Numerical modelling for prediction of ductile fracture of bolted structure under tension shear loading T. Dang Hoang n , C. Herbelot, A. Imad, N. Benseddiq Mechanics Laboratory of Lille, CNRS UMR 8107, Ecole Polytech’Lille, University of Lille—North of France, Cite ´ scientifique, Boulevard Paul Langevin, Villeneuve d’Ascq Ce´dex 59655, France article info Article history: Received 19 March 2012 Received in revised form 11 December 2012 Accepted 20 December 2012 Available online 30 January 2013 Keywords: Bolted assembly Damage Numerical simulation Tightening torque Clearance abstract This paper investigates numerical simulation using the 3D finite elements model to predict the global behaviour of a bolted joint. The tightening torque and clearance will be considered for the analysis of the global mechanical behaviour of the connection. The calculations are carried out both in elasto- plasticity and elasto-plasticity with damage using the energy model of Latham and Crockoft. The numerical results are compared to experimental results. This allows for the explanation of the various phases of the behaviour of the assembly as well as to validate the models and parameters chosen. & 2012 Elsevier B.V. All rights reserved. 1. Introduction The bolted joints are often used in aeronautics, automotive, railway structures and also in several mechanical components (cranes, bridges, etc.). Bolted structures have the advantage of easy implementation. Such assemblies include both metal sheets (aluminum, steely) [2] and composites [3], with body bolts in aluminum, steel and titanium alloys. The use of such structures requires the mastering of their mechanical behaviour in static [4], dynamic [16], and fatigue contexts [5]. Several research works have been focused on the mechanical behaviour of these struc- tures: analytical approach, experimental and numerical simula- tion [6,7]. The numerical simulation of metal sheets assembled by bolted joints presents a difficulty in implementation of the structure real behaviour with all its variants. There is a simplified model, dealing with a 2D structure; a hypothesis regarding the mode of load transmission. We can name the resort model type where the plates and bolted joints are modeled by springs solicited in the applied load direction [8,9]. This type of model is primarily used to deduce the load transfer. Note that the phenomenon called secondary bending can’t be included. Furthermore, we also find models representing the plates by shell elements and bolted joints by beam elements, introducing the contact conditions. Crocombe et al. [10] successfully performed a numerical simula- tion of the bolted assembly using a single-lap joint (two alumi- num plates and a steel bolt). These authors opted for a model using shell elements for the plates, since solid elements make modeling difficult [11]. The authors examined the influence of the friction coefficient in the contacts on the evolution of the applied load versus structure displacement. These authors noted that the elastic phase increases with the friction coefficient. It is well known that the problem with numerical modeling is how to describe the behaviour of plates and the movement of the bolt, particularly in a single-lap tension shear test. The complexity of this model is mainly due to all the phenomena involved in its operation. The eccentricity of loads generates secondary bending creating non-linear stress at the assembled plates level and forcing the rotation of the bolted joint. Taking into account the relative movements of determined surfaces between two ele- ments of the connection leads to define different zones in which the contact should be considered differently [12]. Another sig- nificant parameter of the bolted assembly, the tightening torque, generates pre-stress in the assembly. To introduce this pre-stress into the model, the sheets are solicited in compression corre- sponding to the tension in the bolt [13–15]. In the study done by Langrand et al. [16], finite elements modeling of mechanical assemblies under dynamic loading are examined. The Gurson model is used to describe the damage behaviour of ductile metal. The model’s parameters are identified for the metal sheet plate and rivet aluminum alloys by an inverse method. Dano et al. [17] determined the influence of the failure Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/finel Finite Elements in Analysis and Design 0168-874X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.finel.2012.12.003 n Corresponding author. Tel.: þ33 328767463; fax: þ33 328767301. E-mail address: thong.dang-hoang@polytech-lille.fr (T. Dang Hoang). Finite Elements in Analysis and Design 67 (2013) 56–65