Solid material uniaxial

For linear elastic materials, Hooke s Law is a constitutive relationship between stress and strain. There have been substantial efforts in identifying similar relationships for plastic solids. In uniaxial tests, the portion of the true stress-true strain curve beyond yielding is often described by... 

Stress in crystalline solids produces small shifts, typically a few wavenumbers, in the Raman lines that sometimes are accompanied by a small amount of line broadening. Measurement of a series of Raman spectra in high-pressure equipment under static or uniaxial pressure allows the line shifts to be calibrated in terms of stress level. This information can be used to characterize built-in stress in thin films, along grain boundaries, and in thermally stressed materials. Microfocus spectra can be obtained from crack tips in ceramic material and by a careful spatial mapping along and across the crack estimates can be obtained of the stress fields around the crack. ... 

The material properties used in the simulations pertain to a new X70/X80 steel with an acicular ferrite microstructure and a uniaxial stress-strain curve described by er, =tr0(l + / )", where ep is the plastic strain, tr0 = 595 MPa is the yield stress, e0=ff0l E the yield strain, and n = 0.059 the work hardening coefficient. The Poisson s ratio is 0.3 and Young s modulus 201.88 OPa. The system s temperature is 0 = 300 K. We assume the hydrogen lattice diffusion coefficient at this temperature to be D = 1.271x10 m2/s. The partial molar volume of hydrogen in solid solution is... 

Note 1 For a material specimen which behaves as a Voigt-Kelvin solid under forced uniaxial extensional oscillation with mass added at the point of application of the applied oscillatory force, Av is proportional to the loss modulus (E"). 

A method for measuring the uniaxial extensional viscosity of polymer solids and melts uses a tensile tester in a liquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extruder may be part of the apparatus and may be combined with a device for clamping the extruded material (220). However, most of the more recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is applied, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Although the uniaxial test has traditionally received the most attention, such tests alone may be insufficient to characterize adequately the mechanical capability of solid propellants. This is especially true for ultimate property determinations where a change in load application from one axis to several at once may strongly affect the relative ranking of propellants according to their breaking strains. Since the conditions usually encountered in solid rocket motors lead to the development of multiaxial stress fields, tests which attempt to simulate these stress fields may be expected to represent more closely the true capability of the material. 

The uniaxial failure envelope developed by Smith (95) is one of the most useful devices for the simple failure characterization of many viscoelastic materials. This envelope normally consists of a log-log plot of temperature-reduced failure stress vs. the strain at break. Figure 22 is a schematic of the Smith failure envelope. Such curves may be generated by plotting the rupture stress and strain values from tests conducted over a range of temperatures and strain rates. The rupture locus moves counterclockwise around the envelope as the temperature is lowered or the strain rate is increased. Constant strain, constant strain rate, and constant load tests on amorphous unfilled polymers (96) have shown the general path independence of the failure envelope. Studies by Smith (97) and Fishman (29) have shown a path dependence of the rupture envelope, however, for solid propellants. 

Fig. 46 a Stress contributions of the strained filler clusters for the different pre-strains (upper part), obtained as in Fig. 45b. The solid lines are adapted with the integral term of Eq. (47) and the log-normal cluster size distribution Eq. (55), shown in die lower part. The obtained parameters of the filler clusters are Qe /d 3=26 MPa, =25, and b=0.8. b Uniaxial stress-strain data (symbols) as in Fig. 45c. The insert shows a magnification for the smaller strains, which also includes equi-biaxial data for the first stretching cycle. The lines are simulation curves with the log-normal cluster size distribution Eq. (55) and material parameters as specified in the insert of Fig. 45a and Table 4, sample type C40...

Fig. 47 a Uniaxial stress-strain data in stretching direction (symbols) of S-SBR samples filled with 60 phr N 220 at various pre-strains smax and simulations (solid lines) of the third up- and down-cycles with the cluster size distribution Eq. (55). Fit parameters are listed in the insert and Table 4, sample type C60. b Simulation of uniaxial stress-strain cycles for various pre-strains between 10 and 50% (solid lines) with material parameters from the adaptation in a. The dashed lines represent the polymer contributions according to Eqs. (38) and (44) with different strain amplification factors... 

The strength properties of solids are most simply illustrated by the stress-strain diagram, which describes the behaviour of homogeneous brittle and ductile specimens of uniform cross section subjected to uniaxial tension (see Fig. 13.60). Within the linear region the strain is proportional to the stress and the deformation is reversible. If the material fails and ruptures at a certain tension and a certain small elongation it is called brittle. If permanent or plastic deformation sets in after elastic deformation at some critical stress, the material is called ductile. 

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