load cell was carefully calibrated to measure the loading force, F. With this data, the stress σ, strain ε, and elastic modulus E, were calculated from the following three-point bend equations7
: Equation 1 and Equation 2 thus Equation 3 Results
where L is the support span, b is the specimen width as viewed by the loading head, and d is the specimen depth as viewed by the loading head.
In a typical test, a specimen was placed into the three- point bend apparatus and several measurements of the elastic modulus were first performed at room temperature. The load was kept well below that necessary to break the specimen. Then, the oven was turned on and the oven control system was set such that the temperature of the specimen increased at an approximately constant rate. The heating rate is one of the experimental variables in the present study. Approximately once every minute dur- ing heating (for a heating rate of 8C/min [14.4F/min]), the specimen was loaded and unloaded in order to measure the elastic modulus as a function of temperature. Again, the maximum load was kept to a sufficiently low level that the specimen did not break. A certain minimum load was maintained in order to ensure good contact between the specimen and the loading head. A test concluded when the specimen reached a temperature of approxi- mately 500C (932F). At that temperature, the strength of the bonded sand vanishes because most of the binder has decomposed. Up to 80 elastic modulus measurements were performed in each test.
Validation
In order to validate the present experimental setup and mea- surement procedures, at both room temperature and elevated temperatures, tests were performed using a material with a well-known elastic modulus. The material chosen was ASTM 304 stainless steel. Figure 5 compares the present elastic modulus measurements with the measurements of Sakumoto et al.10
Good agreement can be observed at both
room temperature and 400C (752F). Error Analysis
A simple root-sum-squares (RSS) error analysis was per- formed to estimate the error in the present elastic modulus
International Journal of Metalcasting/Fall 10
Figure 5. Comparison of present measurements of the elastic modulus of ASTM 304 stainless steel as a function of temperature with data from Sakumoto et al.10
11 Stress-Strain Curves
In order to obtain a few complete stress-strain curves, preliminary experiments were conducted in which the load was increased until the specimens broke. The speci- mens were heated from room temperature to the desired test temperature at a rate of 8C/min (14.4F/min). Once the specimens reached the test temperature, the load was increased immediately without any further change in the temperature. Representative stress-strain curves at four different test temperatures are provided in Figure 6. A straight line was fit to the elastic portion of the stress- strain curves, with the slope representing the measured elastic modulus.
measurements. Table 2 shows the sources of error in the individual measurements for a room temperature example. For the specimen deflection and the loading force, only the largest measured values (in the elastic regime) are listed. Table 3 shows the resulting ranges and errors in the elas- tic modulus. It can be seen that the measurement of the specimen deflection is the single largest source of error. The specimen width measurement is also a relatively large source of error, which can be attributed to the roughness of the top surface of the bonded sand specimens. Overall, the error in the present room temperature elastic modulus measurement is estimated to be ±1.5%. A similar accuracy can be expected at elevated temperatures.
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