Numerical modelling of aluminium sheets formability using response surface methodology K. Velmanirajan a , A. Syed Abu Thaheer b , R. Narayanasamy c,⇑ , C. Ahamed Basha d a Department of Mechanical Engineering, Vetri Vinayaha College of Engineering and Technology, Thottiyam, Tiruchirappalli 621 215, Tamil Nadu, India b Department of Mechanical Engineering, PET Engineering College, Vallioor, Tirunelveli 627 117, Tamil Nadu, India c Department of Production Engineering, National Institute of Technology, Tiruchirappalli 620 015, Tamil Nadu, India d Department of Chemical Engineering, Athiyaman College of Engineering, Hosur 620 015, Tamil Nadu, India article info Article history: Received 22 March 2012 Accepted 11 May 2012 Available online 22 May 2012 Keywords: B. Sheet C. Forming G. Fractography G. Scanning electron microscopy abstract This study considers the tensile properties, formability limit strain and void coalescence parameters of the commercially available aluminium alloy sheets in metal forming processes using response surface methodology (RSM). Sheets of three different thickness were chosen for this study. The experimental procedure involved tensile test, forming test and void coalescence study. The effect of important input parameters namely sheet thickness, specimen orientation and annealing temperature (Heat Treatment) were used for the output of tensile test. On the other hand, the sheet thickness, blank width and anneal- ing temperature were used for finding the output of formability cupping test. These input factors and cor- responding output parameters were mathematically evaluated using Design Expert 8.0.7.1, trial software for constructing the numerical modelling on the output parameters namely strain hardening exponent (n-value), plastic strain ratio (r-value), strength coefficient (K-value), product of n-value and r-value (nr-value), fracture and forming limit strain and void coalescence properties like d-factor, ligament thick- ness, length to width (L/W) ratio and void area fraction. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction The application of lightweight Aluminium has increased because of its unique desirable characteristic in many engineering applica- tions. Designers prefer Aluminium, and its alloys. Aluminium alloys, vary by its tensile properties, formability properties and void coalescence properties from one another at different stress state and strain conditions. The outcome of formability analysis of alu- minium with its alloys will be the useful input for designing and manufacturing of modern engineering components, because most of the components are manufactured by forming process. Extensive research on its formability aspects is required to develop useful components of complex shapes [1]. The ability of the sheet metals to be formed into various shapes without failure is termed as form- ability [2]. In the past decade, many researchers investigated the re- sults of mechanical properties and forming and fracture limit strains of various aluminium alloys. These results can be analysed and compared to bring out the common outcomes. An analytical method is presented for predicting the forming limit diagrams, which were achieved during the sheet metal forming operations, for the sheets having isotropy nature [2]. Results from this analysis are compared with the experimental data for AA3105 and AA8011 aluminium alloys. The results indicate good prediction of limit strains for the two alloys when the Vocé and the Tian–Zhang equa- tions are applied [3]. Post-processing of forming models often utilises predicted in-plane principal strains which are directly com- parable to strain measurements using conventional circle grid tech- niques for formability assessment [4]. The mechanical properties of materials like tensile properties and formability properties of aluminium alloys have been discussed in detail by the researchers working on the materials [5]. The impact of annealing process on materials properties are proved through many research articles [6–11]. The works are correlating the tensile properties like strain hard- ening exponent (n-value), plastic strain ratio (r-value), strength co-efficient (K-value), yield strength and tensile strength with the relevant formability anisotropy and void coalescence parameters [5,12]. Forming limit measure is useful in determining the flow property of sheet metals. It has been discussed in many articles stating the findings (or) outcome of different materials and its prop- erties [12–16]. The fracture behaviour is the recent trend in mate- rials and analysis surface studies [17,18]. The scanning electron microscopy (SEM) images are used for analysing the void shape, dimple size, ligament thickness, density of voids and its intensity 0261-3069/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2012.05.027 ⇑ Corresponding author. Tel.: +91 431 2503504, mobile: +91 94439 84160; fax: +91 431 2500133. E-mail addresses: velmanirajan@gmail.com (K. Velmanirajan), pet.engg@gmail. com (A. Syed Abu Thaheer), narayan@nitt.edu (R. Narayanasamy), cab_50@ rediffmail.com (C. Ahamed Basha). Materials and Design 41 (2012) 239–254 Contents lists available at SciVerse ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes