indentation size effect

{{short description|Property of materials at small scales}}

{{Technical|date=November 2019}}

File:Indentation Size Effect Fake Data.svg

The indentation size effect (ISE) is the observation that hardness tends to increase as the indent size decreases at small scales.{{Cite journal|last1=Pharr|first1=George M.|last2=Herbert|first2=Erik G.|last3=Gao|first3=Yanfei|date=June 2010|title=The Indentation Size Effect: A Critical Examination of Experimental Observations and Mechanistic Interpretations|journal=Annual Review of Materials Research|volume=40|issue=1|pages=271–292|doi=10.1146/annurev-matsci-070909-104456|bibcode=2010AnRMS..40..271P|issn=1531-7331}}{{Citation|last=Sargent|first=PM|chapter=Use of the Indentation Size Effect on Microhardness for Materials Characterization|pages=160–160–15|publisher=ASTM International|isbn=978-0-8031-0441-9|doi=10.1520/stp32956s|title=Microindentation Techniques in Materials Science and Engineering|year=1985}} When an indent (any small mark, but usually made with a special tool) is created during material testing, the hardness of the material is not constant. At the small scale, materials will actually be harder than at the macro-scale. For the conventional indentation size effect, the smaller the indentation, the larger the difference in hardness. The effect has been seen through nanoindentation and microindentation measurements at varying depths. Dislocations increase material hardness by increasing flow stress through dislocation blocking mechanisms.{{Cite book|title=The science and engineering of materials|last=Askeland|first=Donald R.|publisher=Cengage Learning|others=Wright, Wendelin J.|year=2016|isbn=9781305076761|edition=Seventh|location=Boston, MA|pages=111–118|oclc=903959750}}{{Clarify|reason=What is a dislocation blocking mechanism|date=November 2019}} Materials contain statistically stored dislocations (SSD) which are created by homogeneous strain and are dependent upon the material and processing conditions.{{Cite journal|last1=Nix|first1=William D.|last2=Gao|first2=Huajian|date=October 1997|title=Indentation size effects in crystalline materials: A law for strain gradient plasticity|journal=Journal of the Mechanics and Physics of Solids|volume=46|issue=3|pages=411–425|doi=10.1016/s0022-5096(97)00086-0|issn=0022-5096|doi-access=free}} Geometrically necessary dislocations (GND) on the other hand are formed, in addition to the dislocations statistically present, to maintain continuity within the material.

These additional geometrically necessary dislocations (GND) further increase the flow stress in the material and therefore the measured hardness. Theory suggests that plastic flow is impacted by both strain and the size of the strain gradient experienced in the material.{{Cite book|title=Introduction to contact mechanics|last=Fischer-Cripps, Anthony C.|date=2000|publisher=Springer|isbn=0387989145|location=New York|oclc=41991465}}{{Cite book|last1=Wu|first1=Theodore|title=Advances in Applied Mechanics|last2=Hutchinson|first2=John|last3=Fleck|first3=N|publisher=Elsevier Science|year=1997|isbn=9780080564111|volume=33|location=|pages=296|chapter=Strain Gradient Plasticity}} Smaller indents have higher strain gradients relative to the size of the plastic zone and therefore have a higher measured hardness in some materials.

File:Geometrical_Necessary_Dislocations_during_Indent.svg

For practical purposes this effect means that hardness in the low micro and nano regimes cannot be directly compared if measured using different loads. However, the benefit of this effect is that it can be used to measure the effects of strain gradients on plasticity. Several new plasticity models have been developed using data from indentation size effect studies, which can be applied to high strain gradient situations such as thin films.{{Cite journal|last1=Voyiadjis|first1=George|last2=Yaghoobi|first2=Mohammadreza|date=2017-10-23|title=Review of Nanoindentation Size Effect: Experiments and Atomistic Simulation|journal=Crystals|volume=7|issue=10|pages=321|doi=10.3390/cryst7100321|issn=2073-4352|doi-access=free}}