Load-indentation curves

Figure 17.4 Displacement-deflection curves and load-indentation curves theoreticaUy produced by the the DMT-M model (a), (b) and the JKR model (c) (d).

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.

Pellicle and tea-immersed pellicle were analyzed using nanoDMA (dynamic mechanical analysis) to see if the tannins had an effect on the viscoelasticity of the pellicle. NanoDMA is a technique used to study and characterize mechanical properties in viscoelastic materials. The method is an extension of nanoindentation testing [58, 59], An analysis of the nanoindentation load-depth curve gives the hardness (H) and reduced elastic modulus (E ), provided the area of contact, A, between the indenter tip and the sample is known [ 13]. By... 

Van Landigham et al. reviewed nanoindentation of polymers, [40, 41] including a summary of the most common analyses of load-indentation data. Chief among these methods is an analysis of indentation load-penetration curves according to the Oliver-Pharr method. [42] This method is based on relationships developed by Sneddon for the penetration of a flat elastic half space by different probes with particular axisymmetric shapes (e.g., aflat-ended cylindrical punch, a paraboloid of revolution, or a cone) [43], More recently, Withers and Aston discussed indentation in the context of plasticity and viscoelasticity [44]. 

In addition to indentation curves, the residual imprints after the application of a defined load force can be images using intermittent contact mode AFM. This is shown below for indentation tests performed on PE, in which the size of the imprint was shown to be reduced to the level of individual lamellae (Fig. 4.23). 

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 2. (a) An example of the indentation curve measured on a 5 pm thick layer of ncTiN/aSi3N4. and are the maximum applied load and indentation depth, Aplastic is the depth of the remanent, plastic deformation. The arrows — and denote the loading and unloading part, (b) Measured values of the hardness against the maximum applied load, (c) Indentation depth at a constant appUed load of 50 mN against time which shows the absence of creep. 

Modern indentometers for the measurement of the hardness of thin films use a computer controlled step-wise increase of the load up to a chosen maximum Zvmax followed by a step-wise unloading. Instead of measuring the diagonal of the plastic deformation, the indentation depth, h, is measured electronically and the indentation curve evaluated (see Fig. 2a). The plastic hardness is calculated from the maximum load, Lmax> d the depth of the plastic indentation. Aplastic,... 

Fig. 4.199 Schematic load-indentation depth curve and section through an indentation (F ax maximum load, -maximum indentation depth, - intersection of the tangent to the unloading curve with the indentation depth-axis, he - contact depth, W piast - plastic energy, If eiast - elastic energy).

Fig. 4.200 Schematic load-time, depth-time and load-depth curves for indentation creep (a, c) and indentation relaxation (b, d) tests.

Table 4.31 Parameters calculated from load - indentation depth curve.

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. 

Figure 7.15 Vickers hardness versus log of indentation load (top curve) four-point flexural strength versus log of indentation loads for fine-grained and coarse-grained Ti3SiC2 and TI3AIC2 with a grain sizeof 25 pm. The inclined dashed line shows the expected behaviorfor brittle solids [104].

In ceramics, the extent of plasticity caused by dislocation, when tension tests are performed, is limited and very often accompanied by microcracking. Many of the tests are consequently performed by low-load indentation, such as microindentation, where the indenter may be focused on a grain. Nevertheless, other testing methods are also used. In the figure below, the stress-strain curves represent compressions at a constant strain rate at several temperatures starting with RT and up to 1423 K (Fig. 5.2). 

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.

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