室温下多晶铍宏观非弹性回复的数学特征

Mathematical characteristics of macroscopic inelastic recovery of polycrystalline beryllium at room temperature

摘要:

采用循环加卸载的单轴拉伸试验,得到室温下不同延伸率的多晶铍试样的塑性变形、弹性回复变形、非弹性回复变形数据。对非弹性回复变形的数学特征进行了分析,建立相应的表达函数。结果表明：完全卸载条件下,铍非弹性回复变形与塑性变形间呈幂函数关联；非完全卸载条件下,二者关系也可用幂函数描述；幂函数所有两个参数与卸载应力水平呈二次函数关系,两个参数间也线性相关；在同一卸载周期内,非弹性回复变形与塑性变形间呈二次函数关系,其中至少两个函数参数表现出超越具体试样的普适性数学特征；弹性模量(或可能延伸率)与各数学模型参数变化趋势的关联明显。

Abstract:

With the uniaxial cyclic loading/unloading test at room temperature, data of the plastic deformation, elastic recovery deformation and inelastic recovery deformation of polycrystalline beryllium samples with different elongation was obtained. Investigation on mathematical characteristics of the inelastic recovery was carried out, and corresponding expression functions were obtained. The result indicates that: after completely unloading, the relationship between inelastic recovery strain and plastic strain of beryllium can be described by the power function; even being incomplete unloading, their relationship can also be described by the power function; all the two function parameters are related to the unloading stress level in analytic form with the square polynomials,and the linear correlativity is presented between the two parameters；in the same unloading cycle, the relationship between inelastic recovery strain and plastic strain can be described by the square polynomials, at least two function parameters show the universal mathematical characteristics beyond specific samples; the modulus of elasticity (also maybe the elongation) is closely relevant to trends of change of all mathematical model parameters..