Nanoindentation load-displacement curves

Nanoindentation load-displacement curves of Ge are not as characteristic as in Si. The only feature discussed in the literature is the formation of numerous small discontinuities ( pop-ins ) in the upper portion of the loading curve (Fig. 30a). As Ge is known to be veiy prone to radial cracking, it has been argued that the pop-ins occur as a result of the discontinuous propagation of radial cracks [13S]. Another explanation of loading discontinuities associated the pop-ins with the nucleation of dislocation slips [121]. 

Fig. 47. Typical nanoindentation load-displacement curve of SiC revealing displacement discontinuity in the loading curve and purely elastic behavior below the pop-in onset. Data from Reference [65].

Like the AFM, load-displacement curves from nanoindentation can also be used to measure tip-sample adhesion. However, because the force resolution of nanoindentation is typically of order tens to hundreds of nanoNewtons, such experiments... 

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... 

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.

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... 

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). 

Similarly, different types of loading and unloading approaches can be used to extract desired properties as a function of penetration depth (Gan et al., 1996 Gan and Ben-Nissan, 1997 Fischer-Cripps, 2002). The apphcation of nanoindentation as suggested by Field and Swain (1993, 1995) can also be used to determine coating adhesion and residual stress from the load at which delamination occurs (taken from the pop-in that corresponds to a plateau or discontinuity in the load—displacement curve). 

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. 

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. 

Conventionally, the compliance method proposed by Oliver and Pharr [153] has been used to determine the hardness (H) and elastic modulus ( ) by means of nanoindentation from the analysis of the load-displacement curve. In this method, the unloading segment of the curve is fitted to a power law function to obtain the contact depth and thus the contact area (A) at the peak load (Pmax) required to determine H H= A typical load-unload displacement curve for a... 

Fig. 2. Typical load vs. displacement curve for a nanoindentation in tooth enamel. The contact depth (Dp), area and stiffness (S) were all determined at the maximum load (P) by fitting a polynomial expression to the upper 70% of the unloading curve, and they were used to quantify hardness (H) and Young s modulus (E) for each nanoindentation according to standard routines [13]. 

Fig. 4.19 Schematic force — displacement curve obtained in a nanoindentation experiment. The tip is pressed into the sample with a load force F to a maximum displacement hmax. The tangent of the unloading curves at hmax represents the stiffness S. (Reprinted with permission from [44]. Copyright 2006. Elsevier)...

Fig. 30. (a) Load-displacement and (b) ACP vs relative contact depth curves for Ge obtained in cyclic nanoindentation at the loading/unloading rate of 1 mN/s. Arrows indicate the loading direction. After Reference [38]. 

FIGURE 8.5 Loading and unloading displacement curves during nanoindentation. 

A representative load/displacement nanoindentation curve for Sample 4 is shown in figure 6. Reduced modulus for Sample 3 and Sample 4 is estimated at 1.6 GPa, while the reduced modulus of Sample 1 and Sample 2 is estimated at 2.5 GPa. These results indicate that for the composite systems studied, the composition of the resin matrix is of greater importance in determining the nanomechanical properties of the composite than the manufacturing release technology. 

Figure 6. Nanoindentation load vs. displacement curve for Sample 4.

Nanoindentation was used to measure the local reduced modulus and hardness in composite samples. Measurements are based on a force curve generated as a stiff probe penetrates the material surface. A force curve plots the applied load to the probe with respect to displacement into the specimen, and information about modulus, hardness, elastic recovery, and plastic deformation is obtained. ... 

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