A Comparative Study on Modified Johnson\u2013Cook and Arrhenius-Type Constitutive Models to Predict the Hot Deformation Behaviour of Molybdenum-Hafnium-Carbide Alloy

Athar Safari,Sabine Weiss,Muhammad Imran

doi:10.1007/s11665-021-05464-2

Abstract

Molybdenum alloys are commonly used as tool material for high-temperature deformation processes like forming or forging. For these types of application, the material has to withstand static load at elevated temperatures. To investigate the high-temperature performance of the material, uniaxial hot tensile tests were performed on a Mo-1.2% Hf-0.1% C alloy (MHC) over the temperature range of 1173-1473 K with intervals of 100 K and strain rates of 0.001, 0.01 and 0.1 s−1 up to the fracture of the specimen. The flow stress decreases with increase in temperature and the reduction in strain rate. This behaviour could be related to the increasing rate of restoration mechanisms, i.e. dynamic recrystallization or recovery as well as to the decrease in the strain hardening rate. Microstructure of the two most critical hot deformation conditions were shown and compared. Based on modified Johnson–Cook and strain-compensated Arrhenius-type models, constitutive equations were established to predict the high-temperature flow stress of the respective MHC alloy. The accuracy of both models was evaluated by comparing the predicted stress values and the values obtained from experiments. Correlation coefficient, average absolute relative error, the number of material constants involved and the computational time required for evaluating the constants were calculated to quantify and compare the precision of both models. The flow stress values predicted by the constitutive equations are in good agreement with the experimental results. At lower strain rates (0.001 and 0.01 s−1), distinct deviation from the experimental results can be observed for the modified Johnson–Cook model. Despite the longer evaluation time and the larger number of material constants, the deformation behaviour, tracked by the Arrhenius-type model is more accurate throughout the entire deformation process.

Highlights

Molybdenum (Mo) is a refractory metal that retains its bodycentred cubic crystal structure from room temperature up to its very high melting temperature of 2610 °C
The flow stress values are affected by deformation temperatures and strain rates
The flow stress rises with increasing strain rate while keeping the temperature constant, whereas the flow stress declines with increasing temperature for constant strain rate

Summary

Introduction

Molybdenum (Mo) is a refractory metal that retains its bodycentred cubic (bcc) crystal structure from room temperature up to its very high melting temperature of 2610 °C. Alloys based on Mo present high creep resistance, high thermal stability and thermal conductivity. They are very notable for many important high-temperature applications (e.g. crucial components in turbines, missiles and fusion reactors) (Ref [1, 2]). Hafnium carbide (HfC), a compound with a NaCI structure and the highest melting temperature (3890 °C) among all carbides, is an ideal particle hardener for Mo, resulting in socalled molybdenum-hafnium-carbide alloy (Ref [3, 4])

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