A Novel Buckling Indicator using the Correlation Between in-Plane and out-of-Plane Displacements N. A. Zanjani A. Dervaric S. Kalyanasundaram Research School of Engineering The Australian National University North Road, Canberra 2601, Australia Abstract— The current article investigates the buckling phenomenon in Aluminium sheets possessing different aspect ratios through a modified Yoshida buckling test. Specimens were uniaxially extended until catastrophic failure. Results of the optical photogrammetry technique revealed the evolution of out-of-plane displacements and in-plane state of strain in specimens during different stages of deformation. A Wrinkling Limit Diagram (WLD) was constructed based on induced principal strains in specimens. It was demonstrated that a specific WLD capable of differentiating between wrinkled and unwrinkled regions does not exist. Based on the cross sectional evolution of the specimen, a novel measure was proposed, showing to be a far more effective indicator of the wrinkling onset. Then, its applicability to some typical forming problems was studied. Keywords— Modified Yoshida Buckling Test, Principal strains, Wrinkling behavior, Wrinkling Limit Diagram. I. INTRODUCTION Wrinkling is a common type of instability during sheet metal forming. It manifests itself as low amplitude, small wavelength waves presented in different regions of the formed part. Underlying source of wrinkling is an increasing compressive stress experienced mostly in unsupported regions during a die forming practice such as sidewalls or flange areas. During a typical stamp forming process, a sheet of material flows into the die and conforms to the punch geometry, causing a reduction in the perimeter of the specimen proportional to its radial displacement. The induced deformations cause significant compressive stresses, triggering onset of instabilities such as local buckling (Wrinkling). Wrinkling is undesirable and deleterious as it affects the normal appearance of the final product, alters the required geometrical tolerances and degrades the mechanical properties of the component. Employing a stringent indicator for wrinkling assists manufacturers to discard the cumbersome trial-and-error procedure during die try-out, increasing manufacturing rate while reducing associated costs and production scraps. One of the earliest attempts aimed at determination of wrinkling in sheet metals was performed by Senior [1]. In this article, a theoretical measure was proposed to predict the onset of wrinkling and to quantify the number of wrinkles observed in the flange area. The analysis was based on the energy method, stress-strain curve of the material and the flange geometry to specify the critical conditions triggering wrinkling. Hill’s early works on stability of solids [2] attempted at formulating the stability condition as a boundary- value problem. It was found that only under some predefined stress conditions, the governing differential equation offers a unique solution. However, if induced strains or deformations are large, the uniqueness of the solution could not be guaranteed. Matsui, Iwata and Mori [3] investigated initiation and development of buckling in a diagonally stretched square specimen. Afterwards, a Finite Element (FE) analysis was conducted, and final results were verified by experimental outcomes. A clear correlation between loading conditions and material properties on buckling initiation and development was found. Szacinski and Thomson [4] investigated the possibility of constructing an empirical Wrinkling Limit Diagram (WLD), although they suggested that a mathematically definable WLD does not exist. In this investigation, detection of wrinkles on the surface of the drawn-sink bowls was done via a laser beam method. Based on experimental results, it was concluded that no definite theoretical WLD can be established to provide a criterion for initiation of wrinkling. Li, Brazil and Chu [5] used an experimental set-up using two strain gauges at both sides of an Aluminium sheet subjected to a non-uniform tensile stress field in a Yoshida Buckling Test (YBT). The evolution of wrinkles height was monitored as a function of stresses and strains developed in the center of sheets. It was found out that plastic anisotropy has the smallest effect on the occurrence of bifurcation phenomenon. Finally, it was concluded that WLD is not a material characteristic, unlike a Forming Limit Diagram (FLD), and therefore cannot be established uniquely for a specific material, simply because it is dependent to other factors such as geometry of the part, thickness of sheets, stress-path and friction. Bayraktar, Isac and Arnold [6] conducted experimental investigations to determine a Buckling Limit Diagram (BLD), conceptually similar to a WLD, for an Interstitial Steel (IFS) through the YBT. Circular blanks having thicknesses varying from 0.7 mm to 1 mm were used in these tests. The heights of wrinkles were measured as a function of extension applied to the specimens. Based on the experimental outcomes, it was concluded that thickness of sheets and yield stress of the material are determinant factors in wrinkling initiation during deep drawing operations. Narayanasamy and Loganthan [7] investigated wrinkling limits of pure Aluminium sheets through drawing process. Three different Aluminum grades, each heat treated by four different methods, were drawn through conical and tractrix International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 www.ijert.org IJERTV3IS100683 (This work is licensed under a Creative Commons Attribution 4.0 International License.) 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