Applied Surface Science 257 (2010) 857–860 Contents lists available at ScienceDirect Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc Regeneration of surface roughness by the Langevin equation using stochastic analysis on AFM image of a carbon fiber Masoud Allahkarami ∗ , Jay C. Hanan, Hrishikesh A. Bale Mechanical and Aerospace Engineering, Oklahoma State University, Tulsa, OK, USA article info Article history: Received 7 February 2010 Received in revised form 9 June 2010 Accepted 25 July 2010 Available online 30 July 2010 Keywords: AFM (atomic force microscopy) Stochastic analysis Surface roughness regeneration Carbon fiber abstract A new method was developed using AFM images of a fiber surface to regenerate the surface roughness in 3D geometry, such as the cylindrical shape of a “model” fiber. The Langevin equation was used to derive the fluctuations of a carbon fiber surface image. The equation contains two quantities, D (1) (h) and D (2) (h) which in physics represent drift and diffusion coefficients. Knowing this coefficient and adding a proper noise function, a similar surface of larger dimension with the same statistical properties of the initial data was created. The generated surface was mapped into cylindrical coordinates, then a mesh generated. The resulting reconstructed surface, input over the geometry of a cylindrical shape, can be implemented for finite element analysis of a single fiber surrounded by matrix and generalized to a many fiber model. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Because of its stiffness, dimensional stability, corrosion resis- tance and low weight, carbon fiber epoxy composites become predominate in space application namely for support structures, antenna and dishes [1,2]. In aerospace and marine industries, car- bon fiber composites have been replaced with structural materials like aluminum or titanium to reduce weight and increase fuel efficiency. Carbon fibers are also used in the automotive indus- try [3], as gas storage cylinders, for robot arms, turbine blades, and sporting goods. Manufacturers can generally reduce the total weight and utilize the stiffness of carbon fiber. Cost was an issue preventing application of carbon fibers in smaller industries, but recently by decreasing the price of such composites, there is an increasing appearance of carbon fiber composites for new appli- cations [4]. Recent fiber reinforced composite technology success benefits from improvement in analytical models for optimiza- tion of fiber to matrix volume fraction, fiber size, orientation, and distribution along with experimental efforts on fiber surface treat- ments to increase interface adhesion and strength [5]. Recently, long thin diameter fibers have become available which have a high ratio of surface to unit volume. This large ratio of surface- to-volume increases the value of development of new methods in the field of composite analysis which considers the surface proper- ties of the fiber/matrix interface. The fact that failure may initiate ∗ Corresponding author. Tel.: +1 918 594 8629; fax: +1 918 594 8628. E-mail address: masoud.allahkarami@okstate.edu (M. Allahkarami). from a weak or defective fiber/matrix interface and consequently reduce ultimate performance, increases current interest in improv- ing and understanding interfacial bonding of the fiber with matrix [6]. Remarkable improvement in the mechanical properties and performance of composites have been achieved using nanofiller- modification in the polymer matrix, which increases the interfacial stress transfer efficiency, and reduces the local stress concentra- tion in the interface between the fiber and matrix [7,8]. Similar enhancement is also obtainable using one of various available sur- face treatments [9]. Statistical analysis on atomic force microscopy (AFM) images of carbon fibers during the surface treatment is an effective tool that can be used to characterize the treatment [10–12]. A problem with this technique is the near impossibility to scan the entire surface of a typical fiber by AFM to produce a profile of surface height in different positions. Since the fiber has a cylindrical curvature, a difficult full range of 360 ◦ scan would be sought. However, just scanning a representative portion of the fiber is possible. This encourages finding a way to reproduce the surface using representative information. To be representative, the regenerated surface must retain the statistical properties of the original. In the current work statistical analyses were done on AFM images to create 3D models of fibers having surface roughness sim- ilar to the actual fibers. One can implement this model to predict the mechanical response of an interface area between fiber and matrix, required for simulating realistic surface geometries. Simi- lar work has been done to input real dental crown geometry for FEA (finite element analysis) analysis using Abaqus software [13]. The change in idea here is using AFM images to reconstruct the geome- try instead of using X-ray tomography to reconstruct the accurate body. 0169-4332/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2010.07.081