Author Contributions
Conceptualisation, L.Z. and W.H., S.G.R.B. and N.P.L.; methodology, L.Z., W.H. and S.M.; software, L.Z. and W.H.; validation, L.Z., W.H. and S.M.; formal analysis, L.Z. and W.H., S.G.R.B. and N.P.L.; investigation, L.Z., W.H. and S.M.; writing—original draft preparation, L.Z. and W.H.; writing—review and editing, L.Z. and W.H.; funding acquisition, S.G.R.B. and N.P.L. All authors have read and agreed to the published version of the manuscript.
Figure 1.
(
a) Standard [
7] and (
b) non-standard [
8] tensile specimens and the strips (
c,
d) obtained from the rapid alloy prototyping routine. The miniaturised non-standard tensile specimen is a better choice due to the limited amount of rapid alloy prototyping materials.
Figure 1.
(
a) Standard [
7] and (
b) non-standard [
8] tensile specimens and the strips (
c,
d) obtained from the rapid alloy prototyping routine. The miniaturised non-standard tensile specimen is a better choice due to the limited amount of rapid alloy prototyping materials.
Figure 2.
Typical microstructure of DP800 steel. The ratio of martensite phase to ferrite phase is about 3:7 for DP800 steel.
Figure 2.
Typical microstructure of DP800 steel. The ratio of martensite phase to ferrite phase is about 3:7 for DP800 steel.
Figure 3.
CAD drawings (a) and photos (b) of different tensile test specimens. , and denote the total length, the parallel section length, the gauge length, the original width, the shoulder radius, and the original thickness of the test piece, respectively.
Figure 3.
CAD drawings (a) and photos (b) of different tensile test specimens. , and denote the total length, the parallel section length, the gauge length, the original width, the shoulder radius, and the original thickness of the test piece, respectively.
Figure 4.
Mesh of the computation domain and definitions of the coordinate system, PW, GL, THK, , , and .
Figure 4.
Mesh of the computation domain and definitions of the coordinate system, PW, GL, THK, , , and .
Figure 5.
Tinius H25KS tensile machine and XSight 9MPX video extensometer.
Figure 5.
Tinius H25KS tensile machine and XSight 9MPX video extensometer.
Figure 6.
The engineering stress strain curves comparison between the experiment (raw data in black) and modelling (in red) of DP800 based on A80 dimension; (a): the whole range of the stress strain curve and (b): the enlargement of Zone A.
Figure 6.
The engineering stress strain curves comparison between the experiment (raw data in black) and modelling (in red) of DP800 based on A80 dimension; (a): the whole range of the stress strain curve and (b): the enlargement of Zone A.
Figure 7.
The plastic strain distribution comparisons between the digital image correlation (a–d) and modelling (e–h) of frames with different engineering strains based on A80 specimen. Both plastic strain distribution and magnitude are matched.
Figure 7.
The plastic strain distribution comparisons between the digital image correlation (a–d) and modelling (e–h) of frames with different engineering strains based on A80 specimen. Both plastic strain distribution and magnitude are matched.
Figure 8.
The engineering stress strain curves comparison for A80 (AR = 16.7), A50 (AR = 10.4), ASTM25 (AR = 5), Mini1 (AR = 2.5), and Mini2 (AR = 1.67).
Figure 8.
The engineering stress strain curves comparison for A80 (AR = 16.7), A50 (AR = 10.4), ASTM25 (AR = 5), Mini1 (AR = 2.5), and Mini2 (AR = 1.67).
Figure 9.
(a): AR effect on the uniform elongation and UTS. (b): AR effect on the uniform and total elongations.
Figure 9.
(a): AR effect on the uniform elongation and UTS. (b): AR effect on the uniform and total elongations.
Figure 10.
The stress triaxiality evolution for A80 (AR = 16.7), A50 (AR = 10.4), ASTM25 (AR = 5), Mini1 (AR = 2.5), and Mini2 (AR = 1.67).
Figure 10.
The stress triaxiality evolution for A80 (AR = 16.7), A50 (AR = 10.4), ASTM25 (AR = 5), Mini1 (AR = 2.5), and Mini2 (AR = 1.67).
Figure 11.
The evolutions of the equivalent plastic strain (PEEQ) (a), the x (U1) displacement (b), and the z (U3) displacement (c) for ARs = 16.7 (A80) and =1.67 (Mini2).
Figure 11.
The evolutions of the equivalent plastic strain (PEEQ) (a), the x (U1) displacement (b), and the z (U3) displacement (c) for ARs = 16.7 (A80) and =1.67 (Mini2).
Figure 12.
The fracture surfaces of DP800 tensile specimens with different AR values. The fracture angle (the acute angle between the pulling direction and the fracture surface plane) increases as the AR value is decreased; (a–e): experiment and (f–j): modelling.
Figure 12.
The fracture surfaces of DP800 tensile specimens with different AR values. The fracture angle (the acute angle between the pulling direction and the fracture surface plane) increases as the AR value is decreased; (a–e): experiment and (f–j): modelling.
Figure 13.
Fracture angle vs. aspect ratio for different steels. For DP800, the transition AR values are located between 10.4 and 5 for the experiment and 5 and 2.5 for the modelling. In the legend, Pham (2018), Kohyama (1991), and Li (2016) are the references of [
9,
35,
36], respectively.
Figure 13.
Fracture angle vs. aspect ratio for different steels. For DP800, the transition AR values are located between 10.4 and 5 for the experiment and 5 and 2.5 for the modelling. In the legend, Pham (2018), Kohyama (1991), and Li (2016) are the references of [
9,
35,
36], respectively.
Figure 14.
Broken A80 (a) and A50 (b) tensile specimens’ appearances. The fracture angles of the A50 bars present a large deviation.
Figure 14.
Broken A80 (a) and A50 (b) tensile specimens’ appearances. The fracture angles of the A50 bars present a large deviation.
Table 1.
Chemical compositions for dual-phase 800 steel (% weight). The data were given by Tata Steel.
Table 1.
Chemical compositions for dual-phase 800 steel (% weight). The data were given by Tata Steel.
C | Si | Mn | P | S | Ni | Cu | Cr |
---|
0.136 | 0.249 | 1.77 | 0.011 | 0.0027 | 0.018 | 0.024 | 0.558 |
Table 2.
Tested tensile bar dimensions. , and denote the total length of the test piece, the parallel length, the gauge length, the original width of the parallel length of a flat test piece, the shoulder radius, and the thickness of the bar, respectively. The slimness ratio (K) and the aspect ratio (AR) are defined as and .
Table 2.
Tested tensile bar dimensions. , and denote the total length of the test piece, the parallel length, the gauge length, the original width of the parallel length of a flat test piece, the shoulder radius, and the thickness of the bar, respectively. The slimness ratio (K) and the aspect ratio (AR) are defined as and .
| | | | | R | | | (−2)/ | | K | | No. of Sample |
---|
| (mm) | (mm) | (mm) | (mm) | (n/a) | (n/a) | (n/a) | (n/a) | (mm) | (n/a) | (n/a) | (n/a) |
---|
A80 | 260 | 120 | 80 | 20 | 25 | 0.67 | 4 | 1 | 1.2 | 16.33 | 16.7 | 6 |
A50 | 200 | 75 | 50 | 12.5 | 15 | 0.67 | 4 | 1 | 1.2 | 12.91 | 10.4 | 6 |
ASTM25 | 76 | 32 | 25 | 6 | 6 | 0.78 | 4.17 | 0.8 | 1.2 | 9.32 | 5 | 6 |
Mini1 | 60 | 12.5 | 10 | 3 | 3 | 0.8 | 3.33 | 0.65 | 1.2 | 5.27 | 2.5 | 6 |
Mini2 | 41 | 9 | 5 | 1.5 | 2 | 0.56 | 2.5 | 1 | 1.2 | 3.23 | 1.67 | 6 |
Table 3.
Details of the four selected meshes. PW, GL, and THK stand for parallel width, gauge length, and thickness of the tensile specimen, respectively.
Table 3.
Details of the four selected meshes. PW, GL, and THK stand for parallel width, gauge length, and thickness of the tensile specimen, respectively.
| Mesh 1 | Mesh 2 | Mesh 3 | Mesh 4 | Increasing Ratio |
---|
No. div. of PW (-) | 11 | 21 | 41 | 81 | ∼2 |
No. div. of GL (-) | 31 | 61 | 121 | 241 | ∼2 |
No. div. of THK (-) | 3 | 5 | 9 | 17 | ∼2 |
Total element. No. (-) | 1023 | 6405 | 44,649 | 331,857 | - |
Total node. No. (-) | 1536 | 8184 | 51,240 | 357,192 | - |
Error of necking strain (-) | 1.87 × 10 | 1.07 × 10 | 8.02 × 10 | 0 | - |
Error of stress at necking strain (-) | 4.22 × 10 | 3.15 × 10 | 2.73 × 10 | 0 | - |
Table 4.
In detail, specimen’s dimensions and element edges for Mesh 3.
Table 4.
In detail, specimen’s dimensions and element edges for Mesh 3.
| PW | dx | GL | dy | THK | dz |
---|
| (mm) | (mm) | (mm) | (mm) | (mm) | (mm) |
---|
A80 | 20 | 0.488 | 80 | 0.661 | 1.2 | 0.133 |
A50 | 12.5 | 0.305 | 50 | 0.413 | 1.2 | 0.133 |
ASTM25 | 6 | 0.146 | 25 | 0.207 | 1.2 | 0.133 |
Mini1 | 3 | 0.073 | 10 | 0.083 | 1.2 | 0.133 |
Mini2 | 2 | 0.049 | 5 | 0.041 | 1.2 | 0.133 |
Table 5.
Research compared to DP800 R-value measurement from 2007.
Table 5.
Research compared to DP800 R-value measurement from 2007.
Lead Author | Ref | Dimension | THK (mm) | r0 | r45 | r90 |
---|
Walp | [25] | ISO-A80 | 1.5 | 0.63 | - | - |
Cardoso | [26] | ∼ISO-A50 | 1.2 | 0.579 | 1.077 | 0.696 |
Cardoso | [27] | ∼ISO-A50 | 1.2 | 0.516 | 1.237 | 0.711 |
Beres | [28] | Nakajima | 1 | 0.65 | 0.77 | 0.72 |
Zaman | [29] | Gauge length 42 cm | 1 | 0.7 | 0.97 | 0.82 |
Kim | [30] | Gauge length 42 cm | 1 | 0.7 | 0.97 | 0.82 |
Almeida | [31] | ∼ASTM25 | - | 0.955 | 0.978 | 0.897 |
Unlu | [32] | - | - | 0.71 | 0.88 | 0.83 |
Current work | - | ISO-A80 | 1.2 | 0.74 | 1.32 | 1.01 |
Current work | - | ISO-A50 | 1.2 | 0.75 | 1.14 | 1.03 |
Current work | - | ASTM25 | 1.2 | 0.97 | 1.23 | 0.93 |
Table 6.
The comparison between the simulation and the experiment of the uniform elongation () and the total elongation (). UB and LB stand for upper and lower bounds, respectively.
Table 6.
The comparison between the simulation and the experiment of the uniform elongation () and the total elongation (). UB and LB stand for upper and lower bounds, respectively.
| | Mean | Exp. Bounds | Mean Discrepancy | Bounds Discrepancy | | Mean | Exp. Bounds | Mean Discrepancy | Bounds Discrepancy |
---|
| (n/a, %) | (n/a, %) | (n/a, %) | (n/a, %) | (n/a, %) | (n/a, %) | (n/a, %) | (n/a, %) | (n/a, %) | (n/a, %) |
---|
A80 | 18.78 | 14.4 | UB: 15.5 | 23.3 | UB: 17.47 | 19.33 | 19.7 | UB: 19.8 | 1.94 | UB: 0.51 |
LB: 13.6 | LB: 27.58 | LB: 17.6 | LB: 10.66 |
A50 | 18.72 | 14.5 | UB: 14.7 | 22.5 | UB: 21.47 | 19.68 | 20.5 | UB: 20.7 | 4.17 | UB: 0.98 |
LB: 13.9 | LB: 25.75 | LB: 17.0 | LB: 17.07 |
ASTM25 | 18.72 | 15.1 | UB: 15.9 | 19.3 | UB: 15.05 | 20.72 | 22.7 | UB: 23.4 | 9.56 | UB: 12.93 |
LB: 14.1 | LB: 24.68 | LB: 21.3 | LB: 2.8 |
Mini1 | 17.4 | 15.3 | UB: 15.9 | 12.1 | UB:10.92 | 26.9 | 25.8 | UB: 26.5 | 4.09 | UB: 2.71 |
LB: 14.9 | LB: 14.37 | LB: 22.4 | LB: 13.18 |
Mini2 | 15.72 | 13.8 | UB: 14.1 | 12.2 | UB: 10.31 | 34.68 | 27.4 | UB: 30.5 | 20.99 | UB: 12.05 |
LB: 12.5 | LB: 20.48 | LB: 25.4 | LB: 29.35 |