Strain saturation

The isolation of cyclopropenones and their undoubtedly increased stability compared to the less-strained saturated cyclopropanones might well be attributed to the validity of the above symbolism of aromatic cyclopropenium contribution to the ground state of 7. It should nevertheless be clear, that the information available on the electronic structure of cyclopropenones demands certain refinements of this very useful qualitative concept. 

Krivdin and Kuznetsova used coupling constants to study strained, saturated heterocycles in an approach... 

The ubiquitous and reversible formation of radical cations in photoelectrochemical transformations allows pericyclic reactions to take place upon photocatalytic activation since the barriers for pericyclic reactions are often lower in the singly oxidized product than in the neutral precursor. For example, ring openings on irradiated CdS suspensions are known in strained saturated hydrocarbons [176], and formal [2 -I- 2] cycloadditions have been described for phenyl vinyl ether [ 177] and A-vinyl carbazole [178]. The cyclization of nonconjugated dienes, such as norbomadiene, have also been reported [179]. A recent example involves a 1,3-sigmatropic shift [180]. 

The reaction is extremely useful for preparing strained cycloalkenes, particularly cyclobutenes. The success of such reactions stems from the fact that they are not ring forming, but involve contraction of a less-strained saturated ring. 

The great number of possible elementary reactions in free radical polymerizations explains why only a fraction of the many thermodynamically polymerizable groups can be converted free radically to un-cross-linked high-molar-mass polymers. Vinyl, vinylidene, and acrylic compounds, as well as some strained saturated rings, belong to this fraction. Allyl compounds only polymerize to branched oligomers, but diallyl and triallyl compounds produce high-molar-mass cross-linked networks. 

The accumulated plastic strains during the cycles were continuously recorded after unloading for the nanocrystalline and the submicron-sized 3Y-TZP ceramics (see Fig. 7.45). This accumulated plastic strain saturated after 100 cycles or so, but was obviously different in nature and extent than that of metal. Such strain accumulation would eventually lead to failure. Under a 50 MPa maximum cyclic-tensile stress, very little strain accumulation was found under fully-cyclic loading... 

The back stress tensor leads to kinematic hardening and must be used to enforce the remanent strain saturation conditions. The approach used to determine the back stresses is based on the assumption that the internal state of the ferroelastic material is completely characterized by the components of the remanent strain tensor. Cocks and McMeeking (1999) and Landis (2002). This assumption leads to the identification of a remanent potential,, such that the back stresses are derived from the... 

Figure 1. The remanent strain saturation curve dividing remanent strain space into regions that are attainable and unattainable by a polycrystal assembled from randomly oriented tetragonal single crystals. Only remanent strain states below the curve are attainable by such a material. The dots are numerical results from Landis (2003a) obtained using a micromechanical self consistent model, and the line is one divided by the function/given in Eqs. (2.7) and (2.8). The remanent strain invariants 4 and are defined in Eq. (2.5) and the results are normalized by the saturation strain in axisymmetric compression s. ...

Here, Wo is a characteristic level of back stress that primarily affects the initial slope of the uniaxial stress versus remanent strain curve, and m is another hardening parameter that controls how abruptly the strain saturation conditions are reached. Figure 2a illustrates the predictions of the effective stress versus the effective remanent strain from the constitutive law for uniaxial compression, pure shear strain, pure shear stress and uniaxial tension. It is interesting to note that the shear strain and shear stress curves do not coincide. This feature is due to the fact that the material can strain more in tension than in compression, and has been confirmed in micromechanical simulations. Figure 2b illustrates the uniaxial stress versus remanent strain hysteresis curves for two sets of the material parameters Wq and m. 

Due to this strain saturation effect, the stresses near the crack tip in the ferroelastic material increase severely. In fact, the numerical results suggest that very close to the crack tip the stresses have a 1 / /r radial dependence. Hence the crack tip stress intensity factor Kiup can be defined such that on the plane ahead of the crack tip... 

Landis, C.M., 2003a, On the strain saturation conditions in polycrystalline ferroelastic ceramics, to appear in Journal of Applied Mechanics. 

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