A review of models for single particle compression and their application to silica microspheres

Advanced Powder Technology

Volumn 25, Issue 1, 2014, Pages 136-153

  Paul, Jonas ^a   Romeis, Stefan ^a   Tomas, Jürgen ^b   Peukert, Wolfgang ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Deformation models; In situ compression; Mechanical properties; Microparticles; Silica

Indexed keywords

COMPRESSIVE STRENGTH; ELASTIC MODULI; MECHANICAL PROPERTIES; MICROSPHERES; PLASTIC DEFORMATION; SCANNING ELECTRON MICROSCOPY; SILICA;

DEFORMATION MODELS; ELASTIC AND PLASTIC DEFORMATION; IN-SITU COMPRESSION; MICRO-PARTICLES; PLASTIC DEFORMATION BEHAVIOR; QUANTITATIVE EVALUATION; SINGLE PARTICLE COMPRESSION; STATISTICAL EVALUATION;

FUSED SILICA;

EID: 84896391442     PISSN: 09218831     EISSN: 15685527     Source Type: Journal    
DOI: 10.1016/j.apt.2013.09.009     Document Type: Review

References (100)

1. P. Toneva, P. Epple, M. Breuer, W. Peukert, and K.-E. Wirth Grinding in an air classifier mill - Part I: characterisation of the one-phase flow Powder Technology 211 2011 19 27
2. P. Toneva, K.-E. Wirth, and W. Peukert Grinding in an air classifier mill - Part II: characterisation of the two-phase flow Powder Technology 211 2011 28 37
3. L. Vogel, and W. Peukert From single particle impact behaviour to modelling of impact mills Chemical Engineering Science 60 2005 5164 5176 (Pubitemid 40906864)
4. S. Romeis, J. Paul, M. Ziener, and W. Peukert A novel apparatus for in situ compression of submicron structures and particles in a high resolution SEM Review of Scientific Instruments 83 2012 095105-095105-9
5. W.C. Oliver, and G.M. Pharr Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments Journal of Materials Research 7 1992 1564 1583
6. L. Kogut Elastic-plastic contact analysis of a sphere and a rigid flat Journal of Applied Mechanics 69 2002 657
7. R.L. Jackson, and L. Kogut A comparison of flattening and indentation approaches for contact mechanics modeling of single asperity contacts Journal of Tribology 128 2006 209
8. M.M. Chaudhri, I.M. Hutchings, and P.L. Makin Plastic compression of spheres Philosophical Magazine A 49 1984 493 503
9. N. Gane The compressive strength of sub-micrometer diameter magnesium oxide crystals Philosophical Magazine 25 1972 25 34
10. W. Gerberich, W. Mook, C. Perrey, C. Carter, M. Baskes, and R. Mukherjee et al. Superhard silicon nanospheres Journal of the Mechanics and Physics of Solids 51 2003 979 992
11. W.M. Mook, J.D. Nowak, C.R. Perrey, C.B. Carter, R. Mukherjee, and S.L. Girshick et al. Compressive stress effects on nanoparticle modulus and fracture Physical Review B 75 2007 214112
12. W.M. Mook, C. Niederberger, M. Bechelany, L. Philippe, and J. Michler Compression of freestanding gold nanostructures: from stochastic yield to predictable flow Nanotechnology 21 2010 055701
13. J. Deneen, W.M. Mook, A. Minor, W.W. Gerberich, and C.B. Carter In situ deformation of silicon nanospheres Journal of Materials Science 41 2006 4477 4483 (Pubitemid 44226127)
14. E. Calvié, L. Joly-Pottuz, C. Esnouf, P. Clément, V. Garnier, and J. Chevalier et al. Real time TEM observation of alumina ceramic nano-particles during compression Journal of the European Ceramic Society 32 2012 2067 2071
15. A.M. Minor, S.A. Syed Asif, Z. Shan, E.A. Stach, E. Cyrankowski, and T.J. Wyrobek et al. A new view of the onset of plasticity during the nanoindentation of aluminium Nature Materials 5 2006 697 702 (Pubitemid 44334983)
16. D.D. Stauffer, A. Beaber, A. Wagner, O. Ugurlu, J. Nowak, and K. Andre Mkhoyan et al. Strain-hardening in submicron silicon pillars and spheres Acta Materialia 60 2012 2471 2478
17. Z.-J. Wang, Z.-W. Shan, J. Li, J. Sun, and E. Ma Pristine-to-pristine regime of plastic deformation in submicron-sized single crystal gold particles Acta Materialia 60 2012 1368 1377
18. K. Zheng, C. Wang, Y.-Q. Cheng, Y. Yue, X. Han, and Z. Zhang et al. Electron-beam-assisted superplastic shaping of nanoscale amorphous silica Nature Communications 1 2010 24
19. J. Deneen Nowak, W.M. Mook, A.M. Minor, W.W. Gerberich, and C.B. Carter Fracturing a nanoparticle Philosophical Magazine 87 2007 29 37 (Pubitemid 44836068)
20. J.Y. He, Z.L. Zhang, M. Midttun, G. Fonnum, G.I. Modahl, and H. Kristiansen et al. Size effect on mechanical properties of micron-sized PS-DVB polymer particles Polymer 49 2008 3993 3999
21. M. Yoshida, H. Ogiso, S. Nakano, and J. Akedo Compression test system for a single submicrometer particle Review of Scientific Instruments 76 2005 093905-093905-5
22. 3 particles Surface and Coatings Technology 201 2007 8180 8184 (Pubitemid 47074252)
23. J.Y. He, Z.L. Zhang, and H. Kristiansen Compression properties of individual micron-sized acrylic particles Materials Letters 63 2009 1696 1698
24. J.Y. He, Z.L. Zhang, H. Kristiansen, K. Redford, G. Fonnum, and G.I. Modahl Crosslinking effect on the deformation and fracture of monodisperse polystyrene-co-divinylbenzene particles Express Polymer Letters 7 2013 365 374
25. J.Y. He, S. Nagao, H. Kristiansen, and Z.L. Zhang Loading rate effects on the fracture of Ni/Au nano-coated acrylic particles Express Polymer Letters 6 2012 198 203
26. J.Y. He, Z.L. Zhang, and H. Kristiansen Nanomechanical characterization of single micron-sized polymer particles Journal of Applied Polymer Science 113 2009 1398 1405
27. H. Zhou, and W. Peukert Modeling Adhesion Forces between Deformable Bodies by FEM and Hamaker Summation Langmuir 24 2008 1459 1468 (Pubitemid 351345868)
28. P. Toneva, and W. Peukert A general approach for the characterization of fragmentation problems Advanced Powder Technology 18 2007 39 51 (Pubitemid 46473725)
29. K.-K. Liu Deformation behaviour of soft particles: a review Journal of Physics D: Applied Physics 39 2006 R189 R199
30. Y. Hiramatsu, and Y. Oka Determination of the tensile strength of rock by a compression test of an irregular test piece International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 3 1966 89 90
31. J. Tomas Assessment of mechanical properties of cohesive particulate solids. Part 1: particle contact constitutive model Particulate Science and Technology 19 2001 95 110 (Pubitemid 34052588)
32. J. Tomas Mechanics of nanoparticle adhesion-a continuum approach Particles on Surfaces 8 2003 183 229
33. K.L. Johnson Contact Mechanics 1987 Cambridge Univ Pr
34. V.I. Mossakovskii Compression of elastic bodies under conditions of adhesion/axisymmetric case/(Compression problem of two elastic bodies, contact surface of which increases with applied compression force) Journal of Applied Mathematics and Mechanics 27 1963 630 643
35. D.A. Spence Self similar solutions to adhesive contact problems with incremental loading Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 305 1968 55 80
36. D.A. Spence The Hertz contact problem with finite friction Journal of Elasticity 5 1975 297 319
37. I.C. Noyan Plastic deformation of solid spheres Philosophical Magazine A 57 1988 127 141
38. H. Krupp Particle Adhesion: Theory and Experiment Advances in Colloid and Interface Science 1 1967
39. H. Rumpf, K. Sommer, and K. Steier Mechanismen der Haftkraftverstä rkung bei der Partikelhaftung durch plastisches Verformen, Sintern und viskoelastisches Fließen Chemie Ingenieur Technik 48 1976 300 307
40. N. Jones Structural Impact 1989 Cambridge University Press
41. J. Hartikainen, K. Kolari, and R. Kouhia Failure simulations with a strain rate dependent ductile-to-brittle transition model S. Repin, T. Tiihonen, T. Tuovinen, Numerical Methods for Differential Equations, Optimization, and Technological Problems 2013 Springer Netherlands 431 444
42. K. Schönert Breakage of spheres and circular discs Powder Technology 143-144 2004 2 18 (Pubitemid 39091922)
43. K.J. Marsh, and J.D. Campbell The effect of strain rate on the post-yield flow of mild steel Journal of the Mechanics and Physics of Solids 11 1963 49 63
44. J. Zhao Applicability of Mohr-Coulomb and Hoek-Brown strength criteria to the dynamic strength of brittle rock International Journal of Rock Mechanics and Mining Sciences 37 2000 1115 1121
45. H. Hertz Ueber die Berührung fester elastischer Körper Journal für die reine und angewandte Mathematik (Crelle's Journal) 1882 156 171
46. K.L. Johnson, and J.A. Greenwood An adhesion map for the contact of elastic spheres Journal of Colloid and Interface Science 192 1997 326 333 (Pubitemid 27475411)
47. S.R. Cohen An evaluation of the use of the atomic force microscope for studies in nanomechanics Ultramicroscopy 42 1992 66 72
48. C.H. Hsueh, and P. Miranda Combined empirical-analytical method for determining contact radius and indenter displacement during Hertzian indentation on coating/substrate systems Journal of Materials Research 19 2004 2774 2781
49. Y. Tatara Extensive theory of force-approach relations of elastic spheres in compression and in impact Journal of Engineering Materials and Technology 111 1989 163 168
50. Y. Tatara Large deformations of a rubber sphere under diametral compression: Part 1: theoretical analysis of press approach, contact radius and lateral extension JSME International Journal Series A, Mechanics and Material Engineering 36 1993 190 196
51. Z. Zhang, H. Kristiansen, and J. Liu A method for determining elastic properties of micron-sized polymer particles by using flat punch test Computational Materials Science 39 2007 305 314 (Pubitemid 46367906)
52. K.K. Liu, D.R. Williams, and B.J. Briscoe The large deformation of a single micro-elastomeric sphere Journal of Physics D: Applied Physics 31 1998 294 303 (Pubitemid 128573983)
53. K.L. Johnson, K. Kendall, and A.D. Roberts Surface energy and the contact of elastic solids Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 324 1971 301 313
54. R.S. Bradley The cohesive force between solid surfaces and the surface energy of solids Philosophical Magazine Series 7 13 1932 853 862
55. B.V. Derjaguin, V.M. Muller, and Y.P. Toporov Effect of contact deformations on the adhesion of particles Journal of Colloid and Interface Science 53 1975 314 326
56. D. Maugis Adhesion of spheres: the JKR-DMT transition using a Dugdale model Journal of Colloid and Interface Science 150 1992 243 269
57. H. Tresca Memoir on the flow of solid bodies under strong pressure Comptes-rendus de L'académie Des Sciences 59 1864 754
58. R. von Mises Mechanik der festen Körper im plastisch- deformablen Zustand, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen Mathematisch-Physikalische Klasse 1913 1913 582 592
59. W. Rankine On the Stability of Loose Earth 1857 Royal Society of London
60. C.A. Coulomb, Essai sur une application des règles de maximis & minimis à quelques problèmes de statique, relatifs à l'architecture, De l'Imprimerie Royale, Paris, 1776.
61. M.T. Huber Zur Theorie der Berührung fester elastischer Körper Annalen der Physik 319 1904 153 163
62. S.D. Mesarovic, and N.A. Fleck Frictionless indentation of dissimilar elastic-plastic spheres International Journal of Solids and Structures 37 2000 7071 7091
63. E.J. Abbott, and F.A. Firestone Specifying surface quality: a method based on accurate measurement and comparison Mechanical Engineering 55 1933 569
64. W.R. Chang An elastic-plastic contact model for a rough surface with an ion-plated soft metallic coating Wear 212 1997 229 237
65. D. Tabor The Hardness of Metals 1951 Oxford University Press
66. A.J. Ishlinsky The axial-symmetrical problem in plasticity and the Brinell test Theoretical Research Translation 2 1944 47
67. M.F. Ashby, and K. Johnson Materials and Design: The Art and Science of Material Selection in Product Design 2009 A Butterworth-Heinemann Title
68. R.L. Jackson, and I. Green A finite element study of elasto-plastic hemispherical contact against a rigid flat Transactions of the ASME-F-Journal of Tribology 127 2005 343 354 (Pubitemid 40664765)
69. W.R. Chang, I. Etsion, and D.B. Bogy An elastic-plastic model for the contact of rough surfaces Journal of Tribology 109 1987 257
70. D.G. Evseev, B.M. Medvedev, and G.G. Grigoriyan Modification of the elastic-plastic model for the contact of rough surfaces Wear 150 1991 79 88
71. Y. Zhao, D.M. Maietta, and L. Chang An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow Journal of Tribology 122 2000 86
72. S. Kucharski, T. Klimczak, A. Polijaniuk, and J. Kaczmarek Finite-elements model for the contact of rough surfaces Wear 177 1994 1 13 (Pubitemid 285002)
73. A. Megalingam, M.M. Mayuram, A FEM Based multiple asperity deterministic contact model, in: ASME, 2009: pp. 375-377.
74. S.S. Wadwalkar, R.L. Jackson, and L. Kogut A study of the elastic-plastic deformation of heavily deformed spherical contacts Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 224 2010 1091 1102
75. K.L. Johnson Adhesion at the contact of solids W.T. Koiter, Theoretical and Applied Mechanics Proc. 4th IUTAM Congress 1976 North Holland Amsterdam 133
76. L. Vu-Quoc, X. Zhang, and L. Lesburg A normal force-displacement model for contacting spheres accounting for plastic deformation: force-driven formulation Journal of Applied Mechanics 67 2000 363 371
77. S.D. Mesarovic, and K.L. Johnson Adhesive contact of elastic-plastic spheres Journal of the Mechanics and Physics of Solids 48 2000 2009 2033
78. K.L. Johnson An experimental determination of the contact stresses between plastically deformed cylinders and spheres J. Heyman, F.A. Leckie, Engineering Plasticity 1968 Cambridge University Press Cambridge 341 461
79. L.-Y. Li, C.-Y. Wu, and C. Thornton A theoretical model for the contact of elastoplastic bodies Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216 2002 421 431 (Pubitemid 34523386)
80. I. Etsion, Y. Kligerman, and Y. Kadin Unloading of an elastic-plastic loaded spherical contact International Journal of Solids and Structures 42 2005 3716 3729 (Pubitemid 40220202)
81. M.A. Hopcroft, W.D. Nix, and T.W. Kenny What is the Young's modulus of silicon? Journal of Microelectromechanical Systems 19 2010 229 238
82. C.A. Klein, and G.F. Cardinale Young's modulus and Poisson's ratio of CVD diamond Diamond and Related Materials 2 1993 918 923
83. T. Adachi, and S. Sakka Dependence of the elastic moduli of porous silica gel prepared by the sol-gel method on heat-treatment Journal of Materials Science 25 1990 4732 4737
84. L. Zhang, M. D'Acunzi, M. Kappl, G.K. Auernhammer, D. Vollmer, and C.M. van Kats et al. Hollow silica spheres: synthesis and mechanical properties Langmuir 25 2009 2711 2717
85. L. Zhang, M. D'Acunzi, M. Kappl, A. Imhof, A. van Blaaderen, and H.J. Butt et al. Tuning the mechanical properties of silica microcapsules Physical Chemistry Chemical Physics 12 2010 15392 15398
86. Micromod Partikeltechnologie GmbH, Technical Data Sheet, 2013. < http://www.micromod.de/pdf/aktuell/43-00-103-tds-en.pdf > (accessed on 10.06).
87. H.R. Philipp Optical transitions in crystalline and fused quartz Solid State Communications 4 1966 73 75
88. J.E. Field, and C.S.J. Pickles Strength, fracture and friction properties of diamond Diamond and Related Materials 5 1996 625 634 (Pubitemid 126355094)
89. KRÜSS: GmbH, Selected Literature Values for Surface Free Energy of Solids, 2013. < http://www.kruss.de/en/theory/substance-properties/solids. html (accessed on 10.06).
90. H. Fessler, and E. Ollerton Contact stresses in toroids under radial loads British Journal of Applied Physics 8 1957 387 393
91. V.L. Popov Contact Mechanics and Friction: Physical Principles and Applications 2010 Springer
92. C. Vass, T. Smausz, and B. Hopp Wet etching of fused silica: a multiplex study Journal of Physics D: Applied Physics 37 2004 2449
93. F. Ullmann, W. Gerhartz, Y.S. Yamamoto, F.T. Campbell, R. Pfefferkorn, and J.F. Rounsaville Ullmann's Encyclopedia of Industrial Chemistry 1985 VCH Verlagsgesellschaft
94. G. Brambilla, and D.N. Payne The ultimate strength of glass silica nanowires Nano Letters 9 2009 831 835
95. S. Antonyuk, J. Tomas, S. Heinrich, and L. Mörl Breakage behaviour of spherical granulates by compression Chemical Engineering Science 60 2005 4031 4044 (Pubitemid 40665429)
96. K. Kendall The impossibility of comminuting small particles by compression Nature 272 1978 710 711
97. Y.H. Lee, J.H. Hahn, S.H. Nahm, J.I. Jang, and D. Kwon Investigations on indentation size effects using a pile-up corrected hardness Journal of Physics D: Applied Physics 41 2008 074027
98. N.P. Suh, R.S. Lee, and C.R. Rogers The yielding of truncated solid cones under quasi-static and dynamic loading Journal of the Mechanics and Physics of Solids 16 1968 357 364
99. P.H. Shipway, and I.M. Hutchings Fracture of brittle spheres under compression and impact loading. I. Elastic stress distributions Philosophical Magazine A 67 1993 1389 1404
100. V.M. Masalov, N.S. Sukhinina, E.A. Kudrenko, and G.A. Emelchenko Mechanism of formation and nanostructure of Stöber silica particles Nanotechnology 22 2011 275718