Determination Of Yield Criterion Of Porous Beryllium And Its Application On Numerical Simulation Of Hot Isostatic Pressing Of Forming Of Beryllium Powder

Beryllium is widely used in aerospace,navigation system,high energy physics and thermal science,for its low density,high melting point high elastic modulus,high specific strength,.etc..In its production,the powder metallurgy process(PMP)is adopted for forming commonly.With different degree,In processes of many materials formed by PMP,such as Ni alloy,W-Cu alloy,Mo,Cu-Cr alloy,Ti-Al-V alloy,.etc.,the computer simulation has been introduced for assisting technological design and optimization,but beryllium is not inside.Relevant domestic enterprises still rely on the traditional trial and error method for process optimization and design,it is a high-cost burden for producers.One of the main reasons causing the lag is that,there is no yield criterion for the porous beryllium,and the yield criterion is the necessary basis of the simulation with high reliability.This research firstly adopted Shima model as the basic mathematical form,and determined the yield criterion of porous beryllium by experiments;secondly accomplished the simulation of hot isostatic pressing of beryllium powder by taking the finite element analysis software MSC.Marc as the platform.The specific work is as follows:1)Determination of yield criterion of porous berylliumThe technical route for establishing the yield criterion of porous material is that,introduce two new parameters to modify the Von Mises yield criterion,both two are functions of the relative density p:the parameterfdescribing the effect of hydrostatic pressure,and the parameter f modifying the stress loaded on the matrix.(a)Through uniaxial compression test of 4 cylindrical specimens of bervllium with difierent initial densities,data series of axial strain increment,transverse strain increment and volume strain increment were measured respectively at different relative densities,from which values of/corresponding to ρ were obtained,then the parameter function f(p)was gotten by fitting with the least square method(LSM).(b)Through uniaxial compression test of 12 cylindrical specimens of beryllium with different initial densities,data series of the first yield stress σ at the different relative density ρ were obtained.The yield stress of compact state σ0 was obtained by extrapolating the ρ-σ curve to ρ=1.Then values of f corresponding to ρ were determined,and finally the parameter functionf(ρ)was obtained by fitting with the least square method.2)Simulation of hot isostatic pressing(HIP)of beryllium powder(a)By utilizing the finite element method(FEM)soft,are MSC.Marc,substituting the yield criterion of porous beryllium obtained above in,and setting process curve according to actual production condition,the simulation of HIP of beryllium powder sealed in cylindrical steel capsule was accomplished.Influences of pressure and temperature on the density,distribution of stress and strain of compressed column were analyzed respectively,the HIP test of beryllium powder was completed,and the outline size of the compressed beryllium column was measured.Then the reliability of simulation was evaluated by comparing the value of measurement with simulation.(b)Substituting several yield criterions of other materials in respectively such as copper,titanium,steel,same simulations of beryllium mentioned above were carried out.Through the comparison of results,the reliability and validity of the yield criterion of porous beryllium were evaluated.Solution1)The stress modified parameter f is associated with the relative density ρ in the form of power function,with power exponent as 2.8866 and coefficient as 1.0;the power function relationship is also existed between hydrostatic pressure influence parameterfand the void ratio 1-ρ,with power exponent as-0.3862 and coefficient as 1/2.89972)Comparing with measurement,relative errors of simulation are:0.44%～1.8%in radial direction,1.58%(maximum value)in axial direction.The maximum compact relative density can be up to 0.98.3)Among simulations of the beryllium process with different yield criterions,only those criterions being close to it of beryllium can finish calculation.It indicates that,the accuracy of yield criterion has a crucial influence on the reliability of simulation.