# Fracture Properties of Concrete in Dry Environments with Different Curing Temperatures
## 3 Results
### Effective Fracture Tougliness  
Fracture toughness characterizes the cracking resistance of concrete, which is usually used for the stress intensity factor criterion. A smaller value of fracture toughness indicates that the concrete is apt to fracture abruptly before the occurrence of obvious unrecoverable deformation. The effective fracture toughness (\(K_{\rm IC}\)) is calculated with the following equation [33]:  
\[K_{\rm IC}=\frac{F_{\rm smax}}{B\sqrt{h}}\frac{3.675[1-0.12(\alpha-0.45)]}{(1- \alpha)^{3/2}}\,\ \ \ \alpha=\frac{a_{\rm c}}{h}\, \tag{2}\]  
where \(F_{\rm smax}\) is the horizontally component of peak load; the meaning of \(h\) and \(B\) is the same as in Equation (1); \(a_{\rm c}\) is the critical effective crack length, which is evaluated by the following equation [33]:  
\[a_{\rm c}=(h+h_{0})\left(1-\sqrt{\frac{13.18}{9.16+CMOD_{\rm c}\cdot E\cdot B/F_ {\rm smax}}}\right)-h_{0}\, \tag{3}\]where \(h_{0}\) is the thickness of clip gauge holder; \(CMOD_{\text{c}}\) is the crack opening displacement corresponding to \(F_{\text{smax}}\); \(E\) is the tensile Young's modulus. Figure 5 depicts the test results of effective fracture toughness against age under four curing conditions investigated. Although each point in Figure 5 denotes the mean values of the three replicate samples, the error bars are not shown again for the sake of brevity. Interestingly, the scattering of data observed in effective fracture toughness was smaller when compared with the case of fracture energy. During the unstable propagation, redundant cracks appeared and the propagation path of the main crack became more random; however, the energy consumed by these extra cracks was difficult to calculate, so these energies were ignored when evaluating fracture energy. As a result, the fracture energy produced larger randomness. As can be presented in Figure 5, for each curing condition investigated, the effective fracture toughness was closely related to age and its value increased with age, which was the same as fracture energy with age. In the beginning, effective fracture toughness improved significantly with the growing age, because at this stage the reaction rate of cement hydration was quite fast. The growth rate increased by degrees and then reduced after maximizing. Subsequently, effective fracture toughness increased slightly with age at a reducing rate and finally reached a constant as the age was further extended. Typically, for 5 \({}^{\circ}\)C, the effective fracture toughness continuously increased from 0.889 MPam\({}^{0.5}\) after 3 d of hydration to 1.043 MPam\({}^{0.5}\) after 7 d of hydration, 1.113 MPam\({}^{0.5}\) after 14 d of hydration, 1.204 MPam\({}^{0.5}\) after 28 d of hydration, and finally 1.306 MPam\({}^{0.5}\) after 60 d of hydration, with a significant increase of 0.417 MPam\({}^{0.5}\) or 46.9%. Similarly, for 60 \({}^{\circ}\)C, the effective fracture toughness was 1.164 MPam\({}^{0.5}\) at the age of 3 d, 1.304 MPam\({}^{0.5}\) at the age of 7 d, 1.395 MPam\({}^{0.5}\) at the age of 14 d, 1.490 MPam\({}^{0.5}\) at the age of 28 d, and 1.509 MPam\({}^{0.5}\) at the age of 60 d. The fracture toughness at the age of 60 d was only 1.3% greater than that at the age of 28 d. This also demonstrated that it takes a shorter time for the effective fracture toughness to reach the constant value under higher temperatures. Figure 5 also shows that, as observed in the fracture energy, there was also a temperature crossover effect in the effective fracture toughness of concrete in dry environments. As the curing temperature increased, concrete effective fracture toughness improved dramatically during the early ages, but this situation did not hold after 28 d, in which greater ultimate value of effective fracture toughness was acquired from the concrete kept at a lower temperature, and vice-versa.