Microstructure Evaluation and Constitutive Modeling of AISI-1045 Steel for Flow Stress Prediction under Hot Working Conditions
<p>Elevated temperature tensile testing set-up and procedures (<b>a</b>) Entire test set-up; (<b>b</b>) Test specimen coupled with thermocouples for temperature measurement; (<b>c</b>) Tested specimens.</p> "> Figure 2
<p>True stress-strain curves acheived from hot tensile tests at various temperatures (<b>a</b>) 750 <math display="inline"><semantics> <msup> <mrow/> <mo>°</mo> </msup> </semantics></math>C; (<b>b</b>) 850 <math display="inline"><semantics> <msup> <mrow/> <mo>°</mo> </msup> </semantics></math>C; (<b>c</b>) 950 <math display="inline"><semantics> <msup> <mrow/> <mo>°</mo> </msup> </semantics></math>C under different strain rates [<a href="#B13-symmetry-12-00782" class="html-bibr">13</a>,<a href="#B14-symmetry-12-00782" class="html-bibr">14</a>,<a href="#B29-symmetry-12-00782" class="html-bibr">29</a>].</p> "> Figure 3
<p>Field emission scanning electron microscopy (FESEM) and energy dispersive X-ray spectroscopy (EDS) mapping images at strain rate 0.5 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> (<b>a</b>–<b>c</b>) 850 <math display="inline"><semantics> <msup> <mrow/> <mo>°</mo> </msup> </semantics></math>C; (<b>d</b>–<b>f</b>) 950 <math display="inline"><semantics> <msup> <mrow/> <mo>°</mo> </msup> </semantics></math>C.</p> "> Figure 4
<p>Relationship plots of <math display="inline"><semantics> <mi>σ</mi> </semantics></math> and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> at <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0.02 (<b>a</b>) ln<math display="inline"><semantics> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </semantics></math> and ln<math display="inline"><semantics> <mi>σ</mi> </semantics></math>; (<b>b</b>) ln<math display="inline"><semantics> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </semantics></math> and <math display="inline"><semantics> <mi>σ</mi> </semantics></math>; for material constant <math display="inline"><semantics> <mi>α</mi> </semantics></math> estimation.</p> "> Figure 5
<p>Relationship plot of <math display="inline"><semantics> <mi>σ</mi> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </semantics></math> at <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0.02 (<b>a</b>) ln<math display="inline"><semantics> <mover accent="true"> <mi>ε</mi> <mo>˙</mo> </mover> </semantics></math> and ln(sinh(<math display="inline"><semantics> <mrow> <mi>α</mi> <mi>σ</mi> </mrow> </semantics></math>)); (<b>b</b>) <math display="inline"><semantics> <mrow> <msup> <mrow/> <msup> <mn>10</mn> <mn>3</mn> </msup> </msup> <mspace width="-0.166667em"/> <msub> <mo>/</mo> <mi>T</mi> </msub> </mrow> </semantics></math> and ln(sinh(<math display="inline"><semantics> <mrow> <mi>α</mi> <mi>σ</mi> </mrow> </semantics></math>)); for material constants <span class="html-italic">n</span> and <span class="html-italic">Q</span> estimation.</p> "> Figure 6
<p>Correlation plot of stress and strain rate at <math display="inline"><semantics> <mi>ε</mi> </semantics></math> = 0.02 for material constant <math display="inline"><semantics> <mrow> <mi>ln</mi> <mi>A</mi> </mrow> </semantics></math> estimation.</p> "> Figure 7
<p>Material constants correlation plots (<b>a</b>) <math display="inline"><semantics> <mi>α</mi> </semantics></math>; (<b>b</b>) <span class="html-italic">n</span>; (<b>c</b>) <span class="html-italic">Q</span>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mi>A</mi> </mrow> </semantics></math>; with true strain.</p> "> Figure 8
<p>Residual plot of material constants (<b>a</b>) <math display="inline"><semantics> <mi>α</mi> </semantics></math>; (<b>b</b>) <span class="html-italic">n</span>; (<b>c</b>) <span class="html-italic">Q</span>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mi>A</mi> </mrow> </semantics></math>.</p> "> Figure 9
<p>Stress-strain curves comparison against the predicted curves from the modified constitutive equation (<b>a</b>) 0.05 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>b</b>) 0.1 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>c</b>) 0.5 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>d</b>) 1.0 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 9 Cont.
<p>Stress-strain curves comparison against the predicted curves from the modified constitutive equation (<b>a</b>) 0.05 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>b</b>) 0.1 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>c</b>) 0.5 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>d</b>) 1.0 s<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>.</p> "> Figure 10
<p>(<b>a</b>) Bar plot comparison using model errors; (<b>b</b>) Correlation plot between test and computed data.</p> "> Figure 11
<p>Graphical validation plots (<b>a</b>) residual plot (at test conditions 750 <math display="inline"><semantics> <msup> <mrow/> <mo>°</mo> </msup> </semantics></math>C and 950 <math display="inline"><semantics> <msup> <mrow/> <mo>°</mo> </msup> </semantics></math>C); (<b>b</b>) Histogram plot.</p> ">
Abstract
:1. Introduction
2. Experiments
3. Microstructure Evaluation of AISI-1045 Medium Carbon Steel
4. Strain Compensated Constitutive Equation for Flow Stress Prediction
4.1. Arrhenius-Type Constitutive Equation
4.2. Higher Order Polynomial Regression Model
4.3. Strain Compensation
5. Constitutive Model Verification
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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C | Fe | Mn | P | S |
---|---|---|---|---|
0.42–0.50 | 98.51–98.98 | 0.60–0.90 | ≤0.04 | ≤0.05 |
Test Conditions | avg() | avg() | ||||
---|---|---|---|---|---|---|
750 C | 21.2241 | 0.1511 | ||||
850 C | 0.05–1.0 s | 9.1810 | 14.1365 | 0.1081 | 0.1522 | 0.0108 |
950 C | 12.0045 | 0.1975 |
T | n | avg(n) | slope | avg(slope) | Q (kJ mol ) | |
---|---|---|---|---|---|---|
750 C | 12.7304 | 0.05 s | 7.1290 | |||
850 C | 7.2567 | 10.1747 | 0.1 s | 6.4418 | 6.7165 | 568.1702 |
950 C | 10.5371 | 0.5 s | 6.4801 | |||
1.0 s | 6.8153 |
lnZ | ln(sinh()) | ||||||
---|---|---|---|---|---|---|---|
750 C | 850 C | 950 C | 750 C | 850 C | 950 C | ||
1.00 s | 66.8025 | 60.8539 | 55.8781 | 0.8863 | 0.2759 | −0.2021 | |
0.50 s | 66.1094 | 60.1608 | 55.1850 | 0.7955 | 0.1227 | −0.2337 | 57.9139 |
0.10 s | 64.4999 | 58.5514 | 53.5756 | 0.6888 | 0.0942 | −0.3389 | |
0.05 s | 63.8068 | 57.8582 | 52.8824 | 0.6472 | −0.1418 | −0.4821 |
() | () | n | Q () | lnA () | |
---|---|---|---|---|---|
0.0108 | 0.1522 | 14.1365 | 10.1747 | 568.1702 | 57.9139 |
Coefficients | / | n | Q/ | lnA/ |
---|---|---|---|---|
0.0142 | 9.484 | 582.9 | 58.62 | |
−0.2474 | 79.16 | 116.6 | 91.64 | |
4.557 | −2961 | −6.386 × 10 | −8930 | |
−46.23 | 3.434 × 10 | 7.02 × 10 | 1.003 × 10 | |
254.2 | −1.859 × 10 | −3.202 × 10 | −4.97 × 10 | |
−711.9 | 4.66 × 10 | 5.877 × 10 | 1.101 × 10 | |
797.0 | −4.311 × 10 | −2.439 × 10 | −8.318 × 10 |
Counts | Test Conditions | Adj. | Overall- | AARE (%) | Overall-AARE (%) | ||
---|---|---|---|---|---|---|---|
1023 K | 0.9516 | 0.9511 | 2.9204 | ||||
24 samples | 0.05–1.0 s | 1123 K | 0.9406 | 0.9400 | 0.9817 | 4.2528 | 3.6781 |
1223 K | 0.9427 | 0.9421 | 3.8609 |
Counts | Test Conditions | Adj. | Overall- | AARE (%) | Overall-AARE (%) | ||
---|---|---|---|---|---|---|---|
1023 K | 0.9720 | 0.9717 | 2.0045 | ||||
24 samples | 0.05–1.0 s | 1123 K | 0.9708 | 0.9705 | 0.9894 | 3.1223 | 2.9840 |
1223 K | 0.9448 | 0.9443 | 3.8251 |
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Murugesan, M.; Sajjad, M.; Jung, D.W. Microstructure Evaluation and Constitutive Modeling of AISI-1045 Steel for Flow Stress Prediction under Hot Working Conditions. Symmetry 2020, 12, 782. https://doi.org/10.3390/sym12050782
Murugesan M, Sajjad M, Jung DW. Microstructure Evaluation and Constitutive Modeling of AISI-1045 Steel for Flow Stress Prediction under Hot Working Conditions. Symmetry. 2020; 12(5):782. https://doi.org/10.3390/sym12050782
Chicago/Turabian StyleMurugesan, Mohanraj, Muhammad Sajjad, and Dong Won Jung. 2020. "Microstructure Evaluation and Constitutive Modeling of AISI-1045 Steel for Flow Stress Prediction under Hot Working Conditions" Symmetry 12, no. 5: 782. https://doi.org/10.3390/sym12050782
APA StyleMurugesan, M., Sajjad, M., & Jung, D. W. (2020). Microstructure Evaluation and Constitutive Modeling of AISI-1045 Steel for Flow Stress Prediction under Hot Working Conditions. Symmetry, 12(5), 782. https://doi.org/10.3390/sym12050782