Effect of a nonuniform temperature field on the distribution of the residual stresses with frontal hardening

Klychnikov, L. V.; Davtyan, S. P.; Khudyaev, S. I.; Enikolopyan, N. S.

doi:10.1007/bf00608342

Cited by 7 publications

(7 citation statements)

References 1 publication

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“…The constitutive relations are derived by differentiating the energy relation with respect to the stress tensor components and are written then in the finite form. The proposed approach to a construction of the physical equations occupies an intermediate position between the models of instantaneously elastic relaxation or phase transition [4][5][6] and the models based on the postulates of the non-isothermal viscous elasticity [7][8][9]. The properties of a solidifying material appear to be smeared out over time and space, which qualitatively agrees with the experimental data.…”

Section: Introductionsupporting

confidence: 61%

“…In the context of this problem, we shall demonstrate that relation (6) provides an appropriate qualitative description of the deformation behavior of a polymeric material during the relaxation transition under different conditions of thermomechanical loading. For the sake of simplicity we also suppose that in the course of one and the same process cooling and heating are conducted with the same constant rate.…”

Section: Model Problem: Analytical Description Of the Simplest Modes mentioning

confidence: 99%

“…Then, at a constant temperature T = T 2 the specimen is loaded by the stress σ 0 , which is held constant up to the time t 6 . In this case, for the state 3 we have σ 3 = σ 0 , N 3 = 1, and from relation (6) we get…”

Section: Model Problem: Analytical Description Of the Simplest Modes mentioning

confidence: 99%

“…3). At stages 4-5, the degree of conversion N decreases from 1 (at T 4 = T g1 ) to zero (at T 5 = T g2 ), following the characteristic law defined by (7-9) and according to (6) we have…”

Section: Model Problem: Analytical Description Of the Simplest Modes mentioning

confidence: 99%

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Models of thermomechanical behavior of polymeric materials undergoing glass transition

et al. 2012

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The phenomenological models of the thermomechanical behavior of polymeric materials in a temperature range including the relaxation transition from the highly elastic to the glassy state (vitrification) and the reverse transition (softening) are considered. A model based on the interpretation of the glass transition as a process of gradual increase in intermolecular bonds in the polymer network, "freezing" the current strain with decreasing temperature is developed. A scalar parameter is introduced-the "degree of vitrification," to establish the quantitative dependence of the relaxation transition completion by temperature. Constitutive relations of thermomechanical behavior of vitrifying polymers in uniaxial and complicated stress states in the "elastic approximation" simplification are obtained. A system of experiments for the identification of the proposed model material functions and constants is formulated and implemented. Analytical model problems are solved, clearly illustrating the mechanism for generation of technological and residual stresses in glass polymers in non-uniform cooling.

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Section: Introductionsupporting

confidence: 61%

Section: Model Problem: Analytical Description Of the Simplest Modes mentioning

confidence: 99%

Section: Model Problem: Analytical Description Of the Simplest Modes mentioning

confidence: 99%

“…3). At stages 4-5, the degree of conversion N decreases from 1 (at T 4 = T g1 ) to zero (at T 5 = T g2 ), following the characteristic law defined by (7-9) and according to (6) we have…”

Section: Model Problem: Analytical Description Of the Simplest Modes mentioning

confidence: 99%

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Models of thermomechanical behavior of polymeric materials undergoing glass transition

et al. 2012

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“…A large number of studies have reported on modeling these effects for the case of small deformations. Two formal groups could be derived from the studies: the models of instantaneous elastic relaxation or phase transition (Bartenev and Barteneva 1992, Bugakov 1989, Klychnikov et al 1980) and the models based on the postulates of the non-isothermal viscous elasticity (Bolotin 1972, Il'ushin and Pobedria 1970, Moskvitin 1972. The approach used in the present study (Matveenko et al 2012) occupies an intermediate position between these two.…”

Section: Introductionmentioning

confidence: 99%

Post-buckled equilibrium state of axially compressed polymeric rod in glass and rubbery transitions

Tikhomirova

Trufanov

2016

Mech Adv Mater Mod Process

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Background: Glass and rubbery transitions under cooling and heating of polymeric materials underlie a shape memory effect, that is a material ability to save temporarily the deformed shape and restore the original one under the external influence. The present work aims to model the shape memory effect for an axially compressed polymeric rod in its post-buckled equilibrium state, which is the generalization of Euler's elastica for a glassy material case. Methods: For modeling, we use a new type of constitutive relations describing the thermomechanical behavior of amorphous polymers over a wide temperature range. To define the model parameters for lightly-linked epoxy resin a series of experiments was conducted using the Dynamic Mechanical Analyzer. Results: Post-buckled states of an epoxy rod equilibrium during the temperature change have been found from numerical simulation. The obtained results illustrate the shape memory effect in case of axially compressed rod buckling. Conclusion: The thermomechanical shape-memory cycle includes the stages of deformation development and preservation and the subsequent recovery of the initial shape. According to the obtained results, maximum deflection corresponds to the first loading step at the rubbery material state, because the elastic modulus is very low. During cooling under a constant load the deformation remains constant. After unloading in glassy state the deflection decreases by a small value, because the glassy elastic modulus significantly exceeds the rubbery one. During subsequent heating the rod recovers its initial undeformed shape.

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Problems of mechanics in the technology of composite materials

Tomashevskii

1982

Mech Compos Mater

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Effect of a nonuniform temperature field on the distribution of the residual stresses with frontal hardening

Cited by 7 publications

References 1 publication

Models of thermomechanical behavior of polymeric materials undergoing glass transition

Models of thermomechanical behavior of polymeric materials undergoing glass transition

Post-buckled equilibrium state of axially compressed polymeric rod in glass and rubbery transitions

Problems of mechanics in the technology of composite materials

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