Abstract
Combined measurements of shear-stress relaxation and differential dynamic storage and loss shear moduli G′ and G″ following a single-step shear strain of 0.4, as well as measurements of dynamic moduli in on-off strain and stress histories, have been made on styrene-butadiene rubber (type 1502) filled with carbon black (N299) at loadings of 40, 50, 60, and 70 phr, with 10 phr Sundex 790 oil. Both cured and uncured compounds were studied at temperatures of 25.0° and −0.5°C respectively. The maximum oscillatory shear strain was 0.005, and the frequency was from 0.4 to 1.8 Hz. The storage shear modulus G′(ω, 0) measured without imposition of static strain was approximately proportional to the fourth power of the volume fraction of black. With imposition of single-step strain, the differential storage modulus G′(ω, γ; t) fell 25% to 35% but slowly recovered somewhat while the strain was maintained for 4 to 5 h. During this period, the static stress relaxed continuously. At the highest content of black, the drop in log G′ was the least, and the final recovery was closest to the initial value of G′(ω, 0). In on-off experiments on uncured compounds, when the strain was “on” for 250 s and then “off” (either stress or strain returned to zero), G′ decreased when the strain was imposed as before and decreased further when it was removed. In the “off” state, G′ recovered partially but did not attain the initial value of G′(ω, 0) even after 7 d. In on-off experiments on cured compounds, removal of stress caused G′ to either increase or decrease depending on the content of black; in any case, in the “off” state, G′ recovered completely to its initial value. Other strain histories involved on-off sequences with different “on” periods and multiple on-off sequences with different “on” periods and multiple on-off sequences. The results are interpreted in terms of a network of black particle aggregates whose contacts can slowly rearrange even in the absence of stress as shown by stress relaxation at very small strains in earlier studies. In large strains, it is postulated that some contacts are broken but can partially reform, especially in the stress-free state; the rate of reformation is similar to that of small-strain stress relaxation. Only in cured compounds is the network fully recovered, presumably because in these the particles are imbedded in a crosslinked matrix and have crosslinked bridges that facilitate reestablishment of interparticle contacts, whereas in uncured compounds the matrix has no crosslinks and the bound rubber on adjacent particles may be merely entangled.
Behavior of Liquefied Sands Under Extremely Large Strain Levels in Cyclic Torsional Shear Tests
