# Fracture Properties of Concrete in Dry Environments with Different Curing Temperatures
## 3 Results
### Fracture Energy  
Fracture energy (\(G_{\text{F}}\)) represents the energy required to generate new cracks per unit area during crack propagation, which is applicable to energy release rate criterion. The simplest method to calculate fracture energy is the fracture work method. Thus, the fracture energy can be evaluated using Equation (1). Note that for a specimen that is not large, the effect of its weight is negligible. Thus, the own weight of the specimen was ignored when evaluating the fracture energy. Besides, the fracture experiment can never reach the zero load level [30]. Therefore, the far-tail constant value was usually used to determine the true fracture energy [31]. In the present paper, the fracture experiments did not stop before the unloading zone of the load-CMOD curve appeared a full tail. The part that was not measured was extended inversely by the fit-best expression in the evaluation of \(G_{\text{F}}\). \[G_{\text{F}}=\frac{W}{B(h-a_{0})}\, \tag{1}\]  
where \(W\) is the fracture work which equals the area below the measured splitting force against CMOD curve; \(a_{0}\) is the length of pre-crack; \(B\) and \(h\) represent the thickness and height of wedge splitting specimen, respectively. Figure 4 shows the fracture energy for concrete exposed to dry environments with different temperatures as a function of the age. In this figure, each point denotes the mean value of fracture energy evaluated by the three companion wedge splitting specimens, and the error bars are not presented to avoid displaying a pell-mell plot. In any case, the difference between one replicate and the mean of the same group was not more than 10% concerning the mean. It can be seen from Figure 4 that the concrete fracture energy increased rapidly during the first 3 d, irrespective of the curing conditions investigated. Over time, fracture energy kept increasing at a  
Figure 4: Fracture energy for concrete exposed to dry environments with different temperatures. reduced rate and gradually stabilized when the age was large enough. For instance, in the case of 5 \({}^{\circ}\)C, the fracture energy was 130.4 N\(\cdot\)m\({}^{-1}\) after 3 d of hydration, 157.2 N\(\cdot\)m\({}^{-1}\) after 7 d of hydration, 174.4 N\(\cdot\)m\({}^{-1}\) after 14 d of hydration, 189.4 N\(\cdot\)m\({}^{-1}\) after 28 d of hydration, and 204.7 N\(\cdot\)m\({}^{-1}\) after 60 d of hydration. The value of fracture energy at 60 d was 8.1% greater than that at 28 d. It means that the fracture energy continuously improved with the increase of age and the growth rate was still relatively great. In other words, in the case of 5 \({}^{\circ}\)C, 60 d of curing time were not sufficient to make the concrete achieve the stable state and there was a lot of un-hydrated cement inside the concrete. A similar phenomenon was observed under elevated temperature, but the fracture energy tended to reach a plateau value in a shorter time. Typically, for 60 \({}^{\circ}\)C, fracture energy was 173.7 N\(\cdot\)m\({}^{-1}\) after 3 d of hydration, 194.4 N\(\cdot\)m\({}^{-1}\) after 7 d of hydration, 207.7 N\(\cdot\)m\({}^{-1}\) after 14 d of hydration, 220.8 N\(\cdot\)m\({}^{-1}\) after 28 d of hydration, and 221.7 N\(\cdot\)m\({}^{-1}\) after 60 d of hydration. Obviously, in this case, the growth rate of fracture energy decreased significantly after 14 d and even stopped increasing after 28 d. At high curing temperature, the shorter stable time is mainly due to a higher temperature accelerating the hydration reaction rate of cement. Figure 4 also reveals that in the early stage, the fracture energy of concrete increased significantly with the increasing temperature; but after 28 d of hydration, the curing temperature had the opposite effect on the fracture energy, that is, the larger later-age value of fracture energy was measured by concrete exposed to the lower temperature, and vice-versa.