Influence of residual stresses in the tensile test of cold drawn wires

Materials and Structures / Mat6riaux et Constructions, Vol. 36, October 2003, pp 548452 Influence of residual stresses in the tensile test of cold drawn wires J. M. Atienza and M. Elices Departamento Ciencia de Materiales, Universidad Polit6cnica de Madrid, E.T.S.I. Caminos, Madrid, Spain. ABSTRACT The aim of this paper is to investigate the influence of residual stresses, due to cold-drawing, on the shape of the tensile stress-strain curve and particularly its influence on the ratio C%.2/~m,~ through a numerical and experimental work. It was found that residual stresses favours the onset of yielding and the ratio cyo.2/c~m~,~ decreases with increasing values of residual stresses. Because of the deleterious effect of residual stresses on fatigue and stress corrosion and because such stresses affect the ratio c~02,"c~ ...... it is reasonable to put a lower limit to ~02/O'm~L-~ in the standards. The ratio O'0.2/~ma x can be increased by relieving residual stresses, a common procedure after drawing. This fact is also ascertained. RESUMF~ L'objectif de cet article est la recherche num&ique et exp&imentale de l'influence des contraintes r&iduelles dues au trdfilage ?~ fi~aid sur la forme de, la courbe contrainte- d~ormation et, plus partic~li&ement, son influence sur le ratio r162 Cet article montre que les contraintes r&iduelles favors la plastification. Le ratio ~o,:/cr~,~ diminue au fur et 27 mesure clue les contraintes r&iduelles augmentent. ~i cause des eflbts ndgatifi' des ~ contraintes r&iduelles sur la fatigue et la corrosion des mat&iaux, il est raisonnable de demander une valeur limite pour Cro,:/c~,,~. Le ratio Cro,:/cL,~.peut Otre augment~ h condition de reldcher les contraintes rOsiduelles, une procddure normale apr& le tr@Tage. 1. INTRODUCTION Standards for cold drawn wires for prestressing concrete [1] require minimum and maximum figures for cr0.j~ma~, where ~0.2 and C~m,x are respectively the conventional yield stress (at a 0.20% offset) and the maximum stress, as measured in a tensile test. The rationale behind these figures seems to be based on good practice and on the idealized behaviour of a prestressing tendon [2, 3]. On the other hand, it is known that the presence of residual stresses due to cold drawing can influence ductility and fracture [4], fatigue [5] and stress corrosion [6]. In addition, residual stress can alter the shape of the stress-strain curve fi'om a tensile test [7]. Therefore, the presence of damaging residual stresses could be reflected in the shape, and in the values of some parameters of the stress strain curve. The purpose of this contribution is to investigate the influence of residual stresses, due to cold-drawing, on the shape of the tensile stress-strain curve and, particularly, its influence on the ratio O'0.2/~ma x. It is hoped that these results may shed some light on the figures required by standards and may help in improving the quality of prestressing wires. 2. EXPERIMENTAL WORK 2.1 Reference bar The material used in this research was intended to be the same as the steel wires used for prestressing concrete, i.e.; eutectoid steel [2], but because it was also intended to measure the stress distribution across the section by neutron diffraction - -as part of another research project-- bars of 20 mm diameter were chosen instead &the usual thinner bars. The bars were produced by hot rolling and we-re aged until no significant residual surface stresses appeared (values less than 50 MPa, fbr longitudinal surfhce stresses measured by Editoria! note Prof Manuel Elices is a RILEM Senior Member. 1359-5997/03 ~ RILEM 548 K 高亮 K 高亮 K 高亮 Materials and Structures / Mat~riaux et Constructions, Vol. 36, October 2003 X-ray diffraction). The average chemical composition is given in Table 1. Table I - Average chemical composition of the reference steel C(~176 I Si(%) I Mn(%) I AI(%) [p(%) I s(%) [ ve 0.75-01S0 10.'5-0.35 10.60-0190 10.0:-0.06 1<0.025 1<0.0:5 I ba'aoce The stress-strain curve, as obtained in a tensile test, is shown in Fig. 1, together with representative values in Table 2. (S~(m~x) is the strain under maximum stress, am~0. 1200 1000 800 600 W [Z CO 400 200 After drawing Before drawing o o 2 4 6 8 lo STP, AtN (%) Fig. 1 - Stress-strain curves of'refErence bar (before drawing) and cold drawn bar. 12 Table 2 - Average tensile values of reference and drawn bars Sample Reference bar Cold drawn bar ...... ~0,z, (M l~a) 515 940 Om~, (MPa) go.~x) (%) 945 8.6 1115 2.2 2.2 Cold drawn bar Reference bars, 20 mm diameter, were cold-drawn under controlled conditions to 18 mm diameter (20% reduction of area), through a wiredrawing die. Die geometry is shown in Fig. 2. To avoid stresses due to bending, drawn wires were kept straight in samples of 3 m length. The average stress-strain curve, from a tensile test, is also shown in Fig. 1. Table 2, compares the ................ main values of the reference and cold drawn I bars obtained in tensile tests. 3. NUMERICAL WORK 3.1 Drawing simulation The steel bar was modelled as an elastoplastic material with strain hardening. Isotropic hardening with a yon Mises criterion was used and, as first approximation, the yield locus was considered independent of strain rate. The drawing process was numerically simulated using the finite element method [8] with the help of ABAQUS code [9]. A three-dimensional Lagangian formulation was used for the wire, where plastic deformation was considered isochoric. Special care was taken in choosing the finite elements to avoid the well known volumetric locking problem [8, 10, 11]. The initial Stress-strain function was the experimental one, for the reference bar shown in Fig. 1. The die was also modelled using the finite element method; the material was treated as linear elastic with a modulus of elasticity of 600 GPa, similar to widia, a common material for dies. The contact between wire and die was modelled as Coulomb friction, with a friction coefficient ranging between 0.2 and 0.01 [12]. A detailed description of numerical modelling can be seen in [7]. One result --particularly interesting for our purpose-- was the steady-state profile of residual stresses. It was found that cold drawing generates an axisymmetrical profile of residual stresses (due to an inhomogeneous plastic deformation through the die). Fig. 3 shows the longitudinal residual stresses as a function of relative depth fiR, where r is the distance from the bar centre and R the bar radius. Tensile stresses appear on the bar surface, and compressive ones in the innermost part to balance the external loads. Fig. 2 - Die geomet-ry used for drawing (die angle 2ct = 15.36~ Fig. 3 - Longitudinal residual stresses as a function of depth. 549 K 高亮 K 高亮 K 高亮 Atienza, Elices 1500 1500 ~'1000 n CO 500 LU n~ O3 . 0 < z g -500 s Z O-1000 - . , (~ _..@ �9 - �9 - (~ @ Loading steps Initial values a WITHOUT RESIDUAL STRESSES -1500 , , , I , , , I , I n I I I I [ I I I 0,0 0,2 0,4 0,6 08 1,0 RELATIVE DEPTH, (r/R) Loading _ , . , . " " ~---'~'~T~ �9 - - " steps ~ �9 �9 "~" "" ~" " " I . f - I , I " ,e" .............. �9 i " I " . - ..... . '~ / -~" - - - " - - . ,~@ ~-" . " ,. ....... J Initial values - i ' , , " ....... I~ b WITH RESlDUALSTRESSES / , , , I , , , I , , i I t I ~ I , I I 1ooo ~- n 500 03 LU n~ 09 0 _j < cn -500 I - (.9 Z O -1000 . j -1500 0.0 02 04 0.6 0.8 t.0 RELATIVE DEPTH, (dR) Fig. 4 - Longitudinal stresses as a function of relative depth during a tensile test: a.- Bar without residual stresses; b.- Bar with residual stresses due to cold drawing. Stresses in both figures correspond to the same loading steps. 3.2 Tensile test s imulat ion The tensile test was modelled using the same procedure as for drawing; the wire was discretized using finite elements and the material was treated as elasto-plastic. Boundary conditions were uniform displacement at the ends of the bar in order to simulate a tensile test under displacement control. Two different initial conditions were considered; a bar free of residual stresses and a bar with residual stresses due to cold- drawing; the residual stresses --longitudinal, circumferential and radial-- previously computed. In a tensile test for a bar wilhout residual stresses, in every section the stress distribution is uniform (Fig. 4a); initially the stress remains within the elastic regime and finally reaches a yield value. At this point the stress-strain curve is no longer a straight line. In a tensile test for a bar with residual stresses, the stress distribution is not uniform across the section, as is shown in Fig. 3. During loading, stress increases and the first yielding appears on the sur&ce because initially the maximum tensile stresses are there. As load increases, yielding extends towards the interior of the bar (Fig. 4b) and the stress-strain curve starts deviating tYom a straight line. Notice that this may happen with a low level of tensile stresses in the inner part of the bar or even with compressive stresses there (Fig. 4b). In practical terms, the presence of tensile residual longitudinal stresses decreases the yield stress - -usual ly measured as or02-- as regards to values without residual stresses. 4. COMPARISON OF EXPERIMENTAL WORK WITH NUMERICAL COMPUTATIONS Tensile tests of cold drawn bars, under controlled conditions, are available and an average value was shown in Fig. 1. Also, a numerical simulation of a tensile test of a cold drawn bar with residual stresses' was performed according to the procedure outlined in the previous section. The stress-strain curve of the reference bar was used for computing residual stresses after drawing, and this profile of residual stresses was the initial stress value for computing the stress-strahq curve of the tensile test. Fig. 5 shows a comparison of both results ---experimental and numerical-- of tensile tests of bars vdth residual stresses. The agreement is very good and this result adds further confidence to the numerical simulations to be discussed in the next section. Table 3 gathers the relevant values of the tensile tests: errs, p was measured as the value where a straight line with the elastic modulus slope separates from the stress-strain curve, 1200 1000 ~, 8OO ~4 ~oo co tit co 400 200 0.5 1.0 1.5 :2,0 STRAIN (%) Fig. 5 - Comparison of tensile tests (experimental and numerical) of bars with residual stresses due to cold drawing. Tab le 3 - Re levant values of tens i le tes ts per fo rmed on bars with res idua l s t resses Sample Experiment Numerical (Yprop (MPa) 460 470 ~0.2 iOma~ (MPa) (MPa) ! 940 i 1115 947 ! 1119 ~om~ (%) { 2.2 1.8 I 550 K 高亮 K 高亮 K 高亮 Materials and Structures I Matdriaux et Constructions, Vol. 36, October 2003 5. INFLUENCE OF RESIDUAL STRESSES ON THE TENSILE TEST CURVE 5.1 Die geometry It is well known that the geometry of the drawing die ~ooc influences the values of residual stresses due to r~ sac drawing [2, 13 ] and, vs therefore, the stress-strain curve of a tensile test will be affected by the die geometry. A significant parameter in ~ .~oo die geometry is the die angle z (see sketch in Fig. 2). Its ~ooo influence on the values of residual stresses is shown through two numerical -~00 0,0 simulations; one with a Die ~prop angle (MPa) 4" 800 [ 8 ~ 445 Table 4 - Relevant values of tensile tests ~erformed on bars drawn with different dies ~om~ (%) ,, . . . . 2_ # 1 Die angle 8" 0.2 0.4 O.B 0.8 ~.0 RELATIVE DEPTH, (dR) ~0.2 (MPa) 1040 ~Dlax (MPa) 1123 1.7 930 1125 1.8 1200 I 10001"- ~ 800 I- B00 b ~ u~ 400~- 200 F ~.0 SII'~S ( O,'~4 y , , l p l / *" H~hmsl~uat O. 5 1.0 1 5 2.~) STRAIN (%) standard die angle of 8 ~ and a second one with a die angle of 4 ~ . Smaller die angles should provide lower values of residual stresses [2, t3]. Profiles of longitudinal residual stresses across the section after drawing with two different dies are shown in Fig. 6a. As expected, it is seen that the die with the lower angle (4 ~ ) induces lower residual stresses than the die with the higher angle (8~ simulation of tensile tests with both wires, bearing residual stresses due to different dies, are sho~al in Fig. 6b, and Table 4 surmnarizes the relevant values. It is clearly seen that the wire with higher residual stresses starts yielding early. It is interesting to notice that a small change in the die angle strongly affects the onset of yielding (ap,~p is halved) and conventional yielding (measured as m~a ) decreases by 10%. Fig. 6 - Influence of die geometry, a) Longitudinal residual stresses due to differences in die angles; b)Tensile tests of wires with different residual stresses due to drawing through dies with different die angles. 5.2 Post-drawing treatments Residual stresses due to cold drawing are known to be detrimental to the pertbrmance of prestressing concrete steel tendons, and different procedures were devised to eliminate or decrease such stresses before delivering steel wires [2]. These changes of residual stress profiles will also affect the shape of the stress-strain curve of a tensile test. To show this effect, two procedures for changing the residual stresses were considered; one --purely mechanical-- consisting in a further drawing with a very small area reduction (about I%), and another, thermomechanical, based on a combination of heating and stretching the wire (commonly known as stabilizing) [2]. Both processes have been numerically simulated: The first one, drawing through a die with 0.01 reduction in area and another by heating at 400~ under a tensile load of 0.4 am~. (A stress-strain curve obtained expeNnentally at 400~ was used as input data tbr computing the second process). Profiles of residual stresses for both procedures are compared in Fig. 7a with the corresponding profile for as-drawn bars. The figure shows clearly that stress relieving was achieved. Tensile tests after post-drawing treatments are also shown in Fig. 7b, and "fable 5 summarizes the relevant Table 5 - Relevant values of tensile tests performed on drawn bars after different post-drawing treatments Treatment t As drawn 1% reduction rhermomech. a~,p(MPa) ao.2 (MPa) 460 940 647 ~ 1065 990 ! 1135 Gmax ~cm~ax (MPa) (%) ...... 1115 2.2 1131 1__2oo ..... .... values difficult to grasp from the figure. It is seen that when relieving residual stresses, the yielding limit (as measured by %,or) increases up to 115%, the conventional yield stress (%.2) may reach values up to 2(PA higher and the maximum stress remain almost the same. 5.3 o0.2/ar~ax ratio In previous sections it was shown that the presence of residual stresses due to cold drawing induces, in a tensile test, a lowering of c~0.2 and has almost no influence on cr~,. Therefore the presence of residual stresses will affect the ratio ao.2/o~, a figure that appears in most standards for steels for prestressing concrete [1]. More precisely, these standards recommend that cro2/C~r~ should be in between 0.85 and 0,95 and some suggest optimum values of about 0.90-0.93. Table 6 gathers all the 60.2/~,~,x values from the difl~rent examples considered, and shows how the presence of residual stresses can alter the a0a/c%a, ratio from 0.95 to less than 0.85. The lowest values are induced by the highest residual stresses. Table 6 - o'0.2/O'ma x ratio of the different examples considered Different dies Post-&awing treatments As High Low "' 1% Yhermomeehanicai ...... drawn residual residual reduction stress stress a0.2/ama~ 0.84 0.83 0.93 0.94 0.95 551 Atienza, Elices 500 ./ o_ c6 0 W -11 < z ~-500 s Z 0 _J ~ditional 1% reduction .'*'*' L , , . , j ........:.*'~ As drawn .,--"" ........ .,..:"'" a -lOOO t I I 1 0,0 0.2 0,4 0,6 0~8 1.0 RELATIVE DEPTH, (r/R) 1200 1000 ~, 8oo 600 400 200 0 0.0 . - " . . . . 7 . . . . ' . . ' . . . . . ' . . . . . . . . . . . . . . - p ,...~ g . : j, .," I S t.," Yhermemeehanical treatment . . . . Additional small reduction (1%) / f . . . . . . . . AS drawn b 0,5 1,0 1.5 STRAIN (%) Fig. 7 - Influence of post-drawing treatments, a) Longitudinal residual stresses due to additional small reduction or to a thermomechanicat treatment; b) Tensile tests of wires with two post-drawing treatments. In both figures, values for as-drawn wires are included fbr comparison. 6. CONCLUSIONS The aim of this contribution, as stated in the introduction, was to investigate the influence of residual stresses, due to cold-drawing, on the shape of the tensile stress-strain curve. It was found that the presence of residual stresses favours the onset of yielding. Notice that longitudinal residual stresses due to cold-drawing are tensile on the wire surface. The higher the residual stresses the lower is the yield stress in a tensile test. Also, it was found that there is almost no effect on the maximum stress. The ratio ~0.2/~rnax decreases with increasing values of residual stresses. Because of the deleterious effect of residual stress on fatigue and stress corrosion [5, 6], it is reasonable to put a lower limit to o0.2/c%~. The ratio o0.2/crm,~ can be increased by relieving residual stresses, a common procedure after drawing, based on mechanical and/or thermomechanical treatments. These techniques may help in placing the ratio G0.2/~m~ within the figures recommended in the standards. Although this research was done with bars of 20 mm initial diameter, it is reasonable to accept that these results also apply to usual drawn wires with initial diameters of about 8 mm. Decreasing wire diameter would not change qualitatively the profile of residual stresses [14, 15] as long as die geometry and drawing procen~ures are scaled. In fact, surface residual stresses measured by neutron diffraction on thinner wires [ 14] (diameters of 1.22 and 0.89 ram) agree quite well with our results. ACKNOWLEDGEMENT The authors gratefully acknowledge the support of Spanish Ministry of Science and Technology. This research was supported by grants MAT2000-1334 and MAT01-3863-C3-1. The authors are very grateful for the help of Mr. Javier del Rio from Bekaert and for the useful comments of Mr. Javier del Pozo from EMESA-ACERALIA. REFERENCES [2] Dove, A~., 'Ferrous Wire' (The Wire Association Int., Inc,, 1991). [3] Libby, J.R., 'Modern Prestressed Concrete' (Van Nostrand Reinhold Co., 1977). [4] Elites, M., 'Fracture of steels for reintbrcing and prestressing concrete' in 'Fracture Mechanics of Concrete' (G.C. Sih, A. DiTommaso Eds, 1985), Chap. 5. [5] Llorca, J. and S~aachez-Gglvez, V., 'Numerical determination of the influence of residual stresses on fatigue', in 'Computational Plasticity', Proceedings of the International Conference, Bascelona, April 1987 (Pineridge Press Limited, 1987) 1123-1136. [6] Elices, M., Maeder, G. and Shnchez-G~ilvez, V., 'Effect of surface residual stress on hydrogen embrittlement of prestressing steels', Br. Corrosion Journal 18 (1983) 80-81. [7] Atienza, J.M., 'Residual stresses in drawn steel wires', PhD Thesis (Polytechnique University of Madrid, 2001). [8] Zienkiewicz, O,C. and Taylor, R,L., 'The Finite Element Method' (McGraw-HiU, Inc., 1989). [9] Hibbitt, H.D., Karlsson, B.I. and Sorensen, 'ABAQUS User's Manual. Version 5.8', (1998). [10] Crook, A.J.L. and Hinton, E., 'Comparison of 2d quadrilateral finite elements for plastici