Concrete strength evaluation using fracture mechanics technology

Transcription

1 (016) DOI: / matecconf/ IPICSE-016 Concrete strength evaluaton usng fracture mechancs technology Valery Poov 1, Dmtry Poov 1, and Anna Davdenko 1. 1 Samara State Techncal Unversty, Insttute of Archtecture and Cvl Engneerng, Molodogvardeyskaya str. 194, Samara, Russa Abstract. Ths aer resents the hyscal henomenon of concrete fracture rocess by statc unaxal comresson. The analyss of strength characterstcs of concrete s carred out usng fracture mechancs technology, and what s more, the actual oeratng condtons of structures are evaluated. The exedency of usng energy aroach and knetc theory s gven to consder materal fracture rocesses wth a large number of defects. 1 Introducton Nowadays, concrete and renforced concrete are wdely sread among buldng materals. What s more, ther alcaton s ncreasng. Ths concluson s based on the analyss of satal arrangement of buldngs and contemorary constructon. It s reflected n a consderable ncrease n the number of storeys, constructon stes and the use of frame - monolthc structure of buldngs that occur manly n resdental constructon. Moreover, the analyss of concrete roertes reduces to determnng the strength characterstcs affectng ts durablty. The man concrete roerty s durablty, that s, the caacty of concrete to resst to dfferent external effects. But not only strength affects durablty, t s also necessary to consder such characterstcs as orosty, crack strength that characterzes the roertes of the materal tself as well as the ntensty of the external load. When we consder concrete fracture rocess the most effectve s the alcaton of the concet and theory of fracture mechancs. Accordng to the roosed method the destructon of any knd of materal s the result of develoment of the already exstng defects n the body materal what s sutable for concrete and takes nto account the heterogenety of ts structure. After all, the concrete already has a sgnfcant number of mcro- and macroscoc defects the formaton of whch s n accordance wth the technologcal features of roducton. The control over the rocess of structure formaton s ossble only after the recet of fnshed roducts. Corresondng author: aezg@mal.ru The Authors, ublshed by EDP Scences. Ths s an oen access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense 4.0 (htt://creatvecommons.org/lcenses/by/4.0/).

2 (016) DOI: / matecconf/ IPICSE-016 Man Part Thus, exstng defects when subjected to external forces ncrease n sze, develo nto macro defects and reach crtcal dsclosure n the form of man cracks. That s, they dvde the materal nto arts destroyng t. Stress redstrbuton, when dsclosng defects, leads to the begnnng of a chan reacton, and s brttle fracture of concrete. The fracture rocess tself can be dvded nto three stages, dscussed n the works 1,, where the energy concet s aled usng knetc theory of fracture mechancs. The energy values of crack formaton, allocated n the destructon, defne three stages of the consdered rocess: 1. characterzng the accumulaton of mcro damages;. the erod of rearaton due to the formaton of numerous mcrocracks;. the erod of rad materal destructon. At the frst stage the energy amount of the materal deformaton s neglgble and ractcally has no effect on the structure and characterstcs of the materal. At the second stage there s more energy amount of destructon than at the frst one. It results n emergence of varously orented mcrocracks affectng the hyscal and mechancal roertes of concrete. At ths stage there s a destructon of the weakest lnks of concrete structures whch are located n the laces of low-strength nclusons or wth a maxmum stress concentraton. At the thrd stage, wth ncrease n load the amount of the released destructon energy far exceeds the caacty of the frst two stages. The release of such amount of energy can be justfed by the rocess of further stress redstrbuton and ts ncrease to such a crtcal value where the ncrease n length and wdth of cracks leads to ther coalescence. Further formaton and ncrease rocesses of large, man cracks absorb all the energy suled to materal and result n loss of stablty and ts dvson nto arts, that s, to the destructon of materal. It should be noted that the rearaton of fracture even under a statc comresson s extended n tme and can be an ndcator of durablty whle the rocess of "destroyng" occurs lke an avalanche. The most mortant nfluence on the duraton of the rearatory destructon rocess has the rate of load alcaton. The use of energy concet makes t ossble to trace the connecton of the characterstcs, crack strength wth the roosed arameters of ts evaluaton. Based on the Grffth's theory of equlbrum cracks, we can assume the develoment of volume damage as flat crack searaton, that s, ndeendent growth of ts length and wdth s allowed. The energy balance characterstc descrbng cracks develoment can be resented as: k l l E k 1 4 l 1 1, (1) where l - the overall length and wdth of gas formed n the concrete samle, m; concrete surface energy, J / m ; Е concrete modulus of elastcty, MPa; workng stress n -th crack, Pa. We smlfy the formula (1) by ntroducng the averaged length and wdth of the crack, so the acton of stress σ wll cause the ncrease of the averaged crack at the secfed length and wdth:

3 (016) DOI: / matecconf/ IPICSE-016 LL E 1 4 L. () We relace the roduct L=S. The second member of equaton () exresses the fracture or crack formaton energy: LS А 1 8E. () Due to ths, t s necessary to nvestgate the behavor of the formed crack deendng on the stress ncrease n the concrete element. Wherefore we use Zhurkov s transformed equaton of knetc theory, resented by K.I. Kuznetsova 6: dl dt a R 0e, (4) where а 0 characterstc reflectng the tendency of the materal to crack formaton under certan condtons of external actons, m / s; characterstc reflectng the ntensty of crack formaton rocesses. Based on the load standard condtons wth lnear varaton of load alcaton rate, we resent the followng equaton: Substtutng ths exresson nto (5) we obtan: d K dt. (5) dl dl dt a ехр d dt d K R, (6) We relace =а р /К, then the exresson (6) takes the form dl ехр d R (7) Integratng the deendence (7) we obtan: R R l ехр d ехр ехр 1 0 R R R 0 (8) The equaton (8) shows the deendence of the crack formaton length from the level of the aled stress. Takng nto account the knetc characterstcs of and consderng varous temerature humdty condtons of concrete destructon we substtute the deendence nto () and obtan the exresson: SR А ехр 1 R 8E. (9)

4 (016) DOI: / matecconf/ IPICSE-016 Takng nto account the relatve level of stresses, the deendence takes the form: R R А SR ехр 1 R 8E. (10) As dscussed above, at the moment of destructon the release of the mcro cracks formaton energy exceeds to the maxmum, whch means that σ = R р, and n consderaton of () the deendence (10) takes the form: SR ехр 1 S 8Е. (11) However, to smlfy the descrtve art, we use the research results of V.A. Kuzmenko [5] showng that n the case of unaxal comresson the maxmum tensle stresses are calculated as "reduced stresses" and are equal to σ com, that s, red tens com. (1) Takng nto account the equvalence of "reduced stresses", we substtute the deendence (11) and derve the crtcal stress, whch led to the destructon of the materal 8Е R com ехр 11. (1) The energy concet and the knetc theory n fracture mechancs are often aled for mert ratng of materals that have a sgnfcant number of mcro- and macroscoc defects n the structure. Concluson Current trends of the roosed method are the smlcty and accuracy of calculatons. The fracture mechancs methods as scence based regulatory framework for evaluaton the roertes of concrete and renforced concrete ganed wdesread wth the ntroducton of GOST n the 1990s,9. That s the result of large-scale exerments comleton conducted by RILEM (Internatonal Unon of Testng and Research Laboratores for Materals and Structures) and the research results of many Russan scentsts 4,7,8. References 1. V. P. Poov, Concrete destructon workng under the cyclc freezng, Dssertaton canddate of techncal scences (MADI, Moscow, 1986). P.G. Komokhov, V.P. Poov, Energy and knetc asects of concrete fracture mechancs (Publ. RIA, Samara, 1999). GOST Concrete. Porosty arameters determnaton methods (Publshng House of Standards, Moscow, 1986) 4

5 (016) DOI: / matecconf/ IPICSE V.P. Poov, A. Yu. Davdenko, Vestnk of the Russan Academy n Constructon, (005) 5. V.A. Kuzmenko, New deformaton schemes of sold bodes (Naukova dumka, Kev, 197) 6. K.I. Kuznetsova, The laws of vscous elastc bodes destructon and some of ther alcaton features to sesmology (Nauka, Moscow, 1969) 7. V.P. Poov, A.Yu. Davdenko, Proceedngs of the X scentfc - techncal conference "The relablty of constructon objects", 4-7 (007) 8. V.P. Poov, A.Yu. Davdenko, Vestnk of the Russan Academy n Constructon, 61-6 (009) 9. GOST Concrete. Defnng the characterstcs of crack strength (toughness) under statc loadng (Publshng House of Standards, Moscow, 199) 5