A model treating tensile deformation of semi-crystalline polymers

Semi-crystalline polymeric solids are usually in a state being built up of crystallites and an amorphous phase. A complex structure changing occurs in the polymer materials during the extension process. Uniaxial stretching of a semi-crystalline polymer sample causes the initial spherulitic structure to be deformed and then destroyed, later a fibrillar structure forms. Employing a video-control in the stretching device, we always measured true stress-true strain dependencies for constant strain rates. From the true stress-true strain curves, it is obvious that after a short range a strain softening occurs, followed by a hardening at large deformations. The true stress-strain dependencies clearly demonstrate that the tensile deformation of semi-crystalline polymers follows a common scheme with changes in the mechanism at critical strains. <br> <br>Our measurements of true stress-true strain relationships were always accompanied by recovery tests. By carrying out a step-wise stretching, interrupted by unloading-loading cycles, it is possible to determine for each imposed strain which part is irreversible and which part recovers. It was found that the recoverable, elastic strain is always limited. It reaches a maximum value exactly at critical strain C, the onset of fibrillation, and stays at this plateau value until critical strain D, the onset of disentangling. <br> <br>Apparently, the crystalline lamellae possess a blocky substructure, and the blocks can slide against each other. This provides the possibility for the crystallites in the sample to take up any imposed strain easily. A emi-crystalline polymer can be viewed as two interpenetrating systems, a skeleton of coupled crystal blocks intermingled with an entangled amorphous network. Both can accommodate any imposed deformation and contribute to the stress. It is obvious that stresses, as observed in tensile stretching tests, can be considered as being composed of three contributions: <br> - the forces transmitted by the skeleton of crystal blocks, <br> - the force brought up by the stressed amorphous network, and <br> - viscous forces. <br> <br>Stress relaxation measurements at constant strain provide a means to determine <br>the viscous forces. Such measurements were carried out for low crystallinity polyethylene and its copolymers. Here, it was found that the stress relaxation followed a logarithmic time-law. This range was not infinite and the stress went to a final value. Additionally, this remaining stress does not depend on the applied strain rate, but on the imposed strain only. The remaining quasi-stationary stress can then be associated with the stress kept up by the crystal skeleton together with the network. A separation of these two contributions from the quasi-static stress becomes possible, considering <br>that in the limit of high strains the network force becomes dominant, and the crystallites may be treated as fillers. Therefore, we separated the network stress from the quasi-static stress. <br> <br>Creep measurements were carried out by stretching the sample at a constant strain rate to a certain stress, whereafter the stress was kept fixed. The measurements showed that creep also followed a logarithmic time-law. During creep the viscous stress decreased. The loss of viscous stress was compensated by the increase of the stress contributed by the network and the skeleton. <br> <br>Based on the experimental observations we constructed a three component model <br>in which one component describes the crystal skeleton behavior in a spring combined with a finite-plastic element. Conventional Gaussian chain statistics were employed to represent in a second component the stress arising from the entanglement network. A Hookean spring in series with an Eyring dashpot represents as the third component the viscous stress. This model description provides a decomposition of the measured stress into the contributions of the crystal skeleton, the amorphous network, and the viscosity; it includes a splitting of the total imposed strain in an elastic and plastic part, describes the kinetics of stress relaxation at fixed strains, represents the kinetics <br>of creep at constant stress, reproduces the experimental stress-strain curves, and deals correctly with the effect of strain rate.

Author dc:creator

• Hong, Ke

Contributors dc:contributor

• Strobl, Gert

• polyethylene
• tensile deformation
• model
• network

Repository record source_url

https://freidok.uni-freiburg.de/data/1817

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:1817