1、A method of modeling residual stress distribution in turning for different materials M.H. El-Axir Department of Production Engineering and Mechanical Design, Menoufia University, Shebin El-Kom, Egypt Received 10 July 2001； received in revised form 7 March 2002； accepted 12 March 2002 Abstract This p
2、aper introduces a more comprehensive experimental model which has the capability of predicting residual stress profile. The main advantage of this model over the existing models that it provides the effect of machining parameters on maximum residual stress and determines both the location and depth
3、of this maximum residual stress. Five different materials namely； stainless steel304, steel-37, 7001 and 2024-aluminum alloys and brass were machined by turning utilizing one of experimental design techniques based on response surface methodology. Tensile strength of these materials and both cutting
4、 speed and feed rates are considered as three input parameters affecting residual stress distribution. The residual stress distribution in the machined surface region was determined using a deflection-etching technique. It is proposed here that the residual stress profile is a deterministic function
5、 of the three input parameters used. Also, it is postulated that the residual stress profile along the depth beneath surface is a polynomial function of the depth beneath surface and the coefficients of this polynomial are, in turn, functions of the input parameters. The model has been developed and
6、 has been checked for accuracy. . 2002 Elsevier Science Ltd. All rights reserved. 1. Introduction Fatigue life is an important dynamic property and it is strongly affected by the surface condition produced during machining 1. The fatigue crack, in general, nucleates at the surface of the part, and t
7、hen propagates into the bulk. As the crack extends the resistant section is reduced, and when the residual section can no longer withstand the applied load component fatigue occurs. Consequently, it is the state of stress at the surface, where the crack nucleates, that is of paramount importance. Th
8、is state is the sum of the stress due to the applied load and of the residual stresses (or self stresses) generated during machining. Residual stress is the result of various mechanical and thermal events, which occur in the surface region during machining. It is usually found that the absolute valu
9、e of the residual stress close to surface it high and decreases continuously with an increase in depth beneath the machined surface eventually vanishing. Residual stress may be tensile or compressive and the stressed layer may be shallow or deep, depending upon the cutting conditions, work material,
10、 and tool geometry. It has been shown 24 that residual stresses may be compressive at the surface and tensile just below the surface or vice versa. Compressive residual stresses are generally improve component performance and life because they reduce service (working) tensile stresses and inhibit cr
11、ack nucleation. On the other hand, tensile residual stresses can significantly increase service (working)stresses which can lead to premature failure of components 510. Sigwart and Fessenmeyer 11, for example, reported that fatigue tests on turned specimens of 42CrMo4 steel presenting high tensile r
12、esidual stresses (up to 600:800 MPa) showed a close to 30% reduction in the fatigue limit. Matsumoto et al. 12 reported that the fatigue strength of hardened AISI 4340 steel specimens (54 HRC) after flycutting was 25% higher that after grinding probably because the compressive residual stress distri
13、bution produced by the single point cutting operation penetrated to a grater work-piece depth. Similarly, Prata Pina et al. 13 found that, when milling annealed hot work die steel (AISI H13), residual stresses close to zero were obtained at the surface, dropping sharply to a maximum compressive stre
14、ss approximately 100 m below the surface, then rising again to the tensile side. Accordingly, It is very clear that the information concerning residual stresses profile (magnitude and direction along the depth) of the machined surface region will be valuable in the design and manufacture of parts. T
15、herefore, it is important that the effect of the machining process parameters on the residual stress profile is determined, and subsequently, such machining parameters may be chosen which would enhance fatigue life by inducing favorable residual stress (compressive stress). The majority of the resea
16、rch existing in literature on the effect of machining parameters on the residual stress profile are experimental in nature. Very few analytical models are available. Liu and Barash 14,15 explained the formation of residual stress by considering the stress strain history that the surface layer experi
17、enced due to the movement of the cutting tool. Lin et al. 9 used finite element techniques to determine residual stress profiles in orthogonal machining. Wu and Matusmoto 16 also used finite element to determine factors, which affect residual stress formation in hardened steel machining. Devarajan e
18、t al. 17 constructed an experimental model for prediction of the surface residual stress. Although the surface residual stress is important, in most machining processes, the subsurface residual stresses are at least equally important. This paper introduces a more comprehensive experimental model to
19、predict surface and subsurface residual stress profiles in turning of five different materials. With the help of this knowledge it will become possible to optimize machining parameters such that the surface integrity of the machined component for these five different materials is maximized under ser
20、vice conditions. 2. Experimental details 2.1. Workpiece materials Workpieces of stainless steel 304, steel37, aluminum alloy 7001, aluminum alloy 2024, and brass were utilized. These materials were selected because they have different machining characteristics and are important in industry. Moreover
21、, both of aluminum alloys 7001 and 2024 are particularly well suited for parts and structures requiring high strength-to-weight ratios. The chemical compositions in weight percent and tensile strength are given in Table 1. The tool material employed was high-speed steel. 2.2. Workpiece preparation T
22、he five different materials were machined into ring shapes with the dimensions shown in Fig. 1a. Fig. 1b shows the tested ring mounted on its mandrel. It is probable that residual stresses are induced in the surface region of the workpiece because of the machining involved in preparation, hence it w
23、as necessary to remove these stresses by annealing the workpieces. Stainless steel 304, steel 37, Al. 7001, Al. 2024 and free machining brass workpieces were heated to 800, 595, 340, 340, and 260C for 3, 6, 2, 2 and 1 h, respectively, and then cooled in air or in furnace. In this investigation, the
24、specimens were machined using one of the experimental designs. According to a central composed second-order rotatable design with three independent variables, the total number of experiments, N, was determined to be 20. The cutting conditions and their coded are summarized in Table 2. The residual s
25、tress distribution in the machined surface was determined utilizing a deflection etching technique where the residual stresses in the removal layer are relived and the remaining residual stresses are redistributed until a new equilibrium position is achieved. This change in shape can be measured fro
26、m which residual stresses can be calculated. A layer of approximately 1525 m was removed with the help of electrochemical etching. Layers were removed until the residual stress state became negligible. The obtained residual stress profiles for 20 different combinations according to Table 3 are shown
27、 in Fig. 2. 3. Proposed model The proposed model postulates that the residual stress profile as well as the depth of residual stress distribution are functions of the machining parameters. The model assumes that profile of residual stress along the depth is polynomial function of the depth. The prof
28、ile can be represented as: where: si is the residual stress, cni are the coefficients of the nth order polynomial term and z is the depth beneath the machined surface. Further, it is proposed that the coefficients of the polynomial are individual functions of the machining parameters. The relation of the coefficient to the machining parameters is where Ci is the coefficient of polynomial for residual stress profile and bxi is the effect of factor (or interaction of factor) x. The values of the code number of each parameter, x, can be obtained from the following transformation equations.
