Modelll- voigt-Kelvin model Total stress. G1+; R,=E train:881=82 2 o=E8+ da For stress relaxation, de/dt=0,O=E,Eo It fails to describe the stress relaxation behavior dc For creep,o=oo Oo=Em8tnmdt At time t=0,=0,柔量E (Em/nm )r Relxauiortimer Retardation time t=nE 6(=( E
Model II - Voigt-Kelvin model V1 H1 Em V2 H2 Km V H 1 1 Em 2 2 m d dt H V K Total stress: V = V1 + V2 ; strain: H= H1 = H2 1 2 m m d E dt H V V V HK For stress relaxation, dH/dt = 0, V H E m 0 It fails to describe the stress relaxation behavior. For creep, V = V0 , 0 m m d E dt H V HK At time t = 0, H = , 0 / 1 m m t m E t e E V K H Relaxation time: Retardation time W = Km/Em: 0 / 1 t m t e E V W H 11 Ḅ䟿
Modell- voigt-Kelvin model Creep compliance 8(tOo For creep recovery,o=0, 0=EmE+n dt Et)=E -t/T e
Model II - Voigt-Kelvin model / 1 t Dt D e W f 0 / 0 0 / /1 t m t e E V W HV V Creep compliance For creep recovery, V = , 0 m m d E dt H H K t / t e W H H f 12
Model I- Burger's Model For creep,O=O0 E,61()=E1+2+53 E Er here T 72 E E2,E2 12y,E2 creep 43 recovery 3 81 81 nLL
Model III – Burger’s Model E1 , H1 E2 , H2 K2 , H2 K3 , H3 V 0 1 2 3 3 / 1 0 0 2 () 1 t E t e t E V V W V H K H H H 2 2 E K W ¾ For creep, V =V0 : where H1 H1 H3 H2 H2 H3 13
粘弹性-分子和力学的松弛行为 力学性能随时间改变而演化,变化的快慢可 由材料本身的松弛时间估算 T= nNe 粘弹性的微观起源: 弹性由熵弹性即构象熵的改变贡献 粘性由构象改变过程中受到的粘滞阻力导致
㋈ᕩᙗⲴᗞ㿲䎧Ⓚ˖ ᕩᙗ⭡⟥ᕩᙗণᶴ䊑⟥Ⲵ᭩ਈ䍑⥞ ㋈ᙗ⭡ᶴ䊑᭩ਈ䗷〻ѝਇࡠⲴ㋈┎䱫࣋ሬ㠤 ㋈ᕩᙗ-࠶ᆀ઼࣋ᆖⲴᶮᕋ㹼Ѫ 14 W = Km/Em ࣋ᆖᙗ㜭䲿ᰦ䰤᭩ਈ㘼╄ॆˈਈॆⲴᘛធਟ ⭡ᶀᯉᵜ䓛Ⲵᶮᕋᰦ䰤ՠ㇇
Dynamical mechanics analysis 高聚物在交变应力作用下,形变落后于应力变化的现象称为 滞后现象 理想液体 粘弹体 0=0 snot σ=(de/d) 弹性体 ot E=Eo sin(ot-8 每一次循环将消耗功一力学损耗或叫内耗 将落后一个δ的相位 δ又称为力学损耗角 即:滞后现象 △W=∮G(s()=no=nsin8 hysteresis and mechanics loss
Dynamical Mechanics Analysis 儎㚐⢟൞Ӛᓊ࣑⭞֒сθᖘ㩳ӄᓊ࣑ौⲺ⧦䊗〦Ѱ └⧦䊗 Zt 0 VV Z sin t HH ZG 0 sin t ሶ㩭ਾањGⲴս ণ˖┎ਾ⧠䊑 ⇿а⅑ᗚ⧟ሶ⎸㙇࣏ˉ࣋ᆖᦏ㙇ᡆਛ㙇ˈ G৸〠Ѫ࣋ᆖᦏ㙇䀂 V H ⨶ᜣ⏢փ ᕩᙗփ ㋈ᕩփ V =K(dH/dt) H=V0 /Ksin(Zt-S/2) 0 0 ' W td t V H SV H G sin v³ 15 hysteresis and mechanics loss