Shear strength prediction of Ni–Ti alloys manufactured by powder metallurgy using fuzzy rule-based model M. Tajdari a, * , A. Ghaffarnajad Mehraban b , A.R. Khoogar c a Department of Mechanical Engineering, Islamic Azad University, Damghan Branch, Damghan, Iran b Department of Energy, Power and Water University of Technology, Tehran, Iran c Department of Mechanical and Aerospace Engineering, Azad University of Science and Research, Hesarak, Tehran, Iran article info Article history: Received 7 July 2009 Accepted 18 September 2009 Available online 1 October 2009 Keywords: Powder metallurgy Ni–Ti alloys Fuzzy logic ANN Prediction abstract Powder metallurgy is an important manufacturing method and developing models that can predict the characteristics of the products is remarkable for researchers. There are many models discussed in the lit- erature for prediction of the product properties however, nonlinear modeling methods including artificial neural networks (ANNs) and fuzzy models have shown better performance. In the present work, a rule-based fuzzy logic model is developed to predict the shear strength of Ni–Ti alloys specimens manufactured by powder metallurgy method. The processing time and temperature are selected as the input variables and a fuzzy model is designed with two inputs and one output variable. Four statistical parameters are used for assessment of the model accuracy. The comparison of this model result and the result of the ANN model that have been reported by previous researchers, shows that the fuzzy model is more accurate and actually better than ANN model for predicting the shear strength of Ni–Ti alloys specimens manufactured by powder metallurgy. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Powder metallurgy (PM) in many industries has not received the praise of which it is worthy, but for many years now, it has been an established process for the manufacture of precision qual- ity engineering components. This method is sometimes the only manufacturing method which can be used for some parts manufac- turing such as composite materials, porous materials, refractory metals and special high duty alloys. The PM method competes with other methods on the basis of cost which can be lowered for high volume production of complicated components. In most cases such components are manufactured using a classical PM route which in- volves deformation of the metal powder followed by sintering. The product manufactured using PM technology can lead to significant material improvements in many cases [1]. Generally, PM technique consists of the production of a con- trolled blend of metal powders, pressing the mixture in suitable dies, and subsequent heating (sintering) the compacted powder in a controlled atmosphere and temperature to obtain the required density and strength. The PM industries have expanded more rap- idly due to the recognition of the distinct advantages in terms of materials utilization, ease of components manufacture, cost/en- ergy saving and other factors [2]. The final quality of prediction in the manufacturing processes is very important. Manufacturing companies are often interested in the foresight of mechanical properties and final quality of products and they use mathematical models for the processing parameters and environment conditions prediction. Many publications have shown models that predict the characteristics of products in vari- ety of size and complexity. They represent the number of control parameters, the employed modeling method, etc. In powder metallurgy as one of the important manufacturing methods, it is highly critical to be able to the predict properties of products. In this method, variations of powder size, metal type, temperature, duration time, pressure, additive materials and other process parameters can affect the mechanical characteristics of the product. Having a model that can describe the relationship be- tween these parameters and the effect of input parameters varia- tions on the output variables, helps to select the optimum input parameters and reach the optimum output. Examples of models that developed for this purpose are submitted by Smitha et al. [3]. In this paper a review of the models that are used for material selection in powder metallurgy is presented. PM method is widely used for production of Ni–Ti alloys. Join- ing of the powder metallurgy products (PM) by diffusion bonding process is important both to protect the micro structural properties of parent materials and bonding behavior of joining materials [4]. 0261-3069/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2009.09.035 * Corresponding author. Tel./fax: +982325233583. E-mail addresses: tajdari@iuim.ac.ir (M. Tajdari), aidinmehraban@yahoo.com (A. Ghaffarnajad Mehraban), khoogar@gmail.com (A.R. Khoogar). Materials and Design 31 (2010) 1180–1185 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes