Stress under compressive shear

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. 

Figure 3. Fracture surface of PMMA impacted under compressive shear stress. Left Magnification X18.5, fracture direction from top to bottom. Right The same spot, magnification XSQ.

Figure 4. Fracture surface of PS impacted under compressive shear stress. Crack propagated from top to bottom. Left magnification X50. Right a different point on same fracture surface,...

The work reported in [381] deals with interlaminar fracture and shear stresses under compression in the plane of the layers, which occurs due to natur d bending of reinforcing fibers as a result of... 

Yielding is more difficult to measure and to model. For strongly flocculated systems, Buscall et al. (1987) measured the yield stress under compression and found a concentration law quite similar to that for the shear modulus. This relation differed, however, from that for the yield stress in shear. Patel and Russel (1988) predicted nearly identical power law indices for modulus and shear yield stress. This prediction has been confirmed experimentally (Figure 10.7.2), albeit for reversibly flocculated systems. The theory is based on the classical yielding criteria. Reversible systems do not follow these criteria as yielding becomes a kinetic phenomenon. The yield stress then depends on shear history (Mewis and Meire, 1984). 

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. 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instmments measure the response of a Hquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduH. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test soHds, melts, and Hquids at frequencies from 10 to 500 rad/s and as a function of strain ampHtude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

The failure of a simple structural element under unidirectional stress (tensile or compressive) is easy to relate to the tensile strength of the material, as determined in a standard tensile test, but for components subjected to combined stresses (normal and shear stress) the position is not so simple, and several theories of failure have been proposed. The three theories most commonly used are described below ... 

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. 

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... 

In equation (1), Tocto corresponds to the shear yield stress under zero pressure and a is a pressure coefficient, which quantifies the yield stress sensitivity to pressure. Such a yield criterion has previously been shown to hold for epoxy resins under a wide range of pressure, temperature and strain rate conditions [10, 11]. The two parameters, Tocto and a were found to be 44 MPa and 0.173 respectively from the uniaxial and plane strain compression results reported in table I. 

Powders can withstand stress without flowing, in contrast to most liquids. The strength or yield stress of this powder is a function of previous compaction, and is not unique, but depends on stress ap ication. Powders fail only under applied shear stress, and not isotropic load, although they do compress. For a given apphed horizontal load, failure can occur by either raising or lowering die normal stress, and two possible values of failure shear stress are obtained (active versus passive failure). 

In the rheological structure of most food systems there is a viscous element present, and the deformation curves are often highly influenced by the rate of the imposed strain. This is due to the fact that the material relaxes (or flows) while tested under compression and the resultant deformation of this flow is dependent on the nature of the viscous element (Szczesniak, 1963 Peleg and Bagley, 1983). In the viscoelastic food systems, where during processing it is caused to oscillate sinusoidally, the strain curve may or may not be a sine wave. In cases when a periodic oscillatory strain is applied on a food system like fluid material, oscillating stress can be observed. The ideal elastic solid produces a shear stress wave in phase with... 

The deformation mode affects the dominant failure mechanism by imposing different stress states on the specimen. For example, at a given temperature and deformation rate, the proclivity to fail by brittle fracture (not to be tough ) is much greater under plane strain tension than under simple shear. Another example is that many thermosets fail by brittle fracture under uniaxial tension while they undergo shear yielding under uniaxial compression. 

In powder technology, the general behavior of powders under compressive stress or compaction due to mechanical motion is relevant in several applications. The tendency of a food powder s physical and chemical properties to change relative to temperature-moisture history is a common feature of all food powders (Peleg, 1978). Intrinsic variables like temperature, moisture, and composition can influence the response of food powders to the stress of deformation from tension, shear, or compression. 

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