In this study, a new expression for the permanent deformation after the impact of a rod with a flat surface is given. Both flat and the surface have been considered elastoplastic. The contact has been considered frictionless and has been divided into three phases, the elastic, the elastoplastic, and the unloading phase. For the normal impact force in the loading phase, we considered a nonlinear expression that satisfies the effect of deformation on both objects by using a finite element model. For the unloading phase, the contact force has been considered to follow the Hertz theory. The simulation and experimental results were conducted for different initial impact velocities of the rod. Permanent deformation after the impact and the motion of the rod has been measured accurately in the experiments. Based on the simulation and experimental results an expression for the permanent deformation has been developed. Finally, the model has been verified and compared with previous contact models in terms of the coefficient of restitution.
Issue Section:
Contact Mechanics
References
1.
Hertz
, C.
, 1882
, “Üher die Berührung Fester Elastischer Körper (On the Contact of Elastic Solids)
,” J. Reine Andegwandte Math.
, 92
, pp. 156
–171
.2.
Johnson
, K.
, 1985
, Contact Mechanics
, Cambridge University
, Cambridge, MA
, pp. 154
–179
.3.
Tabor
, D.
, 1948
, “A Simple Theory of Static and Dynamic Hardness
,” Proc. R. Soc. Lond. Ser. A
, 192
(1029
), pp. 247
–274
.10.1098/rspa.1948.00084.
Tabor
, D.
, 1951
, The Hardness of Metals
, Clarendon Press
, Oxford, UK
.5.
Stronge
, W. J.
, 1990
, “Rigid Body Collisions With Friction
,” Proc. R. Soc. Lond. Ser. A
, 431
(1881
), pp. 169
–181
.10.1098/rspa.1990.01256.
Stronge
, W.
, 1991
, “Unraveling Paradoxical Theories for Rigid Body Collisions
,” ASME J. Appl. Mech.
, 59
(3
), pp. 681
–682
.10.1115/1.28937807.
Stronge
, W.
, 1991
, “Unraveling Paradoxical Theories for Rigid Body Collisions
,” ASME J. Appl. Mech.
, 58
(4
), pp. 1049
–1055
.10.1115/1.28976818.
Chang
, W.-R.
, and Ling
, F. F.
, 1992
, “Normal Impact Model of Rough Surfaces
,” ASME J. Tribol.
, 114
(3
), pp. 439
–447
.10.1115/1.29209039.
Stronge
, W.
, 1995
, “Theoretical Coefficient of Restitution for Planar Impact of Rough Elasto-Plastic Bodies
,” Impact, Waves, and Fracture
, ASME AMD-205, pp. 351
–362
.10.
Thornton
, C.
, and Ning
, Z.
, 1994
, “Oblique Impact of Elasto-Plastic Spheres
,” Proceedings of the First International Particle Technology Forum
, AIChE Publications, Vol. 2, pp. 14
–19
.11.
Thornton
, C.
, 1997
, “Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres
,” ASME J. Appl. Mech.
, 64
(2
), pp. 383
–386
.10.1115/1.278731912.
Mesarovic
, S. D.
, and Johnson
, K.
, 2000
, “Adhesive Contact of Elastic–Plastic Spheres
,” J. Mech. Phys. Solids
, 48
(10
), pp. 2009
–2033
.10.1016/S0022-5096(00)00004-113.
Kharaz
, A.
, Gorham
, D.
, and Salman
, A.
, 1999
, “Accurate Measurement of Particle Impact Parameters
,” Meas. Sci. Technol.
, 10
(1
), pp. 31
–35
.10.1088/0957-0233/10/1/00914.
Kharaz
, A.
, and Gorham
, D.
, 2000
, “A Study of the Recitation Coefficient in Elastic–Plastic Impact
,” Philos. Mag. Lett.
, 80
(8
), pp. 549
–559
.10.1080/0950083005011048615.
Li
, L.
, Wu
, C.
, and Thornton
, C.
, 2002
, “A Theoretical Model for the Contact of Elastoplastic Bodies
,” Proc. Inst. Mech. Eng., Part C
, 216
(4
), pp. 421
–431
.10.1243/095440602152521416.
Wu
, C.-Y.
, Li
, L.-Y.
, and Thornton
, C.
, 2005
, “Energy Dissipation During Normal Impact of Elastic and Elastic–Plastic Spheres
,” Int. J. Impact Engineering
, 32
(1
), pp. 593
–604
.10.1016/j.ijimpeng.2005.08.00717.
Kogut
, L.
, and Etsion
, I.
, 2002
, “Elastic–Plastic Contact Analysis of a Sphere and a Rigid Flat
,” ASME J. Appl. Mech.
, 69
(5
), pp. 657
–662
.10.1115/1.149037318.
Etsion
, I.
, Kligerman
, Y.
, and Kadin
, Y.
, 2005
, “Unloading of an Elastic–Plastic Loaded Spherical Contact
,” Int. J. Solids Struct.
, 42
(13
), pp. 3716
–3729
.10.1016/j.ijsolstr.2004.12.00619.
Shankar
, S.
, and Mayuram
, M.
, 2008
, “Effect of Strain Hardening in Elastic–Plastic Transition Behavior in a Hemisphere in Contact With a Rigid Flat
,” Int. J. Solids Struct.
, 45
(10
), pp. 3009
–3020
.10.1016/j.ijsolstr.2008.01.01720.
Kogut
, L.
, and Komvopoulos
, K.
, 2004
, “Analysis of the Spherical Indentation Cycle for Elastic–Perfectly Plastic Solids
,” J. Mater. Res.
, 19
(12
), pp. 3641
–3653
.10.1557/JMR.2004.046821.
Jackson
, R. L.
, and Green
, I.
, 2005
, “A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat
,” ASME J. Tribol.
, 127
(2
), pp. 343
–354
.10.1115/1.186616622.
Johnson
, K.
, 1968
, “Experimental Determination of the Contact Stresses Between Plastically Deformed Cylinders and Spheres
,” Engineering Plasticity
, Cambridge University
, Cambridge, MA
, pp. 341
–361
.23.
Jackson
, R.
, Chusoipin
, I.
, and Green
, I.
, 2005
, “A Finite Element Study of the Residual Stress and Deformation in Hemispherical Contacts
,” ASME J. Tribol.
, 127
(3
), pp. 484
–493
.10.1115/1.184316624.
Jackson
, R. L.
, Green
, I.
, and Marghitu
, D. B.
, 2010
, “Predicting the Coefficient of Restitution of Impacting Elastic-Perfectly Plastic Spheres
,” Nonlinear Dyn.
, 60
(3
), pp. 217
–229
.10.1007/s11071-009-9591-z25.
Marghitu
, D. B.
, Cojocaru
, D.
, and Jackson
, R. L.
, 2011
, “Elasto-Plastic Impact of a Rotating Link With a Massive Surface
,” Int. J. Mech. Sci.
, 53
(4
), pp. 309
–315
.10.1016/j.ijmecsci.2011.01.01226.
Brake
, M.
, 2012
, “An Analytical Elastic-Perfectly Plastic Contact Model
,” Int. J. Solids Struct.
, 49
(22
), pp. 3129
–3141
.10.1016/j.ijsolstr.2012.06.013Copyright © 2015 by ASME
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