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Recovery ofthe groove

It was not easy to measure the radius of the groove section just after contact, at the beginning of the life span of the groove. Although the contact displayed yielding, if the unloading after contact was elastic and hence reversible, a second passage of the scratching tip along the groove

with a section of concave radius Ro did not increase the yielding. The following analysis may be considered to transfer to scratching the results of previous work on indentation [35]. Provided the elastic sliding may be predicted with the elastic Hertz theory, the radius of the groove can be related to the radius of the tip through the equation:

where E* is the Hertz contact elastic modulus. During recovery, the edges of the groove lie parallel. The mean strain in the matter around the groove may be defined as:

(II)

and the recovery of the groove is described by the ratio:

c(t) _ Ro c;- R(t)

(12)

This recovery is plotted in Figure 14. During contact, the recovery process was not freely stressed because contact between the tip and the surface existed. The start of recovery was defined to occur after contact, i.e. after the maximum strain had been imposed at the maximum

contact width for a time to :

(13)

Results are in agreement with the previous analysis. A comparison of the two curves for the uncoated material indicates that the recovery increases if the tip is smooth, which is related to the fact that the local interfacial strain decreases if there are no micro scratches. A comparison of the two curves for the rough tip indicates that the recovery increases if the sample has been coated. This is linked to a decrease in the yield in the elastic-plastic strain under the contact area as the local friction coefficient decreases.

rough tip - CR39

rough tip - coating 1.1 !Jm smooth tip - CR39

Fig. 14. Recovery of the groove left on the surface as a function of time. The recovery increases if the tip is smooth or if the local friction coefficient is low (coated sample).

CONCLUSIONS

Deposition of a scratch-resistant coating is a common way to improve the scratch behaviour of a polymeric surface. However, a thin scratch-resistant coating cannot prevent yielding on the macroscopic scale of the contact. In-situ photographs show macro grooves with parallel edges, which is an indication of the occurrence of yielding during contact. The mechanical behaviour of a coating on a viscoelastic material is easily described by considering the normalised contact pressure and should be analysed in terms of the shape of the stress field, modified by the effect of the local friction between a scratching tip and the surface, where this local friction will depend on the roughness of the tip and the presence of the coating. A coating decreases the yielding in the elastic-plastic behaviour of the contact if the local friction coefficient between the surface and the tip is low. The major benefit is the reduction of the "scratching contact strain".

The ratio of the thickness of the coating to the roughness of the tip is confirmed to be a critical parameter, which enables one to increase the scratch resistance in the case of a thin coating.

The recovery of the groove left on the surface must be analysed in relation to the contact behaviour. If the local friction coefficient is low and there are no micro scratches along the macro groove, the recovery may be fast.

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The scratch hardness and the surface defonnation mechanisms of materials depend in particular on the rheology of the material, the indenter geometry and the friction at the interface. But the mechanical analysis of this test by analytic models is very intricate and requires many simplifying assumptions especially in three dimensional (3D) conditions [5, 14-17]. First, after having defined our notations we perfonn a preliminary discussion of the various aspects of the problem by considering the two dimensional (2D) case: the plane strain scratching of materials by wedges. After, we present the conditions of the numerical simulations of scratching with conical indenters with a three-dimensional (3D) finite element code. So we compare the behaviour of polymeric and metallic materials in the scratch test at low and high strain and relate their difference in scratch resistance to their rheological properties. In addition, we discuss the reliability of many assumptions commonly used in the interpretation of the scratch test and compare the indentation and scratch testing.

PRELIMINARY: THE SCRATCHING WITH CONICAL INDENTERS

Representative Strain and Indentation Index

In scratch test, as in indentation, the nonnal component of the material displacement Uz is of the order of magnitude of the penetration depth h and this displacement is accommodated on a distance in relation with the contact radius a=bc/2 (Fig. 1). So the order of magnitude of the strain in indentation Ei or scratching Es is:

(1)

Thus the strain increases with the attack angle 13 or as the semiapical angle e decreases. However, we must notice that the representative strain depends on the investigated problem (indentation or scratching, hardness or volume average value... ) and its relation with cote can be rather complex as we shall demonstrate later. For example for metal indentation, following the Tabor's model of indentation pressure with spherical indenter [18], Johnson proposed that the indentation hardness of metals is related to the value of the flow stress cro at the strain 0.2 cote [19]:

So, a first rheological parameter of interest is the yield stress cry to the Young's modulus E ratio:

(3)

Ee defines the order of magnitude of the elastic strain of the material at the point of plastic yielding which is same as the elastic recovery after plastic strain: it is generally very small for metals (0.1-0.5 %) whereas it is much higher for polymers (1-10 %). We may say that the elasticity of the material increases if Ee increases; rigid plastic materials correspond to the limit case Ee =0. If the flow stress of the material does not depend on the strain or the strain rate, case which corresponds to perfectly plastic materials for which the flow stress is always equal to the

yield stress cro= cry, the behaviour in cone indentation or scratch test at constant temperature is characterised by Ei to Ee ratio, a quantity which we call the indentation index X:

We can expect that the elastic effects become more and more negligible as X increases. For example, for a given value of e, in indentation, the constrain factor C (relation (2)) increases steadily with X and tends toward a limit which depends only one (full plastic regime) C3 (9), C3 (9) being an increasing function ofe under zero friction [19]. Following the approach of Hill et. al. [20] for indentation, we define a quantity which characterises the contact geometry: the shape ratio (Fig. 1):

(5)

For elastic contact (very low X) the contact conditions are described by the Hertz's theory: the contact is limited by a full circle, with the radius a=(2ht)h tanS (the material sinks in), c=2ht-0.637. We expect that as in indentation (see below) c is an increasing function of the indentation index.

Scratch Hardness and Representative Strain

On the indenter are applied a normal force W and a tangential force Ft (Fig. 1). Consider the area of the true contact surface projected on the sample surface A and the width b of the residual groove which is the distance between the tops of the shoulders or the scratch pileups (Fig. 1). We can define two types of scratch hardness related to the normal force:

Hs is the average contact pressure if friction between material and indenter is negligible; we name Hs the (true) scratch hardness. The quantity Hs112 defined in [4] is easily measured in experiments. Hsr/2-Hs if bc-b and if the contact is restricted on the frontal part and limited by half of a circle (so this requires particularly hc-hrc)· So we name H,w the apparent scratch hardness. If it is assumed in addition that the contact pressure is uniform, the force ratio or apparent friction coefficient flo is related to the apical angle (Fig. 1) [3]:

This relation is in good agreement with the experimental results of lubricated scratching of metals for 30~9~70 deg [4]. These assumptions on contact geometry are commonly valid for metals because Ee is very small. So the elastic effects are assumed negligible and the contact is considered as restricted to the frontal part [4]. They are not verified for polymers [13]. If, on the