Morphological Developments of the Composite Model

In parallel research to that ofTakayanagi, McCrum and Morris studied the a and a relaxations in high density polyethylene. They proposed that the a relaxation should be attributed to slip at the boundaries of the lamellae, and put forward a model similar to that of Iwayanagi in which elastic lamellae are separated by a viscous liquid. To ensure recoverability, the lamellae are pinned at points along their length. The composite solid then shows linear viscodastic behaviour, with a characteristic relaxation which depends on structural parameters. 

Gupta and Ward found modulus crossover points in drawn and annealed sheets of low density po yethylene and also in the b-c and it-b sheets similar to that observed by Takayanagi in drawn and annealed high density polyethylene. The crossover points were attributed to inter-lamellar shear. When the tensile stress is applied along the draw direction ( measurements in a drawn and annealed sheet) or along either the c or a direction in the special structure sheets ( , and Ea measure- 

The cross-over point in high density polyethylene occurs above the a-relaxation, which it is proposed is an inter-lamellar shear relaxation. This highlights a major difference between high density polyethylene and low density polyethylene, where the a-relaxation is attributed to the c-shear process which gives rise to the anomalous mechanical anisotropy. 

The success of the model for the loss anisotropy led Owen and Ward to use equivalent assumptions to calculate the modulus anisotropy. The loss anisotropy calculations assume simple shear between the lamellae only, which for parallel lamellae sheet would imply that inter-lamellar shear is not activated when the tensile stress is applied along the initial draw direction i.e. parallel to the lamellar plane normals). A very appreciable fall in tensile modulus was. however, observed in this case, although as e.xpected by comparison with the corresponding loss factor in 

The extensional modulus 33 of the uniaxially oriented system is given by 

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