考虑纤维断裂特征的Nb3Sn股线统计拉伸强度和失效概率

Nb₃Sn 超导复合股线在强磁场工程中有着重要的应用，其拉伸强度为保证和评估其长期服役安全的一个关键参数。本文从 “剪滞”理论出发，利用基于Weibull/Possion统计理论的复合材料纤维断裂的Curtin-Zhou模型，较好地描述复合股线中Nb₃Sn超导纤维碎片化过程，建立了分析超导复合股线统计拉伸强度和失效概率的模型。计算结果表明，青铜法Nb₃Sn超导复合股线的拉伸强度随着初始损伤参数的增大而迅速减小；在4.2K服役温度下，当Weibull模量为8时，随着初始损伤参数的增加，股线的拉伸强度约从900MPa衰减至480MPa，与已有实验结果吻合良好；初始损伤参数约为1时，正规化方差最大。初始损伤和Weibull模量对Nb₃Sn复合股线统计拉伸强度和失效概率函数的分布有着显著影响。

The Statistic Tensile Strength and Failure Probability of Nb3Sn Strands under Considering Filament Fragmentation Characteristics

Nb3Sn superconducting composite strands have wide applications high magnetic field engineering, their tensile strength is a key parameter to assure and access the safety of long-time service. Using the Curtin-Zhou model which is on the basis of the Weibull/Poisson statistics as well as the shear lag theory, the fragmentation of filament in composite strands can be well described, and an analytical model is proposed to obtain the statistic tensile strength and the failure probability. The computation results indicate that when the initial damage parameter is rising, the statistic tensile strength is dropping sharply; at the service temperature 4.2 K, when Weibull modulus is equal to 8, the tensile strength decays from 900MPa to about 480MPa, which coincides well with the experimental results; as the initial damage parameter is near 1, the normalized variance reaches to its maximum value. For Nb3Sn superconducting composite strands, the filament initial damage and Weibull modulus both have strong influence on their statistic tensile strength and failure probability.