Inverse Method to Determine Parameters for Time-Dependent and Cyclic Plastic Material Behavior from Instrumented Indentation Tests
Abstract
:1. Introduction
2. Material and Experiments
2.1. Material Specifications
2.2. Experimental Procedure
3. Numerical Model
3.1. Friction Effect
3.2. Rigid and Deformable Indenter
3.3. Constitutive Model
4. Optimization Procedure for Material Parameter Identification
4.1. Parameter Identification by the Inverse Method
4.2. Combined Parameter Identification with Two Back-Stress Terms
4.3. Combined Parameter Identification with Three Back-Stress Terms
4.4. Two-Stage Material Parameter Determination
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Element | Cr | Mo | Si | Mn | N | C | Ni | P | Al | V | Ti | Cu | S |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
wt.% | 15.3 | 1.0 | 0.7 | 0.4 | 0.4 | 0.3 | 0.2 | 0.02 | 0.01 | 0.03 | 0.003 | 0.05 | 0.001 |
Parameter | Minimum | Middle | Maximum |
---|---|---|---|
C1 (MPa) | 25,000 | 125,000 | 225,000 |
γ1 | 100 | 425 | 750 |
C2 (MPa) | 2000 | 3500 | 5000 |
γ2 | 0 | 0 | 0 |
C3 (MPa) | 5000 | 77,500 | 150,000 |
γ3 | 10 | 255 | 500 |
Q (MPa) | −350 | −187 | −25 |
b | 0.1 | 6 | 12 |
(s−1) | 1 × 10−7 | 5 × 10−4 | 1 × 10−3 |
n | 3 | 7.5 | 12 |
m | −0.99 | −0.5 | −0.01 |
2 Back-Stress Terms | 3 Back-Stress Terms | |||||
---|---|---|---|---|---|---|
Parameter | Min | Mid | Max | Min | Mid | Max |
C1 (MPa) | 64,193 | 87,366 | 148,784 | 68,783 | 107,437 | 110,187 |
γ1 | 138 | 171 | 434 | 229 | 253 | 336 |
C2 (MPa) | 3722 | 3616 | 4227 | 3660 | 3628 | 3567 |
γ2 | 0 | 0 | 0 | 0 | 0 | 0 |
C3 (MPa) | -- | -- | -- | 34,543 | 29,012 | 14,582 |
γ3 | -- | -- | -- | 165 | 355 | 75 |
Q (MPa) | −252 | −251 | −55 | −276 | −275 | −247 |
b | 3.31 | 8.39 | 7.87 | 7.97 | 11.09 | 9.54 |
(s−1) | 1.54 × 10−6 | 9.46 × 10−7 | 2.87 × 10−7 | 1.86 × 10−6 | 8.39 × 10−6 | 7.67 × 10−6 |
n | 10 | 11 | 9.8 | 8 | 6.5 | 7.7 |
m | −0.96 | −0.92 | −0.67 | −0.58 | −0.82 | −0.91 |
NMSE | 9.73 × 10−5 | 1.10 × 10−4 | 1.27 × 10−4 | 9.73 × 10−5 | 9.57 × 10−5 | 9.88 × 10−5 |
Two-Stage Optimization | Combined Optimization | |||||
---|---|---|---|---|---|---|
Parameters | Min | Mid | Max | Min | Mid | Max |
C1 (MPa) | 87,646 | 94,140 | 90,260 | 64,193 | 87,366 | 148,784 |
γ1 | 210 | 221 | 210 | 138 | 171 | 434 |
C2 (MPa) | 4000 | 4005 | 4011 | 3722 | 3616 | 4227 |
γ2 | 0 | 0 | 0 | 0 | 0 | 0 |
Q (MPa) | −136 | −189 | −107 | −252 | −251 | −55 |
b | 4.12 | 3.19 | 8.92 | 3.31 | 8.39 | 7.87 |
(s−1) | 7.96 × 10−7 | 1.38 × 10−6 | 1.23 × 10−6 | 1.54 × 10−6 | 9.46 × 10−7 | 2.87 × 10−7 |
n | 11.83 | 10.7 | 10.95 | 10 | 11 | 9.8 |
m | −0.99 | −0.99 | −0.99 | −0.96 | −0.92 | −0.67 |
NMSE | 1.02 × 10−4 | 1.16 × 10−4 | 1.01 × 10−4 | 9.73 × 10−5 | 1.10 × 10−4 | 1.27 × 10−4 |
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Sajjad, H.M.; Chudoba, T.; Hartmaier, A. Inverse Method to Determine Parameters for Time-Dependent and Cyclic Plastic Material Behavior from Instrumented Indentation Tests. Materials 2024, 17, 3938. https://doi.org/10.3390/ma17163938
Sajjad HM, Chudoba T, Hartmaier A. Inverse Method to Determine Parameters for Time-Dependent and Cyclic Plastic Material Behavior from Instrumented Indentation Tests. Materials. 2024; 17(16):3938. https://doi.org/10.3390/ma17163938
Chicago/Turabian StyleSajjad, Hafiz Muhammad, Thomas Chudoba, and Alexander Hartmaier. 2024. "Inverse Method to Determine Parameters for Time-Dependent and Cyclic Plastic Material Behavior from Instrumented Indentation Tests" Materials 17, no. 16: 3938. https://doi.org/10.3390/ma17163938