Indentation load-displacement curves

Figure 7.32 Typical indentation load-displacement curves for pristine PU and its two types of PU nanocomposite thin films with different clay concentrations. Reproduced from Ref. [43] with permission.

A Berkovich diamond tip with a total included angle of 142.3° and a radius of around 150 nm was used for the nanoindentation measurements [1-2]. Indentation load-displacement curves were obtained by applying loads ranging from 1 pN to 1 mN. The hardness and reduced elastic modulus of the tribofilms were determined with Oliver s method [35,36], where fused silica with a Young s modulus of 69.7 GPa was used as a standard sample for tip-shape calibration to determine the function of the contact area with respect to the contact depth in a range of 1.5-50 nm. Figure 9.5 shows indentation load-displacement curves obtained for the MoDTC/ZDDP and ZDDP tribofilms at a maximum load of 600 pN and in situ AFM images of the residual indent. A plastic pileup was clearly observed around the indent on both the MoDTC/ZDDP and ZDDP tribofilms. 

FIGURE 9.5 Indentation load-displacement curves of the MoDTC/ZDDP and ZDDP tribo-fibns at a maximum load of 600 pN and in situ AFM images of the residual indent. No significant differences in hardness and modulus between the MoDTC/ZDDP and ZDDP tribofilms were observed under this loading condition. 

Using instrumented microhardness testing machines, the indentation load-displacement curve can be obtained as shown in Fig. 8.5. They are analysed according to the equation ... 

Figure 15-5. Schematic representation of a typical indentation load-displacement curve (from Malzbender, 2002).

A more generally applicable method is based on the use of nano- or micro-indenters. The indenter load-displacement curve is recorded over both loading and unloading. By assuming that the contact pressure does not change in the presence of elastic residual stresses, equi-biaxial residual stresses can be determined from indentation tests for an elastic coating and substrate [73J. 

Malzbender J, de Witt G (2002) Indentation load-displacement curve, plastic deformation, and energy. J Mater Res 17 502—511... 

Malzbender J, de With G (2000) Energy dissipation, fracture toughness and the indentation load-displacement curve of coated materieds. Surf Coat Technol 135 60... 

The two mechanical properties measured most frequently using indentation techniques are the hardness, H, and the elastic modulus, E. A t5pical load-displacement curve of an elastic-plastic sample during and after indentation is presented in Fig. 30, which also serves to define some of the experimental quantities involved in the measurement. 

Nanoindentation hardness, H, is defined as the indentation load divided by the projected contact area of the indentation. From the load-displacement curve, hardness at the peak load can be determined as... 

In a typical indentation experiment the indenter is pressed onto the surface under investigation and the load is successively increased up to a certain maximum load. In the so-called compliance approach both load and indenter displacement are recorded and plotted as a load-displacement curve, the so-called compliance curve. If the experiment is exclusively run in the compressive load regime, the curve is also referred to as the load-penetration curve. Upon loading, elastic deformations occur succeeded by plastic ones. Upon releasing the imposed stress, elastic strain recovers immediately. 

Figure 2.35. Examples of indentation processes to determine surface hardness. Shown are (a) Vickers indentation on a SiC-BN composite, (b) atomic force microscope images of the nanoindentation of a silver nanowire, and (c) height profile and load-displacement curve for an indent on the nanowire. Reproduced with permission fromNanoLett. 2003, 3(11), 1495. Copyright 2003 American Chemical Society.

Fig. 6 (A) A representative load-displacement curve of an indentation made at 3mN peak indentation load and (B) the hardness and elastic modulus as a function of indentation contact depth for the AI74 gCoig 9Ni8.4 quasicrystal. (Li, X. Zhang, L. Gao, H. Micro/nanomechanical characterization of a single decagonal AlCoNi quasicrystal. J. Phys. D Appl. Phys. 2004, 37, 753-757.)...

An attractive higher-level framework within which to study plasticity during nanoindentation is provided by the dislocation dynamics methods described above. In particular, what makes such calculations especially attractive is the possibility of making a direct comparison between quantities observed experimentally and those computed on the basis of the nucleation and motion of dislocations. In particular, one can hope to evaluate the load-displacement curve as well as the size and shape of the plastic zone beneath the indenter, and possibly the distribution of dislocations of different character. While the... 

Typical load-displacement curves obtained from instrumented indentation experiments are shown in Figure 39.13b. Results are shown for silica E = 72 GPa, v = 0.2) and polystyrene (PS, E = 2 GPa, V = 0.4). The load-displacement curve for PDMS E = 1.5 MPa, v 0.5) involve forces that are too low to appear on the scale used in Figure 39.13b, due to the fact its elastic modulus is three orders of magnitude lower than polystyrene. 

Indentation load and stiffness (i.e., the slope of the load-displacement curve). Temperature and reference temperatures, respectively, of the (th layer the reference temperature is defined as that at which there is no thermal strain, typically the fabrication temperature of the layer. 

Once a specific event in the load-displacement curve has been associated with a particular phase transition, the pressure at which it occurs can be estimated by considering the elastoplastic behavior of the material under the indenter. For the point-force contact, the Sneddon s solution [39] to the problem of the penetration of an axisymmetric punch into an elastic half space predicts the following relation between the applied load P and the indenter displacement A ... 

Fig. 7. (a) Load-displacement curve of a typical elastoplastic material and (b) the schematic of the indentation model of Oliver and Pharr [40]. S—contact stiffness he— contact depth /imax—indenter displacement at peak load hf—plastic deformation after load removal hs—displacement of the surface at the perimeter of the contact. 

Nanoindentation is a powerful technique because the shape of the load-displacement curve can be used to identify effects such as phase transformations, cracking, and film delamination dining indentation. It is also important in studying the mechanical properties of nanomaterials, such as carbon nanotubes. There is reference now to a picoindenter, which is a combination of a nanoindenter and an atomic force microscope (AFM). 

FIGURE 8.12 (a) Load-displacement curves from indentation on faces (0 0 1) and (1 0 0) of aspirin carried out at loading rates of 5 mN/s and at similar depths. Pop-ins can be observed on both curves, indicated by the arrows, (b) Morphological sketch of aspirin drawn using SHAPE and scanning electron micrograph of a representative aspirin particle, (c) SEM image of an indent of aspirin (1 0 0) face. Source Adapted from Olusanmi et al. [79]. Reproduced with permission of Elsevier. 

A typical load-displacement curve is shown in Fig. 2. The loading portion of the curve results from both plastic and elastic deformation response of the contact, while the unloading portion of the curve is related to the elastic recovery of the contact. If the indenter geometry and materials properties are known, the modulus can be obtained by fitting the unloading curve to determine the contact stiffness at maximum load (i4, 17). In this case,... 

Nanoindentation experiments were performed using two different nanoindentation systems to make indents at peak loads from 100 pN to 500 mN. Hardness and Young s Modulus were extracted from the load-displacment curves using the method of Oliver and Pharr. All load displacement curves were corrected for thermal drift and the indenter area functions were carefully calibrated following the Oliver and Pharr approach using a fused silica standard sample prior to testing the coated samples. 

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