Uniaxial-tensile tests

In the following, the relationship between fracture statistics and defect size distribution is discussed for the simple case of tensile tests (uniaxial and homogeneous stress state) on a homogeneous brittle material. The tests are performed on specimens of equal size. It is assumed that the volume of the specimens is V = V. The number of tested specimens (the sample size) isX. In each test the load is increased up to the moment of failure. The strength is the stress at the moment of failure. In each sample the strength values of the individual specimens are different, i.e. the strength is distributed. 

It is not necessary to know the bulk modulus to convert E to G. If the transverse strain, , of a specimen is determined during a uniaxial tensile test in addition to the extensional or longitudinal strain e their ratio, called F oisson s ratio, v can be used ... 

In the [ 45]j tensile test (ASTM D 3518,1991) shown in Fig 3.22, a uniaxial tension is applied to a ( 45°) laminate symmetric about the mid-plane to measure the strains in the longitudinal and transverse directions, and Ey. This can be accomplished by instrumenting the specimen with longitudinal and transverse element strain gauges. Therefore, the shear stress-strain relationships can be calculated from the tabulated values of and Ey, corresponding to particular values of longitudinal load, (or stress relations derived from laminated plate theory (Petit, 1969 Rosen, 1972) ... 

The [10°] off axis tension specimen shown in Fig 3.23 is another simple specimen similar in geometry to that of the [ 45 ]s tensile test. This test uses a unidirectional laminate with fibers oriented at 10° to the loading direction and the biaxial stress state (i.e. longitudinal, transverse and in-plane shear stresses on the 10° plane) occurs when it is subjected to a uniaxial tension. When this specimen fails under tension, the in-plane shear stress, which is almost uniform through the thickness, is near its critical value and gives the shear strength of the unidirectional fiber composites based on a procedure (Chamis and Sinclair, 1977) similar to the [ 45°]s tensile test. 

Fig. 48 Schematics showing (a) the tensile testing rig holding the sample between clamps for uniaxial deformation and (b) deformation stages in the sample, recorded with an optical imaging system. L0 is the original length of the sample, and L the length after deformation...

Blatz and Ko19 added a special attachment to their uniaxial tensile testing equipment (Fig. 5). In this, a sheet specimen of rubber is stretched by chucks attached to its four edges, but, differing from the apparatus of Rivlin and Saunders, the chucks can be moved smoothly on the rigid tracks so that it is possible to strech... 

Very often uniaxial tensile tests are used for polymer characterization. In the case of thermosets, at temperatures below Tg, the stress-strain curve is a straight line (elastic region) and fracture occurs (due to flaws contained in the specimen) well before yielding (Fig. 12.1a). So other tests have to be... 

Figure 12.1 Typical stress-strain curves for thermosets at a temperature below Tg (a) uniaxial tensile test (b) uniaxial compression test. 

Fig. 21. Schematic diagram of process flow stress paths for elements of material undergoing extrusion through a conical die of small semi-angle, and a uniaxial tensile test...

Coherently, as expected for immiscible blends, Tg values measured by DSC show very small variations with respect to the pure components while the mechanical properties degrade with respect to neat sPS. In particular, for minimum polyolefin contents <40 wt%, uniaxial tensile tests revealed a decrease in Young s modulus, elongation at break and energy to break. For higher contents, a phase inversion of the morphology occurs and the blend properties approach progressively those of the pure polyolefins. 

Although the uniaxial tension test is the one most widely used, it has two drawbacks when it is used to provide information on the yielding of polymers. First, the tensile stress applied can lead to brittle fracture before yield takes place, and second, yield occurs in an inhomogeneous way due to the formation of a neck accompanying the tensile test. In any case, given that the section of sample decreases as the stress increases, cj cy . 

Figure 14.5b represents the uniaxial compression test, which uses samples with cylindrical or rectangular cross section. The stress and strain are defined in an analogous way to that of the tensile test. This test overcomes the disadvantages mentioned in relation to a tensile test. The stress is compressive, and consequently there is no possibility of the brittle fracture observed in tensile deformation. Plastic yield can even be seen in thermostable materials, which, under other conditions, can be brittle. In addition, the determination of the yield stress is made under conditions of stable deformation since there is no geometrical reason for the formation of a neck such as occurs in tension. A problem that can arise in this test concerns the diameter/height ratio of the sample. If this ratio is too large friction between plates and sample will introduce a constraint, and if it is very small... 

As mentioned earlier, the Gc value required to define the CZ model is obtained from TDCB tests. The remaining parameter Gm is chosen as the UTS, and was extracted from the stress-strain curves at the corresponding rates. This was an arbitrary choice, since the level of the constraint near the crack tip is higher than that in uniaxial tensile tests used to obtain the stress-strain curves. Therefore, a sensitivity study on this parameter was performed. For illustration purposes, a numerical analysis carried out on TDCB test specimens bonded with the two adhesives under investigation is shown in this section. The value of a was varied from 20 to 80 MPa and numerical predictions of load versus time were compared against the experimental results. Fig. 5 shows a comparison of the FV and experimental results for different values for TDCB tests performed at 0.1 mm/min. The best fit G value should be able to predict correctly both the experimental force and crack history. (Note that the latter was found to be less sensitive to changes of the cohesive strength.)... 

Uniaxial tensile tests were carried out to determine the stress-strain curves and document the damage growth on a computer-controlled Instron model 8516 servo hydraulic testing machine operating at a strain rate of 5% min . The macroscopic tensile yield stress was considered equal to the maximum stress on the loading curve. The Young s modulus was determined as the plateau value of a plot of the secant modulus as a function of the strain. 

Orientation of commercial POM can be carried out using cylindrical samples which are obtained by extruding POM into a thermostatically controlled form. After the form is filled with the melt, it is removed from the extruder and gradually cooled down in a compression-molding press. Cylindrical specimens are then uniaxially stretched in a tensile test instrument at a temperature of 130°C and a stretching rate... 

Fig. 8 Surface of polypropylene bar after 80 weeks of UV exposure followed by uniaxial tensile test. Bar axis is vertical. Cracks formed in degraded layer, perpendicular to stress axis. Degraded surface is very fragile and easily parted from underlying material that is less degraded. Degradation tends to be greatest nearer to the corner, possibly because oxygen can diffuse into the surface layers from two adjacent surfaces. (Courtesy of T.J. Turton. See also Refs. ". )...

In a uniaxial tensile test the volume dilatation simply be-... 

The volume change in a uniaxial tensile test for the orthotropic case simply becomes... 

Light microscopy with Jenaphot 2000, X-ray diffraction analysis with a DRON-3X-ray diffractometer, measurement of Vickers hardness, and longterm hardness were used. The long-term hardness (1 hour at 1 kg load) was carried out at temperatures of 500 °C and 700 °C. Uniaxial tensile tests were done in a temperature range from RT to 800 °C in air at a strain rate of 710"3 s 1. 

The aim of this work is to provide both experimental information and a corresponding formalization in order to elucidate structural propellant grain safety during ignition. The experimental data were obtained from uniaxial tensile tests and simple shear tests performed with an imposed hydrostatic pressure varying from atmospheric pressure to 15 MPa. It is well established that the materials studied exhibit time-temperature and pressure-sensitive properties. The ultimate properties reported here are formalized in a proposed stress-failure criterion capable of including the pressure effect. 

Each type of propellant has specific mechanical characteristics, but the influence of test parameters (temperature, strain rate, and pressure) is the same for all propellants (11). Tensile tests are widely used to analyze propellant behavior as well as examine the manufacturing controls of the propellants. Because their behavior is not linear-elastic, it is necessary to define several parameters that allow a better representation of the experimental tensile curve. The stylistic experimental stress-strain response at a constant strain rate from a uniaxial tensile test is shown in Figure 7, where E is the elastic modulus (initial slope), Sr P is the tensile strength (used later for a failure criterion), and eXj> is the strain at tensile strength. 

Figure 7. Representation of a uniaxial tensile test with T, Vc, and P fixed.

Table I. Comparison of Maximal Stresses for Uniaxial and Equitriaxial Tensile Tests (HTPB Propellant)...

Figure 3 Strain/stress curves for composites in a uniaxial tensile test ...

Figure 4 Uniaxial tensile testing of two cellulose/pectin composites, before (thick lines) and after (thin lines) removal of pectin mediated by calcium chelation with CDTA...

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