Smooth particle hydrodynamics simulation of damage induced by a spherical indenter scratching a viscoplastic material

Abstract We present an implementation of a (mesh-free) smooth particle hydrodynamics (SPH) algorithm, intended for the application to solid bodies, and use it to simulate scratch-induced surface damage on an elasto-viscoplastic material. If conventional SPH is used to simulate solids, an unphysically high artificial viscosity is required to damp strong oscillatory modes and thus stabilize the system. To overcome these intrinsic difficulties associated with modeling solid bodies, the recently implemented so-called total-Lagrangian SPH utilizes an hourglass control scheme similar to what is known from finite element algorithms. Elasto-viscoplastic material properties are modeled by using the Mie–Gruneisen equation of state and the Johnson–Cook model. The material parameters are selected to reproduce the strain-stress behavior of annealed oxygen-free high conductivity copper. The spherical indenter is modeled as a rigid sphere. The topographies of the calculated scratch-induced surface damage are in excellent agreement with experimental scratch tests carried out at comparable normal loads. We also calculate the real contact area between the indenter and the surface, allowing a sound estimation of the scratch hardness.

[1]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[2]  W. Macdonald,et al.  Thermodynamic properties of fcc metals at high temperatures , 1981 .

[3]  S. Attaway,et al.  Smoothed particle hydrodynamics stability analysis , 1995 .

[4]  E. Felder,et al.  Mechanical analysis of the scratch test on elastic and perfectly plastic materials with the three-dimensional finite element modeling , 2001 .

[5]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[6]  V.P.W. Shim,et al.  Effect of strain rate on microstructure of polycrystalline oxygen-free high conductivity copper severely deformed at liquid nitrogen temperature , 2010 .

[7]  S. Sinha,et al.  Scratch and normal hardness characteristics of polyamide 6/nano-clay composite , 2009 .

[8]  H. Rojacz,et al.  The Role Of Temperature And Velocity On Deformation And Wear Mechanisms In Fundamental Abrasive Contacts Up To 800°C , 2015 .

[9]  Georg C. Ganzenmüller,et al.  An hourglass control algorithm for Lagrangian Smooth Particle Hydrodynamics , 2015 .

[10]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Davide Bianchi,et al.  An analysis method for atomistic abrasion simulations featuring rough surfaces and multiple abrasive particles , 2014, Comput. Phys. Commun..

[12]  H. Zahouani,et al.  Understanding and quantification of elastic and plastic deformation during a scratch test , 1998 .

[13]  H. Urbassek,et al.  Nanoscratching of iron: A molecular dynamics study of the influence of surface orientation and scratching direction , 2015 .

[14]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[15]  C. A. Brookes,et al.  Some observations on scratch and indentation hardness measurements , 1972 .

[16]  T. Belytschko,et al.  A uniform strain hexahedron and quadrilateral with orthogonal hourglass control , 1981 .

[17]  Miroslav Piska,et al.  On the SPH Orthogonal Cutting Simulation of A2024-T351 Alloy☆ , 2013 .

[18]  T. Rabczuk,et al.  Discontinuous modelling of shear bands using adaptive meshfree methods , 2008 .

[19]  G. T. Lim,et al.  A new test methodology for evaluating scratch resistance of polymers , 2004 .

[20]  E. Badisch,et al.  Introduction of a novel tribometer especially designed for scratch, adhesion and hardness investigation up to 1000℃ , 2017 .

[21]  Ted Belytschko,et al.  A unified stability analysis of meshless particle methods , 2000 .

[22]  G. R. Johnson,et al.  Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures , 1985 .

[23]  Michel Salaün,et al.  SPH method applied to high speed cutting modelling , 2007 .

[24]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[25]  M. Papini,et al.  Material deformation and removal due to single particle impacts on ductile materials using smoothed particle hydrodynamics , 2012 .

[26]  Kun Sun,et al.  Atomistic scale tribological behaviors in nano-grained and single crystal copper systems , 2013 .

[27]  J. Bonet,et al.  Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations , 1999 .

[28]  E. Felder,et al.  Mechanical analysis of the scratching of metals and polymers with conical indenters at moderate and large strains , 2006 .

[29]  S. Islam,et al.  Novel approach for modelling of nanomachining using a mesh-less method , 2012 .

[30]  B. Briscoe,et al.  Scratch hardness and deformation maps for polycarbonate and polyethylene , 1996 .

[31]  P. Luckham,et al.  Scratch deformations of poly(etheretherketone) , 2011 .

[32]  Oyeon Kum,et al.  Smooth particle applied mechanics , 2006 .

[33]  Sivakumar Kulasegaram,et al.  Remarks on tension instability of Eulerian and Lagrangian corrected smooth particle hydrodynamics (CSPH) methods , 2001 .

[34]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[35]  T. Belytschko,et al.  Stable particle methods based on Lagrangian kernels , 2004 .

[36]  Damian Gąsiorek,et al.  The application of the smoothed particle hydrodynamics (SPH) method and the experimental verification of cutting of sheet metal bundles using a guillotine , 2013 .

[37]  R. Schirrer,et al.  Elastic recovery of a scratch in a polymeric surface: experiments and analysis , 2001 .

[38]  G. Betz,et al.  Applicability of Macroscopic Wear and Friction Laws on the Atomic Length Scale. , 2015, Physical review letters.

[39]  John A. Williams,et al.  Analytical models of scratch hardness , 1996 .

[40]  Morten F. Villumsen,et al.  Simulation of Metal Cutting using Smooth Particle Hydrodynamics , 2008 .