Generalized Constitutive-Based Theoretical and Empirical Models for Hot Working Behavior of Functionally Graded Steels
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FUNCTIONALLY graded materials (FGMs), which have been developed widely in recent decades, can help researchers overcome the shortcomings of composite materials with jumps in material properties.[1] In this area, functionally graded steels (FGSs) are a special group of FGMs with elastic-plastic behavior. Some researchers have studied the fracture characteristics of specimens with this kind of material distribution.[2] For example, Bezensek and Hancock obtained the fracture toughness and the Charpy impact resistance of FGSs produced by the laser welding process.[3] Aghazadeh and Shahossini produced another type of FGSs from austenitic stainless and ferritic steels by means of the electroslag remelting (ESR) process.[4] During the past decades, FGSs with different configurations have been produced and their tensile behavior has been experimentally studied and simulated considering the Vickers microhardness profile of over the material variation direction.[5] Recently, the Vickers microhardness profile of abc FGSs was predicted using the theory of mechanism-based strain gradient plasticity (MSG).[6] In this regard, the dislocation density of each layer in the graded region is related to the Vickers microhardness of the layers. Afterward, the tensile strength,[7] Charpy impact energy,[8] fracture toughness,[9] and behavior of notched structures[10] made of functionally graded steels were analytically obtained by MSG theory. Nevertheless, limited work was done to SEYED ALI SADOUGH VANINI, Professor, MOHAMMAD ABOLGHASEMZADEH, Master of Science Student, and ABBAS ASSADI, Postdoctoral Student, are with the Mechanical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15916, Iran. Contact e-mail: [email protected] Manuscript submitted September 14, 2012. Article published online March 8, 2013 3376—VOLUME 44A, JULY 2013
investigate the hot working characteristic of FGSs. Only in Reference 11 is the mean flow stress of FGSs under hot compression assessed based on a combination of constitutive equations and a mixtures rule based model. This work was related to the parameter of the compression strain to the strains of each individual layer of FGSs considering the variation of volume fractions at each layer. Even though this assumption was justified for abc and cMc FGSs, the results were limited to a compressive strain of 0.5.[11] Hot deformation behavior of metals and their alloys has major importance in the proper design of instrumentations for large deformation processes such as hot rolling, forging, and extrusion. Recently, the finite element method was widely used to study the material forming process. This numerical simulation may be reliable when proper stress-strain relationships are used to model the forging process of mechanical elements under appropriated loading conditions.[12,13] It must be noted that the forming temperature and strain rate change the hardening and softening mechanisms during the process. In general, higher strain rates and lower temperatures increase the resistanc
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