ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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of the evaluated material and an indenter geometry (Ref 188). With the blunt indenters, such as large radii

spheres, cracking initiation would normally precede plasticity onset (Ref 187). In contrast, sharp pyramidal or

conical indenters would initiate plastic deformation prior to cracking (Ref 187). Once yielding takes place

during an indentation test, residual plastic deformation exists after load removal. Accommodation of this

plastically deformed volume by surrounding elastic material results in a residual stress field. These stresses act

to open an indentation crack in a similar way as a center-loaded point force. The stress intensity in this case can

be approximated with (Ref 189, 190):

residual

= χ P/c

3/2

(Eq 6)

where P is an indentation load, c is crack length, and χ is a characteristic constant for a given combination of

material and indenter. It should be noted that with the absence of an additional external load, an indentation-

induced crack is stable as the stress intensity decreases with increasing crack length. With the applied external

load, the total stress intensity becomes (Ref 189, 191):

(Eq 7)

where ψ is a geometrical factor, and σ

is applied stress.

Indentation-Induced Adhesive Fracture. For ductile films on brittle substrates, indentation-induced plastic

deformation in a film provides a driving force for delamination (Ref 192, 193, and 194). With brittle films on

ductile substrates, the delamination driving force more often comes from plastic deformation of the substrate

(Ref 195, 196).

Continuous Scratch. Scratches are produced by traversing a surface at constant or continuously increasing

vertical displacement. While the pattern of indentation cracking is defined by elastic-plastic properties of an

indented material, indenter geometry, and load range, scratch-induced cracking depends on all of the above

parameters plus several others. These factors include scratch velocity, indenter/surface adhesion, and a friction

coefficient. With much more complicated stress/strain state and possible involvement of material time-

dependent behavior, mechanisms of scratch-induced deformation and cracking are not well understood yet.

Given the complexity of the problem, quantitative information gained from a scratch test should be interpreted

very cautiously. To compare two materials, it is preferable to test them both using the same loading conditions.

These would include indenter geometry, loading, and horizontal drive velocity. Similarly, such evaluations

would require testing of both environmentally exposed and nonexposed samples under the same loading

conditions. Theoretical analyses for scratch-induced cohesive and adhesive fracture may be obtained from Ref

197, 198, 199, 200, and 201, respectively.

Indentation or scratch “precracking” followed by application of an external load under exposure to an

environment may be used. Possible geometries include a disk (Ref 202, 203) or cantilever beam specimen (Ref

204). Most commonly used is four-point bending test (Ref 205). Attention should be paid to possible effects of

elastic anisotropy and asymmetry of indentation-induced plastic deformation and fracture (Ref 190). Crack

extension can be monitored with optical microscopy (Ref 206). Crack arrest marking can be generated on the

fracture surfaces by temporary unloading during subcritical crack growth (Ref 207).

Crack extension is driven by a combined action of applied load and residual indentation induced tensile stresses

as given by Eq 7. Analysis of this equation implies stable crack growth providing K ≥ K

and dK/dc < 0.

Instability will occur as dK/dc = 0 and K = K

. From these instability conditions, fracture strength, and critical

crack length under inert conditions may be obtained:

(Eq 8)

(Eq 9)

Fatigue strength of an indented specimen may be expressed by the following function of stressing rate (Ref

208):

= (β′

)

1/(n′ + 1)

(Eq 10)

where n′ = 0.75N + 0.5 and

with N and v* being parameters used in Eq 2.

Values of n′ and β′ may be determined from the slope and the intercept of the dynamic fatigue curve,

respectively. Examples of dynamic curves for soda-lime glass in various environments are shown in Fig. 37

(Ref 209). Here, low susceptibility to environmental crack growth in silicon and motor oils is evident from

large values of n′ exponents.

Fig. 37 Dynamic fatigue results of indented soda-lime glass specimens. Indent load, 19.6 N. Error bars

represent ±1.0 standard deviation. Source: Ref 209

Annealing or surface layer removal may be utilized to remove residual stresses prior to testing. Neglecting

residual stress would result in a significant strength underestimate as shown in Fig. 38 (Ref 210). This in turn

would give an overestimate of environmental susceptibility as determined via crack growth kinetics parameters

from Eq 10.

Fig. 38 Dynamic fatigue response for indented soda-lime glass disks broken in water. Vickers indent

load, 5 N. Source: Ref 210

It should also be stressed that in general, parameters χ and ψ are not constant but may be affected by changing

crack geometry and interference between different crack systems (Ref 211). An example of changes in these

parameters during different crack evolution stages is shown in Fig. 39.

Fig. 39 Complete trends of the shape factor (ψ) and of the residual stress factor (χ) as a function of the

crack size (c). Source: Ref 211

Contact Mechanics Testing under or Following Exposure to an Environment. Environmental effects may be

assessed by measuring an extent of indentation or scratch-induced cracking with and without an environment. A

driving force here would be indentation-induced residual stresses as given by Eq 6. Based on the dynamic

fatigue data, an analytical expression for a time dependent crack extent, c(t) may be obtained (Ref 210). Fatigue

parameters may be determined from plotting c versus t in double-log coordinates. However, values of crack

growth exponents obtained from residual indentation stress driven slow crack growth were significantly

different from these obtained in the same environments with dynamic fatigue (Ref 210). Moreover,

postindentation crack growth in motor oil exhibited a significant environmental susceptibility in contrast to

static fatigue testing. It was suggested that presence of the limited amount of water present in the oil would only

be effective in the small crack regime corresponding to a residual stress driven crack extension. Whatever the

reason, for the observed discrepancy design considerations would require using testing conditions most closely

approximating service conditions. Special considerations required for cohesive and adhesive fracture in thin

films are mentioned below.

Environmentally Assisted Crack Growth in Thin Films. Sensitivity to environmentally assisted cracking for

small volumes often differs from that for bulk materials. Possible reasons include microstructural differences,

one of the most important being nanoscale grain sizes for submicron thick films. With a nanoscale grain size,

the fraction of grain-boundary material increases dramatically. With grain boundaries being the preferred

pathway for diffusion, diffusivity increases with the grain size reduced to the nanoscale. Also, with the grain

boundaries being more prone to preferential dissolution, susceptibility to environmental attack is enhanced for

nanocrystalline materials. In addition, increasing fraction of grain boundaries results in elevated internal

stresses in a film. These stresses combined with the ones produced by substrate constraint may affect resistance

to crack propagation. Similarly, when indentation depth scales with the depth of any surface affected layer,

stresses in this layer may affect indentation-induced crack growth. Tensile stresses would favor indentation

crack propagation as opposed to compressive ones. In addition, stress relaxation could be promoted by either

sign residual stress at higher temperatures. While the initial residual stress would tend to promote slow crack

growth, any relaxation with time would diminish the driving force.

Environmentally Affected Thin-Film Adhesion. Contact mechanics methods provide the following advantages

for thin-film adhesion testing:

• There is no possibility for interfacial property changes.

• Very small amount of material is required for testing.

• Testing can be carried under temperature, potentiostatic, or environmental control.

• Very simple sample preparation and testing procedure.

Indentation-induced blister for charged and noncharged samples are shown in Fig. 40 (Ref 182). Here, the

larger size of an indentation-induced delamination for hydrogen-charged sample indicates hydrogen charging

induced adhesion degradation.

Fig. 40 Indentation-induced delaminations in 500 nm titanium-copper film. (a) Noncharged sample. (b)

Hydrogen-charged sample. Source: Ref 182

References cited in this section

182. Y. Katz, N.I. Tymiak, and W.W. Gerberich, Nano-mechanical Probes as New Approaches to

Hydrogen/Deformation Interaction Studies, An invited paper for Recent Advances in the Engineering

Aspects of Hydrogen Embrittlement of the Engineering Fracture Mechanics, 1999

187. P. Ostojic and R. McPherson, A Review of Indentation Fracture Theory: Its Development,

Principles and Limitations, Int. J. Fract., Vol 33, 1987, p 297–312

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

and Ceramics, J. Am. Ceram. Soc., Vol 73, 1990, p 787–817

189. G.R. Anstis, P. Chantikul, B.R. Lawn, and D.B. Marshall, A Critical Evaluation of Indentation

Techniques for Measuring Fracture Toughness, J. Am. Ceram. Soc., Vol 64, 1981, p 533–538

190. D.B. Marshall and R.B. Lawn, Residual Stress Effect in Sharp Contact Cracking, J. Mater. Sci.,

Vol 14, 1979, p 2001–2012

191. D.B. Marshall, R.B. Lawn, and P. Chantikul, Residual Stress Effects in Sharp Contact Cracking.

Part 2. Strength Degradation, J. Mater. Sci., Vol 14, 1979, p 2225–2235

192. D.B. Marshal and A.G. Evans, Measurement of Adherence of Residually Stressed Thin Film by

Indentation. I. Mechanics of Interface Delamination, J. Appl. Phys., Vol 56, 1984, p 2632–2638

193. M. J. Matthewson, Axi-Symmetric Contact on Thin Compliant Coatings, J. Mech. Phys. Solids,

Vol 29, 1981, p 89–113

194. L.G. Rosenfeld, J.E. Ritter, T.J. Larner, and M.R. Lin, Use of the Microindentation Technique

for Determining Interfacial Fracture Energy, J. Appl. Phys., Vol 67, 1990, p 3291–3296

195. J.J. Vlassak, M.D. Drory, and W.D. Nix, A Simple Technique for Measuring the Adhesion of

Brittle Films to Ductile Substrates with Applications to Diamond-Coated Titanium, J. Mater. Res., Vol

12, 1997, p 1990–1910

196. M.D. Drory and J.W. Hutchinson, Measurement of Brittle-Film Adhesion on a Ductile Substrate

by Indentation, Proc. Roy. Soc. (London) A, 1996, p 2319–2341

197. J.W. Hoehn, S.K. Venkataraman, H. Huang, and W.W. Gerberich, Micromechanical Test

Applied to NiAl, Mater. Sci. Eng. A, Vol A192/193, 1995, p 301–308

198. P.R. Chalker, S.J. Bull, and D.S. Rickerby, A Review of the Methods for the Evaluation of

Coating-Substrate Adhesion, Mater. Sci. Eng. A, Vol A140, 1991, p 583–592

199. S.V. Hainsworth, S.J. Bull, and T.F. Page, Scratch Deformation Response of Thin CNx Coatings

at Ultra-Low Loads, Fundamentals of Nanoindentation and Nanotribology, Symposium. Materials

Research Society, 1998, p 433–438

200. T.W. Wu, Microscratch and Load Relaxation Tests for Ultra-Thin Films, J. Mater. Res., Vol 6,

1991, p 407–426

201. S. Venkataraman, D.L. Kohlstedt, and W.W. Gerberich, Continuous Microscratch Measurements

of the Practical and True Works of Adhesion for Metal/Ceramic Systems, J. Mater. Res., Vol 11, 1996,

p 3133–3145

202. D.B. Marshall and B.R. Lawn, Flaw Characteristics in Dynamic Fatigue: The Influence of

Residual Contact Stresses, J. Am. Ceram. Soc., Vol 63, 1980, p 532–536

203. J. Zhang and A.J. Ardell, Measurement of the Fracture Toughness of Ceramic Materials Using a

Miniaturized Disk-Bend Test, J. Am. Ceram. Soc., Vol 76, 1993, p 1340–1344

204. R.W. Rice, C.C Wu, and K.R. McKinney, Fracture and Fracture Toughness of Stoichiometric

MgAl

Crystals at Room Temperature, J. Mater. Sci., Vol 31, 1996, p 1353–1560

205. Y. Kimura, T. Yagasaki, and T. Kunio, On the Delayed Fracture Characteristics of Vickers

Indented Glass in Deionized Water, Eng. Fract. Mech., Vol 19, 1984, p 1025–1033

206. H. Matzke, Hertzian Indentation of Thorium Dioxide, ThO

, J. Mater. Sci., Vol 15, 1980, p 739–

746

207. P.J. Dwivedi and D.J. Green, Determination of Subcritical Crack Growth Parameters by in Situ

Observation of Indentation Cracks, J. Am. Ceram. Soc., Vol 78, 1995, p 2122–2128

208. E.R. Fuller, B.R. Lawn, and R.F. Cook, Theory of Fatigue for Brittle Flaws Originating from

Residual Stress Concentration, J. Am. Ceram. Soc., Vol 66, 1983, p 314–321

209. S.R. Choi and J.A. Salem, Slow Crack Growth of Indent Cracks in Glass with and without

Applied Stress, Mater. Sci. Eng. A, Vol A149, 1992, p 259–264

210. D.B. Marshall and B.R. Lawn, Flaw Characteristics in Dynamic Fatigue: The Influence of

Residual Contact Stresses, J. Am. Ceram. Soc., Vol 63, 1980, p 532–536

211. V.M. Sglavo and D.J. Green, The Sub-Critical Indentation Fracture Process in Soda-Lime-Silica

Glass, Eng. Fract. Mech., Vol 55, 1996, p 35–46

Evaluation of Environmentally Assisted Crack Growth

Y. Katz, N. Tymiak, and W.W. Gerberich, University of Minnesota

Scanning Probe Microscopy

Scanning probe microscopes (SPM) such as the scanning tunneling microscope (STM) (Ref 212), AFM (Ref

213, 214, 215), and their modifications provide imaging and quantitative evaluation of atomic level surface

features. One important feature is that atomic-scale resolution can be gained without an extensive sample

modification such as thinning and/or polishing. Thus, small-scale aspects of plastic deformation and fracture

can be observed without influence of sample preparation. Also, quantitative information can be obtained from

direct three-dimensional topography measurements. An advantage of SPM is evident when three-dimensional

strain (Ref 216) and stress (Ref 217) fields near a tip of a brittle crack can be obtained directly as compared to a

rather complicated procedure based on digitizing of SEM images (Ref 218). Another example could be

resolving nanoscale plasticity features associated with a brittle crack (Ref 216). Both STM and AFM can be

easily operated in a variety of environments (Ref 219, 220). While the STM cannot be utilized for insulators,

AFM works equally well on conducting, semiconducting, or insulating surfaces such as polymers and ceramics.

With the controlled potential applied to the metallic (Ref 221) or semiconductor (Ref 222) surface, various

solid/electrolyte interactions such as metal dissolution/electrodeposition or passive film evolution can be

visualized and evaluated quantitatively. Here, surface topography mapping provides an accurate spatial

distribution of material removal or deposition rates. Examples include localized dissolution enhanced by

indentation-induced plastic deformation (Ref 223) and grain-boundary sensitization (Ref 224, 225). In the

latter, selectively placed indents have been utilized to reveal preferential dissolution along chromium-depleted

near-boundary regions (Ref 225). With the alternating periods of loading and SPM observations, an insight into

crack initiation and growth can be gained. The above approach has been successively applied to initial stages of

environmentally assisted fatigue (Ref 226, 227). In the latter, number of cycles for crack initiation was

correlated to a damage parameter accounting for global plastic strain alongside with the corresponding local

plasticity characteristics. These include persistent slip band (PSB) spacings and heights as measured with the

SPM. Environmental effects on the fracture onset under increasing monotonic load can be evaluated from

nanoscratch testing combined with the AFM imaging as described in more detail in the preceding section.

Invention of loading devices operated in conjunction with the SPM (Ref 224, 228) enabled a continuous

monitoring of crack initiation and propagation. In situ observations of loaded cracks in vacuo and laboratory air

(Ref 224) show a clear environmental effect apparent from the sharpness of an air-exposed crack as opposed to

blunting occurring at a crack tip in vacuo. Additional advantages come from indentation combined with the

AFM pretest and posttest imaging of an indented area as detailed in the previous section.

References cited in this section

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Using Scanning Tunneling Microscopy, J. Vac. Sci. Technol., Vol B9, 1991, p 673–676

217. T. Kinoshita, Stress Singularity Near the Crack-Tip in Silicon Carbide: Investigation by Atomic

Force Microscopy, Acta Mater., Vol 46, 1998, p 3963–3974

218. K. Jakus, S. Michael, and J.E. Ritter, Measurement of Crack Tip Inelastic Deformations Using

Digital Image Correlation, Adv. Ceram. Mater., Vol 3, 1988, p 268–272

219. S. Manne, J. Massie, V.B. Elings, P.K. Hansma, and A.A. Gewirth, Electrochemistry on a Gold

Surface Observed with the Atomic Force Microscope, J. Vac. Sci. Technol. B, Vol 9, 1991, p 950–954

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R1–23

221. P. Mrozek, Y.-E. Sung, and A. Wieckowski, Silver Deposition on the Au(111) Electrode without

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222. S.-L. Yau, F.-R.F. Fan, and A.J. Bard, In situ STM Imaging of Silicon(111) in HF under

Potential Control, J. Electrochem. Soc., Vol 139, 1992, p 2825–2829

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224. K. Komai and K. Minoshima, Nanometric Visualization of Localized Damage by Scanning

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225. N.I. Tymiak, D.F. Bahr, J.C. Nelson, and W.W. Gerberich, “Micromechanical Probes of a

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on Welding of Stainless Steel Alloys (Indianapolis, IN), Sept 1997

226. G. Venkataraman, T.S. Sriram, M.E. Fine, and Y.W. Chung, STM and Surface Analytical Study

of the Effect of Environment on Fatigue Crack Initiation in Silver Single Crystals I, Surface Chemical

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227. P.G. Marsh, S.E. Harvey, M.D. Kriese, and W.W. Gerberich, Environmental Effects on Fatigue

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Evaluation of Environmentally Assisted Crack Growth

Y. Katz, N. Tymiak, and W.W. Gerberich, University of Minnesota

Acknowledgments

Portions of this article are adapted from the following:

• L. Raymond, Evaluation of Hydrogen Embrittlement, Corrosion, Vol 13, ASM Handbook, ASM

International, 1987, p 283–290

• P.L. Andresen, Corrosion Fatigue Testing, Fatigue and Fracture, Vol 19, ASM Handbook, ASM

International, 1996, p 193–209

• G. H. Koch, Stress-Corrosion Cracking and Hydrogen Embrittlement, Fatigue and Fracture, Vol 19,

ASM Handbook, ASM International, 1996, p 483–506

Evaluation of Environmentally Assisted Crack Growth

Y. Katz, N. Tymiak, and W.W. Gerberich, University of Minnesota

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