Analytical method to predict the pull-out strength of clinched connections S. Coppieters a,n , P. Lava a , S. Baes a , H. Sol b , P. Van Houtte c , D. Debruyne a,c a Department of Mechanical Engineering, Catholic University College Ghent, K.U.Leuven Association, Gebroeders De Smetstraat 1, B-9000 Ghent, Belgium b Department of Mechanics of Materials and Constructions, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium c Department of Metallurgy and Materials Engineering, K.U.Leuven, Kasteelpark Arenberg 44 bus 2450, 3001 Heverlee, Belgium article info Article history: Received 13 July 2011 Received in revised form 19 November 2011 Accepted 1 December 2011 Available online 21 December 2011 Keywords: Clinching Sheet metal Pull-out strength Analytical method abstract Clinching is a mechanical joining technique by which sheet metal parts can be assembled without the use of additional material inserts. The strength of such a connection highly depends on the final geometry of the permanent joint. The assessment of the mechanical strength is conventionally done by conducting simple experiments such as a single shear lap test. However, it is generally recognized that the axial strength of this type of connections is considerably lower than its strength in shear loading. As a consequence, it is clear that applications where the joint is loaded in the axial direction should be handled carefully. The so-called pull-out strength can be investigated by dedicated experiments or sophisticated finite element calculations. In this paper an analytical approach to estimate the pull-out strength is presented. The first part describes the method along with the necessary assumptions. The remainder of this contribution validates this analytical method through a new experimental setup and a finite element model. In addition, a correction curve is derived which enables to adapt the analytical solution accounting for bending effects. Finally, the alternative method is applied to a joint connecting two DC05 sheets. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Manufacturing thin-walled structures inevitably involves the selection of suited joining techniques. The ongoing search for new, sustainable and innovative lightweight materials puts high demands on joining skills. In order to integrate these new materials in structures, products or vehicles, appropriate joining techniques have to be available. In particular for the joining of lightweight metallic sheets, which can be coated and/or dissim- ilar, alternative joining techniques have emerged in recent years [1–4]. Amongst those, clinching – or press-joining – can assemble sheet metal parts by solely relying on local plastic deformation of the combining sheets. Unlike traditional joining techniques, clinching does not use additional material inserts, and, as a consequence, the mechanical strength of such a connection highly depends on the final geometry after forming. This paper focuses on the so-called single stroke round clinch process with a closed die. In this particular process, the joint is formed during one flowing punch movement without perforating the sheets, result- ing in an air-tight joint. Fig. 1 shows the right half cross-section of such a connection between similar materials. This figure depicts some important geometrical parameters of which the thickness of the base of the joint X, introduced by Varis [5,6], can be easily measured. Therefore this parameter is often used as a process parameter in industrial applications. Unlike this X-parameter, the neck-thickness t N and the interlock t U cannot be measured directly, however they certainly play a role of importance in the mechanical behaviour of the joint. The focus in this paper is on the axial strength of such a connection, also referred to as the pull-out strength. To be specific, in this study the possibility to analytically predict the pull-out strength is investigated. The reason for this is threefold. First, since the mechanical behaviour is entirely determined by geometrical parameters such as the amount of interlock t U and the neck-thickness t N , the performance of such a joint can be optimized for a certain loading case by altering the geometry of the tools. The design of such optimal tools can be supported by the finite element method [7] or analytical models [8]. Oudjene et al. [7] have demonstrated this by developing an automatic optimization procedure to maximize the pull-out strength of a single connection. In view of such optimization procedures, the existence of an accurate analytical prediction tool for the joints strength would greatly reduce computation time since then only the forming of the joint requires computer resources. Recently, Lee et al. [8] presented a design method for clinching tools based on analytical models for the pull-out strength. Second, the clinched region is a complex shaped zone where the material properties vary from point to point. If a thin-walled structure contains thousands of Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/tws Thin-Walled Structures 0263-8231/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tws.2011.12.002 n Corresponding author. Tel.: þ32 9 2658615; fax: þ32 9 2658648. E-mail address: sam.coppieters@kahosl.be (S. Coppieters). Thin-Walled Structures 52 (2012) 42–52