3 032 MECHANICAL BEHAVIOR OF MATERIALS FALL 2007 LABORATORY EXPERIMENT 3 Plastic deformation from the micro to nanoscale PreLab Questions 1 Name 2 ways in which instrumented indentation is different from uniaxial mechanical testing of materials 2 Explain the physical meaning of a material s hardness in words I Introduction There are several examples in materials engineering in which materials are available only in small volumes either because they result from new expensive and difficult processing techniques or because they are designed intentionally to be small in one dimension An example of the latter is a thin film or structural coating In such cases mechanical properties cannot be quantified easily through uniaxial force displacement testing of structures e g Laboratory Experiment 1 or stress strain responses of macroscale materials e g Laboratory Experiment 2 One alternative is mechanical testing based on three dimensional contact between the sample surface and a rigid probe of known geometry and mechanical properties In this experiment you will analyze the contact response of several classes of materials via the simple but widely used approach of microscale hardness testing as well as the more quantitative instrumented indentation testing at the nanoscale We analyze the data from such experiments using concepts from contact mechanics In hardness testing a probe such as a cone shaped diamond is pushed into a flat well polished sample surface to a specific maximum load held for a specified duration and then retracted from the surface Figure 1 Hardness Plastic deformation results in a mark indentation for Vickers indentation in the surface and square pyramid measurement of the size of that mark indenter geometry Ares is determined by measuring indicates the material hardness which is the indentation diagonals defined as Image removed due to copyright restrictions Please see H Pmax Ares 1 http www imagemet com images hardness2 Result jpg where Pmax is the maximum load and Ares is the projected 2 dimensional area of the indentation that is observed after unloading residual via optical microscopy As shown in Eq 1 hardness has units of N m2 but is not physically equivalent to stress because the measured projected area of the indentation is not the actual area normal to the applied load of the 3 dimensional indenter One of the early applications of hardness was as an approximate measure of the yield strength y of the material For materials that undergo plastic deformation primarily via slip e g metals for which dislocation motion requires shear stress it has been demonstrated empirically and by slip line theory that H 3 y 2 In instrumented indentation the experimental approach is quite similar but the load P and the depth of penetration h of the indenter are measured continuously during loading and unloading Fig 1 If Pmax 100 nN or hmax 100 nm this is termed nanoindentation but be aware that the term is often used in the literature even when the deformation actually exceeds this range The result is a load displacement response that is similar to that obtained in uniaxial mechanical testing but the loading is multiaxial and thus more complex to analyze in terms of uniaxial mechanical properties such as E and y Most importantly the geometry of the indenter dictates that there is a power law relationship between P and h even during elastic deformation unlike the linear relationship expected for uniaxial testing of a material in the elastic regime 3 032 MECHANICS OF MATERIALS fall 2007 2 LABORATORY 3 Hardness can also be calculated from these data according to Eq 1 but the advantage of this approach is that the actual projected contact area A can be computed from the P h response rather than measured for each experiment For the conical indenter used in this experiment A 24 5 hc 2 3 Images removed due to copyright restriction Please see http www nanoindentation cornell edu pictures schematic nanoindenter gif http www nanoindentation cornell edu pictures DoernerNix schematic 2 gif a b Figure 1 Instrumented indentation enables measurement of mechanical properties of small material volumes a Schematic of one type of indenter b Typical load displacement response where S unloading stiffness dP dh and hc is contact depth Images from http www nanoindentation cornell edu Er 2 S A hc where contact depth hc is given by a semiempirical equation that accounts for material sinking in around the perimeter of the indenter The elastic modulus E is inferred from the instantaneous response of the material upon unloading from Pmax 4 where S dP dh Pmax is the tangent to the unloading portion of the P h response and is also called stiffness S The area between the loading and unloading portions of the P h response directly quantifies the amount of work required to plastically deform the material Wp and therefore the yield strength y can be calculated as a function of Wp Note that instrumented micro and nanoindentation are used for a range of purposes other than mechanical property extraction including fracture toughness and residual stress determination in physically small samples e g enamel dentin junction of teeth as well as dislocation nucleation which requires high stresses and high displacement resolution II Objectives The objectives of this experiment are to 1 Conduct hardness tests on an amorphous ceramic glass 2 ductile metals an alloy brass and a pure metal copper 2 polymers low density polyethylene and ultrahigh molecular weight polyethylene and a heat treated metal for which the microstructure and mechanical properties vary as a function of distance from the surface case hardened steel 2 Conduct and analyze nanoindentation as a function of Pmax for two samples bulk pure copper and a thin film of pure copper on silicon Extract elastic modulus E and indentation hardness H from these data 3 Explore mechanical properties including elastic plastic and fracture behavior for this wide range of materials from the micro to nanoscale Understand how structure 3 032 MECHANICS OF MATERIALS fall 2007 3 LABORATORY 3 composition molecular weight and substrate constraint affect mechanical properties measured in this way 3 032 MECHANICS OF MATERIALS fall 2007 4 LABORATORY 3