# Fatigue in Concrete under Low-Cycle Tensile Loading Using a Pressure-Tension Apparatus
## 2 Materials and Methods  
A total of 22 standard concrete cylinders (100 mm \(\times\) 200 mm) were cast and tested. The concrete used in the cylinders was made using the mix design shown in Table 1. The specimens were molded and compacted based on ASTM C31 [7]. After 24 h of curing in their molds, the cylinders were removed and stored in ambient laboratory conditions for over 2 years. In a pressure-tension test, a destructive test method that specifically evaluates the tensile capacity of concrete, a cylindrical steel jacket is used to hold a concrete cylinder serving as the specimen. A rubber O-ring is used at each end to keep an airtight seal and prevent possible gas leakage. With the ends then left free, gas pressure is incrementally applied to the curved surface of the concrete cylinder until the specimen ultimately fractures across a single plane perpendicular to the axis of the concrete specimen. The value of gas pressure at fracture thus corresponds to the maximum tensile capacity of the concrete. Compressed air is used as the loading medium for all specimens in this experimental work. The air was pressurized using a portable air compressor with a maximum available pressure of about 17 MPa, which was stored in a pressurized gas vessel attached to the compressor and the testing machine. A variable check valve was used to keep the pressure head constant in order to minimize inconsistency in the test caused by pressure variance in the storage tank. A needle valve was used as the controller for the flow rate of the compressed gas into the testing chamber. The valve was operated by a mechanical actuator which was controlled using custom software and monitored using a digital acquisition device (DAQ). Measurement of pressure within the test chamber was obtained using a digital pressure transducer directly adjacent to the chamber, which was used as a control input in the software. The pressure transducer had a measured error of \(\pm\)0.05 MPa. The DAQ had a sensing \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Amount** & **Unit** \\ \hline Water & 15.866 & kg \\ Cement & 29.282 & kg \\ Coarse aggregates & 72.872 & kg \\ Fine aggregates & 79.093 & kg \\ Superplasticizer & 0.146 & Liter \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mix design of the concrete specimens for this study (water-to-cement ratio = 0.45). resolution of approximately 0.1 s [2; 6]. All pressure-time plots were recorded and stored, and the data point immediately preceding failure was used as the failure load. The implemented control algorithm is a modified proportional integral derivative function which automatically varies the valve position based on the detected error between the measured pressure and the set point. The set point is an arbitrary time-dependent function, and all tests carried out in this study used a uniformly increasing pressure-time signal with a rate of about 0.02 to 0.03 MPa/second, comparable to loading rates in both ASTM C 496 and ASTM C 33 [6]. A higher rate of about 0.10 to 0.15 MPa/second was used during the cyclic loading of the specimens to expedite the process. Rubber O-rings with a diameter of 10 mm were used to seal the interface between the test chamber and the concrete sample (Figure 1). One or two layers of polyvinylchloride tape was applied on both ends of the cylinder to provide a better seal between the O-rings and the cylinder, which occasionally had voids or deterioration defects that could cause leakage around the O-rings. The O-rings were torqued with a series of six lug nuts bearing on a steel plate in a manner that applied equal pressure on them and ensured a tight seal for the loading gas. Pressure tension testing is affected by the moisture content of the specimens; samples with a higher water content fail at a higher tensile resistance as compared to dry specimens [2]. For dry samples, the failure mode in pressure tension testing changes from a single crack to a volumetric failure at a lower applied tensile stress [2; 8].