Energy Dissipation and Trapping of Particles Moving on a Rough Surface

We report an experimental, numerical and theoretical study of the motion of a ball on a rough inclined surface. The control parameters are $D$, the diameter of the ball, $\theta$, the inclination angle of the rough surface and $E_{ki}$, the initial kinetic energy. When the angle of inclination is larger than some critical value, $\theta>\theta_{T}$, the ball moves at a constant average velocity which is independent of the initial conditions. For an angle $\theta < \theta_{T}$, the balls are trapped after moving a certain distance. The dependence of the travelled distances on $E_{ki}$, $D$ and $\theta$. is analysed. The existence of two kinds of mechanisms of dissipation is thus brought to light. We find that for high initial velocities the friction force is constant. As the velocity decreases below a certain threshold the friction becomes viscous.Comment: 8 pages RevTeX, 12 Postscript figure

Sliding Blocks Revisited: A simulational Study

A computational study of sliding blocks on inclined surfaces is presented. Assuming that the friction coefficient $\mu$ is a function of position, the probability $P(\lambda)$ for the block to slide down over a length $\lambda$ is numerically calculated. Our results are consistent with recent experimental data suggesting a power-law distribution of events over a wide range of displacements when the chute angle is close to the critical one, and suggest that the variation of $\mu$ along the surface is responsible for this.Comment: 6 pages, 4 figures. submitted to Int. J. Mod. Phys. (Proc. Brazilian Wokshop on Simulational Physics

Thermomechanical material modelling based on a hybrid free energy density depending on pressure, isochoric deformation and temperature

AbstractIn order to represent temperature-dependent mechanical material properties in a thermomechanical consistent manner it is common practice to start with the definition of a model for the specific Helmholtz free energy. Its canonical independent variables are the Green strain tensor and the temperature. But to represent calorimetric material properties under isobaric conditions, for example the exothermal behaviour of a curing process or the dependence of the specific heat on the temperature history, the temperature and the pressure should be taken as independent variables. Thus, in the field of calorimetry the Gibbs free energy is usually used as thermodynamic potential whereas in continuum mechanics the Helmholtz free energy is normally applied. In order to simplify the representation of calorimetric phenomena in continuum mechanics a hybrid free energy density is introduced. Its canonical independent variables are the isochoric Green strain tensor, the pressure and the temperature. It is related to the Helmholtz free energy density by a Legendre transformation. In combination with the additive split of the stress power into the sum of isochoric and volumetric terms this approach leads to thermomechanical consistent constitutive models for large deformations. The article closes with applications of this approach to finite thermoelasticity, curing adhesives and the glass transition

Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction

Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than the expected square of the velocity. It was also found that, for a given inclination of the plane, the velocity of the ball scales as a power of its radius. We present here a one dimensional stochastic model based on the microscopic equations of motion of the ball, which exhibits the same behaviour as the experiments. This model yields a mechanism for the origins of the viscous friction force and the scaling of the velocity with the radius. It also reproduces other aspects of the phase diagram of the motion which we will discuss.Comment: 19 pages, latex, 11 postscript figures in separate uuencoded fil

Kinetics and crystallization path of a Fe-based metallic glass alloy

The thermal stability and the quantification of the different transformation processes involved in the overall crystallization of the Fe50Cr15Mo14C15B6 amorphous alloy were investigated by several characterization techniques. Formation of various metastable and stable phases during the devitrification process in the sequence a-Fe, ¿-Cr6Fe18Mo5, M23(C,B)6, M7C3, ¿-Fe3Mo3C and FeMo2B2 (with M = Fe, Cr, Mo), was observed by in-situ synchrotron high energy X-ray diffraction and in-situ transmission electron microscopy. By combining these techniques with differential scanning calorimetry data, the crystallization states and their temperature range of stability under continuous heating were related with the evolution of the crystallized fraction and the phase sequence as a function of temperature, revealing structural and chemical details of the different transformation mechanisms.Postprint (published version

Complexion-mediated martensitic phase transformation in Titanium

The most efficient way to tune microstructures and mechanical properties of metallic alloys lies in designing and using athermal phase transformations. Examples are shape memory alloys and high strength steels, which together stand for 1,500 million tons annual production. In these materials, martensite formation and mechanical twinning are tuned via composition adjustment for realizing complex microstructures and beneficial mechanical properties. Here we report a new phase transformation that has the potential to widen the application window of Ti alloys, the most important structural material in aerospace design, by nanostructuring them via complexion-mediated transformation. This is a reversible martensitic transformation mechanism that leads to a final nanolaminate structure of α″ (orthorhombic) martensite bounded with planar complexions of athermal ω (a–ω, hexagonal). Both phases are crystallographically related to the parent β (BCC) matrix. As expected from a planar complexion, the a–ω is stable only at the hetero-interface

Plug flow and the breakdown of Bagnold scaling in cohesive granular flows

Cohesive granular media flowing down an inclined plane are studied by discrete element simulations. Previous work on cohesionless granular media demonstrated that within the steady flow regime where gravitational energy is balanced by dissipation arising from intergrain forces, the velocity profile in the flow direction scales with depth in a manner consistent with the predictions of Bagnold. Here we demonstrate that this Bagnold scaling does not hold for the analogous steady-flows in cohesive granular media. We develop a generalization of the Bagnold constitutive relation to account for our observation and speculate as to the underlying physical mechanisms responsible for the different constitutive laws for cohesive and noncohesive granular media.Comment: 8 pages, 10 figure

Complexion-mediated martensitic phase transformation in Titanium

The most efficient way to tune microstructures and mechanical properties of metallic alloys lies in designing and using athermal phase transformations. Examples are shape memory alloys and high strength steels, which together stand for 1,500 million tons annual production. In these materials, martensite formation and mechanical twinning are tuned via composition adjustment for realizing complex microstructures and beneficial mechanical properties. Here we report a new phase transformation that has the potential to widen the application window of Ti alloys, the most important structural material in aerospace design, by nanostructuring them via complexion-mediated transformation. This is a reversible martensitic transformation mechanism that leads to a final nanolaminate structure of α″ (orthorhombic) martensite bounded with planar complexions of athermal ω (a–ω, hexagonal). Both phases are crystallographically related to the parent β (BCC) matrix. As expected from a planar complexion, the a–ω is stable only at the hetero-interface.European Commission. Framework Programme for Research and Innovation (FP7/2007–2013))/ERC Grant agreement 290998 'SmartMet’)Innovative Research Team in University (IRT13034)National Basic Research Program of China (973 Program) (2014CB644003)China. Ministry of Science and Technology. National Key Research and Development Program (2016YFB0701302)National Natural Science Foundation of China (51501145)National Natural Science Foundation of China (51320105014)National Natural Science Foundation of China (51621063