The initial ten cycles of stress-strain loops at different mean stress and stress amplitude show the shifting of the hysteresis loop along the strain axis
with an increase in [[sigma].sub.m] and [[sigma].sub.a] shown in Figure 10.
With increasing number of cycles, the hysteresis loop slightly migrates along the strain axis
. The stress-strain responses during the first five cycles of the test are plotted in Figure 4.
According to the previous studies [14-16], the constitutive energy of the rocks is represented by the area between the complete stress-strain curve and the strain axis
, and the area of O[A.sub.1][A.sub.1]; is surrounded by the first loading curve, and the strain axis
can be defined as absorbed energy; the area of O,[A.sub.1][A'.sub.1] which is surrounded by the first unloading curve and the strain axis
can be defined as released energy.
[[epsilon].sub.1] = 1/2 ([DELTA] + [gamma]) maximum strain axis
6 by discrete displacements of measured values along the shear strain axis
as slip occurs.
The material properties are most easily interpreted on a logarithmic strain axis
so it is advisable to space the strains in the strain sweep so they will be evenly spaced on a log scale.
The path eventually intersects the horizontal strain axis
with an unrecoverable strain that is referred to as plastic strain.
The coefficients in (7) are now derived, as done by Sargin, by imposing the boundary condition; to this aim, three characteristic points of the stress-strain relationship are considered, namely, the normalized strain axis
origin x = 0, the normalized strain value at which the unconfined concrete reaches its peak strength x = 1, and the collapse normalized strain of the confined concrete x = [x.sub.u].
The sample was placed between the polarizer and the quarter-wave plate with their axes at 45[degrees] to the strain axis
in the specimen (13).
Because [e.sup.C + [delta]]([e.sup.[gamma][epsilon]] - 1) = [e.sup.C]([e.sup.[gamma]([epsilon] + [delta]/[gamma])] - [e.sup.[delta]]), varying C implies stretching or shrinking of the curve on the strain axis
, without altering the origin of the plot.
Figures 7 and 8 illustrate typical (4 x 4 [[micro]meter]) SFM images obtained along the principal tensile strain axis
(oriented at [approximately]40 [degrees] of the shear direction for [Gamma] = 0.5 as shown in [ILLUSTRATION FOR FIGURE 1 OMITTED]): collective nanocracks (10-100 nm in width) perpendicular to the tensile strain axis
are observed going through stacks of edge-on lamellae [ILLUSTRATION FOR FIGURE 7 OMITTED] and through stacks of flat-on lamellae as well [ILLUSTRATION FOR FIGURE 8 OMITTED].
Since the strain at each material element is proportional to time, the time axis can be re-scaled into a strain axis
, thereby producing a stress-strain plot for each material element.