Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Improved method to measure the strength and elastic modulus of single aggregate particles

Abstract

The standard methods used to determine the mechanical properties of single aggregate particles have shortcomings. Indeed, methods that are commonly used to measure the strength of irregular particles do not provide their elastic modulus and are also only semi-quantitative. The aim of this work is to determine more accurately both the tensile strength and the elastic modulus of single coarse aggregate particles using the point load test fitted with tungsten carbide semi-spheres and coupled with a linear transducer. In the experiment, the poles of the particles are made flat and parallel at the points of contact with the semi-spheres of the apparatus, allowing to estimate the elastic modulus of aggregates in accordance to Hertz contact theory. Glass particles of different shapes (spheres, cubes, and prisms) were used as reference material to validate the experimental method and establish the optimal conditions to conduct the test. These conditions consisted of a deformation rate of 0.2 mm/min, a blunt 4.0-mm diameter cylinder piston for spherical particles, while two 14.0-mm diameter semi-spheres in the case of rectangular particles (cubes/prisms). It is also hereby proposed to measure the tensile strength of irregularly-shaped particles by a modified version of Hiramatsu and Oka’s formula using the equivalent core diameter. The proposed method was then applied to measure the strength and modulus of coarse granite aggregate particles (25.0 to 9.5 mm). It demonstrated that the variability of the elastic modulus and tensile strengths of the individual aggregate particles was quite significant, confirming the importance of using the proposed improved method to qualify materials for structural (high strength) concrete, or to simulate/predict the mechanical behavior of concrete.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Change history

  • 30 July 2019

    This article was published with an erroneous name of one of the authors and therefore has been corrected.

Abbreviations

A c :

Minimum cross-sectional area

B :

Breakage point

C :

Emprirical constant

D :

Diameter of spherical body

D :

Distance between loading points

D n :

Nominal diameter

D e :

Equivalent core diameter

E * :

Effective modulus of contact

E t :

Elastic modulus of the punch

E p :

Elastic modulus of the particle

E n :

Fracture energy

E v :

Specific-volume fracture energy

F :

Applied force

F b :

Breakage force

F el :

Force during elastic deformation

k p :

Particle stiffness

k t :

Punch stiffness

K N-el :

Contact stiffness during elastic deformation

m p :

Particle mass

s :

Displacement

S :

Total displacement

s :

Displacement variation

V p :

Volume of the particle

W :

Minimum width

Y :

Yield point

σ t :

Tensile strength

μ p :

Poisson’s coefficient of the particle

μ t :

Poisson’s coefficient of the punch

β :

Shape factor

ρ p :

Particle density

References

  1. 1.

    Giaccio G, Rocco C, Violini D, Zappitelli J, Zerbino R (1992) High-strength concretes incorporating different coarse aggregates. Mater J 89:242–246

  2. 2.

    Aitcin PC, Mehta PK (1990) Effect of coarse aggregate characteristics on mechanical properties of high-strength concrete. Mater J 87:103–107

  3. 3.

    Beushausen H, Dittmer T (2015) The influence of aggregate type on the strength and elastic modulus of high strength concrete. Constr Build Mater 74:132–139. https://doi.org/10.1016/j.conbuildmat.2014.08.055

  4. 4.

    Alexander MG, Mindess S (2008) Aggregates in concrete. Taylor & Francis, London

  5. 5.

    Neville AM (2011) Properties of concrete, 5th edn. Pearson, New York

  6. 6.

    Portnikov D, Kalman H, Aman S, Tomas J (2013) Investigating the testing procedure limits for measuring particle strength distribution. Powder Technol 237:489–496

  7. 7.

    Tavares LM (2007) Chapter 1 breakage of single particles: quasi-static. In: Salman A, Ghadiri M, Hounslow M (eds) Handbook of powder technology. Elsevier, Amsterdam, pp 3–68. https://doi.org/10.1016/s0167-3785(07)12004-2

  8. 8.

    Yashima S, Kanda Y, Sano S (1987) Relationships between particle size and fracture energy or impact velocity required to fracture as estimated from single particle crushing. Powder Technol 51:277–282

  9. 9.

    Yashima S, Saito F (1979) Size effects of particle compressive strength of brittle Solids. Sci Rep Res Inst Tohoku Univ Ser Phys Chem Metall 27:31–42

  10. 10.

    Antonyuk S, Heinrich S, Tomas J, Deen NG, Van Buijtenen MS, Kuipers JAM (2010) Energy absorption during compression and impact of dry elastic-plastic spherical granules. Granul Matter 12:15–47. https://doi.org/10.1007/s10035-009-0161-3

  11. 11.

    Antonyuk S, Tomas J, Heinrich S, Mörl L (2005) Micro-macro breakage behavior of elastic-plastic granulates by compression. Chem Eng Technol 28:623–629. https://doi.org/10.1002/ceat.200407060

  12. 12.

    Huang J, Xu S, Yi H, Hu S (2014) Size effect on the compression breakage strengths of glass particles. Powder Technol 268:86–94. https://doi.org/10.1016/j.powtec.2014.08.037

  13. 13.

    Russell A, Schmelzer J, Müller P, Krüger M, Tomas J (2015) Mechanical properties and failure probability of compact agglomerates. Powder Technol 286:546–556. https://doi.org/10.1016/j.powtec.2015.08.045

  14. 14.

    Russel A, Müller P, Tomas J (2013) Material behavior of spherical elastic-plastic granules under diametrical compression. Patiata, India

  15. 15.

    Ahmadi Sheshde E, Cheshomi A (2015) New method for estimating unconfined compressive strength (UCS) using small rock samples. J Pet Sci Eng 133:367–375. https://doi.org/10.1016/j.petrol.2015.06.022

  16. 16.

    Cheshomi A, Sheshde EA (2013) Determination of uniaxial compressive strength of microcrystalline limestone using single particles load test. J Pet Sci Eng 111:121–126. https://doi.org/10.1016/j.petrol.2013.10.015

  17. 17.

    Cheshomi A, Mousavi E, Ahmadi-Sheshde E (2015) Evaluation of single particle loading test to estimate the uniaxial compressive strength of sandstone. J Pet Sci Eng 135:421–428. https://doi.org/10.1016/j.petrol.2015.09.031

  18. 18.

    Lim WL, McDowell GR, Collop AC (2004) The application of Weibull statistics to the strength of railway ballast. Granul Matter 6:229–237

  19. 19.

    McDowell GR, Lim WL, Collop AC (2003) Measuring the strength of railway ballast. Ground Eng 36:25–28

  20. 20.

    Pepe M, Grabois TM, Silva MA, Tavares LM, Toledo Filho RD (2018) Mechanical behaviour of coarse, lightweight, recycled and natural aggregates for concrete. Proc Inst Civ Eng Constr Mater. https://doi.org/10.1680/jcoma.17.00081

  21. 21.

    Portnikov D, Kalman H (2014) Determination of elastic properties of particles using single particle compression test. Powder Technol 268:244–252. https://doi.org/10.1016/j.powtec.2014.08.011

  22. 22.

    Antonyuk S, Tomas J, Heinrich S, Mörl L (2005) Breakage behaviour of spherical granulates by compression. Chem Eng Sci 60:4031–4044. https://doi.org/10.1016/j.ces.2005.02.038

  23. 23.

    Timoshenko S, Goodier JN (1951) Theory of elasticity. McGraw-Hill, New York

  24. 24.

    Hiramatsu Y, Oka Y (1966) Determination of the tensile strength of rock by a compression test of an irregular test piece. Int J Rock Mech Min Sci 3:89–99

  25. 25.

    Callister WD, Rethwisch DG (2014) Materials science and engineering: an introduction, 9th edn. Wiley, Hoboken

  26. 26.

    Kschinka BA, Perrella S, Nguyen HCBR, Bradt RC (1986) Strengths of glass spheres in compression. J Am Ceram Soc 69:467–472

  27. 27.

    Brook N (1985) The equivalent core diameter method of size and shape correction in point load testing. Int J Rock Mech Min Sci Geomech Abstr 22:61–70. https://doi.org/10.1016/0148-9062(85)92328-9

  28. 28.

    Koohmishi M, Palassi M (2016) Evaluation of the strength of railway ballast using point load test for various size fractions and particle shapes. Rock Mech Rock Eng 49:2655–2664. https://doi.org/10.1007/s00603-016-0914-3

  29. 29.

    Johnson KL (1982) One hundred years of hertz contact. ImechE, London

  30. 30.

    Hertz H (1882) Über die Berührung fester elastischer Körper. Reine Angew. 92:156–171

  31. 31.

    Dowling NE (2013) Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue, 4th edn. Pearson, Boston

  32. 32.

    Yashima S, Kanda Y, Saito F, Sasaki T, Iijima M (1973) Mechanical properties of brittle materials and their single fracture under dynamic loads. Sci Rep Res Inst Tohoku Univ Ser A Phys Chem Metal 37:1218–1226

  33. 33.

    Yashima S, Shoichi M, Saito F (1979) Single particle crushing under slow rate of loading. Sci Rep Res Inst Tohoku Univ Ser A Phys Chem Metal 28:116–133

  34. 34.

    American Society of Testing and Materials (2008) ASTM Standard D 5731—Determination of the Point Load Strength Index of Rock and Application to Rock Strength Classifications

  35. 35.

    Sbrighi N (2011) Agregados Naturais, Britados e Artificiais para Concreto. In: Concreto Ciênc. E Tecnol., 1a, Instituto Brasileiro do Concreto, São Paulo

  36. 36.

    Tavares LM, King RP (1998) Single-particle fracture under impact loading. Int J Miner Process 54:1–28. https://doi.org/10.1016/S0301-7516(98)00005-2

Download references

Acknowledgements

Natalia V. Silva and Sérgio C. Angulo received research scholarship grants of FAPESP Numbers 2016/02902-0 and 2016/19974-3, respectively. Sérgio C. Angulo also received a research grant from CNPq, process 305564/2018-8. The information and views set out in this study are those of the authors and do not necessarily reflect the opinion of FAPESP or CNPq. Luís Marcelo Tavares received the research grant from CNPq process 310293/2017-0. David A. Lange received support from the RECAST University Transportation Center established at Missouri University of Science and Technology.

Funding

The study was funded by a research project entitled “Granulometric concepts and advanced processing applied to ecoefficient concrete” between the University of Sao Paulo (USP) and InterCement S.A, as well as by the National Institute of Science and Technology “Advanced Eco-Efficient Cement-Based Technologies”, between USP and CNPq agency.

Author information

Correspondence to Sérgio C. Angulo.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article was published with an erroneous name of one of the authors and therefore has been corrected.

Appendix 1

Appendix 1

See Figs. 7, 8, 9 and 10.

Fig. 7
figure7

Schematic illustration showing nominal diameter and length of particle

Fig. 8
figure8

Typical compression force–displacement curve until breakage (left axis) and calculated contact stiffness (right axis)

Fig. 9
figure9

The pattern of rupture of the glass particles: spheres, cubes and prisms

Fig. 10
figure10

Aggregate particles after the mechanical test. Most particles broke into two pieces

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Silva, N.V., Angulo, S.C., da Silva Ramos Barboza, A. et al. Improved method to measure the strength and elastic modulus of single aggregate particles. Mater Struct 52, 77 (2019). https://doi.org/10.1617/s11527-019-1380-7

Download citation

Keywords

  • Aggregates
  • Single particle
  • Elastic modulus
  • Hertz contact theory
  • Tensile strength
  • Point load test