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- W2330157730 abstract "In the present paper, an equation of nonlinear superposition principle proposed by Schapery is simplified so that the dependences of equilibrium term of relaxation modulus on strain are identical with that of transient term, and this equation is named general model (model G). From this equation, the several nonlinear constitutive equations can be derived as follows.(1) Time-strain factorized model(a) Perfect factorized model (model I)……nonlinearity depends on present strain.(b) Imperfect factorized model (model II)……nonlinearity depends on strain history.(c) Mixed factorized model (model M)……to combine model I with model II.(2) Time-strain reduced model (model III)……the strain to change time scale.(3) General model (model G)……to combine model M with model III.It is difficult to assign nonlinear viscoelastic property of a given material to one of the above five models by single step stress relaxation tests. In particular, it is emphasized for power law's materials.By two step stress relaxation tests, nonlinear characteristics of materials are classified into five models as follows:The time tN, when effects of the first strain e1, decay and hence two step relaxation stress σ2(t′) under e2(=e1+Δe) meets single step relaxation stress σ1(t′) at e2, depends on only t1 (input time of Δe) for the time-strain factorized models. For other models, tN depends on e1, e2 and t1. In each case of model I, II and M, |_??_σ1/_??_e2| is linear to e1, independent of e1, and nonlinear to e1, respectively. The another useful properties are that Δσ/e1 (Δσ=σ2-σ1) decrease with e2, e1, and both e1 and e2, respectively, for model I, 11 and M. The stress increment δσ at t1 has only linear relation to Δe for the model III, while δσ is nonlinear to all e1, e2 and t1 for the model G.The theory is tested for some polyethylenes at room temperature. The samples have nearly power law's properties in single step stress relaxation behavior. The measured values of tN have properties of the model III or G. Only when Δe>0 and e1_??_2%, the experimental curves of o2(t′) agree well with the calculated curves from model III. When e1=3% and Δe>0, the calculated values are less than the experimental values. When Δe<0, the calculated values are greater than experimental values. In this case, if nonlinearized function ae (e) is provided with property of hysteresis, the theory of model III may be improved to approach the experimental results." @default.
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- W2330157730 date "1976-01-01" @default.
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- W2330157730 title "TWO STEP STRESS RELAXATION OF MODIFIED BOLTZMANN'S SUPERPOSITION PRINCIPLE AND ITS PRACTICAL APPLICATIONS" @default.
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- W2330157730 doi "https://doi.org/10.2115/fiber.32.6_t227" @default.
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