Tension-torsion experiments

as well as for mean normal stresses of 4.14, 6.3, and 12.4 MPa at 253 K at different levels of simultaneously applied deviatoric stress s. In all cases craze initiation was considered complete at 10 s, when around 10 crazes per cm had formed. Table 11.1 gives the specific three pairs of a and s for 293 K and 253 K for craze initiation, together with dimensionless representations of stresses by parameters and tj, for and s normalized with appropriate uniaxial compressive yield stresses Tq = 103 MPa at 293 K and 144 MPa at 253 K, respectively. The three combinations of stress parameters and tj for crazing at 293 K and 253 K are given in Fig. 11.3, together with the information on intrinsic crazing in flawless specimens in uniaxial tension. 

Since deviatoric shear stresses and mean normal stresses are expected to play different roles in craze initiation, some conditioning experiments were also performed at 293 K as shown in Fig. 11.4(a) under a pure deviatoric shear stress So = 15.86 MPa for periods of 120, 10, 10 , and 8 x 10 s. Then, a standard mean normal stress of = 4.14 MPa was applied, which initiated crazing. The response on craze initiation after the aging under so alone and upon addition of the ro was 

Fig 11.3 Measurements of craze initiation under combinations of normalized mean normal stress and normalized deviatoric shear stress rj aXT — 293 K (O) and T — 253 ( ) with lines giving model predictions from eqs. (11.19) and (11.22) H gives the intrinsic crazing response at 293 K (from Argon (2011) courtesy of Elsevier). 

---

Table 11.1 Pairs of craze-initiation parameters a- and s in tension-torsion experiments on PS (minerai-oii-free PS...

In eq. (11.15) the concentrated local mean normal stress ai and deviatoric shear stress Si are in the plastic enclaves that result in craze initiation (the time taken for the formation of 10 crazes per cm in 10 s in the tension torsion experiments is taken as the mean period r of craze initiation), which needs to be stated in terms of global stresses a and s through the use of the average stress eoneentrations and of surface grooves. How this is done is discussed below in Section 11.6 comparing the model predictions with the results of the tension torsion experiments. 

The comparison starts with determination of how the applied stresses 022 and an in the tension-torsion experiments are concentrated by the set of surface grooves of semielliptical shape. This is done using specific expressions provided by Neuber (1946). 

The problem of definition of modulus applies to all tests. However there is a second problem which applies to those tests where the state of stress (or strain) is not uniform across the material cross-section during the test (i.e. to all beam tests and all torsion tests - except those for thin walled cylinders). In the derivation of the equations to determine moduli it is assumed that the relation between stress and strain is the same everywhere, this is no longer true for a non-linear material. In the beam test one half of the beam is in tension and one half in compression with maximum strains on the surfaces, so that there will be different relations between stress and strain depending on the distance from the neutral plane. For the torsion experiments the strain is zero at the centre of the specimen and increases toward the outside, thus there will be different torque-shear modulus relations for each thin cylindrical shell. Unless the precise variation of all the elastic constants with strain is known it will not be possible to obtain reliable values from beam tests or torsion tests (except for thin walled cylinders). 

Further work will be focusing on lifetime prediction methods for gas turbine materials (superalloys) and experiments on fracture mechanics in superalloys as well as finite element calculations of multiaxial loaded tubes and validation of multiaxial tests (tension, torsion, internal pressure). 

Rivlin and Saunders carried out experiments in simple tension, torsion, pure shear and pure shear superposed on simple extension to extend the range of combinations of principal extension ratio. This showed behaviour generally consistent with Equation (3.61). Their work illustrates the importance of exploring a wide range of combinations of extension ratio to establish the function U. The traditional form of materials test - the uniaxial stretch -involves a very specific mode of deformation. Finding materials parameters by least squares... 

Material Parameter Characterization Elastic Modulus The first step in the process is to characterize the material model that describes the behavior of axes, flexible gear and rigid gear and also to quantify the variability in the material. Through physical measurements, tension/com-pression and torsional experiments, the material density, elastic and shear moduli were obtained calibrating to represent the dynamic behavior of them at room temperature. Using the data obtained from these samples and from these tests, a probabilistic description of the randomness of them was obtained and subsequently used in more complex system. More specifically, for these components, the elastic modulus is treated as random variable. 

Tension, torsion, and compression experiments can be conducted with equipment having the basic configuration shown in Figure 38. One end of the specimen is gripped in a jaw that can be driven with the appropriate oscillatory motion, while the other is gripped in a jaw attached to a transducer. Due to the viscoelastic nature of polyethylene, the sinusoidal motion of the driven jaw is not transmitted directly by the sample to the transducer. The stress measured by the transducer has a sinusoidal trace that lags behind that of the driven jaw by... 

Hence, the elastic modulus corresponds in principle to the force per square millimeter that is necessary to extend a rod by its own length. Materials with low elastic modulus experience a large extension at quite low stress (e.g., rubber, = 1 N/mm ). On the other hand, materials with high elastic modulus (e.g., polyoxymethylene, s 3500 N/mm ) are only slightly deformed under stress. Different kinds of elastic modulus are distinguished according to the nature of the stress applied. For tension, compression, and bending, one speaks of the intrinsic elastic modulus ( modulus). For shear stress (torsion), a torsion modulus (G modulus) can be similarly defined, whose relationship to the modulus is described in the literature. 

Mechanical Properties. Dynamic mechanical properties were determined both in torsion and tension. For torsional modulus measurements, a rectangular sample with dimensions of 45 by 12.5 mm was cut from the extruded sheet. Then the sample was mounted on the Rheometrics Mechanical Spectrometer (RMS 800) using the solid fixtures. The frequency of oscillation was 10 rad/sec and the strain was 0.1% for most samples. The auto tension mode was used to keep a small amount of tension on the sample during heating. In the temperature sweep experiments the temperature was raised at a rate of 5°C to 8°C per minute until the modulus of a given sample dropped remarkably. The elastic component of the torsional modulus, G, of the samples was measured as a function of temperature. For the dynamic tensile modulus measurements a Rheometrics Solid Analyzer (RSA II) was used. The frequency used was 10 Hz and the strain was 0.5 % for all tests. 

Creep tests are made mostly in tension, but creep experiments can also be done in shear, torsion, flexure, or compression. Creep data provide important information for selecting a polymer that must sustain dead loads for long periods. The parameter of interest to the engineer is compliance (J), which is a time-dependent reciprocal of modulus. It is the ratio of the time-dependent strain to the applied constant stress [J(t) = e(t)/Oo]. Figure 13.3 shows creep curves for a typical polymeric material. 

As noted in Subsection 24.1.2, viscoelasticity of polymers represents a combination of elastic and viscous flow material responses. Dynamic mechanical analysis (DMA, also called dynamic mechanical thermal analysis, DMTA) enables simultaneous study of both elastic (symbol ) and viscous flow (symbol ") types of behavior. One determines the response of a specimen to periodic deformations or stresses. Normally, the specimen is loaded in a sinusoidal fashion in shear, tension, flexion, or torsion. If, say, the experiment is performed in tension, one determines the elastic tensile modulus E called storage modulus and the corresponding viscous flow quantity E" called the loss modulus. 

Erom a practical viewpoint, Eq. (29.4) can be used to describe the stress-strain relation of a material if vi/(A) is known. m/(A) can be obtained in the laboratory in various ways, such as pure shear experiments as described by Valanis and Landel [60], by torsional measurements as described by Kearsley and Zapas [62] and by a combination of tension and compression experiments as also described by Kearsley and Zapas [62]. Treloar and co-workers [63] have also shown that the VL function description of the mechanical response of rubber is a very good one. The reader is referred to the original literature for these methods. 

Rheometers are used in a much larger frequency range than DMA, for a large variety of materials, from liquids to soft solids. Their configurations are plate-plate and cone-plate, whereas torsion and tension attachments are optional. Dynamic mechanical analyzers perform only oscillatory experiments on load-bearing samples (i.e., those that have a shape with well-defined dimensions, such as films, fibers, or bars). The samples can be fixed in specific attachments, such as tension, bending, shear, or compression. A new attachment has been developed for DMA that is intended for non-self-supporting samples—a material pocket (Pinheiro and Mano 2009). The material pocket behaves elastically over the studied temperature... 

In general, the output of a TMA measurement is a plot of sample dimension or dimensional change versus temperature or time recorded in expansion, compression, tension, or flexure. Expansion, compression, and tension experiments are the most common measurements. Table 4.3 summarizes some key TMA applications in different measurement modes using different sample probes. Details of these measurements are discussed further in Sections 4.6 and 4.7 of this chapter. In addition to these basic types of measurement shear and torsional modulus of films, fibers, laminates, and adhesives can be measured using specially designed probes. 

An additional nonlinear effect which appears in extension under high stresses, attributable to the volume expansion associated with the fact that Poisson s ratio is less than i, will be discussed in Chapter 18 it is manifested by a decrease in all the relaxation and retardation times. This effect is especially prominent in more complicated stress patterns such as combined tension and torsion, as studied by Sternstein. ° Nonllnear creep behavior under combined tension and torsion with the additional complication of changing temperature during the experiment has been studied by Mark and Findley. ... 

Experiments with biaxial stresses in varying ratio and combined tension and torsion have been used to distinguish between yielding by shear or normal stress failure. " ... 

---