3.6         Cyclic Loading

 14.1 kg/m³ density specimen was displacement control tested. The displacement rate of this 0.6m cube specimen was 0.06m/min. The same specimen was loaded and reloaded nine times. The total strains for the nine test were 0.87%, 0.87%, 1.8%, 1.8%, 2.7%, 2.7%, 3.5% and 3.5% in sequence. The total and the middle third strains were calculated. The lateral strain was also calculated. The test was run using the Instron machine.

Results for Poisson’s ratio are shown in figure 3-45. Poisson’s ratio is calculated twice, one time for the total height and the other time for the middle third. It can be seen that the Poisson’s ratio is higher for the middle third. The second test gave higher Poisson’s ratio than the first test. After the second test Poisson’s ratio began to decrease. This happens to both the middle third and the total. Poisson’s ratio for the total height tends to level out.

Figure 3-46 shows the value of the initial modulus for all nine tests. The stiffness is slightly higher in the second test. After the second test the modulus began to decrease. There is a significant decrease in the middle third stiffness in the third test. The middle third stiffness tends to approach the total stiffness as the previous total strain increases. An explanation of that phenomenon could be the progressive damage applied  over the middle third portion.

Figure 3‑1 Effect of the Loading History on the Poisson’s Ratio

Figure 3‑2 Effect of the Loading History on the Initial Modulus

A series of cyclic loading tests were performed on four types of 0.05m cube EPS geofoam, type XI, type I, type VIII and type IX. The initial modulus value is shown for the first three cycles in figure 3-47. The specimens are loaded only to 30% of the strength at 5% strain. Equations for the initial modulus for different densities are shown on the charts. The symbol “x” refers to the density in kg/m³. “E” refers to the initial modulus in MPa. From the figure it can be seen that the initial modulus for the first loading is less than that of the second and third one. The second and the third cycles have almost the same initial modulus value.

Figure 3‑3 Pre Yield Cyclic Loading at 10%/min

Figure 3-48 shows the values of the initial tangent modulus for three cycles, each of them is loaded to stresses past yield. The initial tangent modulus in the first cycle is higher than that in the following cycles. The second and the third cycles have almost the same initial tangent modulus. The three cycles reached only 3% strain.

Figures 3-49 and 3-50 shows the values of the initial tangent modulus in MPa for EPS geofoam types XI, I, VIII and IX. The values are obtained from the equations shown in figures 3-48 and 3-49.

Figure 3‑4 Post Yield Cyclic Loading at 10%Strain/min

Figure 3‑5 Commercial EPS Subjected Pre Yield Cyclic Loading

Figure 3‑6 Commercial EPS Types Subjected Post Yield Cyclic Loading

Loading and unloading for more than three cycles did not decrease the initial tangent modulus than the value in the first cycle for any density. This statement is correct as long as the stresses are low. The results in figures 3-52 and 3-53 are for two different frequencies, 1Hz and 0.5Hz. The equations of the initial tangent modulus are shown on the figures for different densities. The “y” symbol refers to the initial tangent modulus in MPa, while the “x” symbol refers to the density in kg/m³. For both frequencies the initial tangent modulus is less than that in the first loading cycle.

Figure 3‑7 Cyclic Loading Effect, 0.5 Hz

Figure 3‑8 Cyclic Loading Effect, 1 Hz

0.6m cube type IX specimens were tested in load controlled cyclic loading. An initial stress value equal to 30% of the strength at 5% strain was applied. A 4kPa stress was applied for a large number of times in a sine curve pattern. The displacements of a typical three cycles are shown in figure 3-53. It can be seen that the displacement profile is the same for the three cycles. Large deformations appear in the top 0.025m.

 The stress strain curves for the three cycles combined are shown in figure 3-54. The curves for three cycles coincide with each other. The figure shows the equations for the total 0.6m height, and for the middle third and for the top 0.025m. Equations for the tangent lines are shown in the figures. The symbol “x” refers to the strain and the symbol “y” refers to the stress. The slope of the straight line is the tangent modulus in kPa. It can be seen that the tangent modulus of the top 0.025m is very low with respect to the middle third tangent modulus. The tangent modulus for the middle third portion is more than 50% higher than the modulus of the total height.

Figure 3-55 shows the stress strain curves of portions of a typical 0.6m specimen measured from the top surface. The tangent modulus is high when portions near the edge are excluded.

Figure 3‑9 Movement of Different Portions of Type IX EPS

Figure 3‑10 Portions of 0.6m Cube Subjected to Cyclic Loading

Figure 3‑11 Portions Measured from the 0.6m Cube under Cyclic Load