The neck-in process is developed to produce very small and thin cylindrical elements by flow forming machine. In this study, neck-in process is applied to the production of thin-walled combustion tube. The purpose of this study is to search for the relations among the processing parameters and find a optimal processing condition to produce precise product. For these purposes, we investigated some of the critical factors in neck-in process and processing parameters by experiment and numerical analysis. FEM analysis is carried out based on elastic-plastic work hardening model using commercially available code ABAQUS/ Standard. The results obtained from the numerical analysis and experimental data can be used to design the optimal production in neck-in process.Key word : neck-in, flow-forming, combustion tube, elastic-plastic FEM I N T R O D U C T I O NThe flow forming technique is unmached in its efficiency for the chipless production of dynamically balanced hollow precision bodies. Neck-in process by flow-forming [1] is developed to produce very small and thin cylindrical elements. In neck-in process, cylindrical workpiece which attached to rotating mandrel deformed by rollers. The deformation of workpiece can be described as reductions in outer diameter, inner diameter, and wall thickness of cylindrical workpiece. In recent days, flow forming is variously applied to the many industrial areas, such as aerospace, medical., printer, automotive and missile industry, etc.[2]The purpose of this study is to search for the critical processing parameters such as filling of tapered part, ~lection of flow forming method (backward or forward method), spring back and wrinkling or fracture possibility. Numerical analysis is carried out based on elastic-plastic work hardening model using commercially available code ABAQUS/Standard and for experiment we used CNC flow forming machine in Samsung Aerospace Industry Inc. D E S C R I P T I O N S F O R N E C K -I N PRO-CESSIn neck-in process of combustion tube, three milers are move to axial direction with a radial preset. By this axial movement cylindrical workpiece contacted with rollers and undergoes a plastic deformation. The l~lastic deformation means decrease in diameter and wall thickness and increase in axial length of workpiece.The dimensions of the workpiece are given 88 mm outer diameter, 78 mm inner diameter and 5 mm wall thickness for the actual combustion tube. After neck-in process, final shape with changed dimensions (outer dia.: 80.7 mm, inner dia.: 73 mm, wall thickness: 4.75 ram). The reduction ratio of wall thickness is 5% and calculated as following equation.reduction ration (%)t o --t -x 1 0 0 = 5 l0 Fig. 1 shows a schematic drawing for neck-in process. Fig. 1. Schematic drawing for Necking-In process.

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In the present work, the formation of shear band under simple shear loading is investigated using the rate-independent elastic-plastic constitutive relations. A small initial perturbation representing material imperfection is introduced into the work piece to develop the post-localization behaviors. Since kinematic hardening rule assumed under a finite deformation regime, the stress rate is co-rotated with respect to the spin of substructure using the plastic spin concept. Moreover, the strain gradient terms are incorporated into the yield function to obtain a non-local plastic constitutive relation and its results are compared with a conventional plasticity model. It is noted that the shear band formation is accompanied by decrease in the magnitude of spatial increment within the regime of localization. Moreover, the strain gradient affects the shear localization behavior significantly such that the intensity of shear band increases as the strain gradient coefficient increases when the J 2 flow theory is employed. The effect of strain gradient on the deformation localization is, however, almost negligible for a material deformed accord with the J 2 deformation theory.

This paper proposes elastic-plastic constitutive relations for a composite material with two phasesinclusion and matrix phases-using a homogenization scheme. A thermodynamic framework is employed to develop non-local plasticity constitutive relations, which are specifically represented in terms of the second-order gradient terms of the internal state variables. A combined two back-stress evolution equation is also established and the degradation of the state and internal variables is expressed by continuum damage mechanics in terms of the damage factor. Then, deformation localization is analyzed; the analysis results show that the proposed model yields a wide range of shear band formation behaviors depending on the evolution of the specific internal state variables. The analysis results also show good agreement with the results of simplified Rice instability analyses.

In the present work, the constitutive relations based on the combination of two back stresses are developed using the Armstrong-Frederick, Phillips and Ziegler's type hardening rules. Various evolutions of the kinematic hardening parameter can be obtained by means of a simple combination of back stress rate using the rule of mixtures. Thus, a wide range of plastic deformation behavior can be depicted depending on the dominant back stress evolution. The ultimate back stress is also determined for the present combined kinematic hardening models. Since a kinematic hardening rule is assumed in the finite deformation regime, the stress rate is co-rotated with respect to the spin of substructure obtained by incorporating the plastic spin concept. A comparison of the various co-rotational rates is also included. Assuming rigid plasticity, the continuum body consists of the elastic deformation zone and the plastic deformation zone to form a hybrid finite element formulation. Then, the plastic deformation behavior is investigated under various loading conditions with an assumption of the J 2 deformation theory. The plastic deformation localization turns out to be strongly dependent on the description of back stress evolution and its associated hardening parameters. The analysis for the shear deformation with fixed boundaries is carried out to examine the deformation localization behavior and the evolution of state variables.