Partial slip contact modeling of heterogeneous elasto-plastic materials

Abstract In this study, a semi-analytic solution is developed for heterogeneous elasto-plastic materials under partial slip contact, and the effects of a single inhomogeneity embedded in the matrix material are investigated. The stick and slip areas are determined by an iterative conjugate gradient method with the assistance of the discrete convolution and fast Fourier transform algorithm. The inhomogeneities within a material are homogenized as homogeneous inclusions with properly determined eigenstrains based on the equivalent inclusion method, and the surface displacements induced by these eigenstrains along with those caused by the shear tractions are then introduced into the gap between the contact bodies to update surface geometry. The accumulative plastic deformation is iteratively obtained by a procedure involving a plasticity loop and an incremental loading process. The model takes into account the interactions among the contact bodies, the embedded inhomogeneities and the plastic zones, thus leading to an accurate solution of the surface pressure distributions, tangential tractions, plastic zones and subsurface stress fields. This solution is of great importance for the analysis of frictional heterogeneous contact coupling the normal and tangential behaviors in the elastic-plastic regime.

[1]  G. Weng,et al.  A secant-viscosity composite model for the strain-rate sensitivity of nanocrystalline materials , 2007 .

[2]  Leon M Keer,et al.  Semi‐analytic solution for multiple interacting three‐dimensional inhomogeneous inclusions of arbitrary shape in an infinite space , 2011 .

[3]  Raymond D. Mindlin,et al.  Compliance of elastic bodies in contact , 1949 .

[4]  L. Gallego,et al.  Modeling of Fretting Wear Under Gross Slip and Partial Slip Conditions , 2007 .

[5]  Daniel Nelias,et al.  A fast and efficient contact algorithm for fretting problems applied to fretting modes I, II and III , 2010 .

[6]  Wei Chen,et al.  Modeling elasto-plastic indentation on layered materials using the equivalent inclusion method , 2010 .

[7]  Q. Fang,et al.  Misfit dislocation dipoles and critical parameters of buried strained nanoscale inhomogeneity , 2008 .

[8]  J. Leroux,et al.  Stick-slip analysis of a circular point contact between a rigid sphere and a flat unidirectional composite with cylindrical fibers , 2011 .

[9]  Sia Nemat-Nasser,et al.  A universal integration algorithm for rate-dependent elastoplasticity , 1996 .

[10]  Tongxi Yu,et al.  Failure of plastic structures under intense dynamic loading: modes, criteria and thresholds , 2000 .

[11]  Y. Mai,et al.  Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate–polymer composites , 2008 .

[12]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13]  Gang Wang,et al.  Interface effects on the diffraction of plane compressional waves by a nanosized spherical inclusion , 2007 .

[14]  Multiple cracks in a half-space under contact loading , 2014 .

[15]  Tongxi Yu,et al.  Forming and failure behaviour of coated, laminated and sandwiched sheet metals: a review , 1997 .

[16]  Xi-Qiao Feng,et al.  Perspectives in mechanics of heterogeneous solids , 2011 .

[17]  Analysis of fluid pressure, interface stresses and stress intensity factors for layered materials with cracks and inhomogeneities under elastohydrodynamic lubrication contact , 2015 .

[18]  Hui Wang,et al.  A Numerical Elastic–Plastic Contact Model for Rough Surfaces , 2010 .

[19]  D. Nélias,et al.  Contact Pressure and Residual Strain in 3D Elasto-Plastic Rolling Contact for a Circular or Elliptical Point Contact , 2011 .

[20]  Elastohydrodynamic lubrication modeling for materials with multiple cracks , 2014 .

[21]  Leon M Keer,et al.  A review of recent works on inclusions , 2013 .

[22]  Daniel Nelias,et al.  A Comprehensive Method to Predict Wear and to Define the Optimum Geometry of Fretting Surfaces , 2006 .

[23]  Daniel Nelias,et al.  Contact analysis in presence of spherical inhomogeneities within a half-space , 2010 .

[24]  D. Nélias,et al.  Contact Fatigue Analysis of a Dented Surface in a Dry Elastic–Plastic Circular Point Contact , 2008 .

[25]  F. Kosior,et al.  Analysis of frictional contact problem using boundary element method and domain decomposition method , 1999 .

[26]  Lv Zhao,et al.  Contact analysis in the presence of an ellipsoidal inhomogeneity within a half space , 2014 .

[27]  Leon M Keer,et al.  A fast method for solving three-dimensional arbitrarily shaped inclusions in a half space , 2009 .

[28]  Philippe Sainsot,et al.  A numerical model for elastoplastic rough contact , 2001 .

[29]  S. Tan,et al.  On the fracture behaviour of an interface crack with plastic zone corrections , 2013 .

[30]  T. X. Yu,et al.  Mechanical Behavior of Metallic Hollow Sphere Materials: Experimental Study , 2008 .

[31]  Krich Sawamiphakdi,et al.  Interaction of multiple inhomogeneous inclusions beneath a surface , 2012 .

[32]  Kun Zhou,et al.  Multiple Inhomogeneous Inclusions and Cracks in a Half Space Under Elastohydrodynamic Lubrication Contact , 2015 .

[33]  Daniel Nelias,et al.  A Three-Dimensional Semianalytical Model for Elastic-Plastic Sliding Contacts , 2007 .

[34]  J. Luo,et al.  On the fracture behavior of a Zener–Stroh crack with plastic zone correction in three-phase cylindrical composite material , 2012 .

[35]  K. Zhou.  Elastic field and effective moduli of periodic composites with arbitrary inhomogeneity distribution , 2012 .

[36]  P. Yarlagadda,et al.  Numerical exploration of plastic deformation mechanisms of copper nanowires with surface defects , 2011 .

[37]  Daniel Nelias,et al.  On the Tangential Displacement of a Surface Point Due to a Cuboid of Uniform Plastic Strain in a Half-Space , 2010 .

[38]  Q. Fang,et al.  Analysis of a screw dislocation inside an inhomogeneity with interface stress , 2007 .

[39]  R. Hill.  The mathematical theory of plasticity , 1950 .

[40]  D. Hills,et al.  On the mechanics of fretting fatigue , 1988 .

[41]  K. Zhou,et al.  Heterogeneous structures with inhomogeneous inclusions under elastohydrodynamic lubrication contact with consideration of surface roughness , 2016 .

[42]  P. Wen,et al.  Dipole of edge misfit dislocations and critical radius conditions for buried strained cylindrical inhomogeneity , 2009 .

[43]  Daniel Nelias,et al.  Fully Coupled Resolution of Heterogeneous Elastic–Plastic Contact Problem , 2016 .

[44]  Wei Chen,et al.  A numerical model for the point contact of dissimilar materials considering tangential tractions , 2008 .

[45]  Daniel Nelias,et al.  Elastic-Plastic Contact Between Rough Surfaces: Proposal for a Wear or Running-In Model , 2006 .

[46]  S. Tan,et al.  On elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under mixed mode loading , 2014 .

[47]  Daniel Nelias,et al.  Rolling contact of a rigid sphere/sliding of a spherical indenter upon a viscoelastic half-space containing an ellipsoidal inhomogeneity , 2015 .

[48]  Z. Xiao,et al.  On the Plastic Zone Size and the Crack Tip Opening Displacement of an Interface Crack Between two Dissimilar Materials , 2012, International Journal of Fracture.

[49]  Xi-Qiao Feng,et al.  An approximate continuum theory for interaction between dislocation and inhomogeneity of any shape and properties , 2011 .

[51]  P. Wen,et al.  Effect of interface stresses on the image force and stability of an edge dislocation inside a nanoscale cylindrical inclusion , 2009 .

[52]  K. Hwang,et al.  Multiscale Analysis of Fracture of Carbon Nanotubes Embedded in Composites , 2005 .

[53]  Wei Chen,et al.  Transient Thermomechanical Analysis of Sliding Electrical Contacts of Elastoplastic Bodies, Thermal Softening, and Melting Inception , 2009 .

[54]  J. Luo,et al.  Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion , 2010 .

[55]  D. A. Hills,et al.  Contact of dissimilar elastic cylinders under normal and tangential loading , 1988 .

[56]  Jian Cao,et al.  A new fast method for solving contact plasticity and its application in analyzing elasto-plastic partial slip , 2013 .

[57]  Analysis and Convenient Formulas for Elasto-Plastic Contacts of Nominally Flat Surfaces: Average Gap, Contact Area Ratio, and Plastically Deformed Volume , 2007 .

[58]  G. Weng,et al.  A micromechanical approach to the stress–strain relations, strain-rate sensitivity and activation volume of nanocrystalline materials , 2013 .

[59]  Daniel Nelias,et al.  Contact Analyses for Bodies With Frictional Heating and Plastic Behavior , 2005 .

[60]  Wei Chen,et al.  Multiple 3D inhomogeneous inclusions in a half space under contact loading , 2011 .

[61]  Daniel Nelias,et al.  Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code , 2002 .