J. Mater. Sci. Technol. ›› 2020, Vol. 45: 35-43.DOI: 10.1016/j.jmst.2019.11.025
• Research Article • Previous Articles Next Articles
Wei Lia,c,*(), Martina Vittoriettib,c, Geurt Jongbloedb, Jilt Sietsmaa
Received:
2019-09-04
Revised:
2019-10-29
Accepted:
2019-11-06
Published:
2020-05-15
Online:
2020-05-27
Contact:
Wei Li
Wei Li, Martina Vittorietti, Geurt Jongbloed, Jilt Sietsma. The combined influence of grain size distribution and dislocation density on hardness of interstitial free steel[J]. J. Mater. Sci. Technol., 2020, 45: 35-43.
Fe | C | Ti | Mn | Al | Si | Cr | Si | P |
---|---|---|---|---|---|---|---|---|
Bal. | 0.005 | 0.081 | 0.077 | 0.055 | 0.052 | 0.016 | 0.011 | 0.003 |
Table 1 Chemical composition (wt%) of the IF steel selected for this study.
Fe | C | Ti | Mn | Al | Si | Cr | Si | P |
---|---|---|---|---|---|---|---|---|
Bal. | 0.005 | 0.081 | 0.077 | 0.055 | 0.052 | 0.016 | 0.011 | 0.003 |
Heat treatment routes | Mean hardness (HV) | Hardness std. (HV) | Dislocation density (1010 m-2) | Dislocation density error (1010 m-2) |
---|---|---|---|---|
1000 °C 10 min 1 °C s-1 | 58.6 | 1.5 | 1 | - |
1000 °C 10 min 750 °C 5 min Q | 60.9 | 2.4 | 1 | - |
1000 °C 10 min 800 °C 5 min Q | 62.0 | 1.3 | 1 | - |
1000 °C 10 min 850 °C 5 min Q | 62.3 | 1.6 | 1 | - |
1000 °C 10 min 700 °C 5 min Q | 64.9 | 0.9 | 1 | - |
1000 °C 10 min 80 °C s-1 | 66.7 | 2.3 | 1 | - |
800 °C 5 min Q | 68.1 | 0.5 | 1 | - |
1000 °C 10 min 200 °C s-1 | 69.1 | 1.7 | 3.1 | 0.9 |
700 °C 5 min Q | 75.9 | 3.2 | 1 | - |
400 °C 5 min Q | 80.1 | 1.3 | 1 | - |
CR 3 mm | 127.3 | 2.3 | 43 | 3 |
CR 1.7 mm | 139.9 | 2.2 | 75 | 4 |
CR 1.13 mm 600 °C 75 min Q | 141.8 | 1.6 | 12 | 2 |
CR 1.13 mm 450 °C 9 min Q | 159.6 | 2.4 | 60 | 4 |
CR 1.13 mm 400 °C 9 min Q | 163.4 | 2.0 | 75 | 5 |
CR 1.13 mm | 167.0 | 1.9 | 72 | 4 |
Table 2 Heat treatment routes with corresponding hardness values and dislocation density. Heat treatment route consists of temperature time and cooling rate, where ‘Q’ means quenching to room temperature, ‘CR’ means cold rolling. The heating rate is 10 °C s-1. The cooling rate, if not stated, is -30 °C s-1.
Heat treatment routes | Mean hardness (HV) | Hardness std. (HV) | Dislocation density (1010 m-2) | Dislocation density error (1010 m-2) |
---|---|---|---|---|
1000 °C 10 min 1 °C s-1 | 58.6 | 1.5 | 1 | - |
1000 °C 10 min 750 °C 5 min Q | 60.9 | 2.4 | 1 | - |
1000 °C 10 min 800 °C 5 min Q | 62.0 | 1.3 | 1 | - |
1000 °C 10 min 850 °C 5 min Q | 62.3 | 1.6 | 1 | - |
1000 °C 10 min 700 °C 5 min Q | 64.9 | 0.9 | 1 | - |
1000 °C 10 min 80 °C s-1 | 66.7 | 2.3 | 1 | - |
800 °C 5 min Q | 68.1 | 0.5 | 1 | - |
1000 °C 10 min 200 °C s-1 | 69.1 | 1.7 | 3.1 | 0.9 |
700 °C 5 min Q | 75.9 | 3.2 | 1 | - |
400 °C 5 min Q | 80.1 | 1.3 | 1 | - |
CR 3 mm | 127.3 | 2.3 | 43 | 3 |
CR 1.7 mm | 139.9 | 2.2 | 75 | 4 |
CR 1.13 mm 600 °C 75 min Q | 141.8 | 1.6 | 12 | 2 |
CR 1.13 mm 450 °C 9 min Q | 159.6 | 2.4 | 60 | 4 |
CR 1.13 mm 400 °C 9 min Q | 163.4 | 2.0 | 75 | 5 |
CR 1.13 mm | 167.0 | 1.9 | 72 | 4 |
Fig. 1. (a) Typical micro-graph of sample ‘CR 3 mm’, (b) the grain boundary outline drawing of (a) and (c) histogram of grain size of (a) with a log-normal fitting.
Fig. 2. Grain size distribution box plot with the increasing order of hardness values from left to right. The dots represent the size of all grains measured in corresponding sample.
Fig. 3. Hardness in relation to (a) mean grain size and (b) dislocation density. The dotted line in (a) is based on the linear fitting of the values for samples without cold rolling. The dotted line in (b) is based on the values of all samples.
Fig. 5. Error as a function of λ for LASSO with all 5 independent variables. The numbers on the top indicate the number of variables included in the fitted model.
Heat treatment routes | μd (μm) | s (μm) | Skewness | Kurtosis |
---|---|---|---|---|
1000 °C 10 min 1 °C s-1 | 159.1 | 94.0 | 0.68 | -0.20 |
1000 °C 10 min 750 °C 5 min Q | 135.8 | 95.5 | 1.02 | 0.51 |
1000 °C 10 min 800 °C 5 min Q | 145.0 | 113.3 | 1.13 | 0.41 |
1000 °C 10 min 850 °C 5 min Q | 92.5 | 59.0 | 0.88 | 0.20 |
1000 °C 10 min 700 °C 5 min Q | 123.9 | 111.7 | 1.59 | 2.24 |
1000 °C 10 min 80 °C s-1 | 71.6 | 53.7 | 0.99 | 0.32 |
800 °C 5 min Q | 32.9 | 18.9 | 1.04 | 0.85 |
1000 °C 10 min 200 °C s-1 | 122.5 | 70.0 | 0.75 | 0.20 |
700 °C 5 min Q | 32.4 | 20.3 | 0.86 | 0.39 |
400 °C 5 min Q | 31.0 | 18.8 | 0.81 | 0.45 |
CR 3 mm | 28.3 | 16.0 | 0.63 | 0.22 |
CR 1.7 mm | 24.2 | 20.1 | 1.25 | 1.42 |
CR 1.13 mm 600 °C 75 min Q | 24.8 | 25.5 | 2.01 | 5.54 |
CR 1.13 mm | 26.8 | 24.5 | 1.51 | 2.19 |
Table 3 Part of the detailed grain size distribution data.
Heat treatment routes | μd (μm) | s (μm) | Skewness | Kurtosis |
---|---|---|---|---|
1000 °C 10 min 1 °C s-1 | 159.1 | 94.0 | 0.68 | -0.20 |
1000 °C 10 min 750 °C 5 min Q | 135.8 | 95.5 | 1.02 | 0.51 |
1000 °C 10 min 800 °C 5 min Q | 145.0 | 113.3 | 1.13 | 0.41 |
1000 °C 10 min 850 °C 5 min Q | 92.5 | 59.0 | 0.88 | 0.20 |
1000 °C 10 min 700 °C 5 min Q | 123.9 | 111.7 | 1.59 | 2.24 |
1000 °C 10 min 80 °C s-1 | 71.6 | 53.7 | 0.99 | 0.32 |
800 °C 5 min Q | 32.9 | 18.9 | 1.04 | 0.85 |
1000 °C 10 min 200 °C s-1 | 122.5 | 70.0 | 0.75 | 0.20 |
700 °C 5 min Q | 32.4 | 20.3 | 0.86 | 0.39 |
400 °C 5 min Q | 31.0 | 18.8 | 0.81 | 0.45 |
CR 3 mm | 28.3 | 16.0 | 0.63 | 0.22 |
CR 1.7 mm | 24.2 | 20.1 | 1.25 | 1.42 |
CR 1.13 mm 600 °C 75 min Q | 24.8 | 25.5 | 2.01 | 5.54 |
CR 1.13 mm | 26.8 | 24.5 | 1.51 | 2.19 |
Heat treatment | N total | Mean | Standard Deviation | SE of mean | Skewness | Kurtosis | Minimum | Median | Maximum | Range (Maximum-Minimum) | P1 | P99 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1000 °C 10 min 1 °Cs-1 | 84 | 159.1 | 94.0 | 10.3 | 0.68 | -0.20 | 23.5 | 145.1 | 402.8 | 379.3 | 23.5 | 402.8 |
1000 °C 10 min 750 °C 5 min Q | 105 | 135.8 | 95.5 | 9.3 | 1.02 | 0.51 | 17.9 | 113.9 | 419.6 | 401.6 | 18.0 | 395.6 |
1000 °C 10 min 800 °C 5 min Q | 93 | 145.0 | 113.3 | 11.7 | 1.13 | 0.41 | 23.3 | 96.8 | 493.0 | 469.7 | 23.3 | 493.0 |
1000 °C 10 min 850 °C 5 min Q | 63 | 92.5 | 59.0 | 7.4 | 0.88 | 0.20 | 14.3 | 87.3 | 242.6 | 228.4 | 14.3 | 242.6 |
1000 °C 10 min 700 °C 5 min Q | 102 | 123.9 | 111.7 | 11.1 | 1.59 | 2.24 | 11.0 | 84.3 | 552.9 | 541.9 | 11.4 | 461.3 |
1000 °C 10 min 80 °Cs-1 | 93 | 71.6 | 53.7 | 5.6 | 0.99 | 0.32 | 3.0 | 55.7 | 236.1 | 233.1 | 3.0 | 236.1 |
800 °C 5 min Q | 214 | 32.9 | 18.9 | 1.3 | 1.04 | 0.85 | 4.5 | 28.4 | 100.6 | 96.1 | 6.5 | 85.0 |
1000 °C 10 min 200 °Cs-1 | 107 | 122.5 | 70.0 | 6.8 | 0.75 | 0.20 | 18.2 | 108.3 | 353.2 | 335.0 | 20.6 | 318.1 |
700 °C 5 min Q | 198 | 32.4 | 20.3 | 1.4 | 0.86 | 0.39 | 1.4 | 29.2 | 102.9 | 101.5 | 2.2 | 92.6 |
400 °C 5 min Q | 214 | 31.0 | 18.8 | 1.3 | 0.81 | 0.45 | 1.5 | 28.3 | 96.3 | 94.7 | 3.1 | 80.2 |
CR 3mm | 195 | 28.3 | 16.0 | 1.1 | 0.63 | 0.22 | 1.6 | 26.4 | 79.8 | 78.2 | 2.1 | 74.3 |
CR 1.7mm | 273 | 24.2 | 20.1 | 1.2 | 1.25 | 1.42 | 1.3 | 19.4 | 94.5 | 93.2 | 1.5 | 92.2 |
CR 1.13 mm 600 °C 75 min Q | 257 | 24.8 | 25.5 | 1.6 | 2.01 | 5.54 | 1.3 | 15.9 | 161.7 | 160.4 | 1.6 | 117.0 |
CR 1.13 mm | 284 | 26.8 | 24.5 | 1.5 | 1.51 | 2.19 | 1.3 | 19.4 | 130.5 | 129.2 | 1.7 | 104.2 |
Table A1. Detailed descriptive statistics of the grain size for all samples.
Heat treatment | N total | Mean | Standard Deviation | SE of mean | Skewness | Kurtosis | Minimum | Median | Maximum | Range (Maximum-Minimum) | P1 | P99 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1000 °C 10 min 1 °Cs-1 | 84 | 159.1 | 94.0 | 10.3 | 0.68 | -0.20 | 23.5 | 145.1 | 402.8 | 379.3 | 23.5 | 402.8 |
1000 °C 10 min 750 °C 5 min Q | 105 | 135.8 | 95.5 | 9.3 | 1.02 | 0.51 | 17.9 | 113.9 | 419.6 | 401.6 | 18.0 | 395.6 |
1000 °C 10 min 800 °C 5 min Q | 93 | 145.0 | 113.3 | 11.7 | 1.13 | 0.41 | 23.3 | 96.8 | 493.0 | 469.7 | 23.3 | 493.0 |
1000 °C 10 min 850 °C 5 min Q | 63 | 92.5 | 59.0 | 7.4 | 0.88 | 0.20 | 14.3 | 87.3 | 242.6 | 228.4 | 14.3 | 242.6 |
1000 °C 10 min 700 °C 5 min Q | 102 | 123.9 | 111.7 | 11.1 | 1.59 | 2.24 | 11.0 | 84.3 | 552.9 | 541.9 | 11.4 | 461.3 |
1000 °C 10 min 80 °Cs-1 | 93 | 71.6 | 53.7 | 5.6 | 0.99 | 0.32 | 3.0 | 55.7 | 236.1 | 233.1 | 3.0 | 236.1 |
800 °C 5 min Q | 214 | 32.9 | 18.9 | 1.3 | 1.04 | 0.85 | 4.5 | 28.4 | 100.6 | 96.1 | 6.5 | 85.0 |
1000 °C 10 min 200 °Cs-1 | 107 | 122.5 | 70.0 | 6.8 | 0.75 | 0.20 | 18.2 | 108.3 | 353.2 | 335.0 | 20.6 | 318.1 |
700 °C 5 min Q | 198 | 32.4 | 20.3 | 1.4 | 0.86 | 0.39 | 1.4 | 29.2 | 102.9 | 101.5 | 2.2 | 92.6 |
400 °C 5 min Q | 214 | 31.0 | 18.8 | 1.3 | 0.81 | 0.45 | 1.5 | 28.3 | 96.3 | 94.7 | 3.1 | 80.2 |
CR 3mm | 195 | 28.3 | 16.0 | 1.1 | 0.63 | 0.22 | 1.6 | 26.4 | 79.8 | 78.2 | 2.1 | 74.3 |
CR 1.7mm | 273 | 24.2 | 20.1 | 1.2 | 1.25 | 1.42 | 1.3 | 19.4 | 94.5 | 93.2 | 1.5 | 92.2 |
CR 1.13 mm 600 °C 75 min Q | 257 | 24.8 | 25.5 | 1.6 | 2.01 | 5.54 | 1.3 | 15.9 | 161.7 | 160.4 | 1.6 | 117.0 |
CR 1.13 mm | 284 | 26.8 | 24.5 | 1.5 | 1.51 | 2.19 | 1.3 | 19.4 | 130.5 | 129.2 | 1.7 | 104.2 |
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