Compressive shear polymers under

Ductile Failure of Brittle Polymers under Compressive Shear Stresses... 

Tphe literature is replete with examples showing that the application of hydrostatic pressure enhances the ductile behavior of strained amorphous polymers. In this paper we present a possible explanation of this effect and two experiments demonstrating the enhanced ductility of polymers under compressive shear stresses applied orthogonally to the plane of shear. 

If the component T of an applied compressive shear stress orthogonal to the plane of fracture combines with the normal component o-yy of the local stress at the tip of a crack, then the combined higher stress will minimize (AH — U0)/ductile failure ensues. This can occur if the orthogonal compressive stress is locally inhomogeneous. Hence, a polymer can fail in a more ductile fashion under orthogonal compressive shear stresses than in their absence. 

In a final chapter a closely related phenomenon, the formation of shear bands in semi-crystalline polymers under compressive load will be described. It is attempted to discuss under which conditions shear bands are formed in semi-crystalline materials and how they interact with each other or with certain microstructural features, finally leading to crack initiation and shear fracture of the bulk polymer. 

The formation of shear bands under compression is found in crystalline polymers when loaded at temperatures lower than 0.75 T. Under such a condition the shear bands interact with certain morphological features such as spherulite boundaries or lamellar arrangements inside the spherulites. The band initiation stress, ct, increases and the strain at break, Cp, decreases with decreasing temperature and increasing stiffness of the tested polymer, i.e. increasing degree of crystallinity. 

For macroscopically isotropic polymers, the Tresca and von Mises yield criteria take very simple analytical forms when expressed in terms of the principal stresses cji, form surfaces in the principal stress space. The shear yield surface for the pressure-dependent von Mises criterion [Eqs (14.10) and (14.12)] is a tapering cylinder centered on the applied pressure increases. The shear yield surface of the pressure-dependent Tresca criterion [Eqs (14.8) and (14.12)] is a hexagonal pyramid. To determine which of the two criteria is the most appropriate for a particular polymer it is necessary to determine the yield behavior of the polymer under different states of stress. This is done by working in plane stress (ct3 = 0) and obtaining yield stresses for simple uniaxial tension and compression, pure shear (di = —CT2), and biaxial tension (cti, 0-2 > 0). Figure 14.9 shows the experimental results for glassy polystyrene (13), where the... 

Althongh fiber-reinforced plastics have good in-plane mechanical properties that are determined by the long fibers, the properties in the transverse and the thickness directions defined by the characteristics of the matrix resin are mnch weaker. Under tension, compression, shear, or inqiact, failure of the polymer matrix may take place. While nanoparticles may reinforce the polymer matrix, the... 

Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different defonnation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the fonnation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]- The reason for these conspicuously different defonnation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

Dimensional stability is one of the most important properties of solid materials, but few materials are perfect in this respect. Creep is the time-dependent relative deformation under a constant force (tension, shear or compression). Hence, creep is a function of time and stress. For small stresses the strain is linear, which means that the strain increases linearly with the applied stress. For higher stresses creep becomes non-linear. In Fig. 13.44 typical creep behaviour of a glassy amorphous polymer is shown for low stresses creep seems to be linear. As long as creep is linear, time-dependence and stress-dependence are separable this is not possible at higher stresses. The two possibilities are expressed as (Haward, 1973)... 

In many applications materials are subjected to compressive stresses. The macroscopic phenomena of collapse under an axial compression are the well-known shear and kink bands. In polymers they are caused by the buckling of chains, accompanied by changes in the chain conformation. The resistance against buckling is expressed by the yield strength under axial compression, ac max. Northolt (1981) found a relationship between c,max and Tg. 

Cross-Linking. A thermoset system is produced when a polymer is cross-linked under static conditions, as in a compression mold. This is the basis of the production of vulcanized articles or cross-linked polyethylene pipe and wire insulation. If the same polymer is lightly cross-linked while it is being sheared in the molten state, however, it will remain thermoplastic. If it is more heavily cross-linked during this process, the final product may contain significant quantities of gel particles, but the whole mass will still be tractable. 

Fig. 32. Shear modulus, G, vs. ratio of undercooling, T/T, (temperature in Kelvin), for various polymers. The modes of deformation which can predominate under compression are indicated...

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