The opening of the crack mouth opening displacement
(CMOD) was measured by the clip gauge.
At the beginning of the inverse analysis, therefore, [[tau].sub.f,max] is assumed, then the section analysis for the section with a notch can be conducted through an iteration procedure, finding the neutral axis depth for a given crack mouth opening displacement
at the bottom of the notch by satisfying force equilibrium along the longitudinal axis.
Figure 8 presents the variations of the critical crack mouth opening displacement
([CMOD.sub.c]) and the critical crack tip opening displacement ([CTOD.sub.c]) of the three-point bending beam specimens of the concrete containing nano-Si[O.sub.2] with different values of relative notch depth, respectively.
This test method, defined by ASTM E1820, uses a measured crack mouth opening displacement
to estimate growing crack size.
where [delta] is crack tip opening displacement; P is applied force; S is span between outer loading points in three point bend test; W is effective width of test specimen; [V.sub.p] is plastic component of crack mouth opening displacement; E is elastic modules; [sigma.sub.s] is yield strength; a is original crack length; z is distance of the crack opening gauge location above the surface of the specimen; B is specimen thickness; [micro] is Poisson's ratio; [Florin] or [Guilder] is a mathematical function of (a/W).
The red points represents the maximum applied forces ([P.sub.c]), and the Plastic crack mouth opening displacements ([V.sub.p]) can also obtained from the figure, as listed in Table 1.
The recorded maximum load [P.sub.u], the recorded crack mouth opening displacement
CMODc at [P.sub.u], the calculated crack tip opening displacement [CTOD.sub.c] based on (20), the initial cracking load Pini determined by graphical method, the calculated residual Young's modulus E based on (18), the double-K fracture parameters, that is, [k.sup.ini.sub.Ic] and [K.sup.un.sub.Ic], and the residual fracture energy [G.sub.F] are summarized in Table 1.
The crack mouth opening displacement
(CMOD) was measured by a TML resistive full bridge transducer astride the notch.
In the Figure 2, it is observed the general configuration of the test that was conducted under control of the crack mouth opening displacements
(CMOD--crack mouth opening displacement) using, for this purpose, an electrical extensometer of the clip gauge type.