Archard derived a simple estimation for the wear volume stating that the wear volume is proportional to the normal load, the sliding distance, and inversely proportional to the hardness of contacting materials (or the smaller one if they are different). The proportionality coefficient is called coefficient of adhesive wear. The physical na-ture of the coefficient of adhesive wear has not been clarified yet. Archard assumed that there is some probability that an asperity contact will lead to the appearance of wear particles. However, he could not specify the detailed physics of this probability. Neither did he make any statement about the size or size distribution of wear particles. However, the amount of wear is not the only quantity that is of interest, the distribution of wear particle size may also be very important. The key physical idea for the problem of size of wear particles (and implicitly for understanding the value of the coefficient of wear) was suggested by Ernest Rabinovich. In 1958, he wrote a short article in Wear, in which he put forward the hypothe-sis of a mechanism determining the size of wear particles [2]. His derivation was based on the con-sideration of the competition between plasticity and fracture. For almost 60 years, this idea was simply retold from one textbook to the other, but did not re-ceive any essential development based on some model ideas until the 2016 the paper of Aghaba-baei, Warner and Molinari appeared in Nature Communications [3]. The authors of this paper con-sidered again the idea of Rabinowicz, but now at the level of physical mechanisms. Molinari and colleagues generated two media with micro heterogeneities and found that the behavior of the sys-tem was strongly dependent on the size of colliding micro heterogeneities. For small enough initial asperity size, the main process was plastic deformation and gradual smoothing of the roughness, while for over-critical size the generation of wear particles was the dominant process. In recent papers [4] and [5], an attempt was undertaken, to formulate, based on the idea of Rab-inowicz, a more general criterion for transition between plastical smoothing and production of wear particles which would be applicable also for asperities of complicated form or which did not use the poorly defined notion of an “asperity”. Here we report the last advancements on this way. References

[1] J. F. Archard, J. Appl. Phys. 24, 981 (1953). [2] E. Rabinowicz, Wear 2, 4-8 (1958). [3] R. Aghababaei, D. H. Warner, J.-F. Molinari, Nat. Commun. 7, 11816 (2016). [4] Q. Li, V.L. Popov, On the possibility of frictional damping with reduced wear: A note

on the applicability of Archard’s law of adhesive wear under conditions of fretting, Fiziheskaya Me-zomechanika, 20, 91-95 (2017).

[5] V. L. Popov, Generalized Rabinowicz’ Criterion for Adhesive Wear for Elliptic Micro Con-tacts, AiP Conf. Proc., Advanced Materials with Hierarchical Structure for New Technologies and Reliable Structures (2017).



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Modeling of detachment in normal and tangential contacts in Discrete Element

Method: an influence of element size

A.V. Dimaki1, E.V. Shilko1, S.G. Psakhie1, V.L. Popov2

1Institute of strength physics and materials science SB RAS, Tomsk, Russia 2Berlin University of Technology, Berlin, Germany

Adhesion plays an important role in friction and wear of materials of different nature. Adhesive forces have a short range of interaction and thus play the most important role in local contacts of micro-asperities of rough surfaces. Attachment and detachment of these micro-contacts determine a macroscopic response of a contact pair. Since different variations of discrete element method (DEM) are widely used for computer-aided modeling of friction, including local fracture and welding, a theoretical investigation of features of DEM simulations of normal and tangential contacts is of high importance. In the present study we have focused on an influence of size of a discrete element on estimates of contact strength under two types of loading conditions, which are typical for friction and wear problems, namely under normal and tangential loading. Here the contact strength means a maximal value of specific reaction force which a contact can sustain before detachment. Suggest an adhesive contact between two linearly elastic bodies (i.e. a contact between an asperity and a counter-body). Suppose the strength of the bodies is much higher than the strength of the interface zone, which is typical for adhesive contacts. Let the asperity move vertically (when simulate a normal contact with tension) or horizontally (when simulate a tangential contact) with constant velocity. We performed a numerical study of this system using a method of movable cellular automata which is a representative of DEM family allowing using a multi-body approximation and various criteria of detachment. We found that model values of tensile and shear strength of the contact depend on the element size in accordance with a power-law. This particularly means that strength of a contact tends to zero with decreasing of the element size. The reason for this non-physical behavior is the fact that DEM provides an element-size-dependent approximation of stress concentrations at the edges of the contact. In the result, the smaller is an element, the higher are stress peaks and the earlier fracture occurs. In order to overcome this artificial effect, we introduced a mesh-dependent fracture criterion which suggests a power-law dependence of a local ultimate stress (i.e. an ultimate stress which a given pair of elements can sustain without detachment) on the element size. The given fracture criterion provides an almost size-independent values of tensile and shear strength for asperity detachment from a counter-body. Although the present form of the obtained fracture criterion isn’t universal, it demonstrates a perspective way of development of discrete-element based models for brittle and elastic-plastic materials.

Why living nature is tolerant to the five-fold symmetry

and inanimate is not too much?

Alexander E. Filippov

Department of Functional Morphology and Biomechanics, Zoological Institute, Kiel University, Am Botanischen Garten 9, D-24118 Kiel, Germany

Department N5, Donetsk Institute for Physics and Engineering, National Academy of Sciences of Ukraine, R. Luxemburg Str. 72, 83114 Donetsk, Ukraine

1. Fibonacci’s rabbits and Fibonacci’s spirals 2. How it relates to the 5-fold symmetry? 3. Penrose tiling and Quasicrystals with 5-fold symmetry in nature 4. Numerical generation of the quasicrystal – periodic contact surface 5. Quasiperiodicity in Islamic ornament 6. Model and its simplification 7. Numerical simulations: results and discussion



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Functionally Graded Materials in Biological Systems with Impact Loading

Emanuel Willert

Technische Universität Berlin, Str. des 17. Juni 135, 10623 Berlin

E-Mail: [email protected]

Functionally Graded Materials (FGM) are increasingly used in technical or biological and, in particular, tribological systems. Within a FGM, one or more mechanical properties vary continuously in one or more directions; thus, these materials can be specifically produced and optimized for their desired application. In contrast to the similar layered materials, FGM usually do not fail against delamination and do not exhibit thermo-cyclic creep. The talk will deal with the influence of the use of FGM in elastic impacts of spheres. As an example, which permits analytical treatment, the focus is on a material model in which the modulus of elasticity increases in depth with the form of a power law. Such forms of FGM have long been used in soil mechanics and are reanalyzed nowadays for example in protheo-synthesis. During the examination of the impact problem, quasi-stationarity and the validity of the half-space hypothesis are assumed, and analytical and numerical methods are used. Coulomb friction without adhesion and JKR-adhesion without slip are considered. The solutions obtained are exact within the framework of the assumptions and within the numerical precision. The rigorous solution of the Hertzian impact problem with and without adhesion for the considered class of inhomogeneous materials is presented and it is demonstrated how by the use of FGM both the maximum normal stresses during the impact (and thus the impact resistance) as well as the critical impact velocity, below which the spheres remain adhered to each other by the effect of adhesion, can be reduced. The general, oblique collision problem is solved numerically using the Method of Dimensionality Reduction. It turns out that, when FGM are used, parameter combinations are possible in which the oblique impact with friction can be completely energy-retaining if the coefficient of friction is large enough. For homogeneous materials, this is impossible even with an infinitely large coefficient of friction.

Simulation of contact of gradient materials with Boundary Element

Q. Li, V.L. Popov

Technical University of Berlin, Berlin, Germany

Since 1990s the functionally graded materials (FGMs) have been developed for improvement of thermomechanical properties of components. The gradually varying composition and structure of FGM result in the continuous changes in properties of materials, thus solving some of typical problems of layered materials as poor interface strength and residual stresses.

For contacts of linearly elastic or viscoelastic materials, the most suitable method for contact problems is the boundary element method (BEM) as it uses discretization only of the two-dimensional surface instead of the whole volume. Recently an effective numerical method based on the BEM was developed by Pohrt and Li for the fast simulation of normal and tangential contacts including indentation test and partial sliding of fractal rough surfaces [1]. This method was further developed by Pohrt and Popov for the adhesive contact by formulating a mesh-dependent stress criterion for detachment of contact elements [2]. In this presentation (or paper [3]), we generalize the method suggested in [2] for the contact of functionally graded materials with power-law dependence of the elastic modulus. Proceeding from the fundamental solution for single force acting on the surface of an elastic half space, first the influence matrix is obtained for a rectangular grid. The inverse problem for the calculation of required stress in the contact area from a known surface displacement is solved using the conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used. For the adhesive contact of graded material, the detachment criterion based on the energy balance is proposed. For verifying the proposed method, several exactly analytically solved problems [4][5] are reproduced numerically. References [1] Pohrt R, Li Q (2014) Complete boundary element formulation for normal and tangential

contact problems. Phys Mesomech 17:334–340. doi: 10.1134/S1029959914040109 [2] Pohrt R, Popov VL (2015) Adhesive contact simulation of elastic solids using local mesh-

dependent detachment criterion in boundary elements method. Facta Univ Ser Mech Eng 13:3–10.

[3] Li Q, Popov VL (2017) Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials, computational mechanics.

[4] Jin F, Guo X (2013) Mechanics of axisymmetric adhesive contact of rough surfaces involving power-law graded materials. Int J Solids Struct 50:3375–3386.

[5] Heß M (2016) A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials. Int J Eng Sci 104:20–33.



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Numerical simulations of the frictional properties of gradient materials

Roberto Guarino1, Gianluca Costagliola2, Federico Bosia2, Nicola Maria Pugno1,3,4,*

1 Laboratory of Bio-Inspired & Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento, Italy

2 Department of Physics and Nanostructured Interfaces and Surfaces Centre, University of Torino, Via Pietro Giuria 1, 10125 Torino, Italy

3 Ket Lab, Edoardo Amaldi Foundation, Italian Space Agency, Via del Politecnico snc, 00133 Rome, Italy

4 School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, E1-4NS London, United Kingdom

* Corresponding author: [email protected]

The precise control of friction coefficients can be of extreme interest in many engineering applications. Recent studies have demonstrated that by realizing surfaces with 2D or 3D textures, it is possible to modify the frictional properties of both dry and of lubricated contacts. Similarly, hierarchical surface structures observed in Nature have stimulated the development of artificial bio-inspired solutions, with outstanding frictional and adhesive properties. Here, we extend previous work on 1D composite surfaces to 2D geometries to show how it is possible to tune the macroscopic tribological properties through local variations of material and surface properties, i.e. friction coefficients and Young’s moduli. Results also allow to compare the predictions of a discrete approach, like the spring-block model, and explicit Finite Element simulations. This provides useful insights to understand the frictional properties of gradient materials, with the aim of designing smart tribo-materials and innovative solutions for sliding interfaces. References Costagliola G., Bosia F., and Pugno N.M., Tuning friction with composite hierarchical surfaces, Tribology International 115 (2017) 261-267.

Costagliola G., Bosia F., and Pugno N.M., 2D Model for friction of complex anisotropic surfaces, arXiv:1706.08055.

A Computational Scheme for Axisymmetric Adhesive Contact of Layered Half-space

Pu Li 1, Xiaoqing Jin 1,2, and Xiangning Zhang 1, Feodor M. Bordich 3

1 State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing,

400044, China 2 College of Aerospace Engineering, Chongqing University, Chongqing, 400040, China

3 School of Engineering, Cardiff University, Cardiff CF24 0AA, United Kingdom

This work presents a computational scheme for treating axisymmetric adhesive contact of layered half-space. A moduli-perturbation method is adopted to estimate the unloading compliance of the Boussinesq flat punch indenting a layered linear elastic half-space. In the framework of the JKR theory, the characteristics of adhesive contact between two spherical solid surfaces may be obtained by employing the energy approach. Benchmark examples are provided to validate the effectiveness of the proposed method, and parametric studies are performed for a moderate range of material combinations of the film/substrate system. Key words: Axisymmetric contact, adhesion, Layered half-space, JKR theory



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Theoretical Analysis of Indentation Between

Elastic Sphere and layered Half-Space

Yiquan Li, Xiaozhou Li, Jinkai Xu and Huadong Yu

School of Mechatronical Engineering, Changchun University of Science and Technology, Changchun 130022, China

Thin films and coatings have been extensively used in engineering to improve mechanical performance of the solid surfaces. For example, hard coatings deposited on tools or parts can protect them against abrasion and wear. In order to optimize the film/substrate structure deign it is necessary to analyze the mechanical properties of the thin film. It is shown that the indentation test with spherical indenter is an effective method to measure the elastic properties of the coating materials. On the other hand, the rough surfaces of solid bodies contain asperities, when two bodies are placed in contact, surface roughness causes contact at discrete summits. The asperity tip is usually assumed to be spherical, the contact problem reduces to a sphere in contact with a flat surface. Therefore, the contact issue between a spherical body and a coated elastic half-space is of great scientific interest.

In this study, the contact problem for the elastic sphere indenting a layered half-space is considered. Analytical methods for solving this problem have been developed on the basis of the 3-D fundamental solution of coated half space subjected to a normal concentrated force on the surface. The normal pressure distribution within the contact zone is assumed as Hertzian type. The solutions are constructed using superposition principle in the form of infinite series. Through comparing with the numerical results of FEM, it can be verified that the exact solutions have rapid convergence rate and the stresses and displacements are mainly determined by the first term, which is corresponding to the solution of homogeneous half-space under Hertzian loading. Applying the method the contact radius can be predicted.

Keywords: Fundamental solution; Image method; Coated half space; Spherical

indentation; Contact radius

A

B C

p(t)

xy

z

φ sr

S O

rz

t

a 0

0

Fig.1 Coated half-space subjected to distributed loading

Application of Micro Texture In Micro cutting Tool

Zhanjiang Yu, Lei Feng

School of Mechatronical Engineering, Changchun University of Science and Technology, Changchun 130022, China

In terms of the serious tool wear during micro cutting process, micro-pit and micro groove is manufactured by laser on lathe tool for high speed micro turning based on the theory of anti-friction and anti-drag of non-smooth micro texture. Relationship between laser processing parameters and morphology of micro-texture are researched and characteristics of friction are analyzed as well. Contrast cutting tests of SUS304 stainless steel with micro-texture and untexture tool are implemented using self-developed high speed Micro-cutting unit. Micro-texture performance is evaluated from cutting force, cutting temperature and tool-chip contact status, chip morphology and machined surface roughness. Experimental results show that micro groove and micro pit can decrease surface friction coefficient effectively, reducing cutting force, cutting temperature and tool-chip contact length, improving chip shape. Especially, micro pits structure can improve surface quality obviously, which can be applied in SUS304 high-speed cutting. Key words: micro texture; SUS304; high speed cutting; micro-turning; lathe tool



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PLASTIC STRAIN LOCALIZATION IN FRICTION STIR WELDED ALUMINUM

R.R. Balokhonov, V.A. Romanova

Institute of Strength Physics and Materials Science, SB, RAS, 634021, Tomsk, Russia

The effect of the microstructures observed in different zones of friction stir welded (FSW) aluminum on the mechanical properties of the alloy is investigated. The microstructure of the material in the thermo-mechanically affected zone (TMAZ) is organized in a complex way [1]. Its special feature observed on the advancing side is that high deformations and mixing during the FSW process cause grains to take quasi-rectangular form and generate grain lamellas oriented in a certain direction (Fig. 1a). This type of microstructure will be referred to as an ordered microstructure, as distinguished from the disordered polycrystalline microstructure formed in the nugget and originally observed in the base material.

FIGURE 1. Experimental microstructures observed in the nugget and TMAZ on the advancing side of the weld a) and corresponding models for different degree of ordering b).

A dynamic boundary-value problem represented in terms of the plane strain is solved numerically by the finite-difference method [2]. A constitutive model accounting for the elastic-plastic behavior of the material experiencing isotropic strain hardening is built. A fracture criterion allowing for crack nucleation and growth in local regions of maximum equivalent plastic strains is formulated. An algorithm was designed to generate ordered and disordered microstructures observed experimentally in the nugget and in the thermo-mechanically affected zone (TMAZ) on the advancing side of the weld and characterized by different shape and arrangement of polycrystalline grains (Fig. 1b). A series of calculations of the elongation of the microstructure were performed for a varying degree of ordering of the microstructure. The ordered lamellar microstructure of the material in the TMAZ on the advancing side of the weld was found to provide more uniform stress and strain distributions under loading and, accordingly, a higher strength as opposed to the disordered polycrystalline microstructure in the base material and in the nugget. This work is financed by Russian Foundation for Basic Research (Grant No. 16-01-00469-a). 1. M. Dumont, A. Steuwer, A. Deschamps, M. Peel, P.J. Withers Microstructure mapping in

friction stir welds of 7449 aluminium alloy using SAXS. Acta Materialia, 54 (2006) 4793–4801.

2. R. Balokhonov, V. Romanova, E. Batukhtina, S. Martynov, A. Zinoviev, O. Zinovieva, A mesomechanical analysis of the stress-strain localisation in friction stir welds of polycrystalline aluminum alloys, Meccanica 51(2), 2016, 319-328,

abstracts - tu berlin...increases the true contact area, and (ii) tangentially to the surface,...

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