Surface roughening of metal-polymer systems during uniaxial plastic deformation
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Surface roughening of metal-polymer systems during uniaxial plastic deformation R. van Tijum, W.P. Vellinga, J.Th.M. De Hosson Department of Applied Physics, Materials Science Centre and the Netherlands Institute for Metals Research, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands ABSTRACT In this paper we present model calculations of the deformation of a glassy polymer film supported by a plastically deforming metal substrate. The focus is on the resulting roughening of the free polymer surface. In the calculations a mixed-mode rate independent cohesive zone has been employed as the interface between the metal and the polymer. The mechanical behavior of the polymer is characterized by an elastic regime, a softening regime and finally a hardening regime. Above the yield point of the polymer shear bands occur that transfer the evolving roughness of the deforming metal through the polymer coating. It turns out that in this regime the resulting rms roughness at the free polymer surface may be higher than that of the underlying metal substrate. For this to occur the thickness of the coating must be higher than the correlation length of the rough metal substrate. INTRODUCTION In an increasing number of applications metal-polymer laminates are produced as plates and afterwards formed to their final shape. During forming large deformations occur that result in roughening of the metal substrate. The polymer coating has to conform to the metal substrate, which may affect the mechanical integrity of the polymer coating. The resulting deformations have an impact on the roughness of the free polymer surface. For applications the optical and mechanical properties of the outer surface are important. In the past various studies were devoted to describe the adhesion between polymers and self-affine rough metals [1] and recent work shows that for all strains the surface during a deformation process of a metal could be seen as a self-affine surface [2,3]. This paper concentrates on the effect of the self-affine roughening process on the polymer coating outer surface. EXPERIMENTAL SETUP During uniaxial tensile tests metal surfaces are self-affine for all strains up to breaking [2,3]. The surface can be characterized by: f (r ) =< (h( x + r ) − h( x)) 2 > (1) where h(r) is the measured height at a certain position r. For self-affine surfaces with a Gaussian distribution of local heights the values of f(r) at a strain ε can be approximated with a single valued continuous function g(r, ) [4]: 2 H (ε ) g (r , ε ) = 2w(ε ) 2 (1 − exp[− ( r / ξ (ε ) ) ]) (2)
This height-height correlation function describes the surface roughness in a statistical sense by defining an rms roughness w above a certain lateral correlation length , and a Hurst exponent H below .
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One of the simplifications proposed here is to parameterize the roughness evolution of a metal surface as a function of strain, and to assume that the roughness evolution at a polymer-metal interface is essentially identical to that of the m
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