Study On Mechanical Behavior Of Polycrystalline Beryllium Under Macro Tensile Test And Nanoindentation At Room Temperature

Polycrystalline beryllium(metal beryllium)has been widely used in nuclear energy,aerospace,optics,high energy physics and other engineering fields due to its excellent atomic properties,low density,high melting point,good dimensional stability,high specific stiffness,and high specific strength.At present,most of the studies on beryllium mechanical problems focus on the analysis of fracture properties,but less attention is paid to its mechanical behavior.In this paper,the constitutive characteristics of the deformation behavior under room temperature are studied at macroscopic and microscopic scales.The specific work is as follows:Macro uniaxial tensile process:(1)Uniaxial tensile tests were carried out on polycrystalline beryllium,and the stress-strain curves were obtained by unloading\loading at different pre-strain positions.Then the plastic and elastic strain information,elastic modulus information and strain hysteresis information at each pre-strain point are obtained;Uniaxial tensile tests of polycrystalline beryllium were carried out to obtain the information of the correlation between yield stage length and yield stress.(2)Based on the assumption of constant elastic modulus,the linear form constitutive equation and energy equation of polycrystalline beryllium strengthening stage were established;Considering the evolution law of elastic modulus with deformation,the quadratic form constitutive equation and energy equation of polycrystalline beryllium strengthening stage are established;Based on the evolution law of secant modulus(?/?),the power form constitutive equation and energy equation in strengthening stage of polycrystalline beryllium were established.By comparing with the measured data,the descriptive efficiency of the three constitutive equations is evaluated.(3)The energy variation law of hysteresis process is calculated,and the proportional relationship between plastic energy and elastic energy is obtained.Nanoindentation process:(4)Nanoindentation were carried out on polycrystalline beryllium surface to obtain force displacement(P-h)curves under eight maximum loads between 6000 and 20000?N.Then the contact depth,elastic modulus and hardness of each indentation point were obtained.(5)Establish a constitutive equation in the form of a power function for the nanoindentation loading process;Determine the residual depth and establish the power function constitutive equation of the nanoindentation and unloading process;Then determine the law of the energy change with the maximum load in the whole process of nanoindentation loading-unloading,and obtain the proportional relationship between plastic properties and elastic energy.Solution:Macro uniaxial tensile process:(1)For the uniaxial stretching process,there is a significant and universal linear relationship between plastic strain and total strain(the slope and intercept are 0.9698 and 0.1652 respectively);The elastic modulus also has a linear relationship between the strengthening stage and the total strain.The equivalent plastic strain(without considering the change in elastic modulus)has a linear relationship with the total strain,the slope value of each sample is basically the same(about 0.97),and the intercept value is roughly the negative value of the yield strain;The ratio of the secant modulus to the reference elastic modulus has a power exponential relationship with the total strain,and its exponent is about 0.95,and its coefficient is roughly the same as the yield strain.The length of the yield stage is positively related to the yield stress.(2)The linear constitutive equation is easy to calculate,but the error is large,and the predicted value is generally smaller than the experimental value;The quadratic constitutive equation has the highest accuracy,but when the ratio of the length of the material at the yield stage to the length of the strengthening stage is large,the accuracy will decrease;The power exponential constitutive equation is easier to handle mathematically,but the predicted value is generally greater than the experimental value.(3)The elastic energy and plastic properties in the hysteresis loop are linearly correlated with each other.The boundary point between the yield stage and the strengthening stage is segmented.The slope of the strengthening stage is greater than the slope of the yielding stage.Nanoindentation process:(4)The power function can well realize the description of the nanoindentation loading curve and the constitutive characteristics of the unloading process.(5)Elastic energy has a good proportional relationship with plastic properties and total energy;There is a universal proportional relationship between the plastic properties and the product of total energy,maximum force and residual indentation depth respectively(the proportional coefficients are 0.7032 and 0.4099 respectively);The residual pressure and the maximum pressure also have a universal proportional relationship(the proportional coefficient is 0.6593).