Stress-induced softening

FIGURE 1.5 Stress-induced softening of a carbon black-filled vulcanizate of a copolymer of styrene and butadiene (25 75) —, stress-strain curve of a coresponding unfilled vulcanizate (from Tobolsky and Mark, 1971). 

Equation (1.5) has also been used to estimate the force at which a rubber molecule will become detached from a particle of a reinforcing filler (e.g., carbon black) when a filled rubber is deformed (Bueche, 1960, 1961). In this way, a general semiquantitative treatment has been achieved for stress-induced softening (Mullins effect) of filled mbbers (shown in Figure 1.5). 

M. Dadfamia, B. P. Somerday, P. Sofronis, and I. M. Robertson, On the Small Scale Character of the Stress and Hydrogen Concentration Fields at The Tip of an Axial Crack in Steel Pipeline Effect of Hydrogen-Induced Softening on Void Growth, Int. J. Mater. Res., to appear (2008). 

Annealing. Annealing has two different purposes to relieve stresses induced by hot- or cold-working, and to soften the steel to improve its machinability or formability. It may involve only a subcritical heating to relieve stresses, recrystallize cold-worked material, or spheroidize carbides alternatively, it may involve heating above the upper critical temperature (A ) with subsequent transformation to peadite or, less commonly, dkectiy to a spheroidized stmcture on cooling. 

At small strains, polymers (both amorphous and crystalline) show essentially linear elastic behavior. The strain observed in this phase arises from bond angle deformation and bond stretching it is recoverable on removing the applied stress. The slope of this initial portion of the stress-strain curve is the elastic modulus. With further increase in strain, strain-induced softening occurs, resulting in a reduction of the instantaneous modulus (i.e., slope decreases). Strain-softening phenomenon is attributed to uncoiling... 

The procedure initially developed by Lee (1974) and later refined by Chaney (1979,1980) and Makdisi et al. (1978) involved the concept that permanent seismic deformations of a slope may be computed by evaluating dynamic-induced softened pseudo slope stiffness values for soil elements with the resultant settling of the slope to a new condition being compatible with pseudo or apparent stress-strain properties of the soils comprising the slope. Figure 11.17 shows an example of the use of the permanent deformation method for evaluating the deformation of the continental slope off Flaifa, Israel, under earthquake loading from a transform fault on the Jordan rift valley. 

Stresses induced by the threads in addition to stress from uncured adhesive outside the joint produce very high stress levels in the part. Surface preparation methods to alleviate stress cracking include abrading the surface with sandpaper, cleaning with isopropyl alcohol, and assembhng the parts immediately after application of alcohol.The use of an incompatible adhesive for the substrates can produce stress cracks. The part surface softens and weakens, creating a crack. Joining materials with different... 

Thus, as indicated above, in the submicron-sized 3Y-TZP ceramic, the stress-induced cyclic hardening, due to transformation taking place, was higher than under static deformation. NanocrystaUine 3Y-TZP softened cyclically, due to the formation of a large number of microcracks. In the submicron structures, this observation basically reflects the effects of dislocations and dislocation-dislocation interactions. In the nanocrystalline 3Y-TZP ceramic, this greater ability to accommodate plastic strain is probably due to grain-boundary sliding, since in nanocrystalline structures dislocations cannot move, because shp distances are on an atomic scale (hke the dimensions of dislocations themselves). 

The Mullins effect [79] is a strain induced softening phenomenon, which is associated mainly with a significant reduction in the stress at a given level of strain during the unloading path as compared with the stress on initial loading in stress-strain cyclic tests [80] (Fig. 18). 

Qi HJ, Boyce MC (2004) Constitutive model for stretch-induced softening of the stress-stretch behavior of elastomeric materials. J Mech Phys Solids 52 2187-2205... 

Qi J H and Boyce M C (2004) Constitutive model for stretch-induced softening of the stress-stretch behavior of elastomeric materials, J Mech Phys Solids 52 2187-2205. Drozdov A A and Dorfmann A (2003) A micro-mechanical model for the response of filled elastomers at finite strains, Int J Plasticity 19 1037-1067. 

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