A two-level system with induced transitions as a model of stress relaxation

Högfors, Christian; Kubát, J.; Rigdahl, Mikael

doi:10.1007/bf01332604

Cited by 5 publications

(6 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In earlier works [6][7][8] it has been shown that the cooperative model gives the time-dependent stress during the relaxation as s~ e -ts/~ -a(t) = EeS/13 1…”

Section: Determination Of the Dynamic-mechanical Propertiesmentioning

confidence: 99%

“…T s=l --where 7: is the relaxation time, sm the maximum size (the multiplicity) of the phonon clusters, fl a parameter determining the shape of the relaxation curve and z a constant related to the physical parameters of the system converting the stress rate &r/dt to pure numbers [8]. In eq.…”

Section: Determination Of the Dynamic-mechanical Propertiesmentioning

confidence: 99%

“…(1) [7]. In [8] it has been shown that both a model based on only a--+ b transitions and an alternative cooperative model, in which transitions between the two energy levels can occur in both directions (ae:~b), produce the same relaxation law. Physically, it may be visualized that a transition is associated with emission of a phonon.…”

Section: Introductionmentioning

confidence: 97%

“…These phonons, which form clusters of different sizes, induce transitions in other elements; the corresponding transition probability being related to the size of the phonon cluster. The cooperative model thus has a spectral character, with the relaxation times determined by the multiplicity of the elementary events (cluster size) [8].…”

Section: Introductionmentioning

confidence: 99%

“…In order to provide a more appropriate description of the relaxation process, a cooperative two-level model has been developed [6][7][8]. According to this model transitions between the upper (a) and the lower (b) energy level 292 are responsible for the relaxation process and the transition of a given element can induce transitions in other elements.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Evaluation of the dynamic-mechanical properties of solids from a cooperative model for stress relaxation

Högfors

Kubát

et al. 1988

Rheol Acta

Self Cite

View full text Add to dashboard Cite

For many solid materials the stress relaxation process obeys the universal relation F = -(da/d In t)max = (0.1 -t-0.01) ((70 --0"i) , regardless of the structure of the material. Here a denotes the stress, t the time, a o the initial stress of the experiment and (7 i the internal stress. A cooperative model accounting for the similarity in relaxation behaviour between different materials was developed earlier. Since this model has a spectral character, the concepts of linear viscoelasticity are used here to evaluate the corresponding prediction of the dynamic mechanical properties, i.e. the frequency dependence of the storage E' (o)) and loss E" (o)) moduli. Useful numerical approximations of E'(~o) and E" (m) are also evaluated. It is noted that the universal relation in stress relaxation had a counterpart in the frequency dependence of E' (co). The theoretical prediction of the loss factor for high-density polyethylene is compared with experimental results. The agreement is good.

show abstract

“…In earlier works [6][7][8] it has been shown that the cooperative model gives the time-dependent stress during the relaxation as s~ e -ts/~ -a(t) = EeS/13 1…”

Section: Determination Of the Dynamic-mechanical Propertiesmentioning

confidence: 99%

Section: Determination Of the Dynamic-mechanical Propertiesmentioning

confidence: 99%