Grain growth prediction with inclination dependence of 〈1 1 0〉 tilt grain boundary using multi-phase-field model with penalty for multiple junctions

► Higher-order multi-phase-field model with grain boundary inclination was proposed. ► The inclination effect was introduced based on molecular dynamics simulations. ► An analytical equilibrium grain shape with Σ3 grain boundary was well reproduced. ► The inclination effects predominantly contributed to triple junction behaviors. ► Σ3 inclination effect characterized a weak anisotropic microstructure for pure Al.