Numerical model about hygro-lock effect in the mechano-sorptive behavior

Transcription

1 Numerical mdel abut hygr-lck effect in the mechan-srptive behavir Jean-Marie Hussn, Frédéric Dubis, Niclas Sauvat, Octavian Pp Labratry GEMH, University f Limges Bulevard Jacques Derche, 93 Egletns, France Research Grup Civil Engineering and Durability Team

2 Scientific Cntext Mechan-srptive test RH (%) T=2,5 C 5 Stress (MPa) Recvery under dry state Time (hur), Time (hur) Free Creep under shrinkage dry state Swelling effect Creep and recvery effects under variable envirnment : mechan-srptin respnse Creep under wet state

3 Strain Scientific Cntext Mechan-srptive test,9%,8%,7%,6% Ttal experimental strain Free shrinkage swelling strain Viscelastic strain Elastic strain,5%,4%,3% Strains lcking : Hygr-lck,2%,%,% Time (hur) Hygr-memry

4 Scientific Cntext Memry Shape Plymer behavir C - applied f a stress lading at high temperature T h pre pre E h 3 2 l B E Stress D 4 pre fix T l Temperature Tg T h A

5 Scientific Cntext Memry Shape Plymer behavir C - applied f a stress lading at high temperature T h pre pre E h l B 2- decrease f the temperature until it lw level Tl T h l s Tl pre dt E T l l E Stress D 4 pre fix T l Temperature Tg T h A

6 Scientific Cntext Memry Shape Plymer behavir C - applied f a stress lading at high temperature T h pre pre E h 2- decrease f the temperature until it lw level Tl l Stress D T h l s Tl pre dt El B T l E 3- lw temperature unlading pre fix fix Tl pre l s Tl T Tl El T l Temperature Tg T h A

7 Scientific Cntext Memry Shape Plymer behavir C - applied f a stress lading at high temperature T h pre pre E h 2- decrease f the temperature until it lw level Tl l Stress D T h l s Tl pre dt El B T l E 3- lw temperature unlading pre fix fix Tl pre l s Tl T Tl El 4- reheating until the initial high level Th T l Temperature Tg T h A

8 Scientific Cntext Memry Shape Plymer behavir C - applied f a stress lading at high temperature T h pre pre E h 2- decrease f the temperature until it lw level Tl l Stress D T h l s Tl pre dt El B T l E 3- lw temperature unlading pre fix fix Tl pre l s Tl T Tl El 4- reheating until the initial high level Th E fix h fix T l Temperature Tg T h A

9 Scientific Cntext Mecan-Srptive behavir = Memry Shape Plymer behavir shape memry shape recvery heating / mistening defrmatin cling / drying shape fixatin heating / mistening cling / drying

10 Outline Mechan-Srptive effects under cnstant lading Mechan-Srptive effects under randm lading Viscelastic behavir and MS cupling Theretical applicatins Experimental applicatin Cnclusins and Perspectives

11 MS effects under cnstant lading Tig between mechanical lading, strain respnse and the elastic mdulus Elastic mdulus Strain Stress f E E E E 2 2 t t t t 2 t t 2 time

12 MS effects under cnstant lading Tig between mechanical lading, strain respnse and the elastic mdulus Stress f Elastic mdulus Strain E E E E 2 2 ( t) f( t) ( t) Mechanical stress Pres-stress t t t t t 2 t time 2 Generalized Hk s law t t E t

13 MS effects under cnstant lading Evlutin f the pre-stress and the ttal stress vs time Stress f Elastic mdulus E E E E 2 Pre-stress E E H t t E E E H t t E E E H t E2 t 2 Ttal stress t H t t E H t E t t t t 2 H t t E H t t E t t 2 E H t t E2 time

14 Memry shape effects under cnstant lading Memry shape behavir Hk s law derivatin : t 2 t t E E t t E t Blcking strain during hardening phases : t E t t E t t E with : t t AE t ( t) A E( t) f( t)

15 MS effects under cnstant lading Memry shape behavir f t E tt t E t t pre t E t t fix with pre fix Elastic mdulus Stress f Strain E E E E 2 2 t t t t t 2 t 2 time

16 MS effects under cnstant lading Memry shape behavir t E tt f t E t t pre t E t t fix with pre fix Stress f E t, t E t tt, t Elastic mdulus Strain E E E E 2 2 E t t t t t 2 t 2 time

17 MS effects under cnstant lading Memry shape behavir t E tt f t E t t pre t E t t fix with pre fix Stress f E t, t E t tt, t Elastic mdulus E E E E 2 E ( t). H t t ( t). H t t, E t, t Et E t, t E t E t t Strain 2 t t t t t 2 t 2 time ( t). H t t E t, t

18 MS under randm lading Incremental frmulatin and integral frm j f t t H t t j H t t j f n j n Linear behavir assumptin Superpsitin principle t t f t t j discretized frm time t t n t. H t t. H t t E t, t E t, t N j j j j

19 MS under randm lading Incremental frmulatin and integral frm j f t t H t t j H t t j f n j n Linear behavir assumptin Superpsitin principle t t f t t j discretized frm time t t n t. H t t. H t t E t, t E t, t N j j j j f t. H t t d E t, t E, t t t

20 MS under randm lading Incremental frmulatin and integral frm j f t t H t t j H t t j f n j n Linear behavir assumptin Superpsitin principle t t f t t j discretized frm time t t n t. H t t. H t t E t, t E t, t N j j j j E t, Specific mechan-srptive spring t t E, t f d

21 Viscelastic behavir and MS cupling Generalized Mechan-srptive Kelvin Vigt Mdel f t E, t f E E m M, t E, t E, t m f E m M f E M f t f m f M f t t m t M t t t E, t f d m t t m E, t m m t t f m E f d with m m t t t f fe f and t t t M m m

22 Viscelastic behavir and MS cupling Generalized Mechan-srptive Kelvin Vigt Mdel E, t f E E m M, t E, t E, t m f E M f E f t H t t f m f m M f M f t H t t t t m t M t t E t, t m Em E t, exp d m t t E t, Em m t d t

23 Viscelastic behavir and MS cupling Generalized Mechan-srptive Kelvin Vigt Mdel f t E, t f E E m M, t E, t E, t m f E m M f E M f t f m f M f t t J t, d J t, f E Em exp t m M E p, t m m E,, E m d d

24 Theretical applicatins Linear apprximatin between misture cntent level and elastic mdulus Lngitudinal elastic mdulus E (Mpa) E l E h t t E t E t w(%)

25 lading ttal strain Theretical applicatins Example ms lading ttal strain t ft t 4.E-3 3.5E-3 3.E-3 2.5E time h E-3.5E-3.E-3 5.E-4.E+

26 lading ttal strain Theretical applicatins Example ms lading ttal strain 2 5 t ft t time h E-3 3.5E-3 3.E-3 2.5E-3 2.E-3.5E-3.E-3 5.E-4.E+ : creep respnse under lw ms level 2: acceleratin f creep prcess during mistening phase 3: hygr-lck effect during drying phase 4: partial recvery phase under lw humidity level 5: acceleratin f recvery phase during mistening phase 6: hygr-lck effect during drying phase 7: ttal recvery at the last high humidity level

27 lading ttal strain Theretical applicatins Example ms lading ttal strain t ft t 8.E-3 7.E-3 6.E E time h E-3 3.E-3 2.E-3.E-3.E+

28 lading ttal strain Theretical applicatins Example ms lading ttal strain t ft t 8.E-3 7.E-3 6.E-3 5.E E-3 3.E-3 2.E-3.E-3.E time h : classic mechan-srptive respnse 2: hereditary effect under a secnd lad increment 3: partial recvery phase 4: final recvery phase 3 4

29 Experimental applicatin Circular bending test Pt /2 Us t Pt /2 3cm Ui t cm

30 Experimental applicatin Mechanical and climatic ladings HR 9% free shrinkage/swelling effects fr lngitudinal and transversal directins 8% 5% T 3 C t C 2% rup t t

31 deflectin (mm) Experimental applicatin Experimental deflectin respnse Time (h) Average deflectin f upper fiber Average deflectin f lwer fiber

32 deflectin (mm) Experimental applicatin Mechan-srptive respnse creep phase recvery phase wet state. dry state Experimental viscelastic deflectin Simulatin Time (h)

33 deflectin (mm) Experimental applicatin Mechan-srptive respnse experimentatin/simulatin wet state. dry state Experimental viscelastic deflectin Simulatin Time (h)

34 Cnclusins Intrductin f the Mechan-Srptive prcess as a Memry Shape behavir Definitin f the hygr-lck effects and memry effects fr elastic behavir Generalizatin fr viscelastic behavir Experimental validatin with creep bending tests Perspectives Implementatin in a finite element sftware Cupling with an heat and mass transfer algrithm Intrductin fr jint behavir predictins Develpment f apprpriate tls in fracture mechanics

35 Numerical mdel abut hygr-lck effect in the mechan-srptive behavir Jean-Marie Hussn, Frédéric Dubis, Niclas Sauvat, Octavian Pp Labratry GEMH, University f Limges Bulevard Jacques Derche, 93 Egletns, France Research Grup Civil Engineering and Durability Team