Thermo–Mechanical Behavior and Constitutive Modeling of In Situ TiB2/7050 Al Metal Matrix Composites Over Wide Temperature and Strain Rate Ranges
Abstract
:1. Introduction
2. Experimental Materials and Procedures
2.1. Materials
2.2. Quasi-Static Uniaxial Compression Experiments
2.3. Dynamic Compressive Experiments
3. Experiment Results
4. Constitutive Modeling
4.1. Johnson–Cook Constitutive Model
- (1)
- By using the experiment result at reference strain rate and temperature, Equation (1) reduces to:The material constant A can be got from the yield stress when plastic strain ε = 0. By the stress data at different plastic strains, B and n can be determined from the intercept and slope of the ln(σ-A) versus lnε fitting line respectively.
- (2)
- At the reference temperature, the third bracket in Equation (1) become unity and the Equation (1) reduces to:By selecting a series of plastic strain at different strain rates, the material constant C can be determined from the above relationship in Equation (7).
- (3)
- At the reference strain rate, the second bracket in Equation (3) become unity and the Equation (3) becomes:By selecting a series of plastic strain at different temperatures, the material constant m can be determined from the above relationship.
4.2. Johnson–Cook Constitutive Model Obtained from Cutting Experiment
4.3. Khan–Liu Constitutive Model
- (1)
- The material constant A can be determined from the yield stress when the current strain rate = , current temperature T = Tr and plastic strain ε = 0.
- (2)
- By using the experimental result at a reference temperature and ε = 0, the yield stress σY at different conditions can be obtained. Equation (16) reduces to:The material constant C1 can be evaluated from the slope of versus .
- (3)
- By using the yield stress σY of the experiment result when the strain rate = , Equation (16) reduces to:The material constant m2 can be determined from relationship between and using the yield stress at different temperature.
- (4)
- By using the experiment result at reference strain rate and temperature, Equation (16) reduces to:The material constant A can be obtained from the yield stress when plastic strain ε = 0. By the stress data at different plastic strains, B and n can be determined from the intercept and slope of the ln(σA) versus lnε fitting line, respectively.
- (5)
- When strain rate = 1, Equation (16) reduces to:Then the material constant m3 can be determined from the above relationship by the stress–strain data at various temperatures and plastic strains.
- (6)
- When the current temperature T = Tr, Equation (16) reduces to:Then the material constant C3 can be determined from the above relationship by the stress–strain date at different strain rate and plastic strain.
5. Comparison of the Constitutive Models
6. Conclusions
- (1)
- The strain rate and temperature have profound effects on the flow stress behavior of TiB2/7050 Al composites. As the increase of temperature, the flow stress decreases at a specified strain rate due to the soften effect. On the other hand, the flow stress increases with the larger strain rate for a specified temperature.
- (2)
- Due to the mismatch of thermal expansion coefficient and elastic modulus of aluminum matrix and TiB2 reinforcement particle, geometrically dislocation occurs around the particles and contributes to the work hardening effect of TiB2/7050 Al composites. The strength of TiB2/7050 Al composites is much larger than the aluminum matrix.
- (3)
- Compared with the JC constitutive model, the KL constitutive model performs better to predict the stress strain behavior of TiB2/7050 Al composites as it has a lower average absolute error (2.61%) and higher correlation coefficient (97.68%) with the experiment result. In addition, the KL model has shown better performance in characterizing the temperature effect and strain effect than JC model.
- (4)
- Although the JC model from an orthogonal experiment can be used to simulate the cutting process, it cannot describe the flow stress exactly during material deformation. For an accurate constitutive model of a material, the basic tensile or compression test is deemed necessary.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Elements | TiB2 | Cu | Mg | Zn | Zr | Al |
---|---|---|---|---|---|---|
Content/wt% | 6 | 2.2 | 2.3 | 6.3 | 0.11 | Balance |
A | B | C | m | n |
---|---|---|---|---|
594 | 446.4538 | 0.0157 | 1.364 | 0.4655 |
A | B | C | m | n |
---|---|---|---|---|
630 | 1127 | 0.004 | 2.4 | 0.972 |
A | B | C1 | C3 | n0 | m2 | m3 |
---|---|---|---|---|---|---|
602.6 | 235.5599 | 4.188 × 10−8 | −4.2151 × 10−8 | 0.2211 | 0.6102 | −1.2285 |
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Lin, K.; Wang, W.; Jiang, R.; Xiong, Y.; Shan, C. Thermo–Mechanical Behavior and Constitutive Modeling of In Situ TiB2/7050 Al Metal Matrix Composites Over Wide Temperature and Strain Rate Ranges. Materials 2019, 12, 1212. https://doi.org/10.3390/ma12081212
Lin K, Wang W, Jiang R, Xiong Y, Shan C. Thermo–Mechanical Behavior and Constitutive Modeling of In Situ TiB2/7050 Al Metal Matrix Composites Over Wide Temperature and Strain Rate Ranges. Materials. 2019; 12(8):1212. https://doi.org/10.3390/ma12081212
Chicago/Turabian StyleLin, Kunyang, Wenhu Wang, Ruisong Jiang, Yifeng Xiong, and Chenwei Shan. 2019. "Thermo–Mechanical Behavior and Constitutive Modeling of In Situ TiB2/7050 Al Metal Matrix Composites Over Wide Temperature and Strain Rate Ranges" Materials 12, no. 8: 1212. https://doi.org/10.3390/ma12081212
APA StyleLin, K., Wang, W., Jiang, R., Xiong, Y., & Shan, C. (2019). Thermo–Mechanical Behavior and Constitutive Modeling of In Situ TiB2/7050 Al Metal Matrix Composites Over Wide Temperature and Strain Rate Ranges. Materials, 12(8), 1212. https://doi.org/10.3390/ma12081212