Critical indentation depth

The results clearly show no delamination of the films from the substrates, indicating good interfacial adhesion. Increasing compaction of the film against the substrate can be found at lai e indentation depth. In this film a critical indentation depth of approximately 2000 nm (hmax/tf = 20%) can be deduced above which the plastic deformation region reached the film/substrate interface and the substrate had a significant effect on the apparent modulus of the film. 

The key point in this method is the determination of the critical load where first irreversible cracks or fractures are generated and which therefore indicates the transition from plastic deformation to significant/lasting damages. For that, the normal load is constantly increased and indentation depth and tangential load are simultaneously recorded. The transition from plastic deformation to the fracture range is indicated e.g. by unsteadiness or fluctuations in the detected load flow and the indentation depth. This transition range can also be evaluated by additional... 

Critical load and indentation depth at 5 mN are the parameters printed as a function of each other to evaluate the scratch resistance (see Fig. 3). A good scratch resistance is the result of high values for the critical load when the values for residual indentation depth are low. 

If the determined indentation depth at 5 mN is used to calculate the ratio of load (5 mN) and depth as a measure for plastic resistance, the result for typical 1 K, 2 K and UV systems is the correlation [20] shown in Fig. 4. It has to be noted that in comparison with Fig. 3 the reciprocal value of the indentation depth is actually plotted on the y-axis. Therefore, a good scratch resistance is the result of high values for the critical load and also high values for the plastic resistance. 

Some difficulties also arise for the interpretation of scratch tests carried out at progressively increasing normal load or indentation depth. Figure 3 indicates, for example, that a transition from ductile deformation to brittle cracking can occur when increasing the normal load whilst the contact strain is nominally fixed by the conical indenter angle. This is indeed observed in many polymer systems and the notion of a critical load at the ductile-brittle transition is largely used to characterize the scratch response. This depth... 

Sun, Y., Bell, T., Zheng, S., 1995. Finite-element analysis of the critical ratio of coating thickness to indentation depth for coating property measurements by nanoindentation. Thin Solid Films 258, 198-204. 

To include the effects of fracture in the model is relatively straightforward if we assume that the coating within the cracked region does not contribute to the plastic work of indentation after fracture occurs. Fracture usually occurs when the plastic zone in the substrate is very well-established so we can consider the volume of coating to be a cylindrical disc with the thickness of the coating. The area of the crack produced is small compared to the volume it encloses so we also assume that the surface energy of the crack plays only a minor part in the work of indentation. For a radial cracked system the cracks have radius kc8 where kc is a constant and 8 is the plastic indentation depth. These form above a critical depth, 8c. The area of material bounded by radial cracks increases linearly with indentation size. In this case the correction for the modelled hardness is given by... 

As it can be noticed on Figure 2, the position of the transition increases with the indentation depth. On Figure 9 this position is plotted versus the indentation depth for a given velocity displacement the transition occurs at a displacement which represents about 3.4 times the indentation depth. Moreover, it is nearly independent of the velocity of the displacement in a range of about 4 decades in velocity (Figure 3). The reason for such a large value of the threshold and of this quasi velocity-independence is not clear, but seems to be linked to a critical deformation in these viscoelastic materials. 

It is worth to mention that, during such measurements, the combined responses of the coating and the substrate are measured. Several relationships have been proposed for modeling this effect (see Pharr, 1992 Fischer-Cripps, 2000 Malzbender et al., 2002 Oliver, 2004). The contribution of the substrate becomes important when the indentation depth exceeds 10-25% ofthe film thickness and, therefore, may become critical when very thin films are measured. 

At a certain critical load, the crack spontaneously breaks through to the free surface (the cut-through ), usually with additional crack depth increase D, and changes into a well developed semicircle (solid-line semicircle). This transformation may also be induced in another, stable, manner, e.g., by the action of rosette type stresses around the strain region while loading the indenter before the cut-through . The model given in Fig. 6.2.8 is described by the equation... 

Nanoscratch tests have been used to simulate the effect of third-body particulate wear debris on component surface scratching during use. The load at which the co-efficient of friction or friction force suddenly increases is identified as the critical load, and is used to evaluate scratch resistance and adhesion strength. The depth-sensing nanoindenter, usually equipped with a conical indenter, can elucidate the mode of failure, whether elastic/plastic deformation, cracking, or delamination. 

The accuracy of the test method relies critically on the accurate determination of the area function, which varies with tip geometry. At the scale of many nanoindentation experiments, minute differences in tip geometry—such as those caused by wear induced by repeated experiments—can have a large effect on the area function. For this reason, the area function is typically measured by indenting a known material to several depths and computing the function from Equation 39.37. This experimentally determined tip function is then used to interpret further tests on unknown materials. Fused silica (or quartz) is commonly used to calibrate the tip, that is, determine the area tip function, because its material response is nearly perfectly elastic and it does not exhibit adhesion with diamond indenter tips. 

Fig. 59. The SEM images of scratches produced in (111) Si by a sharp Vickers indenter. Silicon exhibits (a) ductility on a microscale and (b) brittle fracture at the depth of cut beyond the critical value. Scratching direction from left to right.

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