In-Situ observation of the scratch/indentation true contact area to provide analysis without being model-dependent
One of the major problems in contact mechanics analysis is to convert the stiffness estimated from load versus depth (in the case of indentation) or load contact versus contact radius (in the case of scratching) behaviours into a stress strain relationship. In general, if the load is directly recorded from the load cell, the true contact radius and the true depth depend on a model which depends on the kind of behaviour (elastic, elastic-plastic, plastic). In the case of steel (and for other materials which quickly yield during contact) this difficulty is not a real problem. On the contrary, there are no models at all which take into account the viscoelastic and/or viscoplastic behaviour of the material or an elastic behaviour at large strain, such as in the case of polymeric materials.
To investigate this problem, a new apparatus was built, which control the velocity of the tip over a large range, at a large range of temperatures and an “optical microscope” was fitted to allow in-situ control and measurement of the contact area and of the groove left on the surface. The prototype of this apparatus developed in the Charles Sadron Institute under the name “Micro Visio Scratch”  is now available as an option for all Anton Paar Indentation and Scratch Testers.
Fig. 1: Anton Paar Nanoscratch Nanoindentation tester including the in- situ vision set-up
The prototype Mirau interferometer shown in Fig. 1 is integrated with a Anton Paar Open Platform which is mounted in a vacuum chamber. This optical device may be shifted under the Nanoscratch Module or under the Nanoindentation Tester Module. This Application Bulletin will summarize recent results obtained with this setup. Note that the indenter tip used is of spherical geometry for two reasons: first, there is a uniform
stress distribution around such an indenter and secondly due to the in-situ vision, it is now possible to control the mean contact strain proportional to the ratio a/R (where a is the contact radius and R the radius of the tip).
In-situ observation of the contact area improves the analysis of the scratch behaviour: no model is needed to predict the surface behaviour as in the case of a blind test. In addition, in-situ observations directly provide important information about the bulk material properties. For example, for a polymer having a viscoplastic behaviour, a logarithmic increase of the scratching speed results in a linear decrease of the true contact area without changing the shape of the contact area. So the contact radius decreases alone. The local strain rate during the scratching process may be estimated as the tip speed divided by the contact radius and all experimental measurements of the mean contact pressure may be plotted as a function of this strain rate. The scratch hardness (mean contact pressure in case of plastic contact) therefore appears to be a time and temperature activated processes property like other mechanical properties for this kind of material . A typical image of the contact area and shape of the groove left on the surface is given in Fig. 2. It is easy to see that the diameter of the contact area is larger than the width of the groove. This is due to the elastic unloading just after contact. The rear contact angle seems to be a good parameter to characterize the rate of yielding around and under the scratching tip during the contact phase. This angle is equal to p/2 for an elastic contact and decreases up to about 0.2 to 0.3 rad for a fully plastic contact.
Fig. 2 – Schematics of the constant load scratch on a cross-sectioned sample
Different studies on various polymeric surfaces have shown that the scratch tests are controlled by the imposed elastic- plastic strain in terms of maximum value and size, but also its localization through depth beneath the moving tip. As it is now possible to dissociate the strain dependency from the time and temperature dependencies, it is now possible to use some basic finite element modelling (FEM) to explain the surface behaviour, contrary to the general use of FEM which tries to predict the In-situ observation of the scratch/indentation true contact area to provide analysis without being model-dependent scratch behaviour . Fig. 3 illustrates the strain dependency during a scratch made at increased normal load, applied on a spherical tip.
Fig. 3: Mechanical transitions from elastic sliding to fully plastic scratching observed during experiments with increasing the applied normal load for PMMA (local friction coefficient was estimated at 0.2)
Fig. 4: Equivalent plastic strain maps as computed by simulation for a/R=0.2 with μloc=0 and μloc=0.4 for PMMA.
As a first approximation, the average plastic strain ep increases with the local friction for a given ratio a/R and for a constant local friction with the ratio a/R. FEM results explain experimental results: the average plastic strain ep and then the corresponding plastic strain field are more sensitive to the local friction coefficient for intermediate values of a/R, corresponding to elastic–plastic contacts on polymeric surfaces [4,5]. Fig.5 illustrates the coupled influence of the friction coefficient and of the ratio a/R.
Apparent versus local friction coefficients
When a rigid sphere slides on a soft polymer, the tip penetrates into the material and creates a “ploughing wave” in which a large amount of energy is dissipated. This effect is included in the apparent friction coefficient μapp, the ratio of the measured tangential force over the applied normal load. In order to take into account this phenomenon and accede to a more “local” friction coefficient μloc defined as the ratio between the local shear stress and the local contact pressure, a model was developed  and used to analyze the relationship between the local friction coefficient and the mean contact pressure, the yielding of the surface or the structural recovery of the surface [7,8].
Fig. 5: Experimental in situ observation of the contact geometry and the residual groove during scratch tests (top view) as a function of the mean geometrical strain a/R and the local friction coefficient
The true contact area is therefore the sum of a front area (half disc) and a rear area (part of the rear half disc). The difficulty is to account for this rear contact to relate the true and ploughing frictions to the measured apparent friction. The input data required by the model are the true contact area (contact radius and rear contact angle) and the shape of the rigid sliding tip. The true friction coefficient was easily related to the apparent friction coefficient, using four integrals A, B, C, and D, which are the elementary action integrals of the local pressure and shear, on the normal axis z and on the sliding axis x, as indicated in Fig.6 .
Fig. 6: Rigid sphere sliding on a viscoelastic polymer showing the ploughing effect and the corresponding contact area.
So this model allows an analysis of the interfacial rheological behaviour of the polymer versus the mean contact pressure. Moreover, it is possible to investigate experimentally the interface at the local scale with the control of tip roughness. For example Fig. 7 shows the local friction coefficient, μ, versus the mean contact pressure, Pmean. Results show first that below yield stress ( Pmean<100 MPa) the local friction coefficient follows a master curve for smooth indenters (Δ). Some roughened indenters were realized using chemical etching (fluorhydric acid) which allows monitoring the nanoroughnesses parameters. From 5.5 nm Rms to 140 nm Rms the friction coefficient μ progressively falls to a plastic-like constant value: nano-roughness monitors friction. Due to the in-situ information of the contact area, it is now possible to study the behaviour of confined polymer layers .
Fig. 7: Local friction coefficient μ versus mean contact pressure Pmean during sliding and scratching tests with roughened spherical lenses on a rejuvenated PC surface (v = 30 μm s-1, T = 30°C). (Δ) Rrms = 0.7 nm (reference), (+) Rrms = 5.5 nm, (Δ) Rrms = 8.5 nm, (Δ) Rrms = 140 nm. Snapshots during sliding in the elastic, elasto-plastic and plastic regimes with the measured contact area in diagonal grey hatching.
Scratch damage of uncoated material
By coupling experimental observations and finite element modelling, the scratch behavior of a thermoset polymer exhibiting brittle behavior was investigated. The 3D crack pattern, formed at the rear part of the contact and in the residual groove (due to the high level of tensile stress during scratch tests) has been analyzed using fluorescence confocal microscopy (Fig. 8). By using FEM, the normal contact pressure and the interfacial shear stresses in the contact area at the sample/indenter interface have been computed and used as input data for the 3D crack network analysis based on combined 3D localized multigrid and X-FEM/level set techniques. The fracture process responsible for the crack pattern formation was identified as a complex 3D unloading/reloading process, predominantly driven by mode I. Further, a failure strength around 90 MPa was estimated. It is the value reached by the computed tensile stresses at the rear edge of the contact area for a distance between the last crack and its rear equal to the measured distance between two consecutive actual cracks .
Fig. 8: in-situ photograph of CR39 damage. Cracking appears near the rear edge of the contact area (left) 3D crack pattern reconstruction from confocal microscopy. The surface fracture is roughly a part of a cylinder (right)
Scratch damage of coating
It is generally accepted that the critical load, generating the first damage in a scratch test, is representative of the behaviour of a coating. As the properties of polymers are time and temperature dependent, a single value of the critical load cannot describe the overall mechanical behaviour. It was observed that cracking may appear in the contact area, not always at the rear edge. In the case of thin solid films, the ratio of the contact radius to the radius of the grooving tip proved to be a pertinent parameter to predict the damage and did not depend on the scratching velocity or temperature. The ratio of the thickness of the coating to the roughness of the tip is another critical parameter: the coating prevents the roughness of the diamond tip from creating micro-scratches at the surface of the macro-groove. Therefore, since the absence of micro-scratches is a condition for relaxation of the macro-groove, the thickness of the coating must be greater than the roughness of the tip, as shown Fig. 9 . The second key feature of the durability of coatings submitted to scratching is their interfacial adhesion with the substrate. In-situ observation is key to exploring the damage mechanisms such as blistering and spalling. The fracturing of some thin coatings deposited on various substrates were investigated under different conditions of temperature and scratching speed. Many types of fracture mechanisms were observed , depending on these two variables. A global energy balance model  of the stable blistering process (fig. 10) which is obtained for some experimental conditions, permits an estimation of the adhesion of the ystem. The adhesion can be estimated by following the delaminated area (quantified by image analysis) as a function of the scratching distance during blistering. The adhesion corresponding to different substrate/thin film systems was derived using the global energy balance model and FEM. The study of similar films with different thicknesses proved that some confinement effect occurs and thus leads to an analysis of the results with regard to the probe characteristics: size and roughness.
Fig. 9: Effect of the thickness of the coating on the true contact area (angle increases if no microscratches along the macro groove); R = 110 μm; Tip roughness Rt = 2.5 μm; a/R roughly constant.
Fig. 10: Full sequence of the crescent blister growth during scratching of the material with 10 μm/s scratching speed and a temperature of 90 °C. The indexes 1 to 7 chronologically number the shots. The dashed lines indicate the delamination area.
In-situ observation is a useful tool to study the damage mechanisms which appear during scratching. It is very important to note that post mortem observation cannot give similar information due to the fact that after unloading, the compressive and shearing stress fields disappear after the contact time.
In-situ observation has shown the transition from scratching to sliding during the contact of a moving tip with a polymeric surface as a function of the sliding speed. It would be impossible to analyse such a transition with a blind test as no residual scratch track remains on the surface (in the case of elastic materials) .
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Movies to illustrate this Applications Bulletin
Movies are available at the following address:
Anton Paar would like to thank the Institut Charles Sadron (CNRS Strasbourg) and Prof Christian Gauthier for the results published in this Application Bulletin.
Prof Christian Gauthier
Institut Charles Sadron
Université de Strasbourg
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