The mathematical model of crack growth given by the following equation is proposed,
d(Δa)/dt=K
n/A(Δa)
where Δ
a 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(Δ
a). 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-Δ
a curve obtained indicated a rapid increase in
K at small Δ
a, followed by a gradual decrease in its increasing rate, and finally levelling off of
K above Δ
a=1cm. From this
K-Δ
a curve, the
A(Δ
a) was obtained and found to increase rapidly at small Δ
a and level off above Δ
a=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.
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