The Effect of High Temperatures on Toughness of Concrete

Transcription

1 The Effect of High Temperatures on Toughness of Concrete Vydra V, Trtík K, Vodák F Concrete: Construction s Sustainable Option, Dundee Scotland 8-10 July / 18

2 Introduction Task: To prepare data for concrete containment durability evaluation. Question: Development of the structure after high temperature attack - after the design accident of the reactor (t 150 C )? after a terrorist attack (t 600 C)? Determination of residual properties of concrete after a high temperature treatment. 2 / 18

3 Curing and Heating Subject of investigation: Ordinary Portland Concrete used at concrete containment construction (NPP Temelín). Samples were treated at high temperatures up to 1000 C at age of 90 and 180 days curing: 27 days in a water bath drying: at 105 C, 5 hours rate of heating: 2 C/m heating: 120 minutes cooling: 24 hours 3 / 18

4 Determined Residual Properties 1. Residual mechanical properties compressive strength flexural strength (three point bending) modulus of elasticity (three point bending) 2. Residual fracture properties fracture toughness, critical stress intensity factor, K Ic effective critical stress intensity factor K Ice fracture energy G and few others 3. Porozity of the cement paste 4. Diferencial termal analysis (DTA) 4 / 18

5 Determined Residual Properties 1. Residual mechanical properties compressive strength flexural strength (three point bending) modulus of elasticity (three point bending) 2. Residual fracture properties fracture toughness, critical stress intensity factor, K Ic effective critical stress intensity factor K Ice fracture energy G and few others 3. Porozity of the cement paste 4. Diferencial termal analysis (DTA) 4 / 18

6 Strength compressive strength flexural strength (TPB) 5 / 18

7 Fracture energy determination Fracture energy was determined using several ways 1. G F = A F B(W a 0 ) RILEM recommendations - According to 2. G - as a true fracture energy: a plateau of G(a e ) 6 / 18

8 Fracture energy determination Fracture energy was determined using several ways 1. G F = A F B(W a 0 ) RILEM recommendations - According to 2. G - as a true fracture energy: a plateau of G(a e ) 6 / 18

9 Fracture process zone (FPZ) While the crack propagates energy is consumed in surrounding of the crack in the fracture process zone (FPZ). Materials can be classifies as: Brittle - size of FPZ is insignificant Quasi brittle size of FPZ is comparable with size of the structure size of FPZ is not constant allong the crack 7 / 18

10 Size (in)dependent fracture energy G F determined using standard method depends on size of the sample! Fundamental question arises: Is it possible to determine fracture energy independent on size of the sample? 8 / 18

11 Effective crack model Fracture process zone partially transfers stress, therefore crack length cannot be exactly determined. effective crack length is introduced a e. three point bending: reality: beam with fracture process zone and a crack with length a model: fully elastic beam with an effective crack length a e 9 / 18

12 (Local) fracture energy as a function of eff. crack length Shape of the fracture process zone changes while the crack propagates therefore energy consumption varies, fracture energy G f is a function of effective crack length: G f (a e ) at quasi static crack propagation G f can be determined as: G f (a e ) = G = 1 B dπ da e Function Π(a e ) is unknown so derivation cannot be performed directly! So why not express Π and a e as a function of the beam deviation δ? Then : G f (a e ) = 1 B dπ da e = 1 B dπ dδ ( dae dδ ) 1 10 / 18

13 Summary G f determined using three bend testing: three-linear model: If there is a plateau size independent fracture energy G can be determined! 11 / 18

14 Fracture energy G Age: 90 days 180 days Fracture energy determined using different methods 12 / 18

15 Interpretation - rheological model Fracture energy has two components: 1. break of bonds between gravel and cement matrix model: energy required for dissipative members unlock 2. energy consumed by friction between gravel and the matrix model: dissipative member hypothesis: high temperatures unlock dissipative plastic members 13 / 18

16 Conclusions ❶ New method for true fracture energy determination ❷ Analysis of some residual parameters with temperature dependence temperature in range C steps down fracture energy o f concrete temperature in range C restores original fracture energy temperature higher than 300 C decreases strength and incre ases plasticity of concrete temperature higher than 600 C completely deteriorates con crete Outlook: investigate importance of rate of heating investigate importance of humidity (initial humidity, humidity during heating [autoclaving at t 150 C]) 14 / 18

17 The end Introduction Curing and Heating Determined Residual Properties Strength Fracture energy determination Ladies and gentlemen Thank you for your attention... FPZ Size (in)dependent fracture energy Effective crack model Local fracture energy Summary Fracture energy G Interpretation - rheological model Conclusions The End Determination of potential energy as a function of δ Example of a e and Π determination Determination of effective crack length as a function of δ 15 / 18

18 Determination of potential energy as a function of δ Using effective crack model one can suppose that material is elastic outside of the crack and therefore elastic potential energy is Potential energy of external force is Π el = 1 2 P(δ) δ and therefore Π P = δ 0 P(x)dx Π = Π el + Π P = 1 2 P(δ) δ δ 0 P(x)dx 16 / 18

19 Example of a e and Π determination 17 / 18

20 Determination of effective crack length as a function of δ Only implicit expressions can be found in literature as: E = P 4Bδ ( ) [ S 3 1 0, 387 W ( W W S + 12, 13 S ) 2,5 ] P Bδ ( ) S 2 F 1 (α e ), W where F 1 (α e ) = αe 0 xy 2 (x)dx, Y(x) is complicated function of geometry. Effective crack length can be explicitly expressed only approximately: α e (F 1 ) = arctan(b 1+b 2 ln F 1 +b 3 (lnf 1 ) 2 +b 4 (ln F 1 ) 3 ) π, where b 1 b 4 are simple functions of sample size. Error of the approximation is less than 0,2%! 18 / 18