Torsion Stress-Strain

Shear modulus can be determined by a static torsion test or by a dynamic test using primarily a torsional pendulum (ASTM D 2236). Also used is an oscillatory rheometer test. The torsional pendulum is applicable to virtually all plastics and uses a simple specimen readily fabricated by all commercial fabricating processes or easily cut from fabricated part. The moduli of elasticity, G for shear and E for tension, are ratios of stress to strain as measured within the proportional limits of the material. Thus the modulus is really a measure of the rigidity for shear of a material or its stiffness in tension and compression. For shear or torsion, the modulus analogous to that for tension is called the shear modulus or the modulus of rigidity, or sometimes the transverse modulus. 

---

There are a number of different modes of stress-strain that must be taken into account by the designer. They include tensile stress-strain, flexural stress-strain, compression stress-strain, torsional stress-strain, and/or shear stress-strain (Table 7.9). 

Fig. 1.6 a Tension stress-strain curve b torsion stress-strain curve [23]. With kind permission of Elsevier... 

There have been a number of detailed investigations of the influence of hydrostatic pressure on the yield behaviour of pol3maers. Because it illustrates clearly the relationship between a yield criterion, which depends on hydrostatic pressure, and the Coulomb yield criterion, an experiment will be discussed where Rabinowitz, Ward and Parry [23] determined the torsional stress-strain behaviour of isotropic PMMA under hydrostatic pressures up to 700 MPa. The results are shown in Figure 11.17. 

Many of the methods used for characterizing solid materials are applicable to polymers in the solid state x-ray diffraction and crystallography, thermal analyses such as differential scanning calorimetry, mechanical testing for ductility, brittleness, compressive, tensile, and torsional stress-strain relationships, impact, fatigue, creep, etc. 

On poly(dimethylsiloxane) (PDMS) networks having comb-like crosslinks, torsional vibration experiments and static stress-strain measurements at small deformations were performed as a function of temperature, torsional vibrations also as a function of frequency. 

Relative energy part of the modulus at T = 298K, from stress-strain measurements with X = 1.02-1.04 (ored u red and from torsional vibration experiments (G y/G 5... 

Concepts characteristic of piping flexibility analysis are covered in the following paragraphs. Special consideration is given to displacements (strains) in the piping system, and to resultant bending and torsional stresses. 

The elastic modulus is the slope of the tangent at the origin of the stress/strain curve. The tensile or compression modulus is often called Young s modulus whereas the torsion modulus is often called shear modulus or Coulomb s modulus. 

The hardness of a polymer can also be estimated from the modulus of elasticity E (high E modulus indicates high hardness). The advantage here is that every region of elasticity and every degree of hardness can be detected with a single kind of measurement (determination of stress-strain-behavior or torsional oscillation). 

Stress/strain relationships for other torsional configurations can be found in Engineering Design with Rubber119 and Yeoh120 examined the torsion of cylindrical test pieces by finite element analysis. 

In practice, up to 90% of polyurethanes are used in compression, a few percent in torsion, and very little in tension. There is considerable data on the tensile stress against tensile strain (elongation) for polyurethanes. Most polyurethane specification sheets provide this data. Figure 7.3 and Figure 7.4 show typical stress-strain curves for both polyester and polyether polyurethanes. 

In addition, other measurement techniques in the linear viscoelastic range, such as stress relaxation, as well as static tests that determine the modulus are also useful to characterize gels. For food applications, tests that deal with failure, such as the dynamic stress/strain sweep to detect the critical properties at structure failure, the torsional gelometer, and the vane yield stress test that encompasses both small and large strains are very useful. 

The methods utilized to measure the viscoelastic functions are often close to the stress patterns occurring in certain conditions of use of polymeric materials. Consequently, information of technological importance can be obtained from knowledge of these functions. Even the so-called ultimate properties imply molecular mechanisms that are closely related to those involved in viscoelastic behavior. Chapters 16 and 17 deal with the stress-strain multiaxial problems in viscoelasticity. Application of the boundary problems for engineering apphcations is made on the basis of the integral and differential constitutive stress-strain relationships. Several problems of the classical theory of elasticity are revisited as viscoelastic problems. Two special cases that are of special interest from the experimental point of view are studied viscoelastic beams in flexion and viscoelastic rods in torsion. 

---