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Development of Constitutive Relationship for Thermomechanical Processing of Al-SiC Composite Eliminating Deformation Heating

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Abstract

Constitutive equations are useful for computational or numerical tools in describing the thermomechanical behavior of Al/SiC composites to develop the lightweight component using bulk metal forming. In this study, the uniaxial compression test of powder metallurgy-based Al/7 vol.% SiCp composite samples in the temperature range of 250-500 °C and at the strain rates of 0.001, 0.007, 0.05, 0.3, 2.2 and 15 s−1 was performed on a Gleeble-3800 thermomechanical simulator. An equation correlating actual (measured) temperature with the true stress in real time has been established for each of the strain rates. Further, the true stress was corrected by eliminating the effect of deformation heating using this equation based on the experimental observations. The temperature-corrected true stress data were then used for development of constitutive equations using the Arrhenius model, strain-compensated Arrhenius model and modified Johnson–Cook (m-JC) model. The material parameters in the m-JC model were calculated at different combinations of temperatures and strain rates. The established constitutive equations are validated with temperature-corrected true stress from the experiment. Further, these equations are verified with the experimental true stress that was obtained using different inputs of temperatures and strain rates in a compression test. The correlation coefficient (R) and absolute average relative error reflect the accuracy of constitutive models. The result indicates that the calculated true stress by the established strain-compensated Arrhenius model is in good agreement with that of experimentally measured true stress with a correlation coefficient of 0.996 and relative error of 3.83%.

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Abbreviations

T :

Deformation temperature (°C)

ΔT :

Rise in temperature (°C)

Ε :

True strain or plastic strain

Σ :

True stress (after eliminating effect of deformation heating) (MPa)

σ o :

True stress (MPa)

\(\dot{\varepsilon }\) :

Strain rate (sr) (s−1)

Q :

Deformation activation energy (kJ/mol)

R′ :

Universal gas constant (kJ/mol K)

Α :

Stress multiplier (MPa−1)

n, A, C, λ 1, λ 2 :

Material constant

Z :

Zener–Hollomon parameter (s−1)

\(\dot{\varepsilon }_{\text{r}}\) :

Reference strain rate (s−1)

T r :

Reference deformation temperature (°C)

\(\dot{\varepsilon }^{*}\) :

Ratio of strain rate to reference strain rate

R :

Correlation factor

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Acknowledgments

The authors would like to thank Dr. Subray L. Kamath, CoEST (Centre of Excellence in Steel Technology), IIT Bombay, for technical support during experiments on Gleeble-3800. Also, the authors thank SAIF (Sophisticated Analytical Instrument Facility), IIT Bombay, for providing ESEM for microstructure.

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  1. Indian Institute of Technology Bombay, Mumbai, 400076, India

    Kanhu Charan Nayak & Prashant P. Date

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Correspondence to Kanhu Charan Nayak.

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Nayak, K.C., Date, P.P. Development of Constitutive Relationship for Thermomechanical Processing of Al-SiC Composite Eliminating Deformation Heating. J. of Materi Eng and Perform 28, 5323–5343 (2019). https://doi.org/10.1007/s11665-019-04277-8

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