Research On The Development Of Internal Stress/Strain Field And Damage Law Of Ultra-High-Performance Concrete Under Fatigue Flexural Loading

Ultra-high-performance Concrete?UHPC? was first developed in the 1990 s.Since then,it has attracted a lot of attention from engineers owing to its excellent strength?compressive strength higher than 150 MPa;tensile strength equal to or higher than 8 MPa?,ductility,and fatigue resistance,in addition to its unique strain-hardening response to multiple micro-cracks.With such excellent properties,UHPC applications to pavements,airfield runways,road surfaces,bridge decks,and offshore structures have substantially increased over the last decade.Most of these structures work under cycle loading conditions.Under repeated loading,the intrinsic flaws and micro crack in UHPC would gradually propagate into macro crack.This reduces not only the structural capacity and serviceability but also the durability.Therefore,it is very important to investigate the fracture properties of UHPC under cyclic loading.At present,most studies focus on two aspects: First,quantify the fatigue behavior of UHPC by using the stress-life?S-N?,and the mean fatigue life under given constant-amplitude cyclic stress can be predicted by the S-N curve.The limitation of this method is that the inherent variates,such as the fiber volume fraction and stress level,cannot be included,and fatigue tests must be conducted once the mix design changes.Second,apply the Paris law to describe the crack propagation during the fatigue life.However,the crack propagation theories have not been studied sufficiently which lack of understanding of mechanisms and microstructural parameters responsible for fatigue of UHPC.Fracture mechanics approach was employed in this research for the above reasons.With this approach it is considered that fatigue crack growth is a governing mechanism and is influenced by crack bridging.This study focuses on analyzing the fatigue crack propagation law and investigating the non-uniform stress/strain evolution process to quantify the fatigue damage of UHPC.The obtained results will enhance understanding on the mechanisms and microstructural parameters for fatigue of UHPC.The research significances are described in detail as follows:Firstly,based on the fatigue life obtained from the tests at the different stress levels with varies fiber contents,the Weibull distribution function was used to estimate the mean and design fatigue lives of UHPC;the propagation behavior of fatigue behavior was studied by Paris Law and the fatigue life was predicted.The results indicate that:?1?With regard to crack propagation,three stages can be clearly seen: ?)rapid development stage;?)stable development stage;?) failure stage;Consistently,the loading cycle ratio of stage ? was account for about 5%-10%,and the proportion of stages ? and ? were established as 70%-85% and 10%-20%,respectively.?2?At the end of stage ?,the strain diagrams exhibited a minor strain concentration at the bottom toward the x-direction.The specimen's strain was approximately 300 ?? and reached the level where cracking is considered to occur.At the end of stage ?,the strain extended upward as the loading cycles increased.When the fiber volume fraction was lower than 1.0%,the strain diagrams do not indicate obvious changes in the y-direction;As the fiber volume fraction increased,the y-direction strain diagram exhibited a tendency of slight but not very obvious 45° strain concentration.?3?Moreover,the fatigue crack growth rate can be divided into two distinct stages: deceleration stage and acceleration stage;At the deceleration stage,the slope of the crack propagation rate gradually increased with the increase of the fiber volume fractions.At the acceleration stage,the slope of the crack propagation rate gradually decreased with the increase of the fiber volume fractions.Secondly,pullout tests of single steel fiber were performed to evaluate the effect of fiber inclination angle on the loading direction and an analytical pullout model was derived to characterize the load-slip displacement relation.A three-point bending test was carried out and the fiber orientation distribution was quantitatively estimated by the help of image analysis process.Then,a micromechanics-based analytical technique was adopted to precisely analyze the flexural behavior of UHPC.Based on a micromechanics-based analytical approach and DIC technology,the stress/strain along the surface crack were quantitatively analysed.The results indicate that:?1?The compressive strength and splitting tensile strength were improved with the increase of fiber volume fraction in the matrix of up to 2%;the compressive strength was barely affected by the fiber length and was found to be 168.24 MPa on average;on the other hand,the splitting strength varied with the fiber length.?2?The stress at the first crack is mainly determined by the matrix strength rather than by the fibres.It should be noted that the specimens with the fibre volume fraction 0.5% exhibited deflection-softening and P_LOP> P_MOR,whereas the other test series' exhibited deflection-softening and P_LOP< P_MOR.?3?The fibre dispersion coefficient decreased with the increasing fibre contents;The actual PDF is skewed to perpendicular to the crack surface and the effective length of fibre is 4mm.?4?The steel fiber volume fractions had a limited influence on the tensile strain at cracking.The tensile strain at cracking was extracted from the DIC and was 0.00269 of the UHPC with different fiber contents.The tensile strain at the complete debonding of the fibers extracted from the DIC was 0.0281 of the UHPC.Finally,based on the fracture mechanics and damage mechanics,a cyclic constitutive law of fiber bridging is described,matrix fatigue growth is quantified with Paris law and the interfacial frictional bond degradation is build.The results indicate that:?1?Under the monotonous loading,the CMOD is 0.0299 mm of the fiber completely debonding;When the fiber volume fractions are 0.0%,0.5%,1.0%,1.5% and 2.0%,the maximum fiber bridging force are 4.314MPa?8.628MPa?12.942 MPa and17.256 MPa,respectively.?2?Under the various of stress level?S=0.80,0.75,070 and 0.65?,the normalized displacements of LOP are 0.000586?0.000718?0.000872 and 0.00107;With the cycle loading deceased to the minimum loading,the CMOD reduced to 30.23%?28.92%?27.12% and 26.94%;Once again the cycle loading get to the maximum loading,the CMOD increased to 7.87%?7.43%?7.28% and 6.51%;?4?when failure occurs,the normalized displacements of UHPC are 0.1061?0.1332?0.1639 ?0.1946;The cycle loading reached to minimum value,the CMOD are 0.1061?0.1332?0.1639 and 0.1946;Compared to the unloading values of CMOD,the CMOD have raised to 0.094%?0.075%?0.061% and 0.051% under the failure point.