Torsional test pieces

To calculate fracture toughness using the double torsion test piece, the following equation is used ... 

The authors studied the glassy fracture behavior of the homologous series of DGEBA/DDS networks listed in Table 2. The fracture specimen employed was the double torsion test piece. Fracture data were collected over the temperature range Tg — 120 to Tg — 20 K, and all testing was performed at a single slow crosshead rate of 0.05 cm/min. This test rate was chosen because it minimized hysteretic effects and made all the networks fracture unstably over most of the temperatures investigated. 

Fig. 103. Typical failure surfaces from torsional test pieces with Redux 775 (Ciba-Geigy) (a) broken at -196°C to illustrate brittle failure (b) broken at room temperature to illustrate ductile failure.

The joint shown in Fig. 103(b) failed in the neighbourhood of 70MN.m (data from Foulkes et al., 1970) whilst the yield stress in uniaxial tension of polyvinyl formal at room temperature is given by Whitney and Andrews (1967) as 78MN.m". The uncertainty in the stress failure of torsional test pieces arises from differences in calculation of stress from failure torque. Either plastic or elastic failure must be assumed to make the calculation and which is assumed can only be decided from an examination of the appearance of the failed test piece. 

Double torsion test specimens take the form of rectangular plates with a sharp groove cut down the centre to eliminate crack shape corrections. An initiating notch is cut into one end of each specimen (Hill Wilson, 1988) and the specimen is then tested on two parallel rollers. A load is applied at a constant rate across the slot by two small balls. In essence the test piece is subjected to a four-point bend test and the crack is propagated along the groove. The crack front is found to be curved. 

The double torsion test specimen has many advantages over other fracture toughness specimen geometries. Since it is a linear compliance test piece, the crack length is not required in the calculation. The crack propagates at constant velocity which is determined by the crosshead displacement rate. Several readings of the critical load required for crack propagation can be made on each specimen. 

In principle, the shear modulus could be measured using test pieces strained in torsion and in engineering practice components, such as torsion discs and bushes, do operate in this mode. However, it is not common practice to test rubber in this manner except as a low temperature test (see Chapter 15) when a strip test piece is twisted by means of a torsion wire. The instrument traditionally used is not really accurate enough for precise measurement of modulus at room temperature but it would seem reasonable to suppose that an accurate instrument could be devised. 

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. 

Before considering particular test methods, it is useful to survey the principles and terms used in dynamic testing. There are basically two classes of dynamic motion, free vibration in which the test piece is set into oscillation and the amplitude allowed to decay due to damping in the system, and forced vibration in which the oscillation is maintained by external means. These are illustrated in Figure 9.1 together with a subdivision of forced vibration in which the test piece is subjected to a series of half-cycles. The two classes could be sub-divided in a number of ways, for example forced vibration machines may operate at resonance or away from resonance. Wave propagation (e.g. ultrasonics) is a form of forced vibration method and rebound resilience is a simple unforced method consisting of one half-cycle. The most common type of free vibration apparatus is the torsion pendulum. 

Figure 9-8. Types of torsion pendulum, (a) Free oscillation apparatus with inertia member supported by test piece (b) free oscillation apparatus with inertial member supported by a fine wire. In both types of apparatus, a lamp and scale is used in conjunction with the mirror to observe the oscillations. The broken lines indicate compensation devices to produce a constant amplitude apparatus...

Few details of the apparatus are given in ISO 4663, it is simply stated that means shall be provided to measure frequency to 1% ( 5% in a transition region), amplitude to 1% and, for method C, the supplied energy to 2%. It is suggested that a moment of inertia of about 0.03 gm is suitable for the inertia member which may be a disc or rod. For methods B and C the torsion wire should be of such dimensions that its restoring torque is not more than 25% of the total restoring torque due to the test piece and suspension. BS 903 (equivalent to method B of ISO 4663) suggests that moments of inertia between 50 and 500 g cm are suitable and states that the tensile strain on the test piece should be between 0 and 5%. The British... 

Modulus can be obtained from rotational stiffness by using the formula for static torsion of a strip test piece ... 

The above relationships indicate what may be derived from torsional pendulum measurements. In fact, BS 903 calls for G and G" and the log decrement, although it does not actually say how to calculate the log decrement for the rubber. BS 903 also allows a circular cross section test piece, when the term l/bh3k is replaced by d4n/32 where d is the diameter of the test piece. 

ISO 4663 gives no advice as to the relative merits of the three methods it specifies. Method C, which is not strictly a free vibration method, removes the difficulties associated with changing amplitude through the course of the test but at the expense of a rather more complex apparatus. When the inertia member is supported by a torsion wire, as in method B, the tensile strain in the test piece can be controlled to a low level by means of counterweights. 

Hard viscoelastic solids, which cover a G region of 108-1010 N/m2 test pieces have to be small in torsion and bending tests. 

The Shear Modulus of Elasticity is derived from the torsion of a cylindrical test piece. Its symbol is G. 

Shear, compression, or torsion cycles with constant stress or constant strain amplitude and various cycle shapes are all perfectly feasible but not commonly used except for the heat buildup tests below. A procedure for plastics taken from metals testing invoices rotating a cylindrical test piece with its ends constrained by bearings that are misaligned. The result is that each element of the test piece goes through a sinusoidal cycle from tension to compression. 

K torsional constant of wire, Nm L fiee length of test piece, m a angle of twist measured, "... 

The maximum shear stress that a material is capable of sustaining. The maximum load required to shear a specimen in such a volume manner that the resulting pieces are completely clear of each other. Shear strength (engineering) is calculated from the maximum load during a shear or torsion test and is based on the original cross-sectional area of the specimen. 

FIGURE 2.5 Schematic drawings of experimental setups (AFM) for measuring friction and puU-off forces, (a) The AFM prohe scans along the x-direction, and the torsion and bending of the cantilever are detected by a quad-photodiode detector, (b) Arrangement of probe on a test specimen. The angle between the flat, square tip of the probe and the test piece was 2.5°-3°. 

The slow growth of cracks in poly(methyl methacrylate) is an ideal application of linear elastic fracture mechanics to the failure of brittle polymers. Cracks grow in a very well-controlled manner when stable test pieces such as the double-torsion specimen are used. In this case the crack will grow steadily at a constant speed if the ends of the specimen are displaced at a constant rate. The values of Kc or % at which a crack propagates depends upon both the crack velocity and the temperature of testing, another result of the rate- and temperature-dependence of the mechanical properties of polymers. This behaviour is demonstrated clearly... 

Figure 105 (Wake, 1982) illustrates the temperature limitations of epoxy resins based on bis-phenol A. The two component polyamine cure shows relatively poor performance but these figures refer to torsional shear and the two one-component epoxies here exhibit strengths which would cause gross distortion of lap-shear test pieces of the usual thickness. None is usable above 120°C. By contrast, Fig. 106 (Wake, 1982) shows the very different behaviour of an epoxy-phenolic adhesive supported on a glass cloth carrier. There are two features to be reckoned with when considering the use of adhesives at elevated temperatures. There is the temperature at which they can be used continuously and at which the joint will retain adequate strength...

The shear modulus can be readily obtained from a torsional deformation of a test piece of constant volume. Figure 1(b) shows a cylindrical rod of length L and circular cross-section radius a under the action of equal and opposite torque F applied to its ends. The tangential shear stress acting on the planes of the cross-section at radius r is given by... 

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