Molecular statics study of depth-dependent hysteresis in nano-scale adhesive elastic contacts

Abstract

The contact force—indentation-depth (P–h) measurements in adhesive contact experiments, such as atomic force microscopy, display hysteresis. In some cases, the amount of hysteretic energy loss is found to depend on the maximum indentation-depth. This depth-dependent hysteresis (DDH) is not explained by classical contact theories, such as Johnson–Kendall–Roberts and Derjaguin–Muller–Toporov, and is often attributed to surface moisture, material viscoelasticity, and plasticity. We present molecular statics simulations that are devoid of these mechanisms, yet still capture DDH. In our simulations, DDH is due to a series of surface mechanical instabilities. Surface features, such as depressions or protrusions, can temporarily arrest the growth or recession of the contact area. With a sufficiently large change of indentation-depth, the contact area grows or recedes abruptly by a finite amount and dissipates energy. This is similar to the pull-in and pull-off instabilities in classical contact theories, except that in this case the number of instabilities depends on the roughness of the contact surface. Larger maximum indentation-depths result in more surface features participating in the load–unload process, resulting in larger hysteretic energy losses. This mechanism is similar to the one recently proposed by one of the authors using a continuum mechanics-based model. However, that model predicts that the hysteretic energy loss always increases with roughness, whereas experimentally it is found that the hysteretic energy loss initially increases but then later decreases with roughness. Our simulations capture this non-monotonic dependence of hysteretic energy loss on roughness.

Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials

“…Experiments of Purtov et al [15] and modelling of the experiments by Pepelyshev et al [16], employing Galanov's model of adhesion between rough surfaces [17], showed that consideration of real contact area is a very important factor in adhesive contact problems. This statement is also nicely confirmed by the analysis of nanoscale static friction by Polyakov et al [18], and various works that demonstrate the influence of roughness on the value of adhesive pull-off force (e.g., [19][20][21]).…”

Depth-dependent hysteresis in adhesive elastic contacts at large surface roughness

“…Motivated by the observation of overlapping hysteresis loops during consecutive load-unload cycles both in air and underwater, they hypothesized that DDH was due to the occurrence of a series of small-scale surface, mechanical instabilities that are created due to surface roughness, adhesion, and the large compliance of the soft materials involved 16 . Our recent static molecular simulations showed that this mechanism can operate in adhesive elastic contacts 17 . The surface instabilities through which small-scale roughness gives rise to DDH in the work of Kesari et al 6 and Kesari and Lew 16 are the same as those through which surface undulations cause adhesive toughening in the work of Li and Kim 18 and Guduru 19 .…”

Effects of geometric nonlinearity in an adhered microbeam for measuring the work of adhesion

“…In addition, the adhesion between solids is generally measured using axisymmetric, contact mechanics-based methods [68]. However, surface roughness is known to cause considerable difficulties in unambiguously measuring w using such methods [69][70][71]. Therefore, it would be interesting to see how competitive the proposed vibration-based method for measuring w would be in comparison to the contact mechanics-based methods.…”