ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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Fig. 7 Stress-strain response for metals at quasi-static and high strain rates

Fig. 8 Hardness versus yield stress at 8% strain for metals under (a) static loading and (b) dynamic

loading. The numbers next to the data points refer to metals and alloys listed in Fig. 6.

Characteristics of the Indentation Plastic Zone. To estimate the differences in plastic zone size with respect to

the loading rate, microhardness measurements have been performed within the indentation zones of two

materials that exhibited a strain-rate-sensitive and a strain-rate-insensitive stress-strain response. Static and

dynamic indentations were performed at similar load levels (approximately 490 N) on 2024 aluminum (rate

insensitive) and 316 stainless steel (rate sensitive) (Fig. 7). The specimens were then sectioned just outside of

the indentation zone using a low-speed diamond saw and then carefully ground and polished such that the final

polished surface passed through the midsection of the indentation as shown in Fig. 9 (Ref 20). In the region

surrounding the indentation, static microhardness measurements (which are basically hardness measurements at

much lower load levels) were performed as per ASTM E 384-89 (Ref 25), and the data were contoured to give

an indication of the accumulated plastic strains as a function of depth beneath the indentation. For the present

work, loads of 100 g for aluminum and 200 g for stainless steel were used with microindentation spacing of

0.12 mm and 0.16 mm, respectively.

Fig. 9 Schematic of the plane illustrating the grid of microhardness measurements surrounding the

macroindentation

Contours of microhardness for static and dynamic indentations on aluminum and steel are shown in Fig. 10.

The exact magnitude of the accumulated plastic strains closest to the surface or the tip of indentation could not

be obtained with this procedure due to the constraint imposed by the ASTM standard (Ref 25) (i.e., hardness

measurements should be performed at a distance at least 2.5 times the diagonal of indentation from a free

surface). The position of the free surface of the specimen is denoted by a solid line in the figure. For

comparison purposes, all the contours are plotted on the same scale, with shaded regions representing the area

where the microindentations were performed.

Fig. 10 Contours of microhardness measurements revealing the plastic zone size beneath static and

dynamic indentations. (a) 2024 aluminum, static indentation. (b) 2024 aluminum, dynamic indentation.

Two major observations can be made from these plots. The first observation is that the size of the plastic zone

for 2024 aluminum is almost the same under static and dynamic loads. The contours of microhardness are also

approximately similar in terms of their depth, width, and magnitude of microhardness. This is expected since

this material exhibits no rate sensitivity in both its hardness (Fig. 6) and constitutive response (Fig. 7). The

minor scatter seen in the microhardness contours may be a result of the natural scatter in microhardness

measurements and minor compositional and microstructural variations between the two specimens. In contrast,

the contours of microhardness for 316 stainless steel reveal that the plastic zone size is considerably smaller

under dynamic indentation compared with the static indentation for similar loads. This is consistent with the

rate-sensitive nature of steel—that is, a higher yield stress at higher strain rates (Fig. 7).

The second observation is that the static yield stress at 8% strain for 316 stainless steel is around 750 MPa and

that of aluminum is close to 500 MPa. Correspondingly, the plastic volume size in steel under static indentation

is significantly smaller compared with that of aluminum. A similar result also is seen for dynamic loads where

the effect is further enhanced due to an increase in yield strength in steel and relatively no change in aluminum.

To avoid single crystal effects associated with individual grains, this analysis should be used only when the

grain size is considerably smaller than the size of microindentation. For large-grained materials one can take

advantage of the micromechanisms of deformation (other than dislocation plasticity) to identify the extent of

residual plastic zone. For example, in the case of titanium, which undergoes mechanical twinning during plastic

deformation, the extent of twinned region beneath the indentation can be used to estimate the plastic zone size

(Ref 20). However, caution should be used in interpreting the results based on such microstructural features

because twinning is a preferred mode of plastic deformation at high strain rates in body-centered cubic (bcc)

and hexagonal close-packed (hcp) materials (Ref 26). Moreover, the orientation of individual grains with

respect to the local stress axis may also play a major role in inducing twins in a specific grain irrespective of its

distance from the indentation within the plastic zone. It also is important to be aware of the fact that plastic

strain also is accommodated by the dislocation activity and should be considered before any definite

conclusions can be drawn.

References cited in this section

1. D. Tabor, A Simple Theory of Static and Dynamic Hardness, Proc. R. Soc. (London), Vol 192A, 1948,

p 247–274

2. D. Tabor, The Hardness of Metals, Oxford University Press, London, 1951, p 1–173

17. C.H. Mok and J. Duffy, The Dynamic Stress-Strain Relation of Metals as Determined from Impact

Tests with Hard Ball, Int. J. Mech. Sci., Vol 7, 1965, p 355–371

20. B.J. Koeppell and G. Subhash, Characteristics of Residual Plastic Zone under Static and Dynamic

Indentations, Wear, Vol 224, 1999, p 56–67

24. B.J. Koeppel, “Dynamic Indentation Hardness of Materials,” Ph.D. dissertation, Michigan

Technological University, Houghton, MI, 1997

25. “Standard Test Method for Microhardness of Materials,” E 384–89, Annual Book of ASTM Standards,

Vol 03.01, ASTM, 1996

26. G.T. Gray III, Deformation Substructures Induced by High Strain Rate Deformation, Modeling the

Deformation of Crystalline Solids, T.C. Lowe, A.D. Rollett, P.S. Follansbee, and G.S. Daehn, Ed., The

Minerals, Metals, Materials Society, Warrendale, 1991, p 145–157

Dynamic Indentation Testing

G. Subhash, Michigan Technological University

Dynamic Indentation of Brittle Materials

Static indentation investigations were used extensively to analyze the fracture characteristics of brittle materials

(Ref 27, 28, 29, and 30). The approach also has been extended to model material-removal mechanisms during

grinding and sliding wear of ceramics (Ref 31, 32). In order to develop a representative model of material

removal during machining of brittle materials, the interaction of an abrasive grit with the workpiece has been

viewed as an indentation event where the indenter is attempting to penetrate the workpiece surface in the

normal direction, while being dragged in the lateral direction. Such a premise forms the basis for the

“indentation fracture” models for machining of brittle materials. During static Vickers indentation studies, it

was noted that penny-shaped median cracks develop during loading of the indenter, and lateral cracks parallel

to the surface develop during unloading of the indenter. In a surface-grinding operation, the lateral cracks assist

in chip formation and material removal, whereas median cracks leave residual damage in a workpiece. The role

of these cracks is reversed in a dicing operation (i.e., median cracks assist material separation and lateral cracks

induce surface damage). These model studies were typically performed using static indentations where the rate

effects are not sufficiently captured as described previously. Therefore, a technique for performing dynamic

Vickers indentations is of significant practical value for better characterizing the indentation fracture behavior

of brittle materials at similar strain rates.

Static and dynamic Vickers indentation hardness have been compared for six commercially available brittle

materials: Pyrex (Corning, Inc., Corning, NY) (borosilicate) glass, sintered alumina (Al

), hot pressed pure

aluminum nitride (AlN), 3% yttria-doped AlN (Y

-AlN), maximum-strength-grade magnesia, partially

stabilized zirconia (MgO-PSZ), and yttria tetragonal zirconia polycrystal (Y

-TZP or Y-TZP) (as described

further in Ref 22). A plot of indentation load (P) versus the square of the mean indentation diagonal (d

) is

plotted for all the brittle materials in Fig. 11. A regression line was fit through the static and dynamic data

separately. Note that, similar to metals, the dynamic indentation hardness measurements on brittle materials

were consistently greater than the static hardness measurements, and there seems to be no apparent dependence

of hardness on the indentation load in the range of loads used in this investigation. In the case of AlN, notice

that both the pure and doped AlN had essentially the same static hardness of 11.45 GPa. However, the pure AlN

revealed a 19% increase in the dynamic hardness over the static hardness compared with 8% in the doped AlN.

This may suggest that the addition of the yttria dopant in AlN decreased the rate sensitivity by half. The

commercially sintered alumina exhibited a 12% increase in the dynamic hardness over its static hardness. The

static Vickers hardness for this commercial-grade alumina is around 9.54 GPa, which is considerably lower

than that for a dense and pure alumina, which typically has hardness in the range of 19 to 26 GPa (Ref 33). The

lower hardness of the commercial alumina is attributed to extensive porosity and impurities present in the

material. Similarly, data for zirconia ceramics revealed that there is an increase of 9.0% for MgO-PSZ and a

12% increase for Y-TZP in their dynamic hardness.

Fig. 11 Plots of load versus square of the mean indentation diagonal for brittle materials

The current results on brittle materials (i.e., increase in hardness under dynamic loading compared with that of

static loading) is consistent with the previous results on glass by Fairbanks and others (Ref 34). The hardness

results also are supported by the observed rate-dependent uniaxial strength of structural ceramics where an

increase in fracture strength with increase in loading rate has been observed in Pyrex glass (Ref 35), alumina

(Ref 36), zirconia ceramics (Ref 37, 38), and aluminum nitride ceramics (Ref 9). However, for ceramics, the

Tabor relationship between hardness and fracture strength cannot be established because of absence of

significant plastic strain and the resulting early onset of unstable fracture. Lankford and others (Ref 36)

rationalized the reasons for the nonexistence of Tabor's relationship in ceramics and concluded that, even if

plasticity initiates in ceramics at high confining stresses, the accompanying stress concentration will initiate

microcracking simultaneously and cause catastrophic fracture well before a stress magnitude of H/3 is reached.

Induced Crack Morphology. Typical crack systems induced in brittle materials due to an indentation by a rigid

indenter have been summarized by Cook and Pharr (Ref 27). Of specific interest are radial and median cracks

because these crack systems leave a surface trace on the specimen and can be easily measured for quantification

of damage and fracture toughness calculations. Figure 12 illustrates the effect of loading rate on static and

dynamic indentations in zirconia ceramics. It is clear from the micrographs that the median crack lengths are

considerably larger during static indentations compared with the dynamic indentations at similar load levels.

Fig. 12 Micrographs revealing the extent of induced median cracks in MgO-PSZ under (a) static and (b)

dynamic indentations

A plot of half median crack length, c, versus the half indentation diagonal, a, is presented in Fig. 13 for Pyrex

glass and MgO-PSZ. The inset in this figure gives a pictorial representation of c and a. Similar plots for AlN

and Al

revealed no significant differences in the induced crack sizes between the static and dynamic

indentations (Ref 22). This is because only a limited number of specimens for each ceramic were tested, and the

data did not exhibit any specific trends in the extent of damage with loading rate. From Fig. 13, it can be

noticed that in the case of Pyrex glass, the median crack size induced under dynamic loading is consistently

greater than in the static loading. This is contrary to the observed behavior in zirconia ceramics where the

median crack sizes are significantly smaller under dynamic loads compared with the static loads. This

difference has been attributed to transformation toughening in these ceramics (Ref 39). Under dynamic loading,

the zirconia ceramics exhibit higher yield strength and large inelastic strains close to 2% (Ref 37, 38). Such

large inelastic strains can effectively absorb the imposed dynamic loads and result in the reduced cracking and

enhanced fracture toughness.

Fig. 13 Plots of half median crack length versus half indentation diagonal for (a) Pyrex glass and (b)

MgO-PSZ under static and dynamic indentations

It is interesting to see that the trends in hardness are similar for Pyrex glass and structural ceramics, but the

extent of induced damage in Pyrex glass is contrary to that observed in zirconia ceramics. The fracture behavior

of glasses has been viewed as a representative behavior in brittle ceramics (Ref 27, 29, 30, and 32). Although

the fracture patterns may be similar in glasses and ceramics under static loading, the current study reveals that

the rate effects are significantly different in glasses compared with those in structural ceramics. Similar studies

in glasslike materials (such as ZnS) also confirm these observations (i.e., an increase in hardness as well as

induced damage—or decrease in fracture toughness—under impact loading compared with static loading) (Ref

13). This implies that the use of static models based on the observations on static fracture behavior of glasses

may not be appropriate when modeling the material-removal rates of structural ceramics under high-velocity

grinding and sliding conditions. These results also support the observations of Meng and Ludema (Ref 12) on

erosion model predictions discussed previously. One of the reasons for such contrasting behavior in glasses and

structural ceramics under static and dynamic loads is that glasses are amorphous in structure whereas ceramics

are polycrystalline materials with microstructural features such as grain boundaries, second phases, impurities,

voids, and triple junction, which can promote crack deflection and contribute to radically different crack growth

characteristics and fracture toughness. These inhomogeneities that form during processing have also been found

to be responsible for early fracture as well as the rate-sensitive nature of failure in brittle materials (Ref 6, 40).

Several empirical models for fracture-toughness estimation based on the indentation hardness and the induced

crack sizes have been proposed in the literature. Recently, Ponton and Rawlings (Ref 41, 42) have summarized

these equations and provided standardized indentation toughness equations for several classes of ceramics.

References cited in this section

6. J. Lankford, Mechanisms Responsible for Strain-Rate Dependent Compressive Strength in Ceramic

Materials, J. Am. Ceram. Soc., Vol 64, 1981, p 25–33

9. G. Subhash and G. Ravichandran, Mechanical Behavior of Hot-Pressed Aluminum Nitride under

Uniaxial Compression, J. Mater. Sci., Vol 33, 1997, p 1933–1939

12. H.C. Meng and K.C. Ludema, Wear Models and Predictive Equations: Their Form and Content, Wear,

Vol 181, 1995, p 443–457

13. D.B. Marshall, A.G. Evans, and Z. Nisenholz, Measurement of Dynamic Hardness by Controlled Sharp-

Projectile Impact, J. Am. Ceram. Soc., Vol 66 (No. 8), 1983, p 580–585

22. R.J. Anton and G. Subhash, Dynamic Vickers Indentation of Brittle Materials, Wear, in press

27. R.F. Cook and G.M. Pharr, Direct Observation and Analysis of Indentation Cracking in Glasses and

Ceramics, J. Am. Ceram. Soc., Vol 73 (No. 4), 1990, p 787–817

28. B.R. Lawn and A.G. Evans, Elastic-Plastic Indentation Damage in Ceramics: the Median/ Radial Crack

System, J. Am. Ceram. Soc., Vol 63 (No. 9/10), 1980, p 574–581

29. S.S. Chiang, D.B. Marshall, and A.G. Evans, The Response of Solids to Elastic/Plastic Indentation: (a)

Stresses and Residual Stresses and (b) Fracture Initiation, J. Appl. Phys., Vol 53, 1982, p 298–317

30. D.B. Marshall, B.R. Lawn, and A.G. Evans, Elastic-Plastic Indentation Damage in Ceramics: the Lateral

Crack System, J. Am. Ceram. Soc., Vol 65 (No. 11), 1982, p 561–566

31. A.G. Evans and D.B. Marshall, Wear Mechanisms in Ceramics, Fundamentals of Friction and Wear of

Materials, D.A. Rigney, Ed., American Society for Metals, 1981, p 439–450

32. B.R. Lawn, Fracture of Brittle Solids, Cambridge University Press, 1993, p 249–304

33. M.W. Barsoum, Fundamentals of Ceramics, McGraw-Hill, 1997, p 401

34. C.J. Fairbanks, R.S. Polvani, S.M. Wiederhorn, B.J. Hockey, and B.R. Lawn, Rate Effects in Hardness,

J. Mater. Sci. Lett., Vol 1, 1982, p 391–393

35. J.E. Loukus, G. Subhash, and A. Chandra, “Observations on High Strain Rate Single Grit Scratching of

Brittle Materials,” presented at NSF Grantees Conference (Vancouver, British Columbia), 4–7 Jan 2000

36. J. Lankford, W.W. Predebon, J.M. Staehler, G. Subhash, B.J. Pletka, and C.E. Anderson, The Role of

Plasticity as Limiting Factor in the Compressive Failure of High Strength Ceramics, Mech. Mater., Vol

29, 1998, p 205–218

37. G. Subhash and S. Nemat-Nasser, Dynamic Stress-Induced Transformation and Texture Formation in

Uniaxial Compression of Zirconia Ceramics, J. Am. Ceram. Soc., Vol 76 (No. 1), 1993, p 153–165

38. G. Subhash and S. Nemat-Nasser, Uniaxial Stress Behavior of Y-TZP, J. Mater. Sci., Vol 25, 1993, p

5949–5952

39. D.J. Green, R.H.J. Hannink, and M.V. Swain, Transformation Toughening of Ceramics, CRC Press

Inc., 1989, p 5–93

40. G. Ravichandran and G. Subhash, A Micro Mechanical Model for High Strain Rate Behavior of

Ceramics, Int. J. Solids Struct., Vol 32 (No. 17/18), 1995, p 2627–2650

41. C.B. Ponton and R.D. Rawlings, Vickers Indentation Fracture Test, Part 1: Review of Literature and

Formulation of Standardised Indentation Toughness Equations, Mater. Sci. and Technol., Vol 5, 1989, p

865–960

42. C.B. Ponton and R.D. Rawlings, Vickers Indentation Fracture Test, Part 2: Application and Critical

Evaluation of Standardised Indentation Toughness Equations, Mater. Sci. and Technol., Vol 5, 1989, p

961–976

Dynamic Indentation Testing

G. Subhash, Michigan Technological University

Acknowledgments

This work was supported by the National Science Foundation under Grant DMI 9610545 and NASA/Michigan

Space Grant Consortium.

Dynamic Indentation Testing

G. Subhash, Michigan Technological University

References

1. D. Tabor, A Simple Theory of Static and Dynamic Hardness, Proc. R. Soc. (London), Vol 192A, 1948,

p 247–274

2. D. Tabor, The Hardness of Metals, Oxford University Press, London, 1951, p 1–173

3. H.T. Angus, The Significance of Hardness, Wear, Vol 54, 1979, p 33–78

4. M.A. Meyers, Dynamic Behavior of Materials, John Wiley & Sons, Inc., 1994, p 323–563

5. G. Subhash, The Constitutive Behavior of Refractory Metals as a Function of Strain Rate, JOM, Vol 47

(No. 5), 1995, p 55–58

6. J. Lankford, Mechanisms Responsible for Strain-Rate Dependent Compressive Strength in Ceramic

Materials, J. Am. Ceram. Soc., Vol 64, 1981, p 25–33

7. J. Lankford and C.R. Blanchard, Fragmentation of Brittle Materials at High Rates of Loading, J. Mater.

Sci., Vol 26, 1991, p 3067–3072

8. H.D. Espinosa, G. Raiser, R.J. Clifton, and M. Ortiz, Experimental Observations and Numerical

Modeling of Inelasticity in Dynamically Loaded Ceramics, J. Hard Mater., 1992, Vol 3 (No. 3–4), p

285–295

9. G. Subhash and G. Ravichandran, Mechanical Behavior of Hot-Pressed Aluminum Nitride under

Uniaxial Compression, J. Mater. Sci., Vol 33, 1997, p 1933–1939

10. S. Suresh, T. Nakamura, Y. Yeshurun, K.H. Yang, and J. Duffy, Tensile Fracture Toughness of Ceramic

Materials: Effects of Dynamic Loading and Elevated Temperatures, J. Am. Ceram. Soc., Vol 73 (No. 8),

1990, p 2457–2480

11. K.H. Yang and A.S. Kobayashi, A Hybrid Procedure for Dynamic Characterization of Ceramics at

Elevated Temperatures, Proc. Conf. Hostile Environments and High Temperature Measurements,

Society of Experimental Mechanics, 1989, p 41–44

12. H.C. Meng and K.C. Ludema, Wear Models and Predictive Equations: Their Form and Content, Wear,

Vol 181, 1995, p 443–457

13. D.B. Marshall, A.G. Evans, and Z. Nisenholz, Measurement of Dynamic Hardness by Controlled Sharp-

Projectile Impact, J. Am. Ceram. Soc., Vol 66 (No. 8), 1983, p 580–585

14. G. Sundararajan and P.G. Shewmon, The Use of Dynamic Impact Experiments in the Determination of

the Strain Rate Sensitivity of Metals and Alloys, Acta Metall., Vol 31, 1983, p 101–109

15. Y. Tirupataiah and G. Sundararajan, A Dynamic Indentation Technique for the Characterization of the

High Strain Rate Plastic Flow Behavior of Ductile Metals and Alloys, J. Mech. Phys. Solids, Vol 39,

1991, p 243–271

16. J.P. Nobre, A.M. Dias, and R. Gras, Resistance of Ductile Steel Surface to Spherical Normal Impact

Indentation: Use of Pendulum Machine, Wear, Vol 211, 1997, p 226–236

17. C.H. Mok and J. Duffy, The Dynamic Stress-Strain Relation of Metals as Determined from Impact

Tests with Hard Ball, Int. J. Mech. Sci., Vol 7, 1965, p 355–371

18. “Standard Test Method for Equotip Hardness Testing of Steel Products,” A 956–96, Annual Book of

ASTM Standards, ASTM, Vol 01.05, 1997

19. S. Nemat-Nasser, J.B. Isaacs, and J.E. Starrett, Hopkinson Techniques for Dynamic Recovery

Experiments, Proc. R. Soc. (London) A, Vol 435, 1991, p 371–391

20. B.J. Koeppell and G. Subhash, Characteristics of Residual Plastic Zone under Static and Dynamic

Indentations, Wear, Vol 224, 1999, p 56–67

21. G. Subhash, B.J. Koeppel, and A. Chandra, Dynamic Indentation Hardness and Rate Sensitivity in

Metals, J. Eng. Mater. Technol. (Trans. ASME), Vol 121, 1999, p 257–263

22. R.J. Anton and G. Subhash, Dynamic Vickers Indentation of Brittle Materials, Wear, in press

23. “Standard Test Method for Vickers Hardness of Metallic Materials,” E 92–82, Annual Book of ASTM

Standards, Vol 03.01, ASTM, 1996