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NGHIEN cufu - TRAO D | PREDICTION OF RESIDUAL STRESS AND STRAIN IN COLD FORMING PROCESS TIEN DOAN VE UNG SUAT DU" VA BIEN DANG TRONG QUA TRINH TAO HINH NGUOl Luu Thanh Tung Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology ABSTRACT The cold-forming process significantly enhance the mechanical properties of the profile by strain hardening leading to increased resistance compared to a resistance assessment based on nominal properties It is thus necessary to accurately determine the mechanical properties after the cold process of fabrication In this paper, a spare part of car manufactured by the cold-forming process is introduced The simulation data calculated by finite element analysis (FEA) and analytical solution are presented to solve residual stress and train A comparison between FEA and analytical solution for residual stress and train is then established The solution has the potential to replace laboratory tests to a large extent and can thus be deployed in future research to minimize the need for expensive laboratory testing Keywords: Residual stress, strain TOM TAT Qud trinh tgo hinh nguoi tdng cu&ng ddng ki cdc tinh chdt ca hpc cua chi tiit md hinh thdnh su bien cOng lam gia tdng khd ndng chiu tdc dpng ben ngodi Vi the, cdn thiet de xdc dinh chinh xdc tinh chdt ca hpc cua chi tiet sau qud trinh che tgo bien dgng ngupL Trong bdi bdo ndy segi&i thieu mpt chi tiit phu tung cua to dugc sdn xudt b&i qud trinh biin dgng nguoi Cdc die li^u mo phong tinh todn bdng cdch phdn tich phdn tu hieu hgn (FEA) vd gidi phdp phdn tich dugc trinh bdy di gidi quyit ung sudt du vd bien dgng Mpt so sdnh giica FEA vd gidi phdp phdn tich cho ung sudt du vd biin dgng dugc thiet lap Cdc gidi phdp co khd nang thay the cdc xet nghiim phong thi nghiem v&i quy mo l&n vd do cd thi dugc trien khai cdc nghiin cuu tuang lai de gidm thieu nhu cdu thic nghiem phong thi nghiem ddt tiin Keywords: JJngsudtdu, biin dgng ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, S6 1+2 nam 2015 www.cokhivietnam.vn NGHIEN cufu-TRAOD6I INTRODUCTION Residual stresses in cold-formed steel sections may play a significant role m determinmg their behavior and strength, so they have often been measured by destructive methods in the laboratory The amount of cold work arisingfromthe manufactured process in such a steel member can be quantified using residual stresses and equivalent plastic strains both of which vary over the section as different parts of the section have generally experienced different amounts of cold work [I] Here, the equivalent plastic strains represent the strain hardening effect (i.e material strength enhancement) due to cold work Strain hardening induced by cold work generally has a positive effect on the load carrying capacity of a cold-formed steel member, but residual stresses generally have a negative effect Since residual stresses are always accompanied by material strain hardening, the combined effect of residual stresses and strain hardening on the load-carrying capacity of a cold-formed steel member may thus be either positive or negative [2] Plastic bending, followed by elastic spring back, creates a nonlinear through thickness residual stress distribution, in the direction of bending, as shown in Fig I [3] The presence of nonlinear residual stress distributions in cold formed steel members has been confirmed in experiments [4] and in nonlinear finite element modeling of press-braking steel sheets [5] A closed form analytical prediction method for residual stresses and equivalent plastic strains from coiling, uncoiling, and mechanicalflatteningof sheet steel is presented in [6] In this paper, the residual sfress and strain in a ear spare part (Fig 2) manufactured by cold process is introduced A method for calculating the manufacturing residual stresses and plastic strains in cold-formed steel is proposed here The procedure is founded on common industry manufacturing practices and basic physical assumptions The primary motivation for the development of this method is to define the initial state of a cold-formed steel member for use in a subsequent non-linearfiniteelement analysis Comparison of residual stresses and sfrain between the analytical solution andfiniteelement analysis is also shown to prove the usefiilness in prediction of residual stresses and strain in cold process The result of the method is intended to be accessible to a wide audience including manufacturers, design engineers, and the academic community Elastic sprlngDacK , V J/'l Figure I Forming a bending, nonlinear residual stress [3] ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, S6 I+2nam20I5 www.cokhivietnam.vn NGHIEN cufu-TRAO D | COORDINATE SYSTEM AND NOTATION The sign convention for stress and stram is positive for tension and negative for compression The stress-strain coordinate system and geometric notation used in the forthcoming derivations are defined in Fig.2.The x-axis is referred to as the transverse direction and the z-axis as the longitudinal direction of a structural member ASSUMPTION IN THE COLD PROCESSING Analysis of stress and strain in cold formmg is complicated Thus, some assumptions are used to simpHfy the problem The following assumptions are employed to develop this analytical solution [3]: (a) Plane sections remain plane before and after cold-forming of the sheet steel This assumption permits the use of beam mechanics to derive prediction equations (b) The sheet thickness t remains constant before and after cold forming of the sheet steel A constant sheet thickness is expected after cold bending if the bending is performed without appHed tension Cross section measurements demonstrate modest sheet thinning at the comers, where t in the comers is typically 5% less than in the flange and web This thinning is ignored here to simplify the derivations, although a reduced thickness based on the plastic strain calculations could be used if a higher level of accuracy is required (c) The sheet neutral axis remains constant before and after cross section cold forming Theoretical models used in metal forming theory predict a small shift in the through thickness neutral axis towards the inside of the comer as the sheet plastifies [3] This shift is calculated as 6% of the sheet thickness, t, when assuming a centerlme comer radius, rz, of 2.5t A neutral axis shift of similar magnitude has been observed in the nonlinearfiniteelement model results for thin press braked steel sheets This small shift is ignored here to simplify the derivations (d) The steel stress-sfrain curve is assumed as elastic perfectly plastic when calculating residual stresses More detailed stress-strain models that include hardening are obviously possible, but a basic model is chosen to simplify the derivations The implication of this assumption is that the residual stresses may be under estimated, especially in comer regions where the sheet has yielded completely through the thickness Figure The car spare part and stress-strain coordinate system ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM S6 1+2 nam 2015 www.cokhivietnam.vn NGHIEN cufu-TRAO DOI ANALYTICAL SOLUTION FOR THE COLD PROCESS 4.1 Residual stresses from cold process Some algebraic equations is derived here to predict the transverse and longitudinal residual stresses created by cold processmg in a cross section The residual stresses of cold process are assumed to exist only at the location of the formed comers, between the punch and die reactions, as shown in Fig Some yielding is expected to occur outside of the die and punch reactions as the stress distribution transitions from fiilly plastic to fiilly elastic; however, this transition area is not considered here to simplify the derivation The engineering strain in the steel sheet, e^, and the bend radius, r^, are related for both small and large deformations with the sfrain-eurvature relationship [3] - = ^ Figure Coldforming of the car spare part (1) Figure Force couple applied to simulate the elastic springback of the steel sheet after the imposed radial deformation is removed This geometric relationship is vaHd for elastic and plastic bending of the steel sheet For the small bend radii in the cold-formed steel industry (r^ = 2t to 8t), the steel sheet yields through its thickness during the cold-forming process After the sheet becomes fiiUy plastic through its thickness, the engineering strain continues to increase as the radius decreases When the final bend radius is reached and the imposed radial displacement is remove d, an elastic springback occurs that elastically unloads the comer (see Fig 2) The change in sfress through the thickness from this elastic rebound is derived with the plastic moment force couple (Fig 4) The plastic moment is calculated with the equation: M ™ = fp- (2) Which is then applied elastically through the thickness to simulate the stress distribution from elastic rebound of the sheet steel: _ {^yii,idfP')y _ a^j^tgy ISSN 0866 - 7056 TAP CHi CO KHi VIET NAM, S6 1+2 nam 2015 wTvw.cokhivietnam.vn (3) NGHIEN cufu-TRAO D | And the total predicted longitudinal residual sfress distribution in the flats and comers of each cross-section is integrated to calculate the sectional moment through the thickness: The final transverse sfress state is the summation of the fully plastic sfress distribution through the thickness and the unloading sfress from the elastic spring back of the comer as shown in Fig 1, where a^ is the transverse residual sfress through the thickness from the cold forming of the comer This stress is nonlinear through the thickness and is self-equilibrating, meaning that axial and bending sectional forces are absent in the x-direction after forming The transverse residual sfresses will create stress in the longitudinal dfrection due to the assumed plane strain conditions (^z='V