• K R Y Simha

• Foreword

• Friction tensor concept for textured surfaces

Directionality of grinding marks inﬂuences the coefﬁcient of friction during sliding. Depending on the sliding direction the coefﬁcient of friction varies between maximum and minimum for textured surfaces. For random surfaces without any texture the friction coefﬁcient becomes independent of the sliding direction. This paper proposes the concept of a friction tensor analogous to the heat conduction tensor in anisotropic media. This implies that there exists two principal friction coefﬁcients $\mu_{1,2}$ analogous to the principal conductivities $k_{1,2}$. For symmetrically textured surfaces the principal directions are orthogonal with atleast one plane of symmetry. However, in the case of polished single crystalline solids in relative sliding motion, crystallographic texture controls the friction tensor.

• Study of solid lubrication with MoS2 coating in the presence of additives using reciprocating ball-on-ﬂat scratch tester

Molybdenum disulphide (MoS2) based solid lubricant mixtures containing zirconia and graphite were prepared in the laboratory and coated on steel specimens. The experiments were done using reciprocating scratch test for various numbers of cycles. The results showed that the addition of zirconia and graphite into the MoS2 lubricant has improved its properties in terms of both friction and wear. In addition, it was observed that the presence of moisture affects the life of the lubricating ﬁlm. It was shown that at high temperature the moisture evaporation enhanced the coating performance of the ﬁlm.

• Near surface stress analysis strategies for axisymmetric fretting

Fretting is essentially a surface phenomenon, but bulk stresses and material properties contribute to subsequent failure. This feature of fretting demands a thorough understanding of near surface stresses under the joint action of normal, shear and thermal loading. Axisymmetric fretting is of great concern in piping and coupling design. In this paper, we develop design tools for Near Surface Analysis (NSA) for understanding axisymmetric fretting. Axisymmetric Fretting Analysis (AFA) becomes formidable owing to localised tractions that call for Fourier transform techniques. We develop two different NSA strategies based on two-dimensional plane strain models: 2D strip model (2DS) and half-plane Flamant model (2DF). We compare the results of 2DS and 2DF with the exact results for AFA obtained using Love’s stress function in conjunction with Fourier transform. There is a good correspondence between stress components obtained from 2D-models.

• Axisymmetric fretting analysis in coated cylinder

Fretting is essentially a contact fatigue phenomenon, although bulk stresses and material properties contribute to ﬁnal failure. The near surface state of stress developed under oscillatory contact between machine elements plays a major role in deciding the severity of fretting. It is possible to enhance tribological properties by coating the surface. There is rather scanty literature available on fretting analysis of coated components. Presence of such coatings has a large inﬂuence on the near surface state of stress. The effect of coatings on the severity of fretting is the focus of this paper. Results obtained for both hard and soft coatings are compared with the results obtained for the homogeneous case. The component geometry and loading are chosen to be cylindrical to enable 3D elastic axisymmetric fretting analysis. The results are compared with 2D models (strip and half-plane) to examine their utility and validity for understanding axisymmetric fretting. Contact pressure and frictional shear loading cases are solved separately and superposed appropriately depending on the coefﬁcient of friction considered. Results for different values of coefﬁcient of friction and elastic mismatch are illustrated through contour plots of stresses and strains. These results are expected to be helpful for identifying fretting failure zones and fracture mechanisms in coated components. Analytical results presented here could serve as useful benchmarks for calibrating numerical codes and experimental techniques.

• Micro and macro contact mechanics for interacting asperities

Contact of rough surfaces at micro and macro scales is studied in this paper. The asperities at micro scale are characterised by small radius of curvature whereas the waviness is characterised by large radius of curvature. When two rough surfaces come in contact, on the micro scale, of asperities contacts in a very small area leave large gaps between the surfaces; whereas on the macro scale the surfaces conform to each other under the application of load without gaps. Contact at micro scale is modelled by superposition of Hertzian stress ﬁelds of individual asperity contacts and the waviness at macro scale is modelled as a mixed boundary problem of rough punch indentation where displacements of uneven proﬁle are prescribed along the region of contact. In both the cases for simpliﬁcation the roughness is assigned to one surface making the other surface perfectly ﬂat an assumption often made in contact mechanics of rough bodies.

The motivation for modelling the asperities at micro scales comes from the preliminary results obtained from photoelastic experiments. Numerical results are presented based on the analytical results available for Hertzian contacts. The motivation for modelling the asperities at macro scales comes from the results available in literature for ﬂat contacts from solving mixed boundary elasticity problems. A condition of full stick is assumed along the contact which is a common assumption made for rough contacts. The numerical results are presented for both the cases of rough contact at micro and macro scales.

• Wave propagation in coated cylinders with reference to fretting fatigue

Fretting fatigue is the phenomenon of crack initiation due to dynamic contact loading, a situation which is commonly encountered in mechanical couplings subjected to vibration. The study of fretting fatigue in high frequency regime has gained importance in recent years. However the stress wave effects at high frequency y loading is scanty in the literature. The objective of present investigation is to study stress wave propagation in cylinders with reference to high frequency fretting. The case of a coated cylinder is considered since coating is often provided to improve tribological properties of the component. Rule of mixtures is proposed to understand the dispersion phenomenon in coated or layered cylinder knowing the dispersion relation for the cases of homogeneous cylinders made of coating and substrate materials separately. The possibility of stress wave propagation at the interface with a particular phase velocity without dispersion is also discussed. Results are given for two different thicknesses of coating.