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Understanding of automotive clearcoats scratch resistance
Thin Solid Films 420 – 421 (2002) 281–286
Understanding of automotive clearcoats scratch resistance P. Bertrand-Lambottea,b, *, J.L. Loubeta, C. Verpyb, S. Pavana a
` Ecole Centrale de Lyon, UMR CNRS 5513, Laboratoire de Tribologie et Dynamique des Systemes, 36, avenue Guy de Collongue, F-69134 Ecully, France b ¨ Centre technique de Velizy, ´ ´ ´ ´ – Peinture, Route de Gisy, PSA Peugeot Citroen, Direction Materiaux et Procedes F-78943 Velizy Villacoublay Cedex, France
Abstract Micrometric scratches, mainly due to car wash brushes, decrease the gloss of automotive clearcoats, alter their appearance and prevent them from protecting the car in the best way. Scratch resistance is estimated from the visible damage caused on the clearcoats. As the eye is more sensitive to brittle than to ductile scratches (Microstructures and Microtribology of Polymer surfaces (2000) 428), one way to improve scratch resistance it to decrease the proportion of brittle scratches and to favor healing of ductile scratches. An analysis of the contact during a scratch test shows that the ductileybrittle transition is controlled by both an energetic and a size criterion. The energetic criterion is related to the tensile stress located at the rear of the contact between the indenter and the clearcoat. This stress can enlarge existing cracks, leading to fracture. It depends on the clearcoats viscoelastoplastic properties, the mean deformation imposed by the indenter and the environment (dry tests or tests in water or soapy water). The effect of these parameters on scratch resistance has been studied: indentation and scratch tests with a Nanoindenter XP have been carried out. The healing of ductile scratches has been estimated from scratched samples of clearcoats. The samples have been heated at different temperatures and the remaining scratch depth measured with an atomic force microscope. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Nano-indentation; Nano-scratch; Thermoset resins; Ductile; Brittle; a Relaxation; b Relaxation
1. Introduction Automotive clearcoats compose the outer layer of automotive coatings and consist of thermoset resins w2x. Their thickness ranges from 40 to 50 mm. They make automobiles glossy and protect them from environmental damage such as stone chipping, marring, UV radiations, acid rains w3x, etc« This study focuses on marring brought about by car wash machines brushes. 2. Analysis and experimental procedure 2.1. The samples Automotive clearcoats samples of different chemical *Corresponding author. Tel.: q33-4-72-18-65-96; fax: q33-4-7843-33-83. E-mail address: [email protected] (P. Bertrand-Lambotte).
compositions have been brushed by a car wash simulator. The scratches have been observed with an atomic force microscope (AFM) (Park Instruments䉸 ). In general, the scratches are between 0.05 and 2 mm deep, 1 and 10 mm wide. As the damage is limited to the first few microns of the clearcoats, the latter are considered as semi-infinite materials. There are both ductile and brittle scratches. Ductile scratches present no tearing and we will show that heating can make them disappear. On the contrary, brittle scratches show irreversible damage and the eye is more sensitive to brittle than to ductile scratches w1x. The whole study is based on two reference clearcoats (A and B) chosen from a dozen of available ones. They have been chosen for their difference in mar resistance. ¨ functional tests based According to PSA Peugeot Citroen on loss of gloss measurements, A is the clearcoat with the best scratch resistance while B is the clearcoat with the worst scratch resistance.
0040-6090/02/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 2 . 0 0 9 4 3 - 4
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2.3. The ductileybrittle transition 2.3.1. Analysis Our goal is to relate intrinsic clearcoats parameters to the ductileybrittle transition. This transition is studied from two energetic viewpoints.
Fig. 1. Material containing a crack of width c on which a tensile stress st is applied.
2.2. The ductile scratches Nano-indentation tests w4x have been performed with a Nano-indenter XP (MTS䉸) to determine the clearcoats viscoplastic properties and so to understand ductile scratches. The hardness H is defined as PyAN where AN is the projection of the contact area in a plane normal to the normal applied load P. Continuous stiffness measurement has been used: from an indentation curve (normal load P vs. depth h), the evolution of the hardness H vs. h is determined as a continuous function with only one indent. Each nanoindentation test is performed at a constant strain rate ´˙ ˙ w7x) w5,6x: this is ensured (´˙ is defined as (1y2)(PyP) ˙ by maintaining PyP constant w7x. The maximum load is 15 mN. To enlarge the explored strain rates range and to understand ductile scratch mechanisms, nano-scratch tests and nano-indentation tests at different temperatures (from 0 to 45 8C) have been carried out. In the scratch tests, a Berkovich indenter is used face forward at a constant load (15 mN). Scratch hardness is then defined as FT yAT where FT is the tangential force and AT is the projection of the contact area in a plane normal to v. A thermal chamber used to perform indentation tests at different temperatures was made at our request by Servathin䉸. Additionally, because ductile scratches can heal when heated, experiments were conducted to try and understand these healing mechanisms. To do this, clearcoats with scratches performed with a Berkovich indenter face forward (constant load of 15 mN), have been heated at different temperatures for 1, 5 and 10 min and the scratch depth was then observed via AFM at room temperature.
2.3.1.1. Two energetic viewpoints. (1) A crack of width c in a Hookean material w8x on which a tensile stress st is applied (Fig. 1) will grow if st2cyE0Gc (fracture energy criterion) where E is the elastic modulus and Gc the fracture energy of the material. For ductile materials w9x, the energy released to make the crack grow is used both to create new surfaces and to plastify the material. So Gcs2gqsy´prplastic (g is the surface energy, sy the yield stress, ´p the plastic strain, rplastic the radius of the plastic zone at the tip of the crack). Actually, 2g
Fig. 2. Scheme of the plastic deformation and of the fracture which can occur in a ductile material when a tensile stress st is applied on it.
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Fig. 4. Scratch test geometry for a spherical indenter in elastic contact where A is the contact area, st the tensile stress at the rear of the contact, P the normal applied load, and v the scratch velocity. Fig. 3. Representation of the energy and of the size criteria ruling the ductileybrittle transition of a ductile material containing a crack of width c on which a tensile stress st is applied. The brittle area is reached if s2t)GcEyc (energy criterion) and if the size of the material is higher than 2Gcysy´p (size criterion). Gc is the fracture energy of the material, E its elastic modulus, sy its yield stress and ´p its yield plastic strain.
2.3.1.2. The tensile stress in scratch experiments. (1) In a scratch test, st is the tensile stress at the rear of the contact between the indenter and the clearcoats. (2) In the elastic case and for a sphere–plane contact (Fig. 4), sts
3P B 1y2n 4qn Ft E C q p F 2pa2 D 3 8 PG
w12x (n is the Poisson ratio) where a is the contact radius. The interfacial stress is defined by tsFt yA. Since a 3s3PRy4E* (Hertz theory) and since the strain is proportional to ayR, the tensile stress is proportional to E*´qCt where C is a constant. According to the Way theorem w13x, the stress field out of the contact zone is the same whatever the geometry of the indenter, thus the st expression is valid whatever the indenter. (3) In the plastic case (Fig. 5), we define st as Ft y ANS where ANS is the projection of the contact area in a plane normal to P. Since FtsqmATqtANS (qm is the normal stress and t the tangential stress), stsqm(AT y ANS)qt and as HsFt yAT, qmsHy(ty ´). For spherical and conical indenters, AT yANS is proportional to the strain ´. Thus, the tensile stress is proportional to H´q Dt where D is a constant. (4) Automotive clearcoats are viscoelastoplastic materials, thus when the tensile stress at the rear of the contact is lower than the yield stress, st is proportional to E*(f)´qCt, where f is the exciting frequency. When st is higher than the tensile stress (this is our case in the study of the ductileybrittle transition), st is proportional to H(´˙ )´qDt. Neglecting the interfacial term, st is proportional to H(´˙ )´. Thus the fracture energy criterion becomes (H2 yE)(´˙ )´2c0Gc, putting forward the influence of the viscoelastoplastic properties
of the clearcoats and the influence of the indenter geometry (through ´). 2.3.2. Experimental procedure To highlight the two criteria describing the ductiley brittle transition, nano-scratch tests have been performed with indenters of different geometries: a Berkovich and a trigonal indenter (both face forward) and a spherical indenter (radius Rs10 mm). The normal applied load is increased along the tests and the scratch velocity v is 1 mmys. When using Berkovich and trigonal indenters, the strain ´ remains constant w6,14,15x during the scratch test. The strain rate ´˙ is taken as vyl w4x where l is a characteristic length defined by yANS y yp. In this case, l is close to the scratch width. In contrast, when using a spherical indenter, the strain increases during the test as ´ is proportional to ayR w16x, where a is the contact radius and ´˙ is taken as vy R. 2.4. Method verification Automotive clearcoats are viscoelastoplastic materials, thus their mechanical properties depend on the imposed frequency, as well as temperature. The frequency at which they are strained by car wash brushes is approx-
Fig. 5. Scratch test geometry for a conical indenter in plastic contact where A is the contact area, ANS the projection of the contact area in a plane normal to the normal applied load P, AT the projection of the contact area in a plane normal to the scratch velocity v, Ft the tangential force, qm the normal stress and t the tangential stress.
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Fig. 6. Hardness data of clearcoat A at different strain rates from indentation and scratch tests. One can notice the recovery between indentation and scratch results.
imately 105 ys (calculated from vyl, where v is the linear velocity of the brushes (vs1–2 mys) and l the scratch width (1–10 mm)). However it is less clear what the associated temperature is, namely what is the contact temperature? When two solids are in friction, a great fraction of the dissipated energy is converted into heat. This increase in temperature (DT) with respect to room temperature is short-lived and is called ‘flash temperature’. Flash temperature theory w17,18x gives estimated tables of the temperature increases depending on frictional velocity v, frictional coefficient m, contact radius a, thermal conductivity l and thermal diffusity a. In our case, DT is given by the following expression DTs0.308(mvyl)(Pypa2)pa(ayva)0.5and is estimated to be approximately 43 8C w4x. That means that car wash brushes impose a 105 Hz frequency, at a temperature of 20q43 8C. In contrast, the imposed strain rates at a reference temperature of 20 8C in the nanoindentation and nano-scratch tests, range from 10y3 to 10ys. In order to compare this range of frequencies to those imposed by car wash brushes, the same reference temperature has to be considered. According to the time temperature superposition principle, a one-decade-shift in frequency is analogous to a 6 8C-shift in temperature (Arrhenius equation with activation energy round 300 kJymol w4x). Thus it is equivalent to consider the clearcoat at a temperature of 20q43 8C at a 105 ys, and to consider it at 20 8C at 10y2 ys. This is the approximate frequency range explored during the nano-indentation and the nano-scratch tests, which valids the method.
plasticity in scratch tests is equivalent to study viscoplasticity in indentation tests w4x. From indentation hardness curves determined at different temperatures w3x, a master curve is plotted using the time–temperature principle (Fig. 7). The shift factor, aT, obeys an Arrhenius law, ln aTsyQVP yR((1yT)y (1yT0)), and plotting ln(aT) vs. 1yT allows calculation of the viscoplastic activation energy QVP where R is the perfect gas constant and T0 the reference temperature (20 8C). Activation energies were determined to be QVPs140 and 110 kJymol for clearcoats A and B, respectively. Mechanisms of ductile scratches are ruled by energies which are in the order of magnitude of b secondary relaxations, which would mean that only local motions of the polymer chains are involved (the loss peaks of polymers are often labelled with Greek letters a, b, g« w19x; the a peak corresponds to the relaxation observed at the highest temperature at a given frequency or the lowest frequency at a given temperature; the b and g symbols then apply to the other relaxation regions in order of decreasing temperature or increasing frequency). 3.2. Healing of ductile scratches w3x Master curves of scratch depth vs. time have been determined with a reference temperature of 30 8C (Fig. 8). Almost all clearcoats exhibit the same curve profile with first a plateau, followed by a decrease of the scratch depth (occurring at ‘healing temperature’) and then a second plateau. The first plateau represents the temperature range where scratch healing cannot occur as motions of the polymer chains are limited. Activation energies of the healing process have been determined using the Arrhenius law, and are for clearcoat A, Qhealings470 kJymol and for clearcoat B, Qhealings500 kJymol, respectively. The healing temperature has been compared to the a relaxation temperature of each clearcoat, measured by DMA (tensile tests at 1 Hz) w3x. It appears that the healing temperature is very close to the
3. Results and discussion 3.1. Formation of ductile scratches Scratches created with the Berkovich indenter are ductile and the scratch hardness results are consistent with the indentation hardness results (Fig. 6): that is to say at a given strain rate, the scratch hardness is the same as the indentation hardness. Thus, studying visco-
Fig. 7. Time–temperature superposition curve of hardness data vs. strain rate for clearcoat A. The reference temperature is 20 8C.
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Fig. 8. Time–temperature superposition curve of scratch depth vs. time for clearcoat A. The reference temperature is 30 8C. A first plateau is followed by a decrease of the scratch depth and then by a second plateau. The decrease of the scratch depth occurs at ‘healing temperature’.
Taonset (corresponding to the temperature from which the elastic modulus starts decreasing). Furthermore, healing activation energies are in the order of magnitude of the activation energies of a relaxations. These results show that healing of ductile scratches is ruled by the main relaxation (a relaxation) of the clearcoats. That would mean that healing entails large motions of the polymer chains. 3.3. Ductileybrittle transition When performing scratches with the Berkovich and the trigonal indenter, the strain ´ remains constant: the corresponding tests are represented in Fig. 9 with an horizontal line. Parallel to the first x-axis, a second x-
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axis representing the scratch width is shown. Scratches performed with a Berkovich indenter on clearcoats A and B are ductile whatever the applied load. In contrast, scratches performed with a trigonal indenter on clearcoats A and B are ductile, as long as the scratch width is lower than 3.5–4 mm. Beyond this width, they become brittle. In scratch tests performed with the spherical indenter, the strain increases along the scratch. Since ´ is proportional to ayR and P is proportional to a 2, these tests are represented in Fig. 9 by a parabolic curve. The ductiley brittle transition occurs when the scratch width becomes higher than 11 mm for clearcoat B and higher than 17 mm for clearcoat A: the transition is ruled by the fracture energy criterion. The same tests performed in soapy water show that the ductileybrittle transition occurs later, namely at higher scratch width w4x. 4. Conclusion This paper focuses on marring brought about by car wash machines on automotive clearcoats. Two types of scratches were observed on the clearcoats: ductile and brittle scratches. To improve clearcoats mar resistance, especially brittle scratches occurrence has to be delayed: both the fracture energy criterion and the size criterion can be shifted (s2tcyE is decreased and 2Gc ysy´p increased), which puts forward the significance of viscoplastic properties in fracture mechanics.
Fig. 9. Scratching maps of clearcoats A and B determined from our two criteria (fracture energy and material size criterion), separating ductile and brittle areas. Typical observations of scratch tests performed with indenters of different geometry are reported on the map.
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References w1x Lin L., Blackman G.S., Matheson R.R., in: Tsukruk V.V., Wahl K.L., (Eds.) Microstructures and Microtribology of Polymer Surfaces, 2000, pp. 428–438, Chapter 27, ACS, Washington DC. w2x P. Bertrand-Lambotte, J.L. Loubet, C. Verpy, Tribology Research: from Model Experiment to Industrial Problem, Tribology Series, thiry-ninth ed., Elsevier, Amsterdam, 2000, p. 883. w3x P. Bertrand-Lambotte, J.L. Loubet, C. Verpy, S. Pavan, Thin Solid Films 398–399 (2001) 306–312. w4x Bertrand-Lambotte P., Ph.D. Thesis, Sur les mecanismes ´ de rayure des vernis de finition automobile, Ecole Centrale de Lyon, 2001. w5x D. Tabor, Rev. Phys. Technol. 1 (1970) 145–179. w6x K.L. Johnson, Contact Mechanics, Cambridge University Press, England, 1985. w7x B.N. Lucas, W.C. Oliver, G.M. Pharr, J.L. Loubet, Mater. Res. Soc. Symp. Proc. 436 (1997) 233–238.
w8x A.J. Kinloch, R.J. Young, Fracture Behaviour of Polymers, Elsevier Applied Science, London, New York, 1983. w9x E. Orowan, Rep. Prog. Phys. 12 (1948) 185. w10x K.E. Puttick, M.A. Shadid, M.M. Hosseini, J. Phys. D Appl. Phys. 12 (1979) 195–202. w11x B. Lamy, J. Berlie, J. Mater. Sci. Lett. 3 (1984) 1069–1070. w12x G.M. Hamilton, Proc. Instrum. Mech. Eng. 197C (1983) 53–59. w13x D. Maugis, Course of Ecole des Ponts et Chaussees, ´ Paris, 1987. w14x D. Tabor, The Hardness of Metals, Clarendon Press, Oxford, 1951. w15x B.J. Briscoe, K. Sebastian, Proc. R. Soc. A 452 (1996) 439–457. w16x D. Tabor, Proc. R. Soc. A 192 (1948) 242–274. w17x G.W. Stachowiak, G.W. Batchelor, Engineering Tribology, Tribology Series, twenty-fourth ed., Elsevier, 1993, Chapter 7. w18x J.C. Jaeger, Proc. R. Soc., NSW 76 (1943) 203–224. w19x N.G. Mc Crum, B.E. Read, G. Williams, Anelastic and Dielectric Effects in Polymeric Solids, Wiley, 1967.
Understanding of automotive clearcoats scratch resistance P. Bertrand-Lambottea,b, *, J.L. Loubeta, C. Verpyb, S. Pavana a
` Ecole Centrale de Lyon, UMR CNRS 5513, Laboratoire de Tribologie et Dynamique des Systemes, 36, avenue Guy de Collongue, F-69134 Ecully, France b ¨ Centre technique de Velizy, ´ ´ ´ ´ – Peinture, Route de Gisy, PSA Peugeot Citroen, Direction Materiaux et Procedes F-78943 Velizy Villacoublay Cedex, France
Abstract Micrometric scratches, mainly due to car wash brushes, decrease the gloss of automotive clearcoats, alter their appearance and prevent them from protecting the car in the best way. Scratch resistance is estimated from the visible damage caused on the clearcoats. As the eye is more sensitive to brittle than to ductile scratches (Microstructures and Microtribology of Polymer surfaces (2000) 428), one way to improve scratch resistance it to decrease the proportion of brittle scratches and to favor healing of ductile scratches. An analysis of the contact during a scratch test shows that the ductileybrittle transition is controlled by both an energetic and a size criterion. The energetic criterion is related to the tensile stress located at the rear of the contact between the indenter and the clearcoat. This stress can enlarge existing cracks, leading to fracture. It depends on the clearcoats viscoelastoplastic properties, the mean deformation imposed by the indenter and the environment (dry tests or tests in water or soapy water). The effect of these parameters on scratch resistance has been studied: indentation and scratch tests with a Nanoindenter XP have been carried out. The healing of ductile scratches has been estimated from scratched samples of clearcoats. The samples have been heated at different temperatures and the remaining scratch depth measured with an atomic force microscope. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Nano-indentation; Nano-scratch; Thermoset resins; Ductile; Brittle; a Relaxation; b Relaxation
1. Introduction Automotive clearcoats compose the outer layer of automotive coatings and consist of thermoset resins w2x. Their thickness ranges from 40 to 50 mm. They make automobiles glossy and protect them from environmental damage such as stone chipping, marring, UV radiations, acid rains w3x, etc« This study focuses on marring brought about by car wash machines brushes. 2. Analysis and experimental procedure 2.1. The samples Automotive clearcoats samples of different chemical *Corresponding author. Tel.: q33-4-72-18-65-96; fax: q33-4-7843-33-83. E-mail address: [email protected] (P. Bertrand-Lambotte).
compositions have been brushed by a car wash simulator. The scratches have been observed with an atomic force microscope (AFM) (Park Instruments䉸 ). In general, the scratches are between 0.05 and 2 mm deep, 1 and 10 mm wide. As the damage is limited to the first few microns of the clearcoats, the latter are considered as semi-infinite materials. There are both ductile and brittle scratches. Ductile scratches present no tearing and we will show that heating can make them disappear. On the contrary, brittle scratches show irreversible damage and the eye is more sensitive to brittle than to ductile scratches w1x. The whole study is based on two reference clearcoats (A and B) chosen from a dozen of available ones. They have been chosen for their difference in mar resistance. ¨ functional tests based According to PSA Peugeot Citroen on loss of gloss measurements, A is the clearcoat with the best scratch resistance while B is the clearcoat with the worst scratch resistance.
0040-6090/02/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 2 . 0 0 9 4 3 - 4
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2.3. The ductileybrittle transition 2.3.1. Analysis Our goal is to relate intrinsic clearcoats parameters to the ductileybrittle transition. This transition is studied from two energetic viewpoints.
Fig. 1. Material containing a crack of width c on which a tensile stress st is applied.
2.2. The ductile scratches Nano-indentation tests w4x have been performed with a Nano-indenter XP (MTS䉸) to determine the clearcoats viscoplastic properties and so to understand ductile scratches. The hardness H is defined as PyAN where AN is the projection of the contact area in a plane normal to the normal applied load P. Continuous stiffness measurement has been used: from an indentation curve (normal load P vs. depth h), the evolution of the hardness H vs. h is determined as a continuous function with only one indent. Each nanoindentation test is performed at a constant strain rate ´˙ ˙ w7x) w5,6x: this is ensured (´˙ is defined as (1y2)(PyP) ˙ by maintaining PyP constant w7x. The maximum load is 15 mN. To enlarge the explored strain rates range and to understand ductile scratch mechanisms, nano-scratch tests and nano-indentation tests at different temperatures (from 0 to 45 8C) have been carried out. In the scratch tests, a Berkovich indenter is used face forward at a constant load (15 mN). Scratch hardness is then defined as FT yAT where FT is the tangential force and AT is the projection of the contact area in a plane normal to v. A thermal chamber used to perform indentation tests at different temperatures was made at our request by Servathin䉸. Additionally, because ductile scratches can heal when heated, experiments were conducted to try and understand these healing mechanisms. To do this, clearcoats with scratches performed with a Berkovich indenter face forward (constant load of 15 mN), have been heated at different temperatures for 1, 5 and 10 min and the scratch depth was then observed via AFM at room temperature.
2.3.1.1. Two energetic viewpoints. (1) A crack of width c in a Hookean material w8x on which a tensile stress st is applied (Fig. 1) will grow if st2cyE0Gc (fracture energy criterion) where E is the elastic modulus and Gc the fracture energy of the material. For ductile materials w9x, the energy released to make the crack grow is used both to create new surfaces and to plastify the material. So Gcs2gqsy´prplastic (g is the surface energy, sy the yield stress, ´p the plastic strain, rplastic the radius of the plastic zone at the tip of the crack). Actually, 2g
Fig. 2. Scheme of the plastic deformation and of the fracture which can occur in a ductile material when a tensile stress st is applied on it.
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Fig. 4. Scratch test geometry for a spherical indenter in elastic contact where A is the contact area, st the tensile stress at the rear of the contact, P the normal applied load, and v the scratch velocity. Fig. 3. Representation of the energy and of the size criteria ruling the ductileybrittle transition of a ductile material containing a crack of width c on which a tensile stress st is applied. The brittle area is reached if s2t)GcEyc (energy criterion) and if the size of the material is higher than 2Gcysy´p (size criterion). Gc is the fracture energy of the material, E its elastic modulus, sy its yield stress and ´p its yield plastic strain.
2.3.1.2. The tensile stress in scratch experiments. (1) In a scratch test, st is the tensile stress at the rear of the contact between the indenter and the clearcoats. (2) In the elastic case and for a sphere–plane contact (Fig. 4), sts
3P B 1y2n 4qn Ft E C q p F 2pa2 D 3 8 PG
w12x (n is the Poisson ratio) where a is the contact radius. The interfacial stress is defined by tsFt yA. Since a 3s3PRy4E* (Hertz theory) and since the strain is proportional to ayR, the tensile stress is proportional to E*´qCt where C is a constant. According to the Way theorem w13x, the stress field out of the contact zone is the same whatever the geometry of the indenter, thus the st expression is valid whatever the indenter. (3) In the plastic case (Fig. 5), we define st as Ft y ANS where ANS is the projection of the contact area in a plane normal to P. Since FtsqmATqtANS (qm is the normal stress and t the tangential stress), stsqm(AT y ANS)qt and as HsFt yAT, qmsHy(ty ´). For spherical and conical indenters, AT yANS is proportional to the strain ´. Thus, the tensile stress is proportional to H´q Dt where D is a constant. (4) Automotive clearcoats are viscoelastoplastic materials, thus when the tensile stress at the rear of the contact is lower than the yield stress, st is proportional to E*(f)´qCt, where f is the exciting frequency. When st is higher than the tensile stress (this is our case in the study of the ductileybrittle transition), st is proportional to H(´˙ )´qDt. Neglecting the interfacial term, st is proportional to H(´˙ )´. Thus the fracture energy criterion becomes (H2 yE)(´˙ )´2c0Gc, putting forward the influence of the viscoelastoplastic properties
of the clearcoats and the influence of the indenter geometry (through ´). 2.3.2. Experimental procedure To highlight the two criteria describing the ductiley brittle transition, nano-scratch tests have been performed with indenters of different geometries: a Berkovich and a trigonal indenter (both face forward) and a spherical indenter (radius Rs10 mm). The normal applied load is increased along the tests and the scratch velocity v is 1 mmys. When using Berkovich and trigonal indenters, the strain ´ remains constant w6,14,15x during the scratch test. The strain rate ´˙ is taken as vyl w4x where l is a characteristic length defined by yANS y yp. In this case, l is close to the scratch width. In contrast, when using a spherical indenter, the strain increases during the test as ´ is proportional to ayR w16x, where a is the contact radius and ´˙ is taken as vy R. 2.4. Method verification Automotive clearcoats are viscoelastoplastic materials, thus their mechanical properties depend on the imposed frequency, as well as temperature. The frequency at which they are strained by car wash brushes is approx-
Fig. 5. Scratch test geometry for a conical indenter in plastic contact where A is the contact area, ANS the projection of the contact area in a plane normal to the normal applied load P, AT the projection of the contact area in a plane normal to the scratch velocity v, Ft the tangential force, qm the normal stress and t the tangential stress.
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Fig. 6. Hardness data of clearcoat A at different strain rates from indentation and scratch tests. One can notice the recovery between indentation and scratch results.
imately 105 ys (calculated from vyl, where v is the linear velocity of the brushes (vs1–2 mys) and l the scratch width (1–10 mm)). However it is less clear what the associated temperature is, namely what is the contact temperature? When two solids are in friction, a great fraction of the dissipated energy is converted into heat. This increase in temperature (DT) with respect to room temperature is short-lived and is called ‘flash temperature’. Flash temperature theory w17,18x gives estimated tables of the temperature increases depending on frictional velocity v, frictional coefficient m, contact radius a, thermal conductivity l and thermal diffusity a. In our case, DT is given by the following expression DTs0.308(mvyl)(Pypa2)pa(ayva)0.5and is estimated to be approximately 43 8C w4x. That means that car wash brushes impose a 105 Hz frequency, at a temperature of 20q43 8C. In contrast, the imposed strain rates at a reference temperature of 20 8C in the nanoindentation and nano-scratch tests, range from 10y3 to 10ys. In order to compare this range of frequencies to those imposed by car wash brushes, the same reference temperature has to be considered. According to the time temperature superposition principle, a one-decade-shift in frequency is analogous to a 6 8C-shift in temperature (Arrhenius equation with activation energy round 300 kJymol w4x). Thus it is equivalent to consider the clearcoat at a temperature of 20q43 8C at a 105 ys, and to consider it at 20 8C at 10y2 ys. This is the approximate frequency range explored during the nano-indentation and the nano-scratch tests, which valids the method.
plasticity in scratch tests is equivalent to study viscoplasticity in indentation tests w4x. From indentation hardness curves determined at different temperatures w3x, a master curve is plotted using the time–temperature principle (Fig. 7). The shift factor, aT, obeys an Arrhenius law, ln aTsyQVP yR((1yT)y (1yT0)), and plotting ln(aT) vs. 1yT allows calculation of the viscoplastic activation energy QVP where R is the perfect gas constant and T0 the reference temperature (20 8C). Activation energies were determined to be QVPs140 and 110 kJymol for clearcoats A and B, respectively. Mechanisms of ductile scratches are ruled by energies which are in the order of magnitude of b secondary relaxations, which would mean that only local motions of the polymer chains are involved (the loss peaks of polymers are often labelled with Greek letters a, b, g« w19x; the a peak corresponds to the relaxation observed at the highest temperature at a given frequency or the lowest frequency at a given temperature; the b and g symbols then apply to the other relaxation regions in order of decreasing temperature or increasing frequency). 3.2. Healing of ductile scratches w3x Master curves of scratch depth vs. time have been determined with a reference temperature of 30 8C (Fig. 8). Almost all clearcoats exhibit the same curve profile with first a plateau, followed by a decrease of the scratch depth (occurring at ‘healing temperature’) and then a second plateau. The first plateau represents the temperature range where scratch healing cannot occur as motions of the polymer chains are limited. Activation energies of the healing process have been determined using the Arrhenius law, and are for clearcoat A, Qhealings470 kJymol and for clearcoat B, Qhealings500 kJymol, respectively. The healing temperature has been compared to the a relaxation temperature of each clearcoat, measured by DMA (tensile tests at 1 Hz) w3x. It appears that the healing temperature is very close to the
3. Results and discussion 3.1. Formation of ductile scratches Scratches created with the Berkovich indenter are ductile and the scratch hardness results are consistent with the indentation hardness results (Fig. 6): that is to say at a given strain rate, the scratch hardness is the same as the indentation hardness. Thus, studying visco-
Fig. 7. Time–temperature superposition curve of hardness data vs. strain rate for clearcoat A. The reference temperature is 20 8C.
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Fig. 8. Time–temperature superposition curve of scratch depth vs. time for clearcoat A. The reference temperature is 30 8C. A first plateau is followed by a decrease of the scratch depth and then by a second plateau. The decrease of the scratch depth occurs at ‘healing temperature’.
Taonset (corresponding to the temperature from which the elastic modulus starts decreasing). Furthermore, healing activation energies are in the order of magnitude of the activation energies of a relaxations. These results show that healing of ductile scratches is ruled by the main relaxation (a relaxation) of the clearcoats. That would mean that healing entails large motions of the polymer chains. 3.3. Ductileybrittle transition When performing scratches with the Berkovich and the trigonal indenter, the strain ´ remains constant: the corresponding tests are represented in Fig. 9 with an horizontal line. Parallel to the first x-axis, a second x-
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axis representing the scratch width is shown. Scratches performed with a Berkovich indenter on clearcoats A and B are ductile whatever the applied load. In contrast, scratches performed with a trigonal indenter on clearcoats A and B are ductile, as long as the scratch width is lower than 3.5–4 mm. Beyond this width, they become brittle. In scratch tests performed with the spherical indenter, the strain increases along the scratch. Since ´ is proportional to ayR and P is proportional to a 2, these tests are represented in Fig. 9 by a parabolic curve. The ductiley brittle transition occurs when the scratch width becomes higher than 11 mm for clearcoat B and higher than 17 mm for clearcoat A: the transition is ruled by the fracture energy criterion. The same tests performed in soapy water show that the ductileybrittle transition occurs later, namely at higher scratch width w4x. 4. Conclusion This paper focuses on marring brought about by car wash machines on automotive clearcoats. Two types of scratches were observed on the clearcoats: ductile and brittle scratches. To improve clearcoats mar resistance, especially brittle scratches occurrence has to be delayed: both the fracture energy criterion and the size criterion can be shifted (s2tcyE is decreased and 2Gc ysy´p increased), which puts forward the significance of viscoplastic properties in fracture mechanics.
Fig. 9. Scratching maps of clearcoats A and B determined from our two criteria (fracture energy and material size criterion), separating ductile and brittle areas. Typical observations of scratch tests performed with indenters of different geometry are reported on the map.
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