Hao Sheng-Wang, Zhang Bao-Ju, Tian Ji-Feng
School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, 066004, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):012501. doi: 10.1103/PhysRevE.85.012501. Epub 2012 Jan 3.
We focus on a system consisting of an elastic part and a damageable part in series, to study the relaxation creep rupture of a heterogeneous system subjected to a uniaxial constant strain applied instantaneously. The viscoelastic behavior of the damageable part is modeled by a fiber bundle model consisting of Kelvin-Voigt elements and global load sharing is assumed for the redistribution of load following fiber breaking in the damageable part. Analytical and numerical calculations show that the global relaxation creep rupture appears if the elastic energy stored in the elastic part exceeded the fracture energy of the damageable part. The lifetime of the system strongly depends on the values of the applied external strain and the initial stiffness ratio k between the elastic part and the damageable part. We show that a higher stiffness ratio implies a more brittle system. Prior to complete failure, relaxation creep rupture exhibits a sequence of three stages, similar to creep rupture under constant stress, and the nominal force rate presents a power law singularity with a power index -1/2 near the global rupture time.
我们关注一个由串联的弹性部分和可损伤部分组成的系统，以研究在瞬间施加单轴恒定应变的情况下，非均匀系统的松弛蠕变断裂。可损伤部分的粘弹性行为由一个由开尔文 - 维格纳元件组成的纤维束模型来模拟，并且假设在可损伤部分的纤维断裂后，全局载荷共享用于载荷的重新分配。分析和数值计算表明，如果弹性部分中存储的弹性能超过可损伤部分的断裂能，就会出现全局松弛蠕变断裂。系统的寿命强烈依赖于所施加的外部应变值以及弹性部分和可损伤部分之间的初始刚度比k。我们表明，较高的刚度比意味着系统更脆。在完全失效之前，松弛蠕变断裂呈现出类似于恒定应力下蠕变断裂的三个阶段序列，并且在全局断裂时间附近，名义力率呈现出幂律奇异性，幂指数为 -1/2。
