Load-displacement curves

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... 

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. 

Fig. 40—Typical load-displacement curves during a loading/ unloading cycle. Applied load 1250 /liN, 1-Fe-N(5 nm)/Ti-N(2 nm), 2-Fe-N(20 nm)/Ti-N(2 nm).

T5q)ical load-displacement curves, with maximum applied load of 1,250 /aN are shown in Fig. 40. It can be observed that... 

Fig. 22 Bending load-displacement curve of SA-Tyrannohex using chevron notch spacemen at room temperature...

Fig. 43. Load displacement curves under uniaxial compression for the neat epoxy line a) and macroporous epoxy networks prepared via CIPS with 20 wt % cyclohexane line b)...

Fig. 47. Load-displacement curves of solvent-modified and macroporous epoxy networks prepared with 20 wt % cyclohexane via CIPS with SENB testing at 1 mm/min...

Fig. 49. Load-displacement curves of solvent-modified, semi-porous, and macroporous epoxies prepared with 22 wt % cyclohexane via kinetically controlled CIPS with 1 wt % catalyst...

As for the samples prepared without catalyst, the ability for energy absorption after crack propagation decreases strongly as the solvent is removed. This is reflected in Fig. 49, where the load displacement curves of solvent-modifled, semi-porous, and macroporous epoxies prepared with initially 22 wt % cyclohexane (( )=18.5%) are shown. The crack length is the same in all three cases. Therefore the decrease in maximum load is directly proportional to the decrease in Kj. It is also clearly seen that the fracture behavior changes drastically and that the surface under the load-displacement curve, which is used to calculate the fracture energy is signiflcantly lowered. 

The quantitative results of fracture energy, which are calculated from the total area under load-displacement curves, are presented in Fig. 50. It becomes obvious, that a brittle-tough transition exists at a volume fraction of around 10%. This brittle-tough transition is observed for solvent-modifled as well as semi-porous epoxies. A brittle behavior is observed in macroporous epoxies after complete solvent removal, thus giving low fracture energies similar to the neat epoxy for each porosity. 

The load-displacement curves for the orthogonal interlock fabric composites show a non-linear unloading sequence and an appreciable permanent deformation after unloading, with the crack tip not completely closed (Guenon et al., 1987). These observations are attributed to the crack closure process of the three-dimensional fabric composites where through-the-thickness yarns break near the outer surface of the specimen. 

Fig. 18 a Schematic of probe tack measurements of a thin adhesive film along a temperature gradient, b Compilation of probe tack data during loading and unloading cycles for different temperatures. c Total adhesion energy, calculated from the area under the load-displacement curve shown in b divided by maximum contact area, as a function of temperature. The error bars represent one standard deviation of the data, which is taken as the experimental uncertainty of the measurement. (Reproduced with permission from [86])... 

Figure 5.21 (a) A typical load-displacement curve and (b) the deformation pattern of an elas-... 

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... 

A pendulum may be used (Charpy, Izod, tensile impact) to determine the work of fracture (Brown, 1999). Instrumented devices provided with piezoelectric transducers are also available load-time or load-displacement curves can be recorded (Merle et al., 1985), giving as much information as static tests. Servohydraulic or pneumatic setups and falling weight devices are also used. The drop ball test from the US Food and Drug Administration, is especially useful for optical lenses (acrylate networks). 

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. 

Fig. 2.9 The load-displacement curves for unidirectional SCS-6/Zircon composites versus temperature.58...

Figure 5. Load displacement curve for 3.2 mm diameter spheres.

Figure 3. Load displacement curves at various crack lengths...

From the compliance vs. crack length curve (Figure 5) the instantaneous crack length (a) is obtained. The instantaneous crack length minus the initial crack length (a — a0) corresponding to the point on the load displacement curve is then the amount of crack extension (Aa). 

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.

This energy partition is usually done by considering Wy as the energy under the load-displacement curve up to the maximum load, and W ( as the energy from the maximum load up to final fracture [9,10.16,20,21,24,27]. Similarly to Eq. (4), the authors cited above expressed the variation of Wy and w , with the ligament length as... 

The effects of temperature and displacement rate on the shape of typical load-displacement curves of DENT samples of a given ligament length are illustrated in Fig. 2. 

Fig. 2. Effect of temperature a) and displacement rate b) on the load-displacement curves of DENT specimens.

From Fig. 2a it is evident that as the test temperature raises from 0 up to 70 °C the resulting load-displacement curves display a decrease of the maximum load and an increase of the elongation at failure. On the other hand, as reported in Fig. 2b, when the displacement rate increases the load-displacement curves evidence an increase of the maximum load and, quite surprisingly, also the elongation at break increases. It is worth noting, that this rather unexpected rate effect on the load-displacement curves of notched samples has been already reported by Karger-Kocsis and co-workers for both biaxially oriented filled PET [7] and amorphous copolyester [9], and by Plummer et al. for polyoxymethylene tested at high temperature [14]. 

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