Evaluation of elastic and adhesive properties of solids by depth-sensing indentation

To describe properly interactions between contacting solids at micro/nanometre scales, one needs to know both adhesive and mechanical properties of the solids. Borodich and Galanov have introduced an effective method (the BG method) for identifying both characteristics from a single experiment on depth-sensing indentation by a spherical indenter using optimal fitting of the experimental data. Unlike traditional indentation techniques involving sharp indenters, the Borodich-Galanov methodology intrinsically takes adhesion into account. It is essentially a non-destructive approach. These features extend the scope of the method to important applications beyond the capabilities of conventional indentation. The scope of the original BG method was limited to the classic JKR and DMT theories. Recently, this restriction has been overcome by introducing the extended BG (eBG) method, where a new objective functional based on the concept of orthogonal distance curve fitting has been introduced. In the present work, questions related to theoretical development of the eBG method are discussed. Using the data for elastic bulk samples, it is shown that the eBG method is at least as good as the original BG method. It is shown that the eBG can be applied to adhesive indentation of coated, multilayered, functionally graded media

Insight into mechanics of AFM tip-based nanomachining: bending of cantilevers and machined grooves

Atomic force microscope (AFM) tip-based nanomachining is currently the object of intense research investigations. Values of the load applied to the tip at the free end of the AFM cantilever probe used for nanomachining are always large enough to induce plastic deformation on the specimen surface contrary to the small load values used for the conventional contact mode AFM imaging. This study describes an important phenomenon specific for AFM nanomachining in the forward direction: under certain processing conditions, the deformed shape of the cantilever probe may change from a convex to a concave orientation. The phenomenon can principally change the depth and width of grooves machined, e.g. the grooves machined on a single crystal copper specimen may increase by 50% on average following such a change in the deformed shape of the cantilever. It is argued that this phenomenon can take place even when the AFM-based tool is operated in the so-called force-controlled mode. The study involves the refined theoretical analysis of cantilever probe bending, the analysis of experimental signals monitored during the backward and forward AFM tip-based machining and the inspection of the topography of produced grooves

Scaling of Crack Surfaces and Implications on Fracture Mechanics

The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On the contrary, it appears that an anomalous scaling reflects a R-curve behavior associated to a size effect of the critical resistance to crack growth in agreement with the fracture process of heterogeneous brittle materials exhibiting a microcracking damage.Comment: Revtex, 4 pages, 3 figures, accepted for publication in Physical Review Letter

Size Effect in Fracture: Roughening of Crack Surfaces and Asymptotic Analysis

Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis allows to extend the link to the nominal strength of structures. We show that a Family-Vicsek scaling leads to the classical size effect of linear elastic fracture mechanics. On the contrary, in the case of an anomalous scaling, there is a smooth transition from the case of no size effect, for small structure sizes, to a power law size effect which appears weaker than the linear elastic fracture mechanics one, in the case of large sizes. This prediction is confirmed by fracture experiments on wood.Comment: 9 pages, 6 figures, accepted for publication in Physical Review

Mechanical, Structural and Scaling Properties of Coals: Depth-sensing Indentation Studies

This paper discusses special features of mechanical behaviour of coals discovered using depth-sensing indentation (DSI) techniques along with other traditional methods of material testing. Many of the special features are caused by the presence of multiscale complex heterogeneous internal structures within the samples and brittleness of some coal components. Experimental methodology for studying mechanical properties of coals and other natural extreme materials like bones is discussed. It is argued that values of microhardness of bituminous coals correlate strongly with the maximum load; therefore, the use of this parameter in application to coals may be meaningless. For analysis of the force-displacement curves obtained by DSI, both Oliver–Pharr and Galanov–Dub approaches are employed. It is argued that during nanoindentation, the integrity of the internal structure of a coal sample within a small area of high stress field near the tip of indenter may be destroyed. Hence, the standard approaches to mechanical testing of coals should be re-examined. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.Acknowledgements Research was supported by the Russian Science Foundation (Grant № 16-17-10217)

Conformal Mapping on Rough Boundaries I: Applications to harmonic problems

The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this boundary. We introduce a conformal mapping technique that is tailored to this problem in two dimensions. An efficient algorithm is introduced to compute the conformal map for arbitrarily chosen boundaries. Harmonic fields can then simply be read from the conformal map. We discuss applications to "equivalent" smooth interfaces. We study the correlations between the topography and the field at the surface. Finally we apply the conformal map to the computation of inhomogeneous harmonic fields such as the derivation of Green function for localized flux on the surface of a rough boundary

Development of Barenblatt's scaling approaches in solid mechanics and nanomechanics

The main focus of the paper is on similarity methods in application to solid mechanics and author's personal development of Barenblatt's scaling approaches in solid mechanics and nanomechanics. It is argued that scaling in nanomechanics and solid mechanics should not be restricted to just the equivalence of dimensionless parameters characterizing the problem under consideration. Many of the techniques discussed were introduced by Professor G.I. Barenblatt. Since 1991 the author was incredibly lucky to have many possibilities to discuss various questions related to scaling during personal meetings with G.I. Barenblatt in Moscow, Cambridge, Berkeley and at various international conferences as well as by exchanging letters and electronic mails. Here some results of these discussions are described and various scaling techniques are demonstrated. The Barenblatt- Botvina model of damage accumulation is reformulated as a formal statistical self-similarity of arrays of discrete points and applied to describe discrete contact between uneven layers of multilayer stacks and wear of carbon-based coatings having roughness at nanoscale. Another question under consideration is mathematical fractals and scaling of fractal measures with application to fracture. Finally it is discussed the concept of parametrichomogeneity that based on the use of group of discrete coordinate dilation. The parametric-homogeneous functions include the fractal Weierstrass-Mandelbrot and smooth log-periodic functions. It is argued that the Liesegang rings are an example of a parametric-homogeneous set