Prediction And Optimization Of The Mechanical Properties And Stress-strain Curve Of Multiphase TiB₂-reinforced Steel Composite Using Eshelby-Moritanaka Model

An analytical computational model was built based on the Mori-Tanaka method and Eshelby’s equivalent inclusion principle. It was used to predict the longitudinal and transverse Young’s modulus of the Fe-TiB2 composite material, with a small error about 1%. In addition, combined with Chaboche’s viscoelastic plastic constitutive model, the evolution of tangent stiffness tensor was calculated by the radius return and Newton-Raphson method, which was used to successfully predict the stress-strain curve of the composite under the condition of low plastic deformation and no reinforcement cracks. Finally, the stress sharing between the matrix and reinforcements was calculated by the macro-micro scale approach. Results show that the reinforcements with larger aspect ratios bear more stress and longer fiber reinforcement will help improve the composite’s stiffness, but at the same time it will also cause stress concentration and premature cracks on reinforcements, which diminishes the composite’s strength. With a fixed total volume fraction of reinforcements, the existence of short fibers will hurt the strength and stiffness at the same time.The aspect ratio, volume fraction and orientation of the reinforcements all have an important impact on the mechanical properties of the composite. The longitudinal Young’s modulus increases significantly as the aspect ratio increases, while the transverse one only diminishes a little. As the volume fraction of reinforcements increases, the longitudinal and transverse Young’s modulus increase at the same time. The yield strength mainly depends on the effective stress in the matrix, rather than fractures in the reinforcements. The Young’s modulus increases first but then decreases with the increase of the angle between the loading direction and the reinforcements, while the effective stress in the matrix shows the opposite trend. So according to different design criteria of strength and stiffness, an angle in the range [30, 65] should be chosen.