High-entropy alloy is a new type of alloy system,with high wear resistance,high strength,high hardness,and other good properties,but the production process requires high equipment and technology,the preparation cost is also high,and the study of high-entropy alloy is relatively difficult.In principle,the first-principles calculation does not need to rely on any empirical parameters or specific model assumptions.It only needs to know the type and arrangement of the atoms that constitute the substance to obtain the calculation results,greatly saving research and development costs and shortening the preparation cycle.Therefore,this paper used the first-principles calculation method to study.Firstly,the phase structure of((Ti0.4W0.15Mo0.15Cr0.15)100-xAlx(x=5,10,15,20,25,30,35,40,45 and 50;mass fraction)high-entropy alloys was determined by calculating the mixing entropy,mixing enthalpy,atomic size difference,thermodynamic parameter,and valence electron concentration.Later,in the Materials Studio software,((Ti0.4W0.15Mo0.15Cr0.15)100-xAlx high-entropy alloys crystal models were built.The CASTEP package was used to optimize the structure of the high-entropy alloys,and the elastic constants of the high-entropy alloys under different Al content and pressure were calculated.The bulk modulus,Young's modulus,shear modulus,Poisson's ratio,Cauchy pressure,hardness,and melting point of high-entropy alloys could be calculated using the results of the first principles.After the above calculation,it was found that when Al content was in the range of 5%to 50%,the mixing entropy was between 11.781 and 12.636 J·mol-1·K-1,the mixing enthalpy was between-18.157 and-8.522 kJ·mol-1,the atomic size difference was between 0.044 and 0.052,the thermodynamic parameters were between 1.27 and 3.28,and the valence electron concentration was between 4.296 and 4.945.Except for mixing entropy,the other four terms decreased with the increase in Al content.In the first-principles calculation,the lattice constant of the high-entropy alloys could be obtained by structural optimization.The lattice constants of((Ti0.4W0.15Mo0.15Cr0.15)100-xAlx high-entropy alloys ranged from 0.321 to 0.408 nm,and the lattice constants of high-entropy alloys increased gradually with the increase of Al content in high-entropy alloys.In calculating the elastic constants of((Ti0.4W0.15Mo0.15Cr0.15)100-xAlx high-entropy alloys,only C11,C12,and C44 components were selected for analysis.Based on C11 and C12,C11-C12 and C11+2C12 were calculated.According to the calculation results,both C44 and C11+2C12 were greater than 0,while C11-C12 was greater than 0 only when the Al content was 15%,20%,25%,35%,40%,and 50%.It was proven that the mechanical properties were theoretically stable when the Al content was 15%,20%,25%,35%,40%,and 50%.The bulk modulus,Young's modulus,and shear modulus of((Ti0.4W0.15Mo0.15Cr0.15)100-xAlx high-entropy alloys showed a decreasing trend with increasing Al content.Moreover,when the Al content was 0.1 and 0.3,the shear modulus and Young's modulus appeared to have negative values,which proved that the mechanical structure was unstable and conformed to the judgment of mechanical stability.In the six stable mechanical properties of((Ti0.4W0.15Mo0.15Cr0.15)100-xAlx high-entropy alloys,Poisson's ratio(v),ratio of bulk modulus to shear modulus(B/G),and Cauchy pressure(C12-C44)all increased slowly with the increase of Al content.When Al content was 15%,v0.26,B/G>1.75,C12-C44>0.Calculate(Ti0.4W0.15Mo0.15Cr0.15)85Al15 high-entropy alloy under a pressure of 0~40 GPa.The lattice constant of(Ti0.4W0.15Mo0.15Cr0.15)85Al15 high-entropy alloy slowly decreased from 0.350 to 0.322 nm with increasing applied pressure,and the magnitude of the decrease continuously decreased.The calculated elastic constants C44,C11-C12,and C11+2C12 were all greater than 0.In addition,C12 kept increasing with the increase of pressure,while C11 and C44 increased first and then decreased with the increase of pressure,reaching the maximum value when the pressure was 30 GPa.The bulk modulus of(Ti0.4W0.15Mo0.15Cr0.15)85Al15 high-entropy alloy increased continuously with the pressure increase at 0~40 GPa.Young's modulus and shear modulus both increased first and then decreased with the increase of pressure,reaching their maximum values at pressure of 25 GPa.At pressures ranging from 0 to 40 GPa,Poisson's ratio,the ratio of bulk modulus to shear modulus,and the trend of Cauchy pressure changes were similar,increasing with increasing pressure.When the pressure was 0~10 GPa,v0.26,B/G>1.75,C12-C44>0.The hardness of high-entropy alloy first increased and then decreased with the increase of pressure,and reached the maximum value when the pressure was 25 GPa.At the same time,the melting point of(Ti0.4W0.15Mo0.15Cr0.15)85Al15 high-entropy alloy increased with the increase of pressure.