Mechanical properties simple shear

Torsion property As noted, the shear modulus is usually obtained by using pendulum and oscillatory rheometer techniques. The torsional pendulum (ASTM D 2236 Dynamic Mechanical Properties of Plastics by Means of a Torsional Pendulum Test Procedure) is a popular test, since it is applicable to virtually all plastics and uses a simple specimen readily fabricated by all commercial processes or easily cut from fabricated products. 

Viscoelastic properties have been discussed in relation to molar mass, concentration, solvent quality and shear rate. Considering the molecular models presented here, it is possible to describe the flow characteristics of dilute and semi-dilute solutions, as well as in simple shear flow, independent of the molar mass, concentration and thermodynamic quality of the solvent. The derivations can be extended to finite shear, i.e. it is possible to evaluate T) as a function of the shear rate. Furthermore it is now possible to approximate the critical conditions (critical shear rate, critical rate of elongation) at which the onset of mechanical degradation occurs. With these findings it is therefore possible to tune the flow features of a polymeric solution so that it exhibits the desired behaviour under the respective deposit conditions. 

Visco-elastic models have been developed for the nonlinear mechanical properties of fluids and solids. For a viscous fluid in simple shear flow, the shear stress, r y y), is a function of the effective viscosity, rj(-y) and the shear rate, y, as follows ... 

Analysis of Cure. A simple analysis of the cure results for short term steady flow can be performed by noting that for a number of polymerization reactions, the early stages of cure can be described by a first order type equation (9,10). In the simplest case this would mean that log (n) would vary linearly with time. To examine this possibility the data for various shear rates were analyzed by plotting log (n) vs. time (Figures 13 and 14). If the Initial points (zero cure time data) are excluded, the data for each shear rate can be fit, to a first approximation, with a straight line. The fact that the zero cure time points do not fall near the lines suggests that the mechanical property results show an Initiation time Just as was found previously In thermal experiments (2). 

A simple substance such as water below its freezing point is a hard three-dimensional crystalline solid, and above its freezing point it is a low-viscosity Newtonian liquid. In the liquid state, the mechanical properties of such a substance are specified by its shear viscosity T], which is of course temperature- and pressure-dependent. 

A calibration wire whose shear modulus is known can be used to determine the moment of inertia of the pendulum assembly, so that quantitative measurements of the dynamic mechanical properties of specimens can be made. The shear modulus of the calibration wire is obtained by measuring the period of oscillation of a simple torsion pendulum consisting of an aluminum rod suspended by the wire. The moment of inertia of this system is given by... 

The mechanical properties of a liquid are fundamentally different from the solids discussed in Chapter 7. Solids have stress proportional to deformation (for small deformations). However, the stress in liquids depends only on the rate of deformation, not the total amount of deformation. If we pour water from one bucket into another bucket, there is only resistance during the flow, but there is no shear stress in the water in either bucket at rest. We describe the deformation rate of a liquid in shear by the shear rate 7 = d /dt [Eq. (7.99)]. For the steady simple shear flow of Fig. 7.23, the shear rate is the same everywhere, equal to the way in which velocity changes with vertical position. The stress a in a Newtonian liquid is proportional to this shear rate [Newton s law of viscosity Eq. (7.100), cr = 777], with the viscosity rj being the coefficient of -proportionality. 

We can see that Eqs. (2 101) (2-104) are sufficient to calculate the continuum-level stress a given the strain-rate and vorticity tensors E and SI. As such, this is a complete constitutive model for the dilute solution/suspension. The rheological properties predicted for steady and time-dependent linear flows of the type (2-99), with T = I t), have been studied quite thoroughly (see, e g., Larson34). Of course, we should note that the contribution of the particles/macromolecules to the stress is actually quite small. Because the solution/suspension is assumed to be dilute, the volume fraction is very small, (p 1. Nevertheless, the qualitative nature of the particle contribution to the stress is found to be quite similar to that measured (at larger concentrations) for many polymeric liquids and other complex fluids. For example, the apparent viscosity in a simple shear flow is found to shear thin (i.e., to decrease with increase of shear rate). These qualitative similarities are indicative of the generic nature of viscoelasticity in a variety of complex fluids. So far as we are aware, however, the full model has not been used for flow predictions in a fluid mechanics context. This is because the model is too complex, even for this simplest of viscoelastic fluids. The primary problem is that calculation of the stress requires solution of the full two-dimensional (2D) convection-diffusion equation, (2-102), at each point in the flow domain where we want to know the stress. 

In order to understand the behavior of composite propellants during motor ignition, we conducted a study of the mechanical and ultimate properties of a propellant filled with hydroxy-terminated polybutadiene under imposed hydrostatic pressure. The mechanical response of the propellant was examined by uniaxial tensile and simple shear tests at various temperatures, strain rates, and superimposed pressures from atmospheric pressure to 15 MPa. The experimentally observed ultimate properties were strongly pressure-sensitive. The data were formalized in a specific stress-failure criterion. 

The modulus is the most important small-strain mechanical property. It is the key indicator of the "stiffness" or "rigidity" of specimens made from a material. It quantifies the resistance of specimens to mechanical deformation, in the limit of infinitesimally small deformation. There are three major types of moduli. The bulk modulus B is the resistance of a specimen to isotropic compression (pressure). The Young s modulus E is its resistance to uniaxial tension (being stretched). The shear modulus G is its resistance to simple shear deformation (being twisted). 

The mechanical properties discussed above all have the major common feature of being measured by deforming a specimen continuously at a given rate until it fails. The deformation mode (uniaxial tension, uniaxial compression, plane strain compression, or simple shear) may vary, but these differences can be roughly taken into account by imposing criteria (such as yield criteria) to describe the stress states imposed on specimens by different deformation geometries. 

Viscoelasticity deals with the dynamic or time-dependent mechanical properties of materials such as polymer solutions. The viscoelasticity of a material in general is described by stresses corresponding to all possible time-dependent strains. Stress and strain are tensorial quantities the problem is of a three dimensional nature (8), but we shall be concerned only with deformations in simple shear. Then the relation between the shear strain y and the stress a is simple for isotropic materials if y is very small so that a may be expressed as a linear function of y,... 

Homogeneous, isotropic, elastic materials possess the simplest mechanical properties, and three elementary types of elastic deformation can be observed when such a body is subjected to (1) simple tension, (2) simple shear, and (3) uniform compression. 

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