Investigation On The Energy Dissipation In The Time-dependent Fracture Process Of Concrete

Many structures built of quasi-brittle materials such as concrete,when subjected to sustained loading,can develop cracks which over time propagate and could eventually lead to structural failure.Time-dependent fracture in mass concrete,happening under long-time constant loading,is closely associated with the safety and durability of concrete structures in service.Therefore,it is important to investigate time-dependent fracture under long-time loading.The thesis consists of the experimental study and theoretical analysis by three-point beams:1.The thirty standard three-point bending beams,in which four groups of specimens were cast,with the different heights D=100,200mm,300 and 400mm and same ratio of notch to height a0/D=0.4.Three specimens of each size are used to determine peak loads by means of the monotonic static loading test.The remaining specimens are then tested under different constant load levels.2.Time-dependent crack mouth opening displacement CMOD(t)in concrete under different long-time constant loading are monitored by electronic extensometer.The time-dependent fracture critical crack mouth opening displacement CMOD(tc)of specimens were calculated.Time-dependent fracture lifetime tcr and final crack mouth opening displacement CMODf were reported.The time-dependent critical crack mouth opening displacement CMOD(tc)was compared with critical crack mouth opening displacement of monotonic static loading test.The relation of time-dependent fracture lifetime tcl,final crack mouth opening displacement CMODf and percentage of the peak load P/Pmax Experimental results show that CMOD(t)increases with increasing loading time t.The time curve of crack mouth opening displacementCMOD(t)-tdisplays the features of three stages.CMOD(t)increases rapidly in the primary stage,but the crack mouth opening rate CMOR(t)gradually slows down.In the secondary stage,CMOD(t)increases andCMOR(t)is almost constant.In the tertiary stage,CMOD(t)and CMOR(t)all increase rapidly until the rupture of the specimen.For the test of time-dependent fracture,the critical crack mouth opening displacement CMOD(tc)is relatively higher compared to the monotonic static loading test.The CMOD(tc)decreases with the increasing percentage of the peak load and approaches critical crack mouth opening displacement CMOD。of monotonic static loading test.For the specimens loaded to the different percentage of the peak load,the lifetime decreases with increasing long-term constant load.The time-dependent fracture lifetime tcr and final crack mouth opening displacement CMODf as well as the percentage of the peak load are exponential.3.Crack propagation was observed by means of strain gauges.Equivalent crack length of specimens a(t)at loading time t were discussed.The curves of crack mouth opening displacement versus crack length CMOD(t)-a(t)were analyzed.The crack propagation subjected to sustained loading was compared with that of monotonic static loading test.Experimental results show that the equivalent crack length a(t)at time t can be determined by linear interpolation.The corresponding CMOD(t)-a(t)curve is in accordance with the trend of CMOD(t)-t curve.The crack opening displacement and equivalent crack length at the turning point from CMOD(t)-a(t)curve are approximately equal to that from CMOD(t)-t curve.For the test of time-dependent fracture,the crack mouth opening displacement is relatively higher compared to the monotonic static loading test with the same equivalent crack growth length △a.The critical equivalent crack length,critical crack opening displacement and the values at the final fracture are higher than the critical values corresponding to Pmax of the monotonic static loading test.4.The energy dissipation π(t)in the time-dependent process of specimens are calculated by means of M-θcurves based on the linear elastic method and linear unloading path hypothesis respectively.The critical energy release rate of time-dependent fracture G(tc)is obtained according to the critical crack length.The test results show that the π(t)-t curve,like the CMOD(t)-t curve,displays the features of three stages.Initially the rate of π(t)tends to decrease,but later this rate is almost constant,and then the rate of π(t)increases gradually until the rupture of the specimen.In the time-dependent fracture test,the energy release rate is larger than the critical value of that,G>G(tc),representing the beginning stable crack propagation.The critical energy release rate G(tc),similar to the critical crack mouth opening displacement CMOD(tc),can serve as a stable crack propagation criterion for the time-dependent fracture test.