A Comparative Study of Hot Deformation Behaviors for Sand Casting and Centrifugal Casting Q235B Flange Blanks

Materials

The material used in this investigation is Q235B steel. The Q235B flange blanks with the same dimensions of ϕ270 mm ×ϕ105 mm × 45 mm were produced by sand casting and centrifugal casting at pouring temperature of 1,540 °C [20, 21], respectively, as shown in Figure 1. The measured chemical compositions of the tested as-cast materials are given in Table 1.

Figure 1:

Q235B flange blank.

The initial microstructures of two states materials are mainly composed of a block of ferrite and pearlite, as shown in Figure 2. However, the coarse and inhomogeneous in grains are the main microstructure characteristics of sand casting Q235B. The ferrite is acicular and blocky in centrifugal casting Q235B with finer grain and dense microstructure.

Figure 2:

Initial microstructures of Q235B ring blanks: (a) sand casting and (b) centrifugal casting.

Experimental procedure

The hot compression test’s specimen was cut along the radial of the rings because the flange blank was rolled in the radius direction during hot rolling. Cylindrical specimens were machined with a diameter of 8 mm and a height of 12 mm according to the ASTM E209 standard. In order to minimize the frictions between the specimens and dies during hot deformation, the flat ends of the specimen were placed a graphite of 0.25 mm and a tantalum chip of 0.1 mm. Isothermal compression tests were performed on a Gleeble-1500D thermosimulation machine in four different temperatures (1,150, 1,050, 950 and 850 °C) and four different strain rates (0.01, 0.05, 0.1, 1 and 5 s⁻¹). Each specimen was heated to 1,200 °C at the rate of 10 °C/s and soaked for 5 min. Then, cooled at the rate of 5 °C/s to the corresponding test temperatures and held for 1 min before hot compression so as to obtain the heat balance. The reduction in height is 60 % at the end of the compression tests. After deformation, the specimens were water quenched immediately to keep the deformed microstructure. The detailed experimental procedure is shown in Figure 3. All the specimens were then sectioned parallel to the compression axis, and the cutting surface was prepared using standard polishing and etching techniques for metallographic examination. The microstructures and texture components were observed by optical microscope and electron backscatter diffraction (EBSD) system equipped at Zeiss SEM, respectively. Specimens for EBSD were electropolished using a solution of 5 % KClO₄ alcohol at 20 °C, 30 V and 0.8 A.

Figure 3:

Experimental procedure for hot compression tests and specimens (a) undeformed and (b) deformed.

True stress–strain curves of hot compression

Basically, the intrinsic relationship of flow stress and deformation parameters was articulated by the stress–strain curve, which also indirectly indicates the internal microstructure evolution of materials. Thereby, it is quite helpful to validate the hot deformation mechanisms of materials [22, 23]. The true stress–strain curves of hot compression of sand casting and centrifugal casting Q235B flange blanks under different conditions are shown in Figures 4 and 5. The flow stresses increase quickly to a peak with the increase of strain in the initial stage of compression deformation and gradually decrease to some extent as the deformation exceeds the peak strain. However, the stresses are abnormal within the temperature of 850–950 °C at strain rate of 5 s⁻¹. Subsequently, it shows a steady-state characteristic, which is simultaneously caused by work hardening and softening in the process of hot compression. At the beginning of the deformation, the hardening effect plays a dominant role before reaching the peak stress. As the increase of strain, the driving force of dynamic recrystallization (DRX) increases and thus softening effect gradually increases. After reaching the peak stress, the softening effect turns to a dominant role, resulting in the decrease in stress. Therefore, a dynamic balance is obtained between work hardening and dynamic softening such as dynamic recovery (DRV) and DRX.

Figure 4:

True stress–strain curves of sand casting Q235B under different strain rates with temperatures of (a) 850 °C; (b) 950 °C; (c) 1,050 °C and (d) 1,150 °C.

Figure 5:

True stress–strain curves of centrifugal casting Q235B under different strain rate with temperatures of (a) 850 °C; (b) 950 °C; (c) 1,050 °C and (d) 1,150 °C.

The steady-state stress is greater than 100 MPa at 950 °C and the stress is just 50 MPa at 1,150 °C when strain rate is 0.1 s⁻¹, as depicted in Figure 4. The similar pattern is shown in Figure 5, which indicates that flow stresses decrease with the increase of temperature at constant strain rate. This is mainly because the average kinetic energy of atoms increases and the critical shear stress of crystal slip decreases with the increase of temperature, which reduce the obstruction of dislocation motion and crystal slip [24]. Moreover, with the increase of temperature, the DRV and DRX are more likely to occur, making the density of dislocation decreases and the softening effect turns to a dominant role. The strain rate also has an important effect on flow stress. As illustrated in Figure 4(c), the steady-state stress is 40 MPa under strain rate of 0.01 s⁻¹ at 1,050 °C, while the stress can be up to 100 MPa with increase of strain rate to 1 s⁻¹ and the similar pattern is also shown in Figure 5. It indicates that flow stresses increase with the increase of strain rate at constant temperature. It is attributed to the fact that DRV and DRX have not enough time fully carrying out and cannot offset the hardening effect under high strain rate, so the stress is much higher than that under low strain rate.

However, the variations of the flow stress of centrifugal casting Q235B are relatively smooth at all deformation conditions used in this study, as shown in Figure 5. The work hardening of centrifugal casting Q235B is lower than that of sand casting. It only indicates the interaction of work hardening and DRV at lower temperature and higher strain rate. The stable deformation can contribute to the homogeneous microstructure. Figures 4 and 5 show that the flow stress of sand casting Q235B is higher than that of centrifugal casting at the same deformation conditions. The strain is larger when the stress reached to a peak for sand casting, resulting in the DRX is difficult to occur. The work hardening is quite apparent under low temperature and high strain rate such as 950 °C/1 s⁻¹. The stress value of sand casting Q235B can be up to 224.4 MPa and the stress of centrifugal casting is less than 157.7 MPa under the condition of temperature of 950 °C at 5 s⁻¹. This is mainly because of the centrifugal casting Q235B with dense microstructure and finer grains. Therefore, under the condition of tests, the DRV and DRX in this material are more likely to occur, making the effect of work hardening to be offset comparing with sand casting one.

Characterization of microstructure and texture

Figures 6 and 7 present the microstructures and textures of two as-cast materials under different conditions. Figure 6(a) shows that an apparent DRV occurs, and the microstructure is inhomogeneous existing some new generated grains. The work hardening effect cannot be offset by the slightly softening effect in the process of deformation. When the temperature is 1,050 °C, the grains are refined because the DRV and DRX are higher than that in Figure 6(a). The flow stress value is less than 70 MPa and the grains are about 32.8 μm under this condition. Although the temperature and strain rate is high in Figure 6(c), the material does not have enough time to perform DRV and DRX. Thus, the work hardening effect is severe and the flow stress is 130 MPa under the temperature of 1,050 °C, strain rate of 5 s⁻¹ and true strain of 0.7. Figure 6(a₁)–(c₁) depicts the texture evolution at φ₂ = 45^o section of orientation distribution function (ODF) under the same deformation conditions of Figure 6(a)–(c). As the temperature increases from 950 to 1,050 °C at 0.1 s⁻¹, the intensity of texture slightly weakens and texture components composed of {112}<110> and {111}<112> are shown in Figure 6(a₁), while mainly {111}<112> orientation is shown in Figure 6(b₁). When strain rate reaches 5 s⁻¹, the textures are characterized by strong cube {001}<100> and R-cube {001}<110> orientation, which are related with severe deformation in deformed specimen.

Figure 6:

Microstructures and textures of sand casting Q235B deformed at (a,a₁) 950 °C/0.1 s⁻¹; (b,b₁) 1,050 °C/0.1 s⁻¹; (c,c₁) 1,050 °C/5 s⁻¹.

As illustrated in Figure 7, it can be seen that the microstructural and textural development of centrifugal casting Q235B is similar to that in Figure 6. However, the degree of DRV and DRX for centrifugal casting Q235B is more apparent than the sand casting one at the same conditions, as shown in Figure 7(a)–(c), resulting in the finer grains and lower flow stress. For example, the average size of crystal grains is 22.7 μm and the value of flow stress is less than 60 MPa under the temperature of 1,050 °C, strain rate of 0.1 s⁻¹ and true strain of 0.7. What is more, with the increase of strain rate, the grain distortion cannot be discovered and the approximately equiaxed grains are generated, as presented in Figure 7(c). Similarly, Figure 7(a₁)–(c₁) suggests that texture intensity also slightly weakens with the increase in temperature from 950 °C to 1,050 °C at a strain rate of 0.1 s⁻¹. The texture components are mainly composed of {110}<110> and {111}<112> with the intensity of 4–6, which is different to sand casting Q235B under this condition. The textural development is mainly related with DRV and shear deformation at 1,050 °C when strain rate is 5 s⁻¹.

Figure 7:

Microstructures and textures of centrifugal casting Q235B deformed at (a,a₁) 950 °C/0.1 s⁻¹; (b,b₁) 1,050 °C/0.1 s⁻¹; (c,c₁) 1,050 °C/5 s⁻¹.

The establishment of constitutive model

The hot compression deformation for metals and alloys is a thermally activated process. During hot deformation, the influences of strain rate and temperature on flow stress were described by Arrhenius-type modeling. The Arrhenius constitutive modeling was proposed by Sellars and Tegart [25] according to the similarity of hot deformation and high-temperature creep of materials:

in which ε˙ is the strain rate (s⁻¹); σ is the true stress for a given strain (MPa); Q is the activation energy of hot deformation (kJ/mol); T is the absolute temperature (K); R is the universal gas constant (8.314 J/mol/K); and A is the material constant.

It is the coupled effect of strain rate and temperature on the hot deformation behavior that is represented by Zener–Hollomon parameter (Z) [26]. The impacts of strain rate and temperature on deformation behavior and microstructure evolution were considered in parameter Z, which is a strain rate factor with temperature compensation. And it directly reflected the complexity of the deformation in materials. The parameter Z can be represented as

Then, the parameter Z can be calculated on the basis of deformation activated energy Q. It is obvious that the value of parameter Z increases with the increase of strain rate and the decrease of temperature.

Determination of material constants in constitutive model

In eq. (1), the stress function of F(σ) usually has the following forms [27, 28]:

(3)Fσ=σn(ασ<0.8)

(4)Fσ=expβσ(ασ<1.2)

(5)Fσ=sinhασn(allσ)

where n, β and α are material constants, α = β/n.

For the low stress level (ασ < 0.8) and high stress level (ασ > 1.2), the relationship between strain rate and stress can be expressed as follows:

(6)ε˙=A1⋅σnexp−Q/RT

(7)ε˙=A2⋅expβσexp−Q/RT

where A₁ and A₂ are materials constants.

Taking the logarithm of both sides of eqs (6) and (7), respectively.

(8)1n=∂lnσ∂lnε˙

(9)1β=∂σ∂lnε˙

For all the stress level, substituting eq. (5) into eq. (1), the relationship between strain rate and stress can be presented as,

(10)ε˙=A⋅sinhασnexp−Q/RT

Therefore, the stress can be expressed as a function of parameter Z, as shown in eq. (11).

(11)σ=1αlnZA1/n+ZA2/n+11/2

For the given strain rate conditions, Q can be achieved by differentiating eq. (10) for temperature,

(12)Q=Rn∂lnsinασ∂1/Tε˙

Taking the logarithm of both sides of eq. (10) gives

(13)lnsinhασ=(1/n)lnε˙+Q/(nRT)−(1/n)lnA

It can be concluded from eqs (1) and (2) that the impact of strain on flow stress during hot deformation is not considered, while the material constants n, β, α, Q and A vary with strain in the deformation process. Hence, the effects of strain on the material constants of constitutive equation were studied in this research. The solution procedures of the material constants will be conducted by taking the true strain of 0.05, for example.

The stress values (under the strain of 0.05) and corresponding strain rates of sand casting Q235B are taken into eqs (8) and (9); the relationship between flow stress and strain rate is shown in Figure 8(a) and 8(b). The values of n and β can be derived from the reciprocal of the slope of the lines by linear regression analysis, respectively. As a result, a mean value of n and β can be calculated as 9.0664 and 0.1375  MPa⁻¹. Then, α=β/n=0.01517 MPa⁻¹ is obtained. Therefore, by substituting the values of temperatures and stresses that are obtained from a specified strain rate into eqs (12) and (13), the value of Q can be determined from the average slope of the lines in Figure 8(c) and the value of A can be easily derived from the average intercept on Y-axis of the lines in Figure 8(d). So, the values of Q and A can be evaluated as 482.530 kJ/mol and 1.162 × 10¹⁹ s⁻¹, respectively.

Figure 8:

The relationship between flow stress and strain rate of sand casting Q235B: (a) ln σ–lnε˙; (b) σ–lnε˙; (c) ln[sinhασ]–1,000/T; (d) ln[sinhασ]–lnε˙.

Similarly, the mean value of n and β for centrifugal casting Q235B can be calculated as 10.3621 and 0.1762 MPa⁻¹ according to the relationship between flow stress and strain rate in Figure 9(a) and 9(b). Thus, α = β/n=0.01701 MPa⁻¹ is obtained. As given in Figure 9(c) and 9(d), the values of Q and A can be easily presented as 504.033 kJ/mol and 3.006 × 10¹⁹ s⁻¹ by linear fitting method, respectively.

Figure 9:

The relationship between flow stress and strain rate of centrifugal casting Q235B: (a) ln σ–lnε˙; (b) σ–lnε˙; (c) ln[sinhασ]–1,000/T; (d) ln[sinhασ]–lnε˙.

However, the effect of strain on the plastic flow behavior is unconspicuous and hence not considered by eq. (2). According to the above-mentioned solved method, the values of material constants (n, β, α, Q and A) of the constitutive model for two as-cast Q235B flange blanks were calculated under different strains within the range of 0.05–0.70 and the interval of 0.05. Since the constants determined in the process of derivation are related with strain, the relationship between the material constants and the strain can be fitted employing polynomials. The computed values of the material constants are provided in Tables 2 and 3. The relationships between n, β, α, Q, A and true strain of both Q235B flange blanks (shown in Figure 10) can be polynomial fitted by the compensation of strain, as presented in eq. (14).

Table 2:

Values of the material constants of sand casting Q235B steel at various strains.

Strain	n	β (MPa−1)	α (MPa−1)	Q (kJ/mol)	ln A (s−1)
0.05	9.0664	0.1375	0.01517	492.53	43.93
0.10	8.7771	0.1119	0.01275	516.83	46.04
0.15	8.2087	0.0948	0.01155	511.14	45.61
0.20	7.4077	0.0797	0.01076	497.067	44.8
0.25	7.0964	0.0736	0.01037	490.53	43.62
0.30	6.7512	0.0689	0.01021	477.13	42.91
0.35	6.3661	0.0639	0.01004	468.86	42.09
0.40	6.1826	0.062	0.01003	463.63	41.82
0.45	5.9718	0.0604	0.01011	460.56	41.4
0.50	5.7962	0.0589	0.01016	455.21	41.11
0.55	5.6233	0.0567	0.01008	451.6	40.83
0.60	5.5486	0.056	0.01009	448.83	40.42
0.65	5.5546	0.0557	0.01003	453.96	40.91
0.70	5.5578	0.0559	0.01006	462.84	41.72

Table 3:

Values of the material constants of centrifugal casting Q235B steel at various strains.

Strain	n	β (MPa−1)	α (MPa−1)	Q (kJ/mol)	ln A (s−1)
0.05	10.36	0.1762	0.01701	504.033	44.85
0.10	10.32	0.1426	0.01382	519.163	46.46
0.15	9.675	0.117	0.01209	520.112	46.76
0.20	8.63	0.1013	0.01174	503.181	45.01
0.25	8.015	0.0907	0.01132	491.438	43.9
0.30	7.38	0.083	0.01124	474.266	42.8
0.35	6.985	0.0788	0.01128	464.289	41.47
0.40	6.767	0.0769	0.01136	455.141	40.5
0.45	6.592	0.0756	0.01147	452.785	40.4
0.50	6.535	0.0757	0.01158	454.704	40.6
0.55	6.527	0.0762	0.01167	457.741	40.9
0.60	6.465	0.0761	0.01177	460.283	41.15
0.65	6.458	0.07605	0.01178	458.850	41.05
0.70	6.426	0.0759	0.01181	457.485	40.9

Figure 10:

Variation of (a) n, (b) β, (c) α, (d) Q and (e) ln A with true strain in the range 0.05–0.70 at an interval of 0.05 for sand casting and centrifugal casting Q235B steel.

It can be observed that the material constants of n, β, α, Q and A display apparent variation with true strain. In addition, the levels of the material constants of n, β and α of centrifugal casting Q235B are much higher than that of sand casting, while Q and A show a slight difference only at smaller and larger strains. The deformation activation energies of both steels are found to vary with true strain in the range of 448–516 and 452–520 kJ/mol, respectively. Therefore, in order to predict the flow stress accurately and precisely, a modified constitutive model should be developed by the compensation of strain. Tables 4 and 5 present the coefficients of polynomials of n, β, α, Q and A:

n=B0+B1ε+B2ε2+B3ε3+B4ε4+B5ε5

β=C0+C1ε+C2ε2+C3ε3+C4ε4+C5ε5

(14)α=D0+D1ε+D2ε2+D3ε3+D4ε4+D5ε5

Q=E0+E1ε+E2ε2+E3ε3+E4ε4+E5ε5

lnA=F0+F1ε+F2ε2+F3ε3+F4ε4+F5ε5

Table 4:

Coefficients of polynomials of n, β, α, Q and ln A of sand casting Q235B steel.

	x 0	x 1	x 2	x 3	x 4	x 5
n	9.15472	4.23243	−125.066	431.841	−605.071	308.856
β	0.173	−0.82075	2.41953	−3.42159	2.01494	−0.22736
α	0.01868	−0.08703	0.35283	−0.7142	0.72058	−0.28949
Q	437.294	1639.41	−11734.05	33576.47	−43885.18	21709.72
ln A	38.7963	149.774	−1,067.28	3,071.69	−4,037.01	2,003.96

Note: x represents the undetermined coefficient of the polynomial fitting equations B, C, D, E and F.

Table 5:

Coefficients of polynomials of n, β, α, Q and ln A of centrifugal casting Q235B steel.

	x 0	x 1	x 2	x 3	x 4	x 5
n	9.48227	32.5961	−337.032	1,017.510	−1,295.969	603.627
β	0.22352	−1.0963	3.2875	−5.106	4.2204	−1.5052
α	0.02238	−0.1373	0.6582	−1.532	1.74585	−0.7759
Q	456.818	1,333.898	−8,920.561	21,399.73	−21,761.096	7,867.454
ln A	40.3485	125.702	−803.778	1,828.701	−1,719.601	547.304

Note: x represents the undetermined coefficient of the polynomial fitting equations B, C, D, E and F.

Verification of the developed constitutive model

A comparison between the predicted and experimental results was assessed so as to verify the accuracy of the above-developed constitutive models of two as-cast Q235B flange blanks. So, by applying the computed material constants in constitutive models, the flow stress values were calculated for temperatures of 850, 950, 1,050 and 1,150 °C with strain rates of 0.01, 0.05, 0.1, 1 and 5 s⁻¹. Figures 11 and 12 show the detailed comparisons of predicted values based on the constitutive models and experimental values under the condition of tests. It can be seen in Figures 11 and 12 that the predicted data could agree well with the experimental data throughout the entire strain range toward two as-cast materials. The predicted flow stresses increase with the increase of strain rate and the decrease of temperature, which satisfied the experimental one. Only in the conditions at 0.1 s⁻¹ with 950 and 1,050 °C for sand casting Q235B and at 1 s⁻¹ with 850 and 950 °C for centrifugal casting Q235B, a slight difference between predicted stress values and experimental stress values could be discovered. Both the predicted and experimental stresses indicate that softening effect plays a dominant role after peak strain [8, 29]. Some researchers found that flow stress is lower at low strain rate and high temperature and thus DRX is more likely to occur, leading to a considerable grain refinement [30, 31]. Figures 7, 11 and 12 demonstrate that the developed constitutive models can fit this conclusion well.

Figure 11:

Comparison between the experimental and predicted flow stresses of sand casting Q235B steel at temperatures of (a) 850 °C; (b) 950 °C: (c) 1,050 °C and (d) 1,150 °C.

Figure 12:

Comparison between the experimental and predicted flow stresses of centrifugal casting Q235B steel at temperatures of: (a) 850 °C; (b) 950 °C; (c) 1,050 °C and (d) 1,150 °C.

In this paper, standard statistical parameters such as correlation coefficient (R) and average absolute relative error (AARE) are employed to evaluate the correlation between experimental values and calculated values of the flow stress under all conditions. They are expressed as follows [32, 33]:

(15)R=∑i=1Nσei−σˉeσpi−σˉp∑i=1Nσei−σˉe2∑i=1Nσpi−σˉp2

(16)AARE%=1N∑i=1Nσei−σpiσei×100

where σe is the experimental value of the stress, σp is the calculated data, σˉe and σˉp are the mean values of σe and σp, respectively, and N is the total number of the selected stress data in the equation. As shown in Figure 13(a) and 13(b), a good correlation (R = 0.986) and AARE = 3.76 % between experimental and calculated values is achieved for sand casting Q235B steel, while R and AARE are 0.989 and 4.25 % for centrifugal casting, respectively. This reflects the excellent predictability of the constitutive equations of two states Q235B flange blanks established in the paper by using Arrhenius-type constitutive modeling. Therefore, the proposed constitutive models of sand casting and centrifugal casting Q235B flange blanks are accurate and reliable and can be successfully applied to analyze the deformation in hot rolling of as-cast flange blanks.

Figure 13:

Correlation between the experimental and predicted flow stress values: (a) sand casting and (b) centrifugal casting.