Rock Mechanics and Rock Engineering

, Volume 48, Issue 4, pp 1573–1588 | Cite as

Fracture Toughness Effects in Geomaterial Solid Particle Erosion

  • A. W. MomberEmail author
Original Paper


Effects of fracture toughness on the impingement of geomaterials (rocks and cementitious composites) by quartz particles at velocities between 40 and 140 m/s are investigated experimentally and analytically. If schist is excluded, relative erosion (in g/g) reduces according to a reverse power function if fracture toughness increases. The power exponent depends on impingement velocity, and it varies between −0.64 and −1.33. Lateral cracking erosion models, developed for brittle materials, deliver too high values for relative material erosion. This discrepancy is partly attributed to stress rate effects. Effects of R-curve behavior seem to be marginal. An integral approach E R = K 1 · E R P  + (1 − K 1) · E R L is introduced, which considers erosion due to plastic deformation and lateral cracking. A transition function \(K_{1} = f\left( {K_{\text{Ic}}^{12/4} /\sigma_{\text{C}}^{23/4} } \right)\) is suggested in order to classify geomaterials according to their response against solid particle impingement.


Erosion Fracture toughness Geomaterials Impact 

List of symbols


Distribution shape parameter


Crack length


Material parameter


Fracture toughness exponent


Erodent particle diameter


Kinetic energy erodent particle


Young’s modulus target material


Young’s modulus erodent material


Relative erosion


Hardness target material


Elastic parameter


Erosion parameter


Fracture toughness target material


R-curve parameter


Eroded target mass


Erodent particle mass


Erodent mass flow rate


Stress rate parameter


Contact force


Contact radius


Particle radius


Exposure time


Contact time


Erodent particle velocity


Indenter angle


Transition parameter


Critical energy release rate


Distribution scale parameter


Poisson’s ratio target material


Poisson’s ratio erodent material


Density erodent material


Density target material

\(\dot{\sigma }\)

Stress rate


Compressive strength target material


Contact stress


Yield stress



The author is thankful to the German Academic Exchange Service (DAAD), Bonn, Germany, for providing an Exchange Lecturer Fellowship for a stay at the University of Cambridge, UK. Special thanks is addressed to the Fracture Group, Physics and Chemistry of Solids, Cavendish Laboratory, for its kind hospitality and the permission to use experimental facilities.


  1. Amaral PM, Fernandes JC, Rosa LG (2009) Wear mechanisms in materials with granitic textures—applicability of a lateral crack system model. Wear 266:753–764CrossRefGoogle Scholar
  2. Bertram B (2008) Bruchenergie laufender Risse in Gestein. Dissertation, Bochum: Ruhr-Universität: 1988Google Scholar
  3. Beste U, Lundvall A, Jacobson S (2004) Micro-scratch evaluation of rock types—a means to comprehend rock drill wear. Tribol Int 37:203–210CrossRefGoogle Scholar
  4. Blange JJ, van Nieuwkoop P (2011) Method of drilling and jet drilling system. Interns Patent Application, WO 2011/076845 A1, 30 June 2011Google Scholar
  5. Breder K, Giannakopoulos AE (1990) Erosive wear in Al2O3 exhibiting Mode-I R-curve behavior. Ceram Eng Sci Proc 11:1046–1060CrossRefGoogle Scholar
  6. Breder K, De Portu G, Ritter JE, Fabbriche DD (1988) Erosion damage and strength degradation of zirconia-toughened alumina. J Amer Ceram Soc 71:770–775CrossRefGoogle Scholar
  7. Bujis M (1994) Erosion of glass as modeled by indentation theory. J Amer Ceram Soc 77:1676–1678CrossRefGoogle Scholar
  8. Bushby AJ, Swain MV (1995) Spherical indentations as a means for investigating the plastic deformation of ceramics. In: Bradt RC et al (eds) Plastic Deformation of Ceramics. Plenum Press, New York, pp 161–172CrossRefGoogle Scholar
  9. Chaudri MM, Walley SM (1978) A high-speed photographic investigation of the impact damage in sodalime and borosilicate glasses by small glass and steel spheres. In: Bradt RC et al (eds) Fracture Mechanics of Ceramics, vol 3. Plenum Press, New York, pp 349–364Google Scholar
  10. Chen X, Hutchinson JW, Evans AG (2005) The mechanics of indentation induced lateral cracking. J Amer Ceram Soc 88(5):1233–1238CrossRefGoogle Scholar
  11. Chen P, Cui J, Zhou X (2013) Research on effects of pressure loading on rock lateral cracks under confining pressure. Adv Mater Res 838–841:850–853Google Scholar
  12. Cui M, Zhay Y, Ji G (2011) Experimental study of rock breaking effect of steel particles. J Hydrodyn 23:241–246CrossRefGoogle Scholar
  13. Dai F, Chen R, Iqbal MJ, Xia K (2010) Dynamic cracked chevron notched Brazilian disc method for measuring rock fracture parameters. Int J Rock Mech Min Sci 47:606–613CrossRefGoogle Scholar
  14. Du Y, Wang R, Ni H, Ma L, Zhang S, Han Z (2011) Study on the rock-breaking performance of particles jet drilling technology. Electr J Geomech Engng 16:431–440Google Scholar
  15. Du Y, Wang R, Ni H (2012) Feasibility of particle jet as a drilling medium for the development of deep complicated oil-gas reservoir. Adv Mater Res 361–363:465–468Google Scholar
  16. Erarslan N, Williams DJ (2012) The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks. Int J Rock Mech Min Sci 56:15–26Google Scholar
  17. Evans AG, Gulden ME, Rosenblatt ME (1978) Impact damage in brittle materials in the elastic–plastic response regime. Proc Roy Soc Lond A 361:343–356CrossRefGoogle Scholar
  18. Fischer-Cipps AC (2007) Introduction to Contact Mechanics. Springer, New-YorkCrossRefGoogle Scholar
  19. Gordon AT, Greg GG (2008) Particle drilling alters standard rock-cutting approach. World Oil 229(6):37–44Google Scholar
  20. Gotzmann J (1989) Modellierung des Strahlverschleißes an keramischen Werkstoffen. Schmierungstechnik 20:324–329Google Scholar
  21. Harder NJ, Curlett HB, Padgett O, Hazel B (2010) Impact excavation system and method with injection system. United States Patent, US 7,793,741 B2, 14 Sep 2010Google Scholar
  22. Heßling M (1988) Grundlagenuntersuchungen über das Schneiden von Gestein mit abrasiven Höchstdruckwasserstrahlen. Dissertation, Aachen, RWTH AachenGoogle Scholar
  23. Huang H, Damjanac B, Detournay E (1998) Normal wedge indentation in rocks with lateral confinement. Rock Mech Rock Engng 31(2):81–94CrossRefGoogle Scholar
  24. Hutchings IM (1977) Strain rate effects in microparticle impact. J Phys D Appl Phys 10:L179–L184CrossRefGoogle Scholar
  25. Igrashi S, Bentur A, Mindess S (1996) Microhardness testing of cementitious materials. Advn Cem Bas Mat 4:48–57CrossRefGoogle Scholar
  26. Iqbal MJ, Mohanty B, Xia K (2008) Dynamic tensile strength and mode-I fracture toughness in granitic rocks. In: Proceedings 11th International Congress. Exposition, Orlando; Society for Experimental Mechanics 2–5 June 2008Google Scholar
  27. Jung SJ, Prisbrey K, Wu G (1994) Prediction of rock hardness and drillability using acoustic signatures during indentation. Int J Rock Mech Min Sci Geomech Abstr 31:561–567CrossRefGoogle Scholar
  28. Kleis I, Kulu P (2008) Solid Particle Erosion. Springer, LondonGoogle Scholar
  29. Knight CG, Swain MV, Chaudri MM (1977) Impact of small steel spheres on glass surfaces. J Mater Sci 12:1573–1586CrossRefGoogle Scholar
  30. Lambe TW (1969) Soil Mechanics. John Wiley, New YorkGoogle Scholar
  31. Lambert DE, Ross CA (2000) Strain rate effects on dynamic fracture and strength. Int J Impact Eng 24:985–998CrossRefGoogle Scholar
  32. Marshall DB, Lawn BR, Evans AG (1982) Elastic/plastic indentation damage in ceramics: the lateral crack system. J Amer Ceram Soc 65:561–566CrossRefGoogle Scholar
  33. Maurer WCJ, Rinehart JS (1960) Impact crater formation in rock. J Appl Phys 31:1247–1252CrossRefGoogle Scholar
  34. Momber AW (2003a) Cavitation damage to geomaterials in a flowing system. J Mater Sci 38:747–757CrossRefGoogle Scholar
  35. Momber AW (2003b) An SEM-study of high-speed hydrodynamic erosion of cementitious composites. Compos B 34:135–142CrossRefGoogle Scholar
  36. Momber AW (2004) Damage to rocks and cementitious materials from solid impact. Rock Mech Rock Eng 37:57–82CrossRefGoogle Scholar
  37. Momber AW (2005) Hydrodemolition of concrete surfaces and reinforced concrete. Elsevier, LondonGoogle Scholar
  38. Momber AW (2008) Blast Cleaning Technology. Springer, LondonCrossRefGoogle Scholar
  39. Momber AW (2013) Erosion of schist due to solid particle impingement. Rock Mech Rock Eng 46:849–857CrossRefGoogle Scholar
  40. Momber AW (2014) Effects of target material properties on solid particle erosion of geomaterials at different impingement velocities. Wear 319:69–83CrossRefGoogle Scholar
  41. Momber AW, Kovacevic R (1998) Principles of Abrasive Water Jet Machining. Springer, LondonCrossRefGoogle Scholar
  42. Momber AW, Budidharma E, Tjo R (2011) The separation of reinforced cementitious composites with a stream-line cutting tool. Res Conserv Recycl 55:507–514CrossRefGoogle Scholar
  43. Murakami Y (1987) Stress Intensity Handbook, vol 1. Pergamon Press, Oxford, pp 13–15Google Scholar
  44. Murugesh L, Srinivasan S, Scattergood RO (1991) Models and material properties for erosion of ceramics. J Mater Eng 13:55–61CrossRefGoogle Scholar
  45. Ouchterlony F (1982) Review on fracture toughness testing of rock. SM Archives 71:131–211Google Scholar
  46. Ouchterlony F (1990) Fracture toughness testing of rock with core based specimens. Eng Fract Mech 35:351–366CrossRefGoogle Scholar
  47. Pickering EG, Deshpande VS (2014) The ballistic impact of ceramics—an investigation into the effects of confinement and material properties. In: 4th International Conference on Impact Loading of Lightweight Structures. Cape Town, SA; 12–16 Jan 2014Google Scholar
  48. Ritter JE (1985) Erosion damage in structural ceramics. Mater Sci Eng 71:194–201CrossRefGoogle Scholar
  49. Ritter JE, Strzepa P, Jakus K, Rosenfeld L, Buckman KJ (1984) Erosion damage in glass and alumina. J Amer Ceram Soc 67:769–774CrossRefGoogle Scholar
  50. Rogers CO, Pang SS, Kumano A, Goldsmith W (1986) Response of dry- and liquid-filled porous rocks to static and dynamic loading by variously-shaped projectiles. Rock Mech 19:235–260CrossRefGoogle Scholar
  51. Routbort JL, Matzke HJ (1983) On the correlation between solid-particle erosion and fracture parameters in SiC. J Mater Sci 18:1491–1496CrossRefGoogle Scholar
  52. Ruff AW, Wiederhorn SM (1979) Erosion by solid particle impact. In: Preece CM (ed) Erosion. Academic Press, New York, pp 69–126Google Scholar
  53. Schmidt RA, Lutz TJ (1979) KIc and JIc of Westerley granite—effects of thickness and in-plane dimensions. In: Freiman SW (ed) Fracture Mechanics Applied to Brittle Materials. ASTM, New York, pp 166–182CrossRefGoogle Scholar
  54. Slikkerveer PJ, Verspui M, Skerka E (1999) Erosion and damage by hard spherical particles on glass. J Amer Ceram Soc 82:3173–3178CrossRefGoogle Scholar
  55. Szwedzicki T (1998) Indentation hardness testing of rock. Int J Rock Mech Min Sci 35:825–829CrossRefGoogle Scholar
  56. Tabor D (1951) The hardness of metals. Clarendon Press, OxfordGoogle Scholar
  57. Tandon S, Faber KT (1999) Effects of loading rate on the fracture of cementitious materials. Cem Concr Res 29:397–406CrossRefGoogle Scholar
  58. Tibbitts GA, Galloway G, Vuyk A, Terry J (2009) Methods of using a particle impact drilling system for removing near-borehole damage, milling objects in a wellbore, under reaming, coring, perforating, assisting, annular flow, and associated methods. United States Patent Application Publication, US 2009/0218098 A1, 3 Sep 2009Google Scholar
  59. Timoshenko S, Goodier JN (1970) Theory of Elasticity. McGraw-Hill, New YorkGoogle Scholar
  60. Verhoef PN (1987) Sandblast testing of rock. Int J Rock Mech Min Sci 24:185–192CrossRefGoogle Scholar
  61. Verhoef PN, Kuipers TJ, Verwaal W (1984) The use of the sand-blast test to determine rock durability. Bull Int Assoc Engng Geol 29:457–461CrossRefGoogle Scholar
  62. Wallin K (2013) A simple fracture mechanical interpretation of size effects in concrete fracture toughness tests. Eng Fract Mech 99:18–29CrossRefGoogle Scholar
  63. Wang QZ, Yang JR, Zhang CG, Zhou Y (2014) Rock dynamic fracture toughness measured by using crack propagation gauge and universal function. In: 16th International Conference on Experimental Mechanics, Cambridge, UK; European Society Experimental Mechanics: 7–8 July 2014Google Scholar
  64. Wiederhorn SM, Hockey BJ (1983) Effect of material parameters on the erosion resistance of brittle materials. J Mater Sci 18:766–780CrossRefGoogle Scholar
  65. Winslow DN (1984) A Rockwell hardness test for concrete. Cement Concr Aggreg 6:137–141CrossRefGoogle Scholar
  66. Zhang ZX, Kou SQ, Yu J, Yu Y, Jiang LG, Lindqvist PA (1999) Effects of loading rate on rock fracture. Int J Rock Mech Min Sci 36:597–611CrossRefGoogle Scholar
  67. Zhang ZX, Kou SQ, Jiang LG, Lindqvist PA (2000) Effects of loading rate on rock fracture: fracture characteristics and energy partitioning. Int J Rock Mech Min Sci 37:745–762CrossRefGoogle Scholar
  68. Zhang H, Song H, Kang Y, Huabng G, Qu C (2013) Experimental analysis on deformation evolution and crack propagation of rock under cyclic indentation. Rock Mech Rock Eng 46:1053–1059CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.Faculty of Georesources and Materials TechnologyAachen University of Technology (RWTH Aachen)HamburgGermany

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