FEM simulation of quenching process in A357 aluminum alloy cylindrical bars and reduction of quench residual stress through cold stretching process

Computational Materials Science 69 (2013) 396–413

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FEM simulation of quenching process in A357 aluminum alloy cylindrical bars and reduction of quench residual stress through cold stretching process Xiawei Yang, Jingchuan Zhu ⇑, Zhisheng Nong, Zhonghong Lai, Dong He National Key Laboratory for Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China

a r t i c l e

i n f o

Article history: Received 29 February 2012 Received in revised form 8 September 2012 Accepted 14 November 2012 Available online 16 January 2013 Keywords: Quenching process A357 aluminum alloy FEM simulation Residual stresses Cold stretching process

a b s t r a c t The quenching process of A357 aluminum alloy cylindrical bars with 80 mm diameter and with heights of 40, 80, 120, 160, 200 and 240 mm were investigated by using finite element method (FEM) simulation. Heat transfer coefficient was accurately calculated by using a traditional method of inverse heat transfer. Residual stresses caused by quenching of A357 alloy cylindrical bars are inevitable. Residual stresses reduction through cold stretching process was studied by using FEM simulation. Three numerical examples were used to illustrate the accuracy and efficiency of our method. The results show that this quenching model is able to predict the residual stress with high precision. The influence of some factors (quenching water temperature, aspect ratio of cylindrical bar, pre-stretching ratio and stretching rate) on the residual stress of quenched cylindrical bars after cold stretching was investigated. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction A357 (Al–7Si–0.6Mg) alloy is widely used in aerospace applications and automotive industries because of its excellent castability, good corrosion resistance and high strength-to-weight ratio in the heat treated condition [1–3]. In most cases, A357 alloy castings are used in the T6 condition, which requires solution heat treatment, quenching and artificial aging. Rapid cooling during quenching of A357 alloy is necessary to inhibit the formation of Mg–Si precipitates [4]. The inner stress and strain produced by rapid cooling during quenching is the basic reason of formation of quench-distortion of parts. Residual stresses occur for a variety of reasons, including inhomogeneous plastic deformations and heat treatment. Residual stresses are known to influence a material’s mechanical properties such as stress corrosion and fatigue life, and to cause distortion and dimensional variation [5–8]. Distortion frequently occurs during subsequent machining of aluminum alloys due to residual stresses developed during the quenching operation. Therefore, the investigation and understanding of residual stress prediction and reduction is important to improve the quality of many A357 alloy workpieces. ⇑ Corresponding author at: National Key Laboratory for Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China. Tel.: +86 451 86413792; fax: +86 451 86413922. E-mail address: [email protected] (J. Zhu). 0927-0256/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2012.11.024

Residual stresses in the quenching operation for aluminum alloys are usually investigated by numerical simulation using the finite element method (FEM) [9–12] and by measurement, using experimental methods such as X-ray [13,14] and hole drilling [15,16]. The residual stress reduction through stretching or cold compression immediately after quenching has been widely investigated [9,10,17,18]. The thermo-mechanical response of various surface treatments on forgings and aluminum cylindrical missiles during warm water quench has been investigated using experimental and FE modeling techniques [19,20]. Numerical simulation of quenching process and prediction of residual stresses of quenched parts have been widely studied since experimental investigations of these problems are time-consuming and costly. In order to obtain high accurate prediction of quenching residual stresses, some factors of quenching (the heat transfer coefficient, the preheat temperature and the quenchant temperature) must be fully taken into account. Compared with these two factors (preheat temperature and quenchant temperature), the heat transfer coefficient is the most decisive factor that influences the quenching results [21]. The inverse heat transfer method has been widely used to calculate the heat transfer coefficient of quenching medium [22,23]. This approach is a traditional method, so in this investigation, the authors do not give a detailed description of how to calculate the heat transfer coefficient of the quenching medium. The authors directly give the calculation result of heat transfer coefficient. Water is the most commonly used liquid

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

quenchant. Water temperature is an important parameter of heat transfer coefficient, but at the same time surface roughness and condition (oxidized or not) of workpiece can greatly affect heat transfer coefficient. In actual production, the surface roughness and stability of a simple casting is easier to control than a large complicated workpiece. A357 aluminum alloy cylindrical bars were used in the present investigation, so the authors ignored the effects of surface roughness and condition of workpiece on heat transfer coefficient. To compare the effect of water temperature on the quenching process of aluminum parts is of great importance to control residual stresses and distortion from quenching. Therefore, the accurate calculation of heat transfer coefficient between water and workpiece will be very valuable for this study. In this paper, the study involves combining FEM analysis with experimental methods to investigate the quenching process and residual stress reduction. Cooling curves of probe quenched in different water temperatures (25, 45, 60 and 80 °C) were obtained according to international standard ISO9950. Based on the cooling curves of an inconel probe, the heat transfer coefficients between probe and different water temperatures were solved by using an inverse heat transfer method. The quenching process of A357 aluminum alloy cylindrical bars and the distribution/magnitude of residual stress of quenched cylindrical bars were simulated by using ABAQUS CAE software. The authors used three numerical examples from two publications [9,11] to validate the accuracy and efficiency of this method. To validate the efficiency of this method using the data from publications is an effective method, which has been more widely adopted in many research fields. In addition, it is important and necessary for researchers to avoid a large number of tests. Finally, the influence of water temperature, aspect ratio of cylindrical bar, pre-stretching ratio and stretching rate on the residual stress of A357 as quenched cylindrical bars were investigated using simulation.

2. Experimental procedure The main chemical composition of commercial A357 aluminum alloy used in the present investigation is as follows: 6.83Si, 0.51Mg, 0.18Ti, 0.04Cu, 0.03Fe, 0.02Be and Al balance (wt.%). The quenchant used in this paper is water. In order to calculate the heat transfer coefficient, cooling curves and cooling rate curves of quenchant must be measured. According to ISO9950 1995(E), the international standard specifies a laboratory test using an Inconel 600 probe for the determination of the cooling characteristics of industrial quenchants [24]. The schematic diagram of probe of 12.5 mm diameter and 60 mm length used in this instrument is shown in Fig. 1. As shown in Fig. 1, a cylindrical probe has a thermocouple at its geometric center. According to ISO9950 1995(E), the standard probe temperature should be heated to 850 ± 5 °C. The probe was used at temperatures much greater than those experienced by the aluminum alloy. But when import the values of heat transfer coefficient into ABAQUS software, only select the values of heat transfer coefficient when the standard probe is at low temperatures (6550 °C). The probe shall be conditioned prior to its initial use with any quenchant by carrying out a minimum of six dummy quenches, or a greater number if required to achieve a constant result, in a general-purpose machine oil from 850 °C. Upon completion of each quenching test, the probe shall be removed from the quenchant and allowed to cool below 50 °C. The probe surface shall be cleaned using detergent alcohols, followed by wiping with a dry lint-free cloth. The probe has a specific surface finish. It is probably machined and polished. It will be different to the aluminum alloy surface finish. Surface finish is known to affect the heat transfer coefficient. If the authors do the experiment, they can adopt surface treatment approach

397

Fig. 1. Schematic diagram of the probe.

equivalent to that of inconel probe. So when doing the numerical simulation of the quenching process of A357 aluminum alloy cylindrical bars, the authors suppose the surface finish of the aluminum alloy same to the probe. The probe is heated in a furnace to 850 ± 5 °C, and then transferred into the water (25, 40, 60 and 80 °C) under test. The change in temperature at the center of the probe is recorded as a function of time. The authors can then create a ‘‘cooling curve’’ by plotting the temperature and time data as x–y coordinates and drawing a curve through the data points. After obtaining the temperature– time curve of inner point A (Fig. 1), the temperature history and the heat flux of the probe outer point B can be calculated by using the inverse heat transfer method. Then the heat transfer coefficients of water at different temperatures (25, 45, 60 and 80 °C) can be calculated by Newton’s law of cooling.

3. FEM modeling of quenching process In this study, the ABAQUS software is used to carry out FEM simulation of quenching process in A357 alloy cylindrical bars and the reduction of quench induced residual stress through a cold stretching process. Quenching is a thermo-elastic-plasticity problem within a non-linear material and temperature field, phasetransformation field and stress/strain field affecting each other during quenching operation. Thermal stress in a work piece during the quench operation is caused by a temperature difference in one part of the work piece compared to another part. The greater the temperature difference, the greater the thermal stress. The quenching process of A357 alloy is to inhibit the formation of Mg–Si precipitates [4]. So the phase transformations of A357 alloy during quenching operation can be ignored.

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The distortion of the part is very small during quenching operation, so the heat produced by stress/deformation of the part is also very small and the influence of stress field on temperature field can be discounted. The stress/deformation field of the part during quenching process depends on the temperature field. Therefore, a sequential analysis of coupled temperature-stress was employed in this investigation. It is performed by first conducting an uncoupled heat transfer analysis and then a stress/deformation analysis. After uncoupled heat transfer analysis, nodal temperatures are stored as a function of time in the heat transfer results. Then carrying out stress/deformation analysis, the nodal temperatures are read into the stress analysis as a predefined field. The basic governing equations of FEM modeling include heat conduction equation, initial condition, boundary condition and total strain equation. The heat conduction equation is an important partial differential equation which describes the distribution of heat (or variation in temperature) in a given region over time. According to the first law of thermodynamics and the Fourier model, for a function T(x, y, z, and t) of three spatial variables (x, y, and z) and the time variable t, the equation can be written as

      @T @ @T @ @T @ @T k þ k þ k þ qv qc ¼ @t @x @x @y @y @z @z

ð1Þ

where q, c, k, T and t are density, specific heat capacity, thermal conductivity, temperature and time, respectively. qv is the latent heat of phase transformation. Because the purpose of quenching of A357 alloy is inhibit the formation of Mg–Si precipitates, the authors can set the value of qv to zero.

The initial condition is an initial value problem, which is an ordinary differential equation together with specified value. In this investigation, the initial condition is the initial temperature of quenching parts. The equation of initial condition at time t = 0 is as follows:

Tjt¼0 ¼ T 0 ðx; y; zÞ

ð2Þ

where T0(x, y, z) is the initial temperature function. The boundary condition is a boundary value problem, which is a differential equation together with a set of additional constraints. In this investigation, boundary condition is the way of heat transfer between quenching parts and medium. It is given by

q ¼ hk ðT w  T c Þ þ hs ðT 4w  T 4c Þ ¼ hðT w  T c Þ

ð3Þ

where q, hk, hs and h are thermal flux, convection coefficient, radiation coefficient and total heat transfer coefficient, respectively, Tw and Tc are temperature of boundary and ambience, respectively. Using a small deformation theory, the total strain (e) can be additively decomposed into five components as

e ¼ ee þ ep þ eth þ eDV þ etr e

p

th

DV

ð4Þ tr

where e , e , e , e and e are elastic strain tensor, plastic strain tensor, thermal plastic strain tensor, volumetric strain tensor and transformation induced plastic strain tensor, respectively. Because the purpose of quenching for A357 alloy is limit phase transitions, the authors can set the value of etr to zero. So the strain increment can be given by

De ¼ Dee þ Dep þ Deth þ DeDV

(a)

(b) Unit: mm

(c)

Fig. 2. The mesh diagram of quench cylindrical bar. (a) Three-dimensional model; (b) simplification of model; and (c) mesh generation.

ð5Þ

399

X. Yang et al. / Computational Materials Science 69 (2013) 396–413 Table 1 Dimensions of A357 alloy cylindrical bars.

Cooling rate ( /s)

Height (mm)

Aspect ratio of cylinder

80

40 80 120 160 200 240

1:2 1:1 3:2 2:1 5:2 3:1

where Dee, Dep, Deth and DeDV are elastic strain increment, plastic strain increment, thermal plastic strain increment and volumetric strain increment, respectively. The casting cylindrical bars of A357 alloy were selected for the heat treatment simulation, and the dimensions of these A357 alloy bars are shown as in Table 1. According to symmetrical features of bars, an axisymmetric model can be used instead of a three-dimensional model and a half model can be used instead of a whole model. Here an A357 bar with £80 mm  160 mm was selected to illustrate how to develop the FEM model of the quenching process. Fig. 2 shows the dimensions and the mesh grid of simulation model. A 4-node linear axisymmetric heat transfer quadrilateral element (DCAX4 in ABAQUS) and a 4-node bilinear axisymmetric quadrilateral, reduced integration, hourglass control element (CAX4R in ABAQUS) were adopted in the simulations for heat transfer analysis and stress/strain analysis, respectively. The numerical simulations of stress/deformation analysis and of thermal analysis were carried out by using the same finite element mesh, except for different element type and boundary conditions. The total nodes and the total elements are 1891 and 1800, respectively.

900

50

100

150

200

250

300

800 700

Temperature

Diameter (mm)

0

600 500 400 300 200 100 0

0

20

40

60

80

100

120

140

160

time (s) Fig. 3. Cooling curves and cooling rate curves for water at 25, 45, 60 and 80 °C.

temperature from FEM simulation results accord with experimental data. Therefore, heat transfer coefficient calculated in the present paper can be used as the accurate thermal parameter of FEM simulation for quenching process of A357 alloy. 4.2. FEM simulation results

4. Results and discussion

4.2.1. Temperature field results Here an A357 alloy cylindrical bar with £80 mm  160 mm was selected to investigate the quenching process by using FEM simulation method. Constitutive equation is commonly incorporated into the FE model for deformation simulation. Hyperbolic sine constitutive equation that is used to is usually shown below [25–27]:

4.1. Heat transfer coefficient calculation results

e_ ¼ A½sinhðarÞn  exp Z ¼ e_ exp



Q RT



Q RT

 ð6Þ

¼ A½sinhðarÞn

ð7Þ

where A, n, and a are material constants. Q is deformation activation energy in kJ/mol. R is gas constant (R = 8.3154 J/K/mol). T is absolute temperature in K. Z is Zener–Hollomon parameter in s1. r is the yield stress in MPa. e_ is the strain rate in s1. a is an adjustable constant. The ABAQUS provide interfaces for users to implement general constitutive equations. In ABAQUS/Standard, user subroutine UHARD is called at all material calculation points of elements for

25 45 60 80

25

2

Heat transfer coefficient kW/m K

The cooling curves and the cooling rate curves of water at 25, 45, 60 and 80 °C obtained from experiments, as shown in Fig. 3. It is seen that the cooling rate largely depends on the water temperature (decreasing with increasing water temperature). For the high water temperature (80 °C), cooling rate curve show a very different trend compared with the other three lower temperatures (25, 45 and 60 °C). As can be seen from Fig. 3, the maximum cooling rates inside the probe at water temperatures of 25, 45, 60 and 80 °C are 227, 189, 149 and 75 °C/s, respectively, and temperatures inside the probe corresponding to the maximum quenching rates are 650, 592, 531 and 455 °C, respectively. It is important that cooling rates during quenching be sufficiently fast to minimize precipitation phase in A357 alloy during cooling. The supersaturated solid solution will be retained. But at the same time, owing to the fast quenching rate, large residual stress of A357 parts will occur after quenching operation. Cooling rate of probe during quenching is determined by the values of heat transfer coefficients. In order to calculate and analyse the residual stress of workpieces during quenching treatment, an accurate solution for the heat transfer coefficients should be determined. Fig. 4 shows the heat transfer coefficient values calculated by using inverse heat transfer method and Newton’s law of cooling. As shown in Fig. 4, the heat transfer coefficient is a function of water temperature. The values of heat transfer coefficient were imported into the property module of ABAQUS software. Then, temperature at node in probe center (point A in Fig. 1) was calculated by using ABAQUS software. Fig. 5 shows comparison of temperature at inconel probe center (point A) between experimental data and FEM simulation results. It can be seen that the



20 15 10 5 0 0

100

200

300

400

500

600

700

800

Temperature Fig. 4. Heat transfer coefficient for water quenching.

900

400

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

900

700

Experimental Calculated 600

600

500

Temperature

800

45

60

80

25

45

60

80

80 60

500

400

400

300

300

45 25

200

200

100

100 0

25

0

20

40

5

10

15

60

20 80

25 100

30 120

time (s) Fig. 5. Comparison between experimental data and FEM simulation results of cooling curves during quenching process for the inconel probe. Fig. 6. Schematic curve of solution heat treatment and water quenching process.

which the material definition includes user-defined isotropic hardening or cyclic hardening for metal plasticity. It can be used to define a material’s isotropic yield behavior and can include material behavior dependent on field variables or state variables [28]. A hyperbolic sine equation (Eq. (6)) is a relation among three physical quantities (strain rate, flow stress and temperature). In this paper, the authors do subroutine UHARD of hyperbolic sine equation (Eq. (6)) by themselves. Four variables (SYIELD, HARD (1), HARD (2), HARD (3)) need to be defined in subroutine UHARD. SYIELD is yield stress for isotropic plasticity. HARD (1) is variation of SYIELD with respect to the equivalent plastic strain. HARD (2) is variation of SYIELD with respect to the equivalent plastic strain rate. HARD (3) is variation of SYIELD with respect to temperature. The user subroutine interface is as follows: 

USER SUBROUTINES SUBROUTINE UHARD(SYIELD,HARD,EQPLAS,EQPLASRT, TIME,DTIME,TEMP, 1 DTEMP,NOEL,NPT,LAYER,KSPT,KSTEP,KINC,CMNAME, NSTATV, 2 STATEV,NUMFIELDV,PREDEF,DPRED,NUMPROPS,PROPS) C INCLUDE ‘ABA_PARAM.INC’ C CHARACTER80 CMNAME DIMENSION HARD(3),STATEV(NSTATV),TIME(), $ PREDEF(NUMFIELDV),DPRED(),PROPS() user coding to define SYIELD,HARD(1),HARD(2),HARD(3)

HARD ð2Þ ¼

  @r ¼ @ e_ T

HARD ð3Þ ¼

  @r ¼ @T e_

Q  sinh ðarÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi anRT 2 1 þ sinh2 ðarÞ

ð11Þ

The yield strength at different temperature for A357 alloy can be obtained from publication [29]. The hyperbolic sine equation can be written as [29]:

e_ ¼ 2:803  1016 ½sinh ð0:027rÞ9:034  exp

  252095 RT

ð12Þ

Therefore, the material constants in Eqs. (8), (10), and (11) were determined, and then expressions of these four variables (SYIELD, HARD (1), HARD (2), HARD (3)) in subroutine UHARD were determined. The heat transfer coefficients values of different water temperature were shown in Fig. 4. The solution heat treatment and water quenching process of the bar are given in Fig. 6. This is a simulation of the heat treatment process, not a real experiment. As shown in Fig. 6, the cylindrical bar was heated to 540 °C at a heating time of 3 h. Then, it was maintained at 540 °C for 8 h. After 10 s air quench-

600

600

ð8Þ

Because there is no strain parameter in hyperbolic sine constitutive equation, HARD (1) can be expressed as

ð9Þ

At constant deformation temperature, by partial differentiation of Eq. (8), HARD (2) can be expressed as

400

400

Axis of symmetry

Temperature ( )

In Eq. (6), the yield stress is the dependent variable. In order to determine values of four variables (SYIELD, HARD (1), HARD (2), HARD (3)) in subroutine UHARD, explicit expression for yield stress must be given. According to Eqs. (6) and (7), SYIELD in subroutine UHARD can be expressed as

5 4 3

500

500

HARD ð1Þ ¼ 0

ð10Þ

At constant strain rate, by partial differentiation of Eq. (8), HARD (3) can be expressed as

RETURN END

" 1 # 1 Z n 1 SYIELD ¼ r ¼ sinh A a

  sinhðarÞ1n Q qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  exp RT 2 a  A  n 1 þ sinh ðarÞ

2

300

1

200

300 100

0

2

4

6

8

200

10

5 4 3 2 1 Plane of symmetry

100 0

0

50

100

150

200

Time (s) Fig. 7. Cooling curves at different locations in cylindrical bar when 60 °C water was adopted as a quenching medium.

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

ing transfer time, it was immersed in water at a temperature of 60 °C until it was cooled down to a uniform temperature. The surface heat transfer coefficient between the bar and the 60 °C water was obtained from Fig. 4. In this paper, residual stresses reduction through cold stretching process was studied by using FEM simulation. At a given prestretching ratio, the stretching amount of a cylindrical bar must be calculated accurately. Cylindrical bar expands when it heats. It shrinks when it cools. The distortion of cylindrical bar happens due to thermal expansion and quenching. Therefore, it was necessary to simulate heating of cylindrical bar. When 60 °C water was adopted as a quenching medium, the FEM results of temperature-time curves at different locations in cylindrical bar are shown in Fig. 7. Here five locations from symmetry plane of cylindrical bar were chosen to obtain the temperature–time curves. As shown in Fig. 7, the temperature of location decreases with increasing the distance between location and center node of cylindrical bar. In the present investigation, the authors did not do experimental test for temperature-time curves at different locations in cylindrical bar. The inconel probe with dimension £12.5 mm  60 mm and the cylindrical bar with £80 mm  160 mm belong to typical cylindrical parts. Therefore, the accuracy of FEM model for temperature calculations of inconel probe during quenching process can be indirectly verified the accuracy of FEM results of temperature field of cylindrical bar during quenching operation. As shown in Fig. 5, the authors compared the FEM and experimental results of cooling curves during quenching process for inconel probe, which indicates that the calculated cooling curves from FEM model are in good agreement with experimental results. Therefore, the accuracy of FEM results of temperature field of cylindrical bar should be acceptable and satisfactory.

4.2.2. Prediction of residual stress after quenching Fig. 8 shows the distribution of the r-, z- and t-component residual stresses after quenching at the axial plane of symmetry of cylindrical bar with £80 mm  160 mm. Fig. 9 shows r-, z- and t-component residual stresses after quenching along the r- and zaxis direction at the axial plane of symmetry. In Fig. 8, S11, S22 and S33 represent radial residual stress (rr), axial residual stress (rz) and hoop residual stress (rt), respectively. In Fig. 9a, OA and OB represent the path that along r- and z-direction, respectively. As shown in Figs. 8 and 9, the surface of cylindrical bar exhibits compressive stress, while the center is tensile stress. It can be seen from Fig. 8, the rr ranges between 132 MPa and 148 MPa (Fig. 8b), the rz ranges between 144 MPa and 241 MPa (Fig. 8c) and the rt ranges between 152 MPa and 149 MPa (Fig. 8d). As shown in Fig. 9b, at the cylindrical bar center, the values of r-, zand t-component residual stress along r-direction were 108, 239 and 108 MPa, respectively, while at the cylindrical bar surface, these values were 1, 142 and 116 MPa, respectively. As shown in Fig. 9c, at the cylindrical bar center, the values of r-, z- and tcomponent residual stress along z-direction were 108, 239 and 108 MPa, respectively, while at the cylindrical bar surface, these values were 132, 0 and 132 MPa, respectively. Based on FEM simulation during quenching, the residual stress in any cross-section of cylindrical bar can be given. 4.2.3. Relief of quenching residual stress through cold stretching process Fig. 10 shows the distribution of the r-, z- and t-component residual stresses of quenched cylindrical bar after 1.5% stretching at the axial plane of symmetry of cylindrical bar with £80 mm  160 mm. Fig. 11 shows r-, z- and t-component residual stresses after 1.5% stretching along the r- and z-direction at the axial plane

Unit: mm

(b)

Axis plane of symmery

(a)

(c)

401

(d)

Fig. 8. Distribution of r-, z- and t-component residual stresses after quenching. (a) Three-dimensional model; (b) rr; (c) rz; and (d) rt.

402

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

(a)

Unit: mm z B

O

σr

250 200

(c)

σz

150

σt

100

r

σr

250 200

Residual stress (MPa)

Residual stress (MPa)

(b)

A

50 0 -50 -100

σz

150

σt

100

σr

50

σt

0 -50 -100 -150

-150 0

10

20

30

40

50

0

10

20

30

40

50

60

70

80

90

Distance to z-axis direction (mm)

Distance to r-axis direction (mm)

Fig. 9. r- And z-axis direction residual stresses on cylindrical bar after quenching. (a) The map of coordinate orientation; (b) r-direction; and (c) z-direction.

of symmetry. Here the stretching velocity was 0.5 mm/s. The rr ranges between 0.04 MPa and 13.57 MPa (Fig. 10b), the rz ranges between 9 MPa and 12 MPa (Fig. 10c) and the rt ranges between 28 MPa and 14 MPa (Fig. 10d). As shown in Figs. 8–11, the residual stresses of quenched cylindrical bar after 1.5% stretching are largely reduced compared with the values of the as quenched cylindrical bar, confirming that the cold stretching approach is a highly effective method for stress removal of quenched parts. In the present paper, reduction ranges of residual stress were calculated by comparing the maximum tensile residual stress of cylindrical bar after quenching and as quenched cylindrical bar after cold stretching, and by comparing the maximum compressive residual stress of cylindrical bar after quenching and quenched cylindrical bar after cold stretching. The reduction percentage of tensile and compressive residual stress were used to assess the effect of the cold stretching to stress relief, and the equations of reduction percentage can be described as

pðtrsÞ ¼

rQ ðmtÞ  rS ðmtÞ  100% rQ ðmtÞ

ð7Þ

pðcrsÞ ¼

rQ ðmcÞ  rS ðmcÞ  100% rQ ðmcÞ

ð8Þ

where p(trs) and p(crs) are reduction percentage of tensile residual stress and reduction percentage of compressive residual stress, respectively. r can be replaced by the three stress components, rr, rz and rt, respectively. rQ(mt) and rQ(mc) are maximum tensile and compressive residual stress of cylindrical bar after quenching, respectively. rS(mt) and rS(mc) are maximum tensile and compressive residual stress of quenched cylindrical bar after cold stretching, respectively. Table 2 shows the residual stress reduction percentage

of quenched cylindrical bar after cold stretching. As shown in Table 2, the range of stress reduction percentage of quenched cylindrical bar through cold stretching is 81.5–94.9%.

4.3. Numerical examples of FEM simulation In this study, three numerical examples from two publications [9,11] were used to evaluate the validity of the prediction the residual stress after quenching and of reduction of the residual stress through the cold working process. In publication [9], ABAQUS software was used to predict residual stresses of aluminum 7050 forged block after quenching, and the numerical predictions were compared with experimental measurements. Then cold compression and cold stretching were used to reduce the residual stresses. Coupled temperature–displacement analysis includes two types: sequentially coupled thermal-stress analysis and fully coupled thermal-stress analysis. It is uncertain which type was used in publication [9]. While in the present study, sequentially coupled thermal-stress analysis was carried out for heat transfer analysis and stress analysis. In publication [11], neutron diffraction was used to measure the magnitude and distributions of residual stresses of aluminum 7449 block after quenching. Cold compression was used to reduce the residual stresses and then residual stresses values were again measured by neutron diffraction. Fig. 12 shows comparison of the authors simulated residual stresses on Block A after quenching along x-locus with published data [9]. Here, Block A is a 7050 aluminum block of 340 mm  127 mm  124 mm [9]. Fig. 13 shows comparison of our simulation residual stresses on Block A after quenching along y-locus with published data. Figs. 12 and 13a show the middle plane of quenching model where residual stresses were simulated and

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

(b) Unit: mm

Axis plane of symmery

(a)

403

(c)

(d)

Fig. 10. Distribution of r-, z- and t-component residual stresses after 1.5% stretching. (a) Three-dimensional model; (b) rr; (c) rz; and (d) rt.

measured. It can be seen from Figs. 12 and 13 that compared with the published simulation data, our simulation results show a higher accuracy in predicting the residual stresses of aluminum block after quenching. In addition, the trends of residual stresses curves from our simulation also coincide with the publication experimental curves. In order to investigate the capability of FEM quenching model thoroughly, a second model (Block B) from publication [9] was used not only for comparison of residual stresses of block B after quenching between publication experimental data and our simulation results, but also for comparison of residual stresses of quenched block B after cold compression. Fig. 14 shows comparison of present simulation residual stresses on as-quenched Block B with published data. Fig. 15 shows comparison of present simulation residual stresses on Block B along x-locus with published data at different conditions (66 °C quenched water, 1% cold compression and 2% cold compression). Fig. 16 shows comparison of present simulation residual stresses on block B along y-locus with published data at different conditions. As can be seen from Figs. 14–16, not only the prediction of residual stresses of block B after quenching but also the prediction of residual stresses of asquenched block B after cold working process (cold compression and cold stretching) are all in very good agreement with the simulation data from the published data [9]. Based on the above two blocks from publication [9], the authors established the FEM quenching model to predict the residual stress of blocks after quenching and to predict the residual stress of asquenched blocks after cold working process (cold compression and cold stretching). The results show that the FEM model proposed in our paper is suitable to predict the residual stress of the blocks and as-quenched blocks aluminum alloy, with a higher precision. The authors have also used another publication [11] model

to test the validity of the FEM quenching model. Fig. 17 shows comparisons of present simulation residual stresses on Block C with published [11] data. In publication [11], the 7749 alloy was used for investigation of residual stress after quenching. In our analyses, material parameters and physical properties of 7449 aluminum forged blocks were not available. So instead of 7449 aluminum, the authors used data of 7075 aluminum for investigation. The 7449 and 7075 alloys belong to the Al–Zn–Mg–Cu alloys, but the main chemical compositions of these two alloys are somewhat different. Fig. 17 shows comparison of present simulation residual stresses on Block C after quenching with published [11] data. It is seen that the results obtained from present simulation have little different from the data from published data, and the changing trend of each curve is roughly the same. Based on the above investigation in this paragraph, after qualitative and quantitative analysis of the residual stresses curves, the authors can conclude that the performance of the FEM model for prediction the residual stresses after quenching should be satisfactory and the simulation results are credible.

4.4. Influence of some factors on residual stress after stretching process In this part, the authors used the approach of ABAQUS simulation to research the influence of some factors on residual stress of quenched cylindrical bars. These factors include pre-stretching ratio, stretching rate, quenching water temperature and aspect ratio of cylindrical bar. In this part, the authors used two paths to investigate the residual stress after stretching. The two paths were OA-path and OB-path (see Figs. 9 and 11a), respectively.

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(a)

Unit: mm z B

O

20

Stretching- 1.5%

Residual stress (MPa)

15

(c)

σr

10

σz

5

σt

Residual stress (MPa)

(b)

0 -5 -10

20

r

A

Stretching- 1.5% σr

15

σr

σt

σz σt

10

5

0

-15 -20

0

10

20

30

40

50

Distance to r-axis direction (mm)

-5

0

10

20

30

40

50

60

70

80

90

Distance to z-axis direction (mm)

Fig. 11. r- And z-axis direction residual stresses on quenched cylindrical bar after 1.5% stretching. (a) The map of coordinate orientation; (b) r-direction; and (c) z-direction.

Table 2 Stress reduction percentage of quenched cylindrical bar after cold stretching. Maximum residual stress (MPa)

After quenching

After stretching-1.5%

rr

Tensile stress Compressive stress

148.3 131.7

–

rz

Tensile stress Compressive stress

rt

Tensile stress Compressive stress

Stress reduction percentage (%)

13.6

90.8 –

241.1 144

12.4 8.6

94.9 94

149 151.9

13.6 28.1

90.9 81.5

4.4.1. Influence of pre-stretching ratio In order to clarify the influence of pre-stretching ratio on quenching residual stress, eleven simulation cases have been performed by the authors in this part and the stretching ratios were 0.4%, 0.7%, 1.0%, 1.3%, 1.5%, 1.7%, 2%, 2.3%, 2.5%, 2.7% and 3%, respectively. Here the cylindrical bar with £80 mm  160 mm was selected, the quenching water temperature was 60 °C and the stretching rate was 0.5 mm/s. Fig. 18 shows residual stresses of the quenched cylindrical bar along r-direction under different stretching ratio conditions. As shown in Fig. 18, residual stress along r-direction decreases with increasing stretching ratio. At low stretching ratios (61.5%), the residual stress along r-axis direction decreases greatly as the stretching ratio increases. While for high stretching ratios (>1.5%), the residual stress along r-axis direction decreases not sharply as the stretching ratio increases. Therefore, when considering the selected stretching ratio to minimize the residual stress along r-axis direction greatly, a lower limit to

stretching ratio is set 1.5%. Fig. 19 shows residual stresses of the quenched cylindrical bar along z-axis direction under different stretching ratio conditions. The authors can reach the conclusion from Fig. 19 similar to the conclusion from Fig. 18. When considering the selected stretching ratio to minimize the residual stress along z-axis direction greatly, a lower limit to stretching ratio is also set 1.5%.

4.4.2. Influence of stretching rate In this part, six simulation cases have been performed by the authors for investigation of the influence of stretching rate on residual stress of quenched cylindrical bar, and the stretching rates were 0.05, 0.25, 0.5, 0.75, 1 and 10 mm/s, respectively. Here the cylindrical bar with £80 mm  160 mm was selected, the quenching water temperature was 60 °C. Based on the results of Section 4.4.1, stretching ratio of 1.5% was selected in this part. Fig. 20 shows residual stresses of the quenched cylindrical bar along r-axis direction under different stretching rate conditions. As shown in Fig. 20, residual stress along r-axis direction increases with increasing stretching rate. For the high stretching ratio (10 mm/ s), residual stress along r-axis direction is more higher compared with the low stretching ratio (61 mm/s). Therefore, when considering the selected stretching rate to minimize the residual stress along r-axis direction greatly, an upper limit to stretching rate is set 1 mm/s. Fig. 21 shows residual stresses along z-axis direction of the quenched cylindrical bar under different stretching rate conditions. The authors can reach the conclusion from Fig. 19 similar to the conclusion from Fig. 20. When considering the selected stretching rate to minimize the residual stress along z-axis direction greatly, an upper limit to stretching rate is also set 1 mm/s.

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X. Yang et al. / Computational Materials Science 69 (2013) 396–413

(a)

(b) 300 Residual Stress (MPa)

Unit: mm

Koc's Simulation [9] Koc's Experimental [9] Present simulation

200 100 0

x-component

-100 -200 -300 0.0

0.2

0.4

Middle plane

(d) 300

300

Residual Stress (MPa)

Residual Stress (MPa)

(c)

200 100

y-component

0

Koc's Simulation [9] Koc's Experimental [9] Present simulation

-100 -200 -300 0.0

0.2

0.4

0.6

0.6

0.8

1.0

x/W

0.8

100 0

z-component

-100 -200 -300 0.0

1.0

Koc's Simulation [9] Koc's Experimental [9] Present simulation

200

0.2

0.4

0.6

0.8

1.0

x/W

x/W

(a)

Unit: mm

(b)

300

Residual Stress (MPa)

Fig. 12. Comparison of present simulation residual stresses of quenched Block A along x-locus with published data. (a) Schematic of coordinate and middle plane of model; (b) x-component; (c) y-component; and (d) z-component.

200

Koc's Simulation [9] Koc's Experimental [9] Present simulation

100 0

x-component -100 -200 -300 0.0

0.2

0.4

300 200

(d)

100

y-component 0

Koc's Simulation [9] Koc's Experimental [9] Present simulation

-100 -200 -300 0.0

0.2

0.4

0.6

0.8

0.6

0.8

1.0

y/H

Residual Stress (MPa)

(c) Residual Stress (MPa)

Middle plane

1.0

y/H

300

Koc's Simulation [9] Koc's Experimental [9] Present simulation

200 100 0

z-component

-100 -200 -300 0.0

0.2

0.4

0.6

0.8

1.0

y/H

Fig. 13. Comparison of present simulation residual stresses of quenched Block A along y-locus with published data. (a) Schematic of coordinate and middle plane of model; (b) x-component; (c) y-component; and (d) z-component.

4.4.3. Influence of quenching water temperature The most common quenchant used for aluminum alloys is water. In this part, four simulation cases have been performed by the authors to investigate the influence of water temperature on

residual stress of quenched cylindrical bar, and water temperatures were 25, 45, 60 and 80 °C, respectively. Here the cylindrical bar with £80 mm  160 mm was selected. Based on the results of Sections 4.4.1 and 4.4.2, stretching ratio of 1.5% and stretching

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X. Yang et al. / Computational Materials Science 69 (2013) 396–413

(a)

Unit: mm

Middle plane

(c) 300

200

Residual Stress (MPa)

Residual Stress (MPa)

(b) 300 100 0

x-component [11] y-component [11] z-component [11] x-component [Present] y-component [Present] z-component [Present]

-100 -200 -300

0.0

0.2

0.4

0.6

0.8

200 100 0 -100 -200 -300

1.0

0.0

0.2

x-component [11] y-component [11] z-component [11] x-component [Present] y-component [Present] z-component [Present] 0.4 0.6 0.8

1.0

y/H

x/W

(a)

Unit: mm

(b)

300

Residual Stress (MPa)

Fig. 14. Comparison of present simulation residual stresses on Block B after quenching with published data. (a) Schematic of coordinate and middle plane of model; (b) xlocus; and (c) y-locus.

200

Middle plane

x-component residual stress

100 0 66 1% 2% 66 1% 2%

-100 -200 -300 0.0

0.2

water quenched [11] cold compression [11] cold stretching [11] water quenched [present] cold compression [present] cold stretching [present]

0.4

0.6

0.8

1.0

x/W

(d) 300

300

y-component residual stress

Residual Stress(MPa)

Residual Stress (MPa)

(c)

200 100 0 66 water quenched [11] 1% cold compression [11] 2% cold stretching [11] 66 water quenched [present] 1% cold compression [present] 2% cold stretching [present]

-100 -200 -300 0.0

0.2

0.4

0.6

0.8

x/W

1.0

z-component residual stress

200 100 0 66 water quenched [11] 1% cold compression [11] 2% cold stretching [11] 66 water quenched [present] 1% cold compression [present] 2% cold stretching [present]

-100 -200 -300 0.0

0.2

0.4

0.6

0.8

1.0

x/W

Fig. 15. Comparison of present simulation residual stresses on Block B along x-locus with published data (66 °C water quenched, 1% cold compression and 2% cold compression). (a) Schematic of coordinate and middle plane of model; (b) x-component; (c) y-component locus; and (d) z-component.

rate of 0.5 mm/s were selected in this part. Figs. 22–24 show the predicted residual stresses contours after quenching under different water temperature. And the residual stresses include radial

residual stresses, axial residual stresses and hoop residual stresses. As can be seen from Fig. 22, the radial residual stresses decrease obviously with increasing water temperature, especially water

407

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

Unit: mm Unit: mm

(a)

300 200

(c) 300

y-component residual stress

Residual Stress (MPa)

(b) Residual Stress (MPa)

Middle plane

100 0 66 water quenched [11] 1% cold compression [11] 2% cold stretching [11] 66 water quenched [present] 1% cold compression [present] 2% cold stretching [present]

-100 -200 -300 0.0

0.2

0.4

0.6

0.8

z-component residual stress

200 100 0 66 water quenched [11] 1% cold compression [11] 2% cold stretching [11] 66 water quenched [present] 1% cold compression [present] 2% cold stretching [present]

-100 -200 -300 0.0

1.0

0.2

0.4

0.6

0.8

1.0

y/H

y/H

Fig. 16. Comparison of present simulation residual stresses on Block B along y-locus with published data (66 °C water quenched, 1% cold compression and 2% cold compression). (a) Schematic of coordinate and middle plane of model; (b) x-component; (c) y-component locus; and (d) z-component.

(b) Residual Stress (MPa)

(a)

400

7449 alloy was used in literature 11 7075 alloy was used in present simulation

300 200 100 0

σx [11]

-100

σy [11]

-200

σz [11]

-300

σx[Present simulation] σy[Present simulation]

-400

σz[Present simulation]

0

10

20

30

40

50

60

70

80

Distance from center in x direction /mm

(d)

7449 alloy was used in literature 11 7075 alloy was used in present simulation

300

Residual Stress (MPa)

Residual Stress (MPa)

(c) 400 200 100 0

σx [11]

-100

σy [11]

-200

σz [11]

-300

σx [Present simulation] σy [Present simulation]

-400

10

20

30

40

7449 alloy was used in literature 11 7075 alloy was used in present simulation

300 200 100 0

σx [11]

-100

σy [11]

-200

σz [11]

-300

σx [Present simulation] σy [Present simulation]

-400

σz [Present simulation]

0

400

50

60

70

Distance from center in y direction /mm

σz [Present simulation]

0

50

100

150

200

250

Distance from center in z direction /mm

Fig. 17. Comparison of present simulation residual stresses on Block C with published data. (a) Schematic of coordinate and middle plane of model; (b) x-direction; (c) y-direction; and (d) z-direction.

temperature above 60 °C. As can be seen from Fig. 24, the hoop residual stresses also decrease obviously with increasing water temperature, especially water temperature above 60 °C. As can

be seen from Fig. 23, at lower water temperatures (660 °C), the axial residual stresses decrease slightly with increasing water temperature, but when the temperature above 60 °C, the axial

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

Unit: mm

(a)

z B

O

r

A

(b)

150

Residual stress/MPa

408

120

0.4% 0.7% 1.0% 1.3% 1.5% 1.7% 2% 2.3% 2.5% 2.7% 3%

σr

90 60 30 0 0

5

10 15 20 25 30 35 40 45 50 55

Distance/mm

σz

Residual stress/MPa

100 50 0 -50 -100 -150

0

5

(d) 150

0.4% 0.7% 1.0% 1.3% 1.5% 1.7% 2% 2.3% 2.5% 2.7% 3%

0.4% 0.7% 1.0% 1.3% 1.5% 1.7% 2% 2.3% 2.5% 2.7% 3%

σt

100

Residual stress/MPa

(c) 150

50 0 -50 -100 -150

10 15 20 25 30 35 40 45 50 55

-200

0

5

10 15 20 25 30 35 40 45 50 55

Distance/mm

Distance/mm

Fig. 18. Residual stresses of quenched cylindrical bar along r-direction under different stretching ratio conditions: (a) radial residual stress; (b) axial residual stress; and (c) hoop residual stress.

(b)

Unit: mm

150

z B

O

A

r

0.4% 0.7% 1.0% 1.3% 1.5% 1.7% 2% 2.3% 2.5% 2.7% 3%

σr

120

Residual stress/MPa

(a)

90 60 30 0 -30 -60

0

10

20

30

40

50

60

70

80

90 100

Distance/mm

σz

Residual stress/MPa

120

0.4% 0.7% 1.0% 1.3% 1.5% 1.7% 2% 2.3% 2.5% 2.7% 3%

90 60 30 0 -30

0

20

40

60

Distance/mm

80

100

(d) 150

σt

120

Residual stress/MPa

(c) 150

0.4% 0.7% 1.0% 1.3% 1.5% 1.7% 2% 2.3% 2.5% 2.7% 3%

90 60 30 0 -30 -60

0

20

40

60

80

100

Distance/mm

Fig. 19. Residual stresses of quenched cylindrical bar along z-axis direction under different stretching ratio conditions: (a) radial residual stress; (b) axial residual stress; and (c) hoop residual stress.

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X. Yang et al. / Computational Materials Science 69 (2013) 396–413

(a)

20

(b)

Unit: mm

Residual stress/MPa

z B

O

12 8 4

r

A

0.05mm/s 0.25mm/s 0.5mm/s 0.75mm/s 1mm/s 10mm/s

σr

16

0 -4

0

5

10

15

20

25

30

35

40

45

50

Distance/mm 20

σz

Residual stress/MPa

16

(d)

0.05mm/s 0.25mm/s 0.5mm/s 0.75mm/s 1mm/s 10mm/s

12 8 4 0 -4 -8 -12

20

0.05mm/s 0.25mm/s 0.5mm/s 0.75mm/s 1mm/s 10mm/s

σt

15

Residual stress/MPa

(c)

10 5 0 -5 -10 -15 -20

0

5

10

15

20

25

30

35

40

45

-25

50

0

5

10

15

20

25

30

35

40

45

50

Distance/mm

Distance/mm

Fig. 20. Residual stresses of quenched cylindrical bar along r-axis direction under different stretching rate conditions: (a) radial residual stress; (b) axial residual stress; and (c) hoop residual stress.

(a)

(b) 24

Unit: mm

20

B

O

r

A

Residual stress/MPa

z

0.05mm/s 0.25mm/s 0.5mm/s 0.75mm/s 1mm/s 10mm/s

σr

16 12 8 4 0 -4

0

10

20

30

40

50

60

70

80

90

Distance/mm 24 20

Residual stress/MPa

0.05mm/s 0.25mm/s 0.5mm/s 0.75mm/s 1mm/s 10mm/s

σz

16 12 8 4

0.05mm/s 0.25mm/s 0.5mm/s 0.75mm/s 1mm/s 10mm/s

σt

20 16 12 8 4 0

0 -4

(d) 24 Residual stress/MPa

(c)

0

10

20

30

40

50

60

Distance/mm

70

80

90

-4

0

10

20

30

40

50

60

70

80

90

Distance/mm

Fig. 21. Residual stresses of quenched cylindrical bar along z-axis direction under different stretching rate conditions: (a) radial residual stress; (b) axial residual stress; and (c) hoop residual stress.

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X. Yang et al. / Computational Materials Science 69 (2013) 396–413

Fig. 22. Predicted radial residual stresses contours (a) 25 °C; (b) 45 °C; (c) 60 °C; and (d) 80 °C.

Fig. 23. Predicted axial residual stresses contours (a) 25 °C; (b) 45 °C; (c) 60 °C; and (d) 80 °C.

Fig. 24. Predicted hoop residual stresses contours (a) 25 °C; (b) 45 °C; (c) 60 °C; and (d) 80 °C.

residual stresses decrease obviously with increasing water temperature. Fig. 25 shows histogram of maximum residual stresses of cylindrical bar after quenching and of quenched cylindrical bar after 1.5% stretching at the axis plane of symmetry. As can be seen from Fig. 25, it is very obvious that stretching eliminate the residual stress of quenched cylindrical bar greatly. As can be seen from

Fig. 25b and c, the maximum residual stress decreases with increasing water temperature. As can be seen from Fig. 25d, at lower water temperatures (660 °C), the maximum tensile residual stresses in three directions of quenched cylindrical bar after stretching were all reduced to approximately 11 MPa. While at water temperature 80 °C, they were reduced to approximately

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X. Yang et al. / Computational Materials Science 69 (2013) 396–413

Axis plane of symmetry

Unit: mm

(a)

z B

O

A

r

280

Maximum tensile stress (MPa)

(b)

Quenched cylindrical bar

S11 S22 S33

240

(c)

200 160 120 80 40 0 25

45

60

Temperature (

80

Maximum compressive stress (MPa)

Temperature ( 0

25

45

-100

-150

14 12

S11 S22 S33

10 8 6 4 2 45

60

Temperature (

80

(e)

Maximum compressive stress (MPa)

Maximum tensile stress (MPa)

Quenched bar after Stretching

25

S11 S22 S33

Quenched cylindrical bar -200

)

16

0

80

-50

Temperature (

(d)

)

60

0.0

25

45

)

60

80

-0.2 -0.4 -0.6 -0.8 -1.0 -10 -20 -30 -40

Quenched bar after stretching

S11 S22 S33

)

Fig. 25. Histogram of maximum residual stresses of cylindrical bar after quenching and of quenched cylindrical bar after 1.5% stretching at the axis plane of symmetry. (a) Axis plane of symmetry; (b) maximum tensile residual stress of cylindrical bar after quenching; (c) maximum compressive residual stress of cylindrical bar after quenching; (d) maximum tensile residual stress of quenched cylindrical bar after 1.5% stretching; and (e) maximum compressive residual stress of quenched cylindrical bar after 1.5% stretching.

5 MPa. As can be seen from Fig. 25e, the maximum compressive residual stresses in three directions of quenched cylindrical bar after stretching were all below 30 MPa. 4.4.4. Influence of aspect ratio of cylindrical bar The aspect ratio is an important structural parameter for aluminum alloy parts. So it is necessary to carry out the investigation of influence of aspect ratio on quenching residual stress. In this part, the diameter of cylindrical bar was 80 mm and the heights were 40, 80, 120, 160, 200, 240 mm, respectively. So the aspect ratio of cylindrical bars are 1:2, 1:1, 3:2, 2:1, 5:2, 3:1, respectively. Here the quenching water temperature was 60°C, the stretching rate

was 0.5 mm/s and the stretching ratio was 1.5%. Fig. 26 shows histogram of maximum residual stresses of cylindrical bar after quenching and of quenched cylindrical bar after 1.5% stretching. As can be seen from Fig. 26, it is found that releasing residual stresses of quenched cylindrical bar by using stretching process is very effective. As can be seen from Fig. 26b, the maximum radial/hoop residual tension stress of quenched cylindrical bar at low aspect ratios (61:1) is higher than the value in high aspect ratios (P3:2), while the maximum axial residual tension stress of quenched cylindrical bar at low aspect ratios (61:1) is lower than the value in high aspect ratios (P3:2). As shown in Fig. 26b, at high aspect ratios (P3:2), with the increase of aspect ratio, the change trend

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

(a)

Unit: mm Axis plane of symmetry

412

z B

O

A

r

320

S11 S22 S33

280

(c)

240 200 160 120 80 40 0 2:1

5:2

3:1

Maximum compressive stress (MPa)

(b)

Maximum tensile stress (MPa)

Aspect ratio of cylindrical bar 0

-50

-100

-150 S11 S22 S33

-200

Aspect ratio of cylinder

20

Maximum tensile stress (MPa)

(d)

S11 S22 S33

18 16 14 12 10 8 6 4 2 0

1:2

1:1

3:2

2:1

5:2

3:1

(e)

Maximum compressive stress (MPa)

Aspect ratio of cylinder 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -10 -20 -30 -40 -50

S11 S22 S33

Aspect ratio of cylinder Fig. 26. Histogram of maximum residual stresses of cylindrical bar after quenching and of quenched cylindrical bar after 1.5% stretching. (a) Axis plane of symmetry; (b) maximum tensile residual stress of cylindrical bar after quenching; (c) maximum compressive residual stress of cylindrical bar after quenching; (d) maximum tensile residual stress of quenched cylindrical bar after 1.5% stretching; and (e) maximum compressive residual stress of quenched cylindrical bar after 1.5% stretching.

of the maximum radial/axial/hoop residual tension stress is not obvious. As can be seen from Fig. 26c, with the increase of aspect ratio, the change trend of the maximum radial/axial/hoop residual compression stress is not obvious. As shown in Fig. 26d, it is found that the effectiveness of releasing residual stresses for quenched cylindrical bar at low aspect ratio (1:2) is better than the effectiveness in high aspect ratios (P1:1). As can be seen from Fig. 26e, the maximum compressive residual stresses in three directions of quenched cylindrical bar after stretching were all below 30MPa. 5. Conclusions ABAQUS CAE software has been used to research the magnitude and distribution of residual stress of cylindrical bars after quench-

ing and of quenched cylindrical bars after cold stretching process. Heat transfer coefficient of water at different temperature was accurately calculated by using an inverse heat transfer method. The validity and correctness of the quenching model were testified by using three numerical examples from two publications. The influence of some factors (pre-stretching ratio, stretching rate, water temperature and aspect ratio of cylindrical bar) on the magnitude of residual stress of cylindrical bars after quenching and of quenched cylindrical bars after cold stretching was investigated. The results of this paper were described as follows: (1) Prediction of residual stress of cylindrical bars after quenching and of quenched cylindrical bars after cold stretching by using FEM simulation is credible because of accurately

X. Yang et al. / Computational Materials Science 69 (2013) 396–413

(2)

(3)

(4)

(5)

calculated for heat transfer coefficient of water and testified for quenching model by using three numerical examples from two publications. When water temperature is 60 °C, the maximum tensile residual stresses of quenched cylindrical bar along r-direction, z-direction and t-direction are 148, 241 and 149 MPa, respectively, while the maximum compressive residual stresses along these three directions are 132, 144 and 152 MPa, respectively. The residual stress of quenched cylindrical bar after cold stretching process (1.5% stretching ratio and 0.5 mm/s stretching rate) is decreased largely and the range of stress reduction percentage is 81.5–94.9%. In order to decrease the residual stress of quenched cylindrical bar greatly, an upper limit to stretching rate is set 1 mm/s and a lower limit to stretching ratio is set 1.5%. The maximum tensile and compressive residual stress of quenched cylindrical bar decrease with increasing water temperature. While for the high water temperature (80 °C), the maximum tensile and compressive residual stress show much smaller than the values in the other temperatures (25, 45 and 60 °C). The maximum tensile and compressive residual stress of quenched cylindrical bar after cold stretching (1.5% stretching ratio and 0.5 mm/s stretching rate) reduced to less than 14 and 28 MPa, respectively. The maximum radial/hoop residual tension stress of quenched cylindrical bar at low aspect ratios (61:1) is higher than the value in high aspect ratios (P3:2), while the maximum axial residual tension stress of quenched cylindrical bar at low aspect ratios (61:1) is lower than the value in high aspect ratios (P3:2). At high aspect ratios (P3:2), with the increase of aspect ratio of cylindrical bar, it is not obvious about the change trend of the maximum radial/axial/hoop residual tension stress. The effectiveness of releasing residual stresses for quenched cylindrical bar at low aspect ratio (1:2) is better than the effectiveness in high aspect ratios(P1:1). After stretching for quenched cylindrical bar, the maximum compressive residual stresses along r-direction, z-direction and t-direction were all below 30 MPa.

Acknowledgement The authors would like to express their sincere thanks to the School of Materials Science and Engineering, Harbin Institute of Technology for supporting the research work.

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