两个基本原理-s.pptVIP

* * * * * * * * * * * * * * * * * * * * * * * * * * * 3.9 两个基本原理 3.9.1 Boltzmann’s superpositon 波尔兹曼叠加原理 Ludwig Eduard Boltzmann was born February 20, 1844, in Vienna? and died on September 5, 1906, in Duino, Italy. Tombstone 墓碑 He was a physicist whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms such as mass, charge, and structure determine the visible properties of matter such as viscosity, thermal conductivity, and diffusion. Boltzmann于1876年提出 1．每个应变或应力对材料的贡献是互相独立的、可线性加和的； 2．材料当前的应变或应力是全部受力史的函数。 Basic contents 波尔兹曼叠加基本内容 2MPa 1MPa 2MPa 1MPa 3MPa 2MPa G = 2MPa ? = ? /G= 1 ? = ?1/G+ ?2/G =3/2= 1.5 ? = （2+1+3）/2=6/2= 3 = ?1/G+ ?2/G + ?3/G =2/2+1/2+3/2 = 3 方法1 方法2 ??1 ??2 ??3 J1(t-s1) J2(t-s2) J3(t-s3) 0 s1 s2 s3 Time Stress Strain Input Response 输入 响应 ??1在时刻s1施加，形变 ??2在时刻s2施加，形变 蠕变 Creep …………… ??i – 应力的增量 si – 施加力的时间 如果受力为时间的连续函数，可写为积分形式： 应力松弛 ??1 ??2 ??3 G1(t-s1) G2(t-s2) G3(t-s3) 0 s1 s2 s3 Time Stress Strain Input Response 输入 响应 ??1在时刻s1施加，应力 …………… ?? 2在时刻s2施加，应力 如果应变为时间的连续函数，可写为积分形式： Results of Boltzmann superposition --- 蠕变，后边项代表聚合物对过去历史的记忆效应 --- 应力松弛，后边项代表聚合物应力松弛行为的历史效应 粘弹性固体常被称为“记忆减退材料” 例题：一聚合物样品可用Kelvin模型描述，其弹簧模量为2Pa，粘壶粘度为100Pa.s，s=10sec时加应力0.5Pa，s=40sec时再加应力0.8Pa，求t=80sec时的应变 3.9.2 粘弹性的时温等效原理Time temperature superposition 升高温度与延长时间能够达到同一个结果。 —— 时温等效 Fast noodle 模量变化 E(?,?,T,t) 即模量为时间和温度的函数 低温 = 短时 长时=高温 Time-Temperature superpostion It was found in the 1940s that the mechanical properties of a polymer at a given temperature could be related directly (by a constant shift factor) to the behavior at another temperature. Similarly, the behavior at a given rate could be related directly to another rate by a similar shift factor. Rate and temperature are inversely related for these materials by the Time-Temperature superposition principle which is based on the William