ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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Fig. 9 A typical load-displacement trace for instrumented hardness testing

Sometimes ordinary microindentation hardness machines may be retrofitted with displacement transducers, but

care must be taken to measure displacement as close to the indenter-specimen contact point as possible. Frame

compliance is an important source of error with retrofitted machines. Severe variability (up to a factor of 2) in

instrumented hardness results were recently demonstrated in a VAMAS round-robin exercise with a

borosilicate crown glass and NIST SRM 2830 silicon nitride blocks (Ref 33, 34). Dedicated low-load

instrumented hardness or even extremely low-load nanohardness machines are now commercially available.

This emerging technology has great promise, but consensus on the analyses, standard procedures, and reference

materials are sorely needed.

References cited in this section

33. C. Ullner and G. Quinn, “Round Robin on Recording Hardness,” Report No. 33, VAMAS (Versailles

Advanced Materials and Standards), BAM, Berlin/NIST, Feb 1998

34. C. Ullner and G. Quinn, Interlaboratory Study on Depth Sensing Hardness on Ceramics, to be presented

at IMEKO XV Conference (Osaka, Japan) as Reference No. 269, June 1999

Indentation Hardness Testing of Ceramics

G.D. Quinn, Ceramics Division, National Institute of Standards and Technology

Hardness and Brittleness

Much of the ceramics literature has thus far emphasized the effect of load and hardness on fracture processes

and fracture toughness. It has not considered in detail the reverse effect of fracture on hardness. This article

notes that the hardness of a brittle material is a measure of the resistance of the material to deformation,

densification, displacement, and fracture. Local fracture around and under an indentation can affect the

impression size and can be considered an intrinsic part of the indentation process. The degree of fracture at

ceramic indentations is load dependent. Deformation is predominant at low loads, while fracture is more

evident at high loads. The Meyer law is:

W = cd

(Eq 6)

where W is the load, c is a constant, and n is the Meyer or logarithmic index. As noted previously, for ceramics

and glasses, n < 2 and hardness decreases with increasing load. The hardness-load curves for many ceramics

deviate somewhat from the empirical Meyer law. This has prompted alternative attempts to achieve improved

curve fits to hardness-load or hardness-indentation size data. Bückle (Ref 35) and later Mitsche (Ref 36)

suggested a power series expansion that was later simplified to only two terms:

W = a

d + a

(Eq 7)

where a

and a

are constants. This equation alternatively may be expressed as an energy balance by

multiplying both sides by d:

Wd = a

+ a

(Eq 8)

The term Wd is proportional to the external work done by the indenter, Wℓ, where ℓ is the indenter penetration

depth, which is proportional to d for self-similar indentations. A number of investigators have attempted to

correlate surface energy processes to the a

term (Ref 37, 38, 39, 40), while Li et al. (Ref 41, 42) have related

this term to frictional and elastic contributions in their “proportional specimen resistance” model. The a

term, on the other hand, is considered to be the “work of permanent deformation” (Ref 39) or the “volume

energy of deformation” (Ref 42).

Close examination of experimental ceramic Vickers hardness-load curves (on either HV versus load or HV

versus diagonal size graphs) suggests a discrete transition point may exist where hardness changes from being

load dependent to load independent as shown in Fig. 10 (Ref 43). The Meyer relationship and energy models

(Eq 2 3 4) do not predict a specific transition point to constant hardness. The transition point, which is usually

overlooked, appears to be associated with the onset of extensive cracking around and underneath the

indentation. Cracking, an integral response of the ceramic to indentation even at small loads, may either be

localized or, at higher loads, massive to the extent that crushing occurs. Yurkov and Bradt (Ref 44) detected

significant acoustic emission activity at the indentation load where the constant hardness plateaus were reached

for five sialon ceramics. Knoop hardness does not exhibit an abrupt transition to a constant hardness plateau,

presumably because there is less cracking. The Vickers hardness transition point is related to a new index of

ceramic brittleness defined as (Ref 43):

(Eq 9)

where HV

is Vickers hardness at the plateau, E is the elastic modulus, and K

is the fracture toughness.

Fig. 10 Vickers hardness versus load (indentation size effect) curve for ceramics, showing a distinct

transition to a plateau hardness, H

, at W

B may also be expressed as:

(Eq 10)

where γ

is the fracture surface energy. B is the ratio of hardness to the fracture surface energy. Hardness has

units of work per unit volume and may be considered the work to create unit deformed volume, whereas γ

the work to create unit surface area. In other words, B is a ratio of volume deformation energy to surface

fracture energy. Figure 11 shows some hardness versus indentation load data for three ceramics of varying

brittleness. The transition point is easy to detect in brittle ceramics such as silicon carbide but may require very

careful measurements in less brittle materials.

Fig. 11 Hardness versus load for three ceramics. The silicon carbide is the most brittle of the three.

References cited in this section

35. H. Bückle, Mikrohärteprüfung, Berliner Union Verlag, Stuttgart, 1965

36. R. Mitsche, Über die Eindringhärte Metallischer Fest und Lockerkörper, Osterr. Chem. Z., Vol 49,

1948, p 186 (in German)

37. E.O. Bernhardt, On Microhardness of Solids at the Limit of Kick's Similarity Law, Z. Metallkd., Vol 33,

1941, p 135–144

38. K. Hirao and M. Tomozawa, Microhardness of SiO

Glass in Various Environments, J. Am. Ceram.

Soc., Vol 70 (No. 7), 1987, p 497–502

39. F. Fröhlich, P. Grau, and W. Grellmann, Performance and Analysis of Recording Microhardness Tests,

Phys. Status Solidi (a), Vol 42, 1977, p 79–89

40. M. Swain and M. Wittling, The Indentation Size Effect for Brittle Materials: Is There a Simple Fracture

Mechanics Explanation, Fracture Mechanics of Ceramics, Plenum, 1996, p 379–388

41. H. Li and R.C. Bradt, The Microhardness Indentation Load/Size Effect in Rutile and Cassiterite Single

Crystals, J. Mater. Sci., Vol 28, 1993, p 917–926

42. H. Li, A. Ghosh, Y.H. Han, and R.C. Bradt, The Frictional Component of the Indentation Size Effect in

Low Hardness Testing, J. Mater. Res., Vol 8 (No. 5), 1993, p 1028–1032

43. J. Quinn and G. Quinn, Indentation Brittleness of Ceramics: A Fresh Approach, J. Mater. Sci., Vol 32,

1997, p 4331–4346

44. A.L. Yurkov and R.C. Bradt, Load Dependence of Hardness of SIALON Based Ceramics, Fracture

Mechanics of Ceramics, Vol 11, R. Bradt, et al., Ed., Plenum, 1996, p 369–378

Indentation Hardness Testing of Ceramics

G.D. Quinn, Ceramics Division, National Institute of Standards and Technology

Summary

Hardness testing of ceramics, while conceptually simple, has many pitfalls. Sound metrological practices using

quality equipment (microscopes and optical controls with aperture and diaphragm stops) coupled with the use

of ceramic reference blocks will dramatically improve the quality of conventional test data. High-quality

ceramic or glass standard test methods that have been backed by major international round-robins are on the

books. New schemes for designating conventional hardness will rationalize the reporting of results. Hardness in

SI units is widely used and is codified in several world standards. The indentation load should always be

reported with the hardness data. New interpretations of conventional tests (such as brittleness, or fracture

toughness) and emerging new instrumented hardness technologies hold great promise for the future.

Indentation Hardness Testing of Ceramics

G.D. Quinn, Ceramics Division, National Institute of Standards and Technology

References

1. “Standard Specification for High-Purity Dense Yttria Tetragonal Zirconium Oxide Polycrystal (y-TZP)

for Surgical Implant Applications,” E 1873-98, Annual Book of ASTM Standards, Vol 13.01, ASTM,

1999

2. J.T. Hagan and M.V. Swain, The Origin of Median and Lateral Cracks around Plastic Indents in Brittle

Materials, J. Phys. D: Appl. Phys., Vol 11, 1978, p 2091–2102

3. “Standard Test Method for Knoop Indentation Hardness of Glass,” C 730-98, Annual Book of ASTM

Standards, Vol 15.02, ASTM, 1999

4. “Standard Test Method for Knoop Indentation Hardness of Ceramic Whitewares,” C 849-88, Annual

Book of ASTM Standards, Vol 15.02, ASTM, 1999

5. “Standard Test Method for Knoop Indentation Hardness of Advanced Ceramics,” C 1326-99, Annual

Book of ASTM Standards, Vol 15.01, ASTM, 1999

6. I.J. McHolm, Ceramic Hardness, Plenum, 1990

7. “Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics), Test Method for Hardness at

Room Temperature,” ISO 14705, International Organization for Standards, Geneva, Switzerland

8. D.M. Butterfield, D.J. Clinton, and R. Morrell, “The VAMAS Hardness Tests Round-Robin on Ceramic

Materials,” Report No. 3, Versailles Advanced Materials and Standards/National Physical Laboratory,

April 1989

9. R. Morrell, D.M. Butterworth, and D.J. Clinton, Results of the VAMAS Ceramics Hardness Round

Robin, Euroceramics, Vol 3, Engineering Ceramics, G. de With, R.A. Terpstra, and R. Metselaar, Ed.,

Elsevier, London, 1989, p 339–345

10. N. Thibault and H. Nyquist, The Measured Knoop Hardness of Hard Substances and Factors Affecting

Its Determination, Trans. ASM, Vol 38, 1947, p 271–330

11. L. Tarasov and N. Thibault, Determination of Knoop Hardness Numbers Independent of Load, Trans.

ASM, Vol 38, 1947, p 331–353

12. B.W. Mott, Micro-Indentation Hardness Testing, Butterworth, London, 1955

13. F. Knoop, C. Peters, and W. Emerson, A Sensitive Pyramidal-Diamond Tool for Indentation

Measurements, J. Res. Nat. Bur. Std., Vol 23, July 1939, p 39–61

14. C.G. Peters and F. Knoop, Resistance of Glass to Indentation, Glass Ind., Vol 20, May 1939, p 174–176

15. “Standard Test Method for Microhardness of Materials,” E 384-89 (1997)e2, Annual Book of ASTM

Standards, Vol 3.01, ASTM, 1999

16. “Advanced Technical Ceramics, Monolithic Ceramics, Mechanical Properties at Room Temperature,

Part 4. Vickers, Knoop and Rockwell Superficial Hardness Tests,” CEN EN 843-4, European

Committee for Standardization, Brussels, 1994

17. “Knoop Hardness Testing, Glass and Glass Ceramic,” DIN 52333, Entwurf German Institute for

Standards, Berlin, 1987

18. “Glass and Glass-Ceramics, Knoop Hardness,” ISO 9385, International Organization for Standards,

Geneva, 1990

19. R.J. Gettings, G.D. Quinn, A.W. Ruff, and L.K. Ives, Development of Ceramic Hardness Reference

Materials, New Horizons for Materials, P. Vincenzini, Ed., Proc. Eighth World Ceramic Congress,

CIMTEC (Florence, Italy), July 1994, Techna, Florence, 1995, p 617–624

20. R.J. Gettings, G.D. Quinn, A.W. Ruff, and L.K. Ives Hardness Standard Reference Materials (SRMs)

for Advanced Ceramics (No. 1194), Proc. Ninth International Symposium on Hardness Testing in

Theory and Practice, (Dusseldorf), Nov 1995, VDI Berichte 1995, p 255–264

21. “Standard Test Method for Vickers Indentation Hardness of Advanced Ceramics,” C 1327–99, Annual

Book of ASTM Standards, Vol 15.01, ASTM, 1999

22. “Testing Method for Vickers Hardness of High Performance Ceramics,” JIS R 1610, Japanese

Standards Association, Tokyo, 1991

23. R.W. Rice, C.C. Wu, and F. Borchelt, Hardness-Grain Size Relations in Ceramics, J. Am. Ceram. Soc.,

Vol 77 (No. 10), 1994, p 2539–2553

24. D.J. Clinton and R. Morrell, Hardness Testing of Ceramic Materials, Mater. Chem. Phys., Vol 17, 1989,

p 461–473

25. A. Krell and P. Blank, Grain Size Dependence of Hardness in Dense Submicrometer Alumina, J. Am.

Ceram. Soc., Vol 78 (No. 4), 1995, p 1118–1120

26. S.D. Skrovanek and R.C. Bradt, Microhardness of a Fine-Grain-Size Al

, J. Am. Ceram. Soc., Vol 62

(No. 3–4), 1979, p 215–216

27. A. Evans and E. Charles, Fracture Toughness Determination by Indentation, J. Am. Ceram. Soc., Vol 59

(No. 7–8), 1976, p 371–372

28. G. Anstis, P. Chantikul, B. Lawn, and D. Marshall, A Critical Evaluation of Indentation Techniques for

Measuring Fracture Toughness: I, Direct Crack Measurements, J. Am. Ceram. Soc., Vol 64 (No. 9),

1981, p 533–538

29. C.B. Ponton and R.D. Rawlings, Dependence of the Vickers Indentation Fracture Toughness on the

Surface Crack Length, Br. Ceram. Trans. J., Vol 88, 1989, p 83–90

30. H. Awaji, T. Yamada, and H. Okuda, Results of the Fracture Toughness Test Round Robin on

Ceramics, VAMAS Project, J. Ceram. Soc. Jpn., Int. Ed., Vol 99 (No. 5), 1991, p 403–408

31. G. Quinn, J. Salem, I. Bar-on, K. Chu, M. Foley, and H. Fang, Fracture Toughness of Advanced

Ceramics at Room Temperature, J. Res. NIST, Vol 97 (No. 5), Sept–Oct 1992, p 579–607

32. Z. Li, A. Ghosh, A. Kobayashi, and R. Bradt, Reply to Comment on Indentation Fracture Toughness of

Sintered Silicon Carbide in the Palmqvist Crack Regime, J. Am. Ceram. Soc., Vol 74 (No. 4), 1991, p

889–890

33. C. Ullner and G. Quinn, “Round Robin on Recording Hardness,” Report No. 33, VAMAS (Versailles

Advanced Materials and Standards), BAM, Berlin/NIST, Feb 1998

34. C. Ullner and G. Quinn, Interlaboratory Study on Depth Sensing Hardness on Ceramics, to be presented

at IMEKO XV Conference (Osaka, Japan) as Reference No. 269, June 1999

35. H. Bückle, Mikrohärteprüfung, Berliner Union Verlag, Stuttgart, 1965

36. R. Mitsche, Über die Eindringhärte Metallischer Fest und Lockerkörper, Osterr. Chem. Z., Vol 49,

1948, p 186 (in German)

37. E.O. Bernhardt, On Microhardness of Solids at the Limit of Kick's Similarity Law, Z. Metallkd., Vol 33,

1941, p 135–144

38. K. Hirao and M. Tomozawa, Microhardness of SiO

Glass in Various Environments, J. Am. Ceram.

Soc., Vol 70 (No. 7), 1987, p 497–502

39. F. Fröhlich, P. Grau, and W. Grellmann, Performance and Analysis of Recording Microhardness Tests,

Phys. Status Solidi (a), Vol 42, 1977, p 79–89

40. M. Swain and M. Wittling, The Indentation Size Effect for Brittle Materials: Is There a Simple Fracture

Mechanics Explanation, Fracture Mechanics of Ceramics, Plenum, 1996, p 379–388

41. H. Li and R.C. Bradt, The Microhardness Indentation Load/Size Effect in Rutile and Cassiterite Single

Crystals, J. Mater. Sci., Vol 28, 1993, p 917–926

42. H. Li, A. Ghosh, Y.H. Han, and R.C. Bradt, The Frictional Component of the Indentation Size Effect in

Low Hardness Testing, J. Mater. Res., Vol 8 (No. 5), 1993, p 1028–1032

43. J. Quinn and G. Quinn, Indentation Brittleness of Ceramics: A Fresh Approach, J. Mater. Sci., Vol 32,

1997, p 4331–4346

44. A.L. Yurkov and R.C. Bradt, Load Dependence of Hardness of SIALON Based Ceramics, Fracture

Mechanics of Ceramics, Vol 11, R. Bradt, et al., Ed., Plenum, 1996, p 369–378

Miscellaneous Hardness Tests

Edward L. Tobolski, Wilson Instrument Division, Instron Corporation

Introduction

MISCELLANEOUS HARDNESS TESTS encompass, for the purpose of this article, a number of test methods

that have been developed for specific applications. These include dynamic, or “rebound,” hardness tests using a

Leeb tester or a Scleroscope, static indentation tests on rubber or plastic products using the durometer or IRHD

testers, scratch hardness tests, and ultrasonic microindentation testing. This article reviews the procedures,

equipment, and applications associated with these alternate hardness test methods.

Miscellaneous Hardness Tests

Edward L. Tobolski, Wilson Instrument Division, Instron Corporation

Dynamic (Rebound) Test Methods

Hardness can be empirically related to either the elastic response of a material or the plastic deformation of a

material. Indentation hardness tests determine hardness in terms of plastic behavior, while dynamic test

methods relate hardness to the elastic response of a material.

A number of dynamic hardness test methods have been developed, but only a few have common use. The two

most common methods of dynamic hardness testing are the Shore Scleroscope and the Leeb tester. These two

methods are rebound-type tests and are described further here. Other dynamic hardness tests include a

pendulum test method and dynamic indentation hardness testing using a Hopkinson-bar technique (the article

“Dynamic Indentation Testing” in this Volume contains details).

Scleroscope Hardness Testing

The Scleroscope (Instron Corporation, Canton, MA) dynamic hardness tester was invented by Albert F. Shore

in 1907 and was the first commercially available metallurgical hardness tester produced in the United States.

While Scleroscopes are not currently manufactured in the United States, the unit is still used frequently for

testing very large specimens such as forged steel or wrought alloy steel rolls. In this procedure, a diamond-

tipped hammer is dropped from a fixed height onto the surface of the material being tested. The height of

rebound of the hammer is a measure of the hardness of the metal.

The Scleroscope scale consists of units determined by dividing into 100 units the average rebound of a hammer

from a quenched (to maximum hardness) and untempered water-hardened tool steel. The scale is continued

above 100 units to permit testing of materials with hardnesses greater than that of fully hardened tool steel.

Testers. Two types of Scleroscope hardness testers were manufactured. The model C Scleroscope (Fig. 1)

consists of vertically disposed barrel containing a precision-bore glass tube. A scale, graduated from 0 to 140, is

set behind the tube and is visible through it. Hardness is read from the vertical scale, usually with the aid of a

reading glass attached to the tester. A pneumatic actuating head, affixed to the top of the barrel, is manually

operated by use of a rubber bulb and tube. The hammer drops and rebounds within the glass tube.

Fig. 1 Model C Scleroscope hardness testers mounted in stands

The model D Scleroscope hardness tester (Fig. 2) may have either analog (dial) or digital readouts. The tester

consists of a vertically disposed barrel that contains a clutch to arrest the hammer at the maximum height of

rebound. This is possible because of the short rebound height. The hammer is longer and heavier than the

hammer used in the model C Scleroscope, developing the same striking energy even through dropping a shorter

distance.

Fig. 2 Model D Scleroscope hardness testers mounted in stands

Models C, D, and D digital Scleroscopes were available in two calibrations: standard and roll. Standard

calibration, which conforms to ASTM E-448, “Standard Practice for Scleroscope Hardness Testing of Metallic

Materials,” has a direct correlation to Rockwell C, Brinell, and Vickers hardness values (Table 1). Roll

calibration conforms to ASTM A 427, “Standard Specification for Wrought Alloy Steel Rolls for Cold and Hot

Reduction,” and is used to determine hardness values of homogeneous wrought hardened alloy steel rolls for

use in reduction of flat-rolled products. This calibration is symbolized by HFRSc or HFRSd. The model C

Scleroscope can also be calibrated in accordance with ASTM C 886, “Standard Test Method for Scleroscope

Hardness Testing of Fine-Grained Carbon and Graphite Materials.” This is referred to as model C carbon

calibration.

Table 1 Approximate hardness conversion numbers for nonaustenitic steels

Brinell hardness number, HB

Scleroscope

hardness

Rockwell C

hardness

number,

HRC

Vickers

hardness

number,

10 mm

standard ball,

3000 kgf

load

10 mm

carbide ball,

3000 kgf

load

97.3 68 940 …

…

95.0 67 900 …

…

92.7 66 865 …

…

90.6 65 832 …

739

88.5 64 800 …

722

86.5 63 772 …

705

84.5 62 746 …

688

82.6 61 720 …

670

80.8 60 697 …

654

79.0 59 674 …

634

77.3 58 653 …

615

75.6 57 633 …

595

74.0 56 613 …

577

72.4 55 595 …

560

70.9 54 577 …

543

69.4 53 560 …

525

67.9 52 544 500

512

66.5 51 528 487

496

65.1 50 513 475

481

63.7 49 498 464

469

62.4 48 484 451

455

61.1 47 471 442

443

59.8 46 458 432

432

58.5 45 446 421

421

57.3 44 434 409

409

56.1 43 423 400

400

54.9 42 412 390

390

53.7 41 402 381

381

52.6 40 392 371

371

51.5 39 382 362

362

50.4 38 372 353

353

49.3 37 363 344

344

48.2 36 354 336

336

47.1 35 345 327

327

46.1 34 336 319

319

45.1 33 327 311

311

44.1 32 318 301

301

43.1 31 310 294

294

42.2 30 302 286

286

41.3 29 294 279

279

40.4 28 286 271

271

39.5 27 279 264

264

38.7 26 272 258

258

37.8 25 266 253

253

37.0 24 260 247

247