PSI - Issue 5

Igor Shardakov et al. / Procedia Structural Integrity 5 (2017) 210–216 Igor Shardakov / Structural Integrity Procedia 00 (2017) 000 – 000

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The results of numerical modeling (solid line) compared with the experimental data (dashed line) are shown in Fig. 3. Their analysis indicates the changes in accelerations normal to the beam surface at the points located at different distance from the point of impact impulse excitation (D1 – at a distance L, and D2 – at a distance L+2l). It is seen that numerical and experimental acceleration results agree well in the limits of the first half-wave, i.e. within the time interval where the signal (not being distorted by secondary reflected signals) is recorded. The maximum acceleration amplitudes of the first half – wave at the location points of the accelerometers D1 and D2 are observed just in this time interval. Note that the above mentioned values are required for computing the criterion K from relation (1). Hence it can be concluded that the proposed mathematical model can be used in the numerical experiments, which provide the reliable registration of signal distortion caused by the presence of a crack in the area between the accelerometers D1 and D2 and demonstrate the possibility of using the criterion K to assess this distortion.

Fig.3. Change in a normal acceleration on the beam surface at the location points of the accelerometers D1 and D2.

3. Results of numerical experiments and their analysis

Application of the developed mathematical model made it possible to perform a numerical experiment aimed to determine the values of the criterion K for a beam with a crack in its middle section and to compare the obtained value with that found for the entire beam. Besides, the experiment allowed us to trace how the criterion K changed at the stage of crack elimination through its filling with an epoxy composition during the repair of the beam. Four states of the beam labeled I, II, III, and IV were investigated: (I) – entire beam, (II) – beam with a fully opened crack, (III) – crack filled with a healing agent to 5-10 mm depth along the entire length of the surface of the crack, (IV) – crack completely filled with the injected material. Figure 4 gives a schematic representation of the beam fragment (cross-section 220×120mm) in the vicinity of the crack of dimensions 175×120×1mm and the beam cross-section configuration for its 4 states. Numerical data on the physical-mechanical properties of concrete, the reinforcement, and the injected material (epoxy resin) used for mathematical modeling are summarized in the Table given below.

Fig.4 Area of a crack at different stages of its growth and elimination (1 – concrete, 2 – crack cavity, 3 - epoxy resin