Abstract
The mathematical model of crack growth given by the following equation is proposed,
d(Δa)/dt=Kn/A(Δa)
where Δa is the crack extention and K is the stress intensity factor.
The proposed equation has been applied to the three-point-bending tests on beam specimens under the condition of a constant rate of load-point-displacement, u. The results calculated showed a linear increase in Kmax with u1/(n+1). The experiments have been carried out by changing u from 10-6 to 10-1cm/sec. The experimental results also showed a linear increase in Kmax with u1/(37+1).
Subsequently, the experiment has been carried out in order to determine the function A(Δa). The experimental procedure starts at loading a specimen up to K under a constant u, and then the specimen is unloaded measuring the compliance (COD)/(LOAD) to calculate the crack length. By changing the level of K, a total of 28 tests have been carried out. The K-Δa curve obtained indicated a rapid increase in K at small Δa, followed by a gradual decrease in its increasing rate, and finally levelling off of K above Δa=1cm. From this K-Δa curve, the A(Δa) was obtained and found to increase rapidly at small Δa and level off above Δa=1cm.
Through various simulations by a computer, the proposed model was found to explain the behaviour of Sanjome Andesite specimen with a crack subjected to three-point-bending under the condition of a constant u. It is remained for future research to verify the equation in the cases of creep and relaxation.
