Double-torsion specimen

Fig. 2 a and b. Schematic load versus displacement curves for crack propagation in epoxy polymers obtained using a double torsion specimen a Stable continuous propagation, b Unstable stick/slip propagation... 

Fig. 12. Stoichiometric DGEBA/DDS network fracture toughness versus temperature. Fracture toughness from double torsion specimen at crosshead rate of 0.05 cm/min. Network T, s shown by dashed lines. O Initiation Arrest 9 Stable crack growth. (After LeMay...

The techniques and test geometries that have been used to measure subcritical crack growth in ceramics are several, but they share a common principle, namely, the subjection of a well-defined crack to a well-defined stress intensity Ki, and a measurement of its velocity v. The technique considered here, the advantages of which are elaborated upon below, is the double torsion geometry shown in Fig. 12.8. For the double torsion specimen, K is given by... 

Detailed derivations of the relationship similar to Eq. 14 can be found in the literature [16.54.55]. Double-torsion specimens [56.57] are convenient, because of their geometry and the mode of loading, for the study of crack growth rates under a fixed load, where G and K remain constant, i.e., independent of the crack length. 

Another geometry that has been found useful in some situations is the double torsion specimen, which is shown in Fig. 8.21. The crack front is rather complicated in this geometry as the upper surface is in compression. This geometry is, however, a constant K specimen, with K being independent of crack length, i.e.,... 

The value of Kc at which crack propagation occurs in a specimen of finite size depends upon the applied load, crack length and specimen dimensions. It is only given by Equation (5.194) for a crack of length 2a in an infinite plate. At other times it must be determined from an elastic analysis of the particular specimen used and this so-called / -calibration has only been done for certain specific specimens. The formulae for K which have been determined for the three specimens in Fig. 5.55 are given in Table 5.5. It should be noted that for the double-torsion specimen the crack length, a does not appear in the formula. 

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... 

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 the study of crack growth in epoxy polymers the double-torsion and compact-tension specimens have been the most widely used. The values of KIc may be obtained from 1,2)... 

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. 

The load-relaxation method of Double-Torsion (DT) test is adopted in this study (Evans, 1972). A schematic illustration of a DT specimen is shown in Figure /, where the notations of the specimen are noted. In this study, the guide groove was set upward. 

Glassy fracture energies were measured using single edge notch (sen) and double torsion (DT) specimens (Figure 3). Rubbery fracture measurements above Tg en5)loyed only the SEN specimen. 

Figure 3. Fracture test specimens (a) Single edge notch (sen) (h) Double torsion (DT).

Figure 4. Typical schematic load-displacement traces for double torsion test specimen (a) continuous (stable) crack growth (b) discontinuoxis (unstable) crack growth showing initiation and arrest loads.

Since it is usually convenient to measure the crack speed in a specimen in which K does not vary with a for a given load or loading rate, the double-torsion and tapered-cantilever beam tests are used (Fig. 16). In the first we have... 

Fig. 5.55 Schematic representation of different fracture mechanics specimens used with brittle polymers and load-displacement curves for each specimen for a constant displacement rate. SEN, single-edge notched DT, double torsion DCB, double-cantilever beam.

The WOL and the double-cantilever beam (DCB) specimens are suitable to determine the arrest of an initially unstable crack the double-torsion (DT) specimen permits the investigation of crack propagation under constant Kj [7—15]. 

NOTE - there are other testing specimens that are suitable for fracture toughness or fracture energy measurements of brittle materials. These include for instance compact tension (CT) and double torsion (DT) specimens. Readers will find more details in [CHE 75]. 

Find the energy release rate G for the split-bar specimen loaded in double torsion as shown. 

Because strain measurements are difficult if not impossible to measure, few values of yield strength can be determined by testing. It is interesting to note that tests of bolts and rivets have shown that their strength in double shear can at times be as much as 20% below that for single shear. The values for the shear yield point (kPa or psi) are generally not available however, the values that are listed are usually obtained by the torsional testing of round test specimens. 

The double extrapolation procedure invoked involves firstly extrapolation of measurements of torque on specimens with various known axial tensions to zero axial tension. These extrapolated values were then used in the St. Venant expression for torsion of non-circular cylinders to obtain apparent values of 566 for rectangular prisms of various aspect ratios (width rthickness). If the theory was rigorous these values of 566 would be independent of aspect ratio. However, this was not the case and a second extrapolation was made to obtain a value for 5166 at the limiting aspect ratio at which the theory could be regarded as most rigorous. 

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