An analytical elastic plastic contact model with strain hardening and frictional effects for normal and oblique impacts

Brake, M. R. W.

doi:10.1016/j.ijsolstr.2015.02.018

An analytical elastic plastic contact model with strain hardening and frictional effects for normal and oblique impacts

Journal Article · Tue Feb 17 04:00:00 EST 2015 · International Journal of Solids and Structures

DOI:https://doi.org/10.1016/j.ijsolstr.2015.02.018· OSTI ID:1146110

Brake, M. R. W. ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Impact between metallic surfaces is a phenomenon that is ubiquitous in the design and analysis of mechanical systems. We found that to model this phenomenon, a new formulation for frictional elastic–plastic contact between two surfaces is developed. The formulation is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The constitutive model for normal contact is developed as two contiguous loading domains: the elastic regime and a transitionary region in which the plastic response of the materials develops and the elastic response abates. For unloading, the constitutive model is based on an elastic process. Moreover, the normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. Frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact. This model is validated through comparisons with experimental results reported in the literature, and is demonstrated to be significantly more accurate than 10 other normal contact models and three other tangential contact models found in the literature.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1146110

Report Number(s):: SAND--2014-4365J; PII: S002076831500058X

Journal Information:: International Journal of Solids and Structures, Journal Name: International Journal of Solids and Structures Journal Issue: C Vol. 62; ISSN 0020-7683

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (61)

The elasto-plastic indentation of a half-space by a rigid sphere Hardy, C.; Baronet, C. N.; Tordion, G. V. International Journal for Numerical Methods in Engineering, Vol. 3, Issue 4 https://doi.org/10.1002/nme.1620030402	journal	October 1971
A Numerical Study of an Impact Oscillator with the Addition of dry Friction Cone, K. M.; Zadoks, R. I. Journal of Sound and Vibration, Vol. 188, Issue 5 https://doi.org/10.1006/jsvi.1995.0617	journal	December 1995
Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres Jackson, Robert L.; Green, Itzhak; Marghitu, Dan B. Nonlinear Dynamics, Vol. 60, Issue 3 https://doi.org/10.1007/s11071-009-9591-z	journal	September 2009
The role of epistemic uncertainty of contact models in the design and optimization of mechanical systems with aleatoric uncertainty Brake, M. R. Nonlinear Dynamics, Vol. 77, Issue 3 https://doi.org/10.1007/s11071-014-1350-0	journal	April 2014
An elastic–plastic contact model of ellipsoid bodies Jamari, J.; Schipper, D. J. Tribology Letters, Vol. 21, Issue 3 https://doi.org/10.1007/s11249-006-9038-3	journal	March 2006
In situ investigation of the contact area in elastic–plastic spherical contact during loading–unloading Ovcharenko, A.; Halperin, G.; Verberne, G. Tribology Letters, Vol. 25, Issue 2 https://doi.org/10.1007/s11249-006-9164-y	journal	November 2006
Quasi-static normal indentation of an elasto-plastic half-space by a rigid sphere—I Follansbee, P. S.; Sinclair, G. B. International Journal of Solids and Structures, Vol. 20, Issue 1 https://doi.org/10.1016/0020-7683(84)90078-7	journal	January 1984
Quasi-static normal indentation of an elasto-plastic half-space by a rigid sphere—II. Results Sinclair, G. B.; Follansbee, P. S.; Johnson, K. L. International Journal of Solids and Structures, Vol. 21, Issue 8 https://doi.org/10.1016/0020-7683(85)90039-3	journal	January 1985
Cross-flow-induced chaotic vibrations of heat-exchanger tubes impacting on loose supports Païdoussis, M. P.; Li, G. X. Journal of Sound and Vibration, Vol. 152, Issue 2 https://doi.org/10.1016/0022-460X(92)90363-3	journal	January 1992
The correlation of indentation experiments Johnson, K. L. Journal of the Mechanics and Physics of Solids, Vol. 18, Issue 2 https://doi.org/10.1016/0022-5096(70)90029-3	journal	April 1970
An analysis of fully plastic Brinell indentation Biwa, S. Journal of the Mechanics and Physics of Solids, Vol. 43, Issue 8 https://doi.org/10.1016/0022-5096(95)00031-D	journal	August 1995
The oblique impact of elastic spheres Maw, N.; Barber, J. R.; Fawcett, J. N. Wear, Vol. 38, Issue 1 https://doi.org/10.1016/0043-1648(76)90201-5	journal	June 1976
Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree of freedom impact oscillator Cusumano, J. P.; Bai, B. -Y. Chaos, Solitons & Fractals, Vol. 3, Issue 5 https://doi.org/10.1016/0960-0779(93)90003-J	journal	September 1993
On frictional effects at inelastic contact between spherical bodies Carlsson, S.; Biwa, S.; Larsson, P. -L. International Journal of Mechanical Sciences, Vol. 42, Issue 1 https://doi.org/10.1016/S0020-7403(98)00110-6	journal	January 2000
The dynamics of loosely jointed structures Wilson, James F.; Callis, Eric G. International Journal of Non-Linear Mechanics, Vol. 39, Issue 3 https://doi.org/10.1016/S0020-7462(02)00219-6	journal	April 2004
Normal and tangential force–displacement relations for frictional elasto-plastic contact of spheres Vu-Quoc, Loc; Zhang, Xiang; Lesburg, Lee International Journal of Solids and Structures, Vol. 38, Issue 36-37 https://doi.org/10.1016/S0020-7683(01)00065-8	journal	September 2001
The correlation of the indentation size effect measured with indenters of various shapes Swadener, J. G.; George, E. P.; Pharr, G. M. Journal of the Mechanics and Physics of Solids, Vol. 50, Issue 4 https://doi.org/10.1016/S0022-5096(01)00103-X	journal	April 2002
The measurement of particle rebound characteristics Gorham, D. A.; Kharaz, A. H. Powder Technology, Vol. 112, Issue 3 https://doi.org/10.1016/S0032-5910(00)00293-X	journal	October 2000
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations Ascher, Uri M.; Ruuth, Steven J.; Spiteri, Raymond J. Applied Numerical Mathematics, Vol. 25, Issue 2-3 https://doi.org/10.1016/S0168-9274(97)00056-1	journal	November 1997
Modeling the dependence of the coefficient of restitution on the impact velocity in elasto-plastic collisions Zhang, Xiang; Vu-Quoc, Loc International Journal of Impact Engineering, Vol. 27, Issue 3 https://doi.org/10.1016/S0734-743X(01)00052-5	journal	March 2002
Nonlinear dynamics of parts in engineering systems Jerrelind, Jenny; Stensson, Annika Chaos, Solitons & Fractals, Vol. 11, Issue 15 https://doi.org/10.1016/S0960-0779(00)00016-3	journal	December 2000
Effects of material strain rate sensitivity in low speed impact between two identical spheres Minamoto, Hirofumi; Kawamura, Shozo International Journal of Impact Engineering, Vol. 36, Issue 5 https://doi.org/10.1016/j.ijimpeng.2008.10.001	journal	May 2009
Moderately high speed impact of two identical spheres Minamoto, Hirofumi; Kawamura, Shozo International Journal of Impact Engineering, Vol. 38, Issue 2-3 https://doi.org/10.1016/j.ijimpeng.2010.09.005	journal	February 2011
Smooth dynamics of oblique impact with friction Stronge, W. J. International Journal of Impact Engineering, Vol. 51 https://doi.org/10.1016/j.ijimpeng.2012.08.001	journal	January 2013
Unloading of an elastic–plastic loaded spherical contact Etsion, I.; Kligerman, Y.; Kadin, Y. International Journal of Solids and Structures, Vol. 42, Issue 13 https://doi.org/10.1016/j.ijsolstr.2004.12.006	journal	June 2005
Reassessing spherical indentation: Contact regimes and mechanical property extractions Alcalá, J.; Esqué-de los Ojos, D. International Journal of Solids and Structures, Vol. 47, Issue 20 https://doi.org/10.1016/j.ijsolstr.2010.05.025	journal	October 2010
An analytical elastic-perfectly plastic contact model Brake, M. R. International Journal of Solids and Structures, Vol. 49, Issue 22 https://doi.org/10.1016/j.ijsolstr.2012.06.013	journal	November 2012
An accurate tangential force–displacement model for granular-flow simulations: Contacting spheres with plastic deformation, force-driven formulation Vu-Quoc, L.; Lesburg, L.; Zhang, X. Journal of Computational Physics, Vol. 196, Issue 1 https://doi.org/10.1016/j.jcp.2003.10.025	journal	May 2004
An accurate elasto-plastic frictional tangential force–displacement model for granular-flow simulations: Displacement-driven formulation Zhang, Xiang; Vu-Quoc, Loc Journal of Computational Physics, Vol. 225, Issue 1 https://doi.org/10.1016/j.jcp.2006.12.028	journal	July 2007
Modal analysis of a continuous gyroscopic second-order system with nonlinear constraints Brake, M. R.; Wickert, J. A. Journal of Sound and Vibration, Vol. 329, Issue 7 https://doi.org/10.1016/j.jsv.2009.10.004	journal	March 2010
The effect of the contact model on the impact-vibration response of continuous and discrete systems Brake, M. R. Journal of Sound and Vibration, Vol. 332, Issue 15 https://doi.org/10.1016/j.jsv.2013.02.003	journal	July 2013
Theoretical and experimental analysis of contact radius for spherical indentation Bartier, Olivier; Hernot, Xavier; Mauvoisin, Gérard Mechanics of Materials, Vol. 42, Issue 6 https://doi.org/10.1016/j.mechmat.2010.03.003	journal	June 2010
On the tangential contact behavior at elastic–plastic spherical contact problems Olsson, E.; Larsson, P. -L. Wear, Vol. 319, Issue 1-2 https://doi.org/10.1016/j.wear.2014.07.016	journal	November 2014
Surface Roughness and Contact: An Apology Greenwood, J. A.; Wu, J. J. Meccanica, Vol. 36, Issue 6, p. 617-630 https://doi.org/10.1023/A:1016340601964	journal	January 2001
A simple theory of static and dynamic hardness Tabor, David Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 192, Issue 1029, p. 247-274 https://doi.org/10.1098/rspa.1948.0008	journal	February 1948
An elastoplastic contact force–displacement model in the normal direction: displacement–driven version Vu-Quoc, Loc; Zhang, Xiang Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 455, Issue 1991 https://doi.org/10.1098/rspa.1999.0488	journal	November 1999
Linearity of amplitude and phase in tapping-mode atomic force microscopy Salapaka, M. V.; Chen, D. J.; Cleveland, J. P. Physical Review B, Vol. 61, Issue 2 https://doi.org/10.1103/PhysRevB.61.1106	journal	January 2000
Coefficient of normal restitution of viscous particles and cooling rate of granular gases Schwager, Thomas; Pöschel, Thorsten Physical Review E, Vol. 57, Issue 1 https://doi.org/10.1103/PhysRevE.57.650	journal	January 1998
Coefficient of restitution of colliding viscoelastic spheres Ramírez, Rosa; Pöschel, Thorsten; Brilliantov, Nikolai V. Physical Review E, Vol. 60, Issue 4 https://doi.org/10.1103/PhysRevE.60.4465	journal	October 1999
A micromachined impact microactuator driven by electrostatic force Mita, M.; Arai, M.; Tensaka, S. Journal of Microelectromechanical Systems, Vol. 12, Issue 1 https://doi.org/10.1109/JMEMS.2002.802906	journal	February 2003
A Normal Force-Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force-Driven Formulation Vu-Quoc, L.; Zhang, X.; Lesburg, L. Journal of Applied Mechanics, Vol. 67, Issue 2 https://doi.org/10.1115/1.1305334	journal	September 1999
Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat Kogut, L.; Etsion, I. Journal of Applied Mechanics, Vol. 69, Issue 5 https://doi.org/10.1115/1.1490373	journal	August 2002
A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces Kogut, Lior; Etsion, Izhak Journal of Tribology, Vol. 126, Issue 1 https://doi.org/10.1115/1.1609488	journal	January 2004
A Finite Element Study of the Residual Stress and Deformation in Hemispherical Contacts Jackson, Robert; Chusoipin, Itti; Green, Itzhak Journal of Tribology, Vol. 127, Issue 3 https://doi.org/10.1115/1.1843166	journal	June 2005
A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat Jackson, Robert L.; Green, Itzhak Journal of Tribology, Vol. 127, Issue 2 https://doi.org/10.1115/1.1866166	journal	April 2005
A New Method for Elastic-Plastic Contact Analysis of a Deformable Sphere and a Rigid Flat Lin, Li Po; Lin, Jen Fin Journal of Tribology, Vol. 128, Issue 2 https://doi.org/10.1115/1.2164469	journal	October 2005
Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat Jamari, J.; Schipper, D. J. Journal of Tribology, Vol. 128, Issue 2 https://doi.org/10.1115/1.2164470	journal	December 2005
Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres Thornton, C. Journal of Applied Mechanics, Vol. 64, Issue 2 https://doi.org/10.1115/1.2787319	journal	June 1997
Fractal Model of Elastic-Plastic Contact Between Rough Surfaces Majumdar, A.; Bhushan, B. Journal of Tribology, Vol. 113, Issue 1 https://doi.org/10.1115/1.2920588	journal	January 1991
Energy Dissipation in Normal Elastoplastic Impact Between Two Spheres Du, Yanchen; Wang, Shulin Journal of Applied Mechanics, Vol. 76, Issue 6 https://doi.org/10.1115/1.3130801	journal	July 2009
Extensive Theory of Force-Approach Relations of Elastic Spheres in Compression and in Impact Tatara, Yoichi Journal of Engineering Materials and Technology, Vol. 111, Issue 2 https://doi.org/10.1115/1.3226449	journal	April 1989
An Elastic-Plastic Model for the Contact of Rough Surfaces Chang, W. R.; Etsion, I.; Bogy, D. B. Journal of Tribology, Vol. 109, Issue 2 https://doi.org/10.1115/1.3261348	journal	April 1987
Compliance of Elastic Bodies in Contact Mindlin, R. D. Journal of Applied Mechanics, Vol. 16, Issue 3 https://doi.org/10.1115/1.4009973	journal	September 1949
An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow Zhao, Yongwu; Maietta, David M.; Chang, L. Journal of Tribology, Vol. 122, Issue 1 https://doi.org/10.1115/1.555332	journal	May 1999
Experimental Validation of an Elastic-Plastic Contact Model Brake, M. R.; Reu, P. L.; VanGoethem, D. J. ASME 2011 International Mechanical Engineering Congress and Exposition, Volume 7: Dynamic Systems and Control; Mechatronics and Intelligent Machines, Parts A and B https://doi.org/10.1115/IMECE2011-65736	conference	August 2012
Finite element analysis of cyclic indentation of an elastic-perfectly plastic half-space by a rigid sphere Yan, S. L.; Li, L. Y. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 217, Issue 5 https://doi.org/10.1243/095440603765226795	journal	May 2003
Study on Impact of Equivalent Two Bodies : Coefficients of Restitution of Spheres of Brass, Lead, Glass, Porcelain and Agate, and the Material Properties Tatara, Yoichi; Moriwaki, Nobuyasu Bulletin of JSME, Vol. 25, Issue 202 https://doi.org/10.1299/jsme1958.25.631	journal	January 1982
Ueber die Berührung fester elastischer Körper. Hertz, Heinrich crll, Vol. 1882, Issue 92, p. 156-171 https://doi.org/10.1515/crll.1882.92.156	journal	January 1882
An elastic-plastic indentation model and its solutions Yu, Weiping; Blanchard, James P. Journal of Materials Research, Vol. 11, Issue 9 https://doi.org/10.1557/JMR.1996.0299	journal	September 1996
Continuous measurements of load-penetration curves with spherical microindenters and the estimation of mechanical properties Alcalá, J.; Giannakopoulos, A. E.; Suresh, S. Journal of Materials Research, Vol. 13, Issue 5 https://doi.org/10.1557/JMR.1998.0197	journal	May 1998
IMEX-a: An Adaptive, Fifth Order Implicit-Explicit Integration Scheme Brake, Matthew Robert https://doi.org/10.2172/1089990	report	May 2013

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36 MATERIALS SCIENCE
constitutive behavior
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An analytical elastic plastic contact model with strain hardening and frictional effects for normal and oblique impacts

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