RESEARCH PAPER
Calculating post-uniform deformation energy using tensile parameters S. Khani Moghanaki1,2, H. Pouraliakbar*1,2, M. R. Jandaghi1,2, R. Bagheri1 and G. Khalaj2 Post-uniform deformation energy of materials is defined as absorbed energy per unit area after necking. The energy is constant for a material type and its experienced specific processing history and also depends on its mechanical parameters as workhardening exponent, strain rate sensitivity, post-necking extension and inhomogeneity factor. Different methods such as single and multiple tensile testing had been proposed in the literature to calculate tearing energy, but the effect of post-necking extension had not been expressed explicitly. A new model by implementing uniform and failure elongations with the combination of Unwin theory is introduced. Based on the model, it was shown that tearing energy was a constant portion of uniform deformation energy in every specific material, and its value for alloys of aluminium, copper and brass was calculated through previous and new developed models. Keywords: Post-uniform deformation energy, Post-necking extension, Tearing energy, Metal forming, Modelling
Introduction The total absorbed energy in ductile deformation of materials consists of two components: one is uniform deformation energy (UDE), which occurs in the workhardening stage, and the second is post-uniform deformation energy (PDE) that results in material tearing. In structure designs for higher energy absorption, the value of PDE is critical.1 This energy could be obtained through single and multiple tensile testing (STT and MTT) methods.2–5 In STT, PDE can be calculated by subtracting the UDE from the total absorbed energy. In MTT, tensile tests are carried out on specimens with different gauge lengths, it can be calculated by plotting the total absorbed energy divided by cross-sectional area against gauge lengths and it results in a straight line in which the slope is UDE per unit volume and the intercept is PDE per unit area of material. Askariani et al.6 compared the tearing energy of interstitial free and low carbon steel by MTT method, and their findings showed that interstitial free steel with lower strength and higher uniform extention (UE) exhibited higher UDE and lower PDE than that of low carbon steel. In another study by similar method, they reported that the PDEs obtained for annealed AZ31 sheets were comparable to those of AA 5010 sheets, while the UDEs were much higher than those of aluminium sheets.7
Mahmudi8 showed that PDE was related to the neck breadth parameter N, which was proposed first by Ghosh,9 influenced by the workhardening exponent n and strain rate sensitivity m. Mahmudi3 demonstrated that PDE increased when N increased. N relates to postuniform extension (PE); consequently, PDE relates to PE. In metal forming processes, PE is important due to the possibility of continuing the forming even after plastic instability occurs.10 Hatakeyama et al.11 indicated that PE in tensile test is related to the degree of strain localisation along the tensile axis. According to the literature, the effect of PE on absorbed PDE had not been stated explicitly, while the aim of the present study is to show this correlation explicitly. In order to demonstrate the direct effect of PE, a previous model for calculating PDE in uniaxial tensile test was modified using Unwin12 theory, and finally a new mathematical model that correlated it to parameters of UE, PE, specimen gauge length and workhardening parameters was proposed and discussed.
Calculating PDE Ductile materials deformations consist of two parts of elastic and plastic straining. The plastic part includes yielding, uniform deformation and non- or post-uniform deformation. The non-uniform deformation stage occurring after necking results in tearing. Any material absorbs energy during all stages, which could be shown as follows
1
Department of Materials Science and Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran Department of Advanced Materials, WorldTech Scientific Research Center (WT-SRC), Tehran, Iran
W ~Weld zWpld zWpud
(1)
2
*Corresponding author, email
[email protected] and
[email protected]
ß 2013 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute Received 25 July 2013; accepted 27 August 2013 DOI 10.1179/1743284713Y.0000000390
where W is the total absorbed energy of the bulk material, Weld is the absorbed energy in the elastic deformation stage, Wpld is the UDE and Wpud is the
Materials Science and Technology
2013
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