利用努氏硬度表征金属的弹性模量和屈服强度

Characterization of elastic modulus and yield strength of metals by Knoop hardness

为利用努氏硬度表征金属材料弹性模量和屈服强度,提出了Marshall和Conway的修正模型表征弹性模量,以及Lockett、Yu、Marsh、Johnson和Vandeperre的修正模型表征屈服强度,开拓了努氏硬度表征金属材料力学性能的新应用。选取35种金属进行努氏硬度试验,利用Meyer定律、弹塑性变形模型、Hays-Kendall模型和比例试样模型对努氏硬度的正压痕尺寸效应(硬度随载荷的减小而增大)进行了分析,可以用大载荷下趋于稳定的硬度值代表材料的真硬度。首次考虑金属材料在努氏压痕短对角线处材料堆积的影响,Marshall模型和Conway模型进行了修正:Marshall模型中原有的常参数α修正为b/d(努氏压痕短对角线与长对角线的比值)的二次函数;Conway模型引入了与b/d的平方呈线性关系修正系数β。通过比较文献中与原模型计算的屈服强度,引入修正系数k,首次获得了基于努氏硬度利用Lockett、Yu、Marsh、Johnson和Vandeperre模型计算金属屈服强度的修正模型。结果表明:除Ti6Al4V和Sn外,修正模型与仪器化压入得到的弹性模量一致,置信度不低于0.94;除60Si2Mn弹簧钢外,修正后得到的屈服强度与文献值一致,置信度不低于0.90。

To characterize the elastic modulus and yield strength of metallic materials by Knoop hardness,the modified Marshall model and Conway model were proposed to characterize the elastic modulus,and the modified Lockett,Yu,Marsh,Johnson and Vandeperre models were proposed to characterize the yield strength,broadening the new application of Knoop hardness to the characterization of mechanical properties of metallic materials.Knoop hardness tests were carried out on 35 metals.The positive indentation size effect of Knoop hardness(hardness increases with the decrease in load) was analyzed by Meyer's law,elastic-plastic deformation(EPD) model,Hays-Kendall model,and proportional specimen resistance(PSR) model.It was found that the hardness under large loads can be approximated to be constant,and can be used to represent true hardness of the material.For the first time,the influence of pile-up around the short diagonal of Knoop indent was considered to modify Marshall model and Conway model as follows:the constant parameter α in the original Marshall model was modified as a quadratic function of b/d(the ratio of the short diagonal to the long diagonal of the residual Knoop imprint),and a correction coefficient β linearly increasing with the square of b/d was introduced to Conway model.By comparing the values of yield strength in the literature and those calculated by original models,a correction coefficient k was introduced to modify Lockett,Yu,Marsh,Johnson and Vandeperre models for the calculation of yield strength of metals for the first time.The results showed that except for Ti6Al4V and Sn,values of elastic modulus obtained from the modified models were consistent with those from instrumented indentation,with a confidence degree no less than 0.94.Similarly,except for spring steel 60Si2Mn,values of yield strength obtained from the modified models were consistent with those in the literature,with a confidence degree no less than 0.90.