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Stress history

The diagnostics applied to shock experiments can be characterized as either prompt or delayed. Prompt instrumentation measures shock velocity, particle velocity, stress history, or temperature during the initial few shock transits of the specimen, and leads to the basic equation of state information on the specimen material. Delayed instrumentation includes optical photography and flash X-rays of shock-compression events, as well as post-mortem examinations of shock-produced craters and soft-recovered debris material. [Pg.69]

In a given motion, a particular material particle will experience a strain history The stress rate relation (5.4) and flow rule (5.11), together with suitable initial conditions, may be integrated to obtain the eorresponding stress history for the particle. Conversely, using (5.16) instead of (5.4), may be obtained from by an analogous ealeulation. As before, may be represented by a continuous curve, parametrized by time, in six-dimensional symmetric stress spaee. [Pg.127]

Unloading. The stress lies on the elastic limit surface and the tangent to the stress history points inward into the elastic region/= 0,/< 0. Then ic = 0 and the elastic limit surface is stationary. [Pg.128]

If a motion is specified with satisfies the continuity condition, the velocity, strain, and density at each material particle are determined at each time t throughout the motion. Given the constitutive functions (e, k), c(e, k), b( , k), and a s,k) with suitable initial conditions, the constitutive equations (5.1), (5.4), and (5.11) may be integrated along the strain history of each material particle to determine its stress history. If the density, velocity, and stress histories are substituted into (5.32), the history of the body force at each particle may be calculated, which is required to sustain the motion. Any such motion is termed an admissible motion, although all admissible motions may not be attainable in practice. [Pg.131]

Impact of a thin plate on a sample of interest which is, in turn, backed by a lower impedance window material leads to an interaction of waves which will carry an interior planar region into tension. Spall will ensue if tension exceeds the transient strength of the test sample. A velocity or stress history monitored at the interface indicated in Fig. 8.4 may look as indicated in Fig. 8.5. The velocity (stress) pull-back or undershoot carries information concerning the ability of the test material to support transient tensile stress and, with appropriate interpretation, can provide a reasonable measure of the spall strength of the material. [Pg.272]

These latter curves are particularly important when they are obtained experimentally because they are less time consuming and require less specimen preparation than creep curves. Isochronous graphs at several time intervals can also be used to build up creep curves and indicate areas where the main experimental creep programme could be most profitably concentrated. They are also popular as evaluations of deformational behaviour because the data presentation is similar to the conventional tensile test data referred to in Section 2.3. It is interesting to note that the isochronous test method only differs from that of a conventional incremental loading tensile test in that (a) the presence of creep is recognised, and (b) the memory which the material has for its stress history is accounted for by the recovery periods. [Pg.52]

The simplest theoretical model proposed to predict the strain response to a complex stress history is the Boltzmann Superposition Principle. Basically this principle proposes that for a linear viscoelastic material, the strain response to a complex loading history is simply the algebraic sum of the strains due to each step in load. Implied in this principle is the idea that the behaviour of a plastic is a function of its entire loading history. There are two situations to consider. [Pg.95]

Example 2.13 A plastic which can have its creep behaviour described by a Maxwell model is to be subjected to the stress history shown in Fig. 2.43(a). If the spring and dashpot constants for this model are 20 GN/m and 1000 GNs/m respectively then predict the strains in the material after 150 seconds, 250 seconds, 350 seconds and 450 seconds. [Pg.96]

Superposition Principle that the entire stress history of the material contributes to the subsequent response. [Pg.99]

Example 2.14 A plastic is subjected to the stress history shown in Fig. 2.45. The behaviour of the material may be assumed to be described by the Maxwell model in which the elastic component = 20 GN/m and the viscous component r) = 1000 GNs/m. Determine the strain in the material (a) after u seconds (b) after 1/2 seconds and (c) after 3 seconds. [Pg.99]

A plastic which behaves like a Kelvin-Voigt model is subjected to the stress history shown in Fig. 2.87. Use the Boltzmanns Superposition Principle to calculate the strain in the material after (a) 90 seconds (b) 150 seconds. The spring constant is 12 GN/m and the dashpot constant is 360 GNs/m. ... [Pg.164]

It is instructive to describe elastic-plastic responses in terms of idealized behaviors. Generally, elastic-deformation models describe the solid as either linearly or nonlinearly elastic. The plastic deformation material models describe rate-independent behaviors in terms of either ideal plasticity, strainhardening plasticity, strain-softening plasticity, or as stress-history dependent, e.g. the Bauschinger effect [64J01, 91S01]. Rate-dependent descriptions are more physically realistic and are the basis for viscoplastic models. The degree of flexibility afforded elastic-plastic model development has typically led to descriptions of materials response that contain more adjustable parameters than can be independently verified. [Pg.31]

Thermoplastic polymer macromolecules usually tend to become oriented (molecular chain axis aligns along the extrusion direction) upon extrusion or injection moulding. This can have implications on the mechanical and physical properties of the polymer. By orienting the sample with respect to the coordinate system of the instrument and analysing the sample with polarised Raman (or infrared) light, we are able to get information on the preferred orientation of the polymer chains (see, for example, Chapter 8). Many polymers may also exist in either an amorphous or crystalline form (degree of crystallinity usually below 50%, which is a consequence of their thermal and stress history), see, for example, Chapter 7. [Pg.528]

The sum in this expression can be replaced by an integral which will enable us to describe the strain response to any stress history ... [Pg.121]

Apply the Boltzmann superposition principle for the case of a continuous stress application on a linear viscoelastic material to obtain the resulting strain y(t) in terms of J(t — t ) and ih/dt, the stress history. Consider the applied stress in terms of small applied At,-, as shown on the accompanying figure. [Pg.142]

Cogswell (1985) expressed it in the following words "To make the connection from the basic material properties to the performance in the final product, industrial technologists had to learn a new science". It is more or less so, that - for liquid crystal polymers -properties like stress history, optical and mechanical anisotropy, and texture seem to be independent variables this in contradistinction to the situation with conventional polymers. [Pg.581]

This test may be useful for a rapid comparison of a number of polymers. A theoretical interpretation of the results is almost impossible, however, because temperature and stress history of the polymer are completely undefined. [Pg.812]

Figure 9-33a shows the predicted shear stress as a function of strain for the initial foam orientation depicted in Fig. 9-32. The stress grows continuously until at y = 1.15 a T1 reorganization occurs which brings the cell structure back to its starting state, and the stress jumps back to zero. Thereafter, the stress history repeats itself. Similar periodic stress patterns and stress jumps have been predicted for the three-dimensional tetrakaidecahedron foam model (Reinelt 1993). If the initial orientation is rotated through an angle of r/12 with respect to that shown in Fig. 9-32, the stress history also has jumps, but is aperiodic (see Fig. 9-33b). Aperiodic behavior is the norm, and periodic stress histories occur only for special initial orientations (Kraynik and Hansen 1986). These unsteady, discontinuous stress... Figure 9-33a shows the predicted shear stress as a function of strain for the initial foam orientation depicted in Fig. 9-32. The stress grows continuously until at y = 1.15 a T1 reorganization occurs which brings the cell structure back to its starting state, and the stress jumps back to zero. Thereafter, the stress history repeats itself. Similar periodic stress patterns and stress jumps have been predicted for the three-dimensional tetrakaidecahedron foam model (Reinelt 1993). If the initial orientation is rotated through an angle of r/12 with respect to that shown in Fig. 9-32, the stress history also has jumps, but is aperiodic (see Fig. 9-33b). Aperiodic behavior is the norm, and periodic stress histories occur only for special initial orientations (Kraynik and Hansen 1986). These unsteady, discontinuous stress...
Owing to the entropic changes that take place in a viscoelastic system perturbed by a force field, the response does not vanish when the perturbation field ceases. A consequence of this fact is that the deformation depends not only on the actual stress but also on the previous stresses (mechanical history) undergone by the material in the past. Under the linear behavior regime, the responses to different perturbations superpose. Let us assume that the stresses Aa(0i) and A(t(02) are applied on the material at times 0j and 02, respectively. This stress history is shown schematically in Figure 5.12. The response is given by... [Pg.207]

Figure 5.12 Schematic representation of the response of a viscoelastic material (b) to the shear stress history (a). Figure 5.12 Schematic representation of the response of a viscoelastic material (b) to the shear stress history (a).
For reasons that will become clear, it is important to obtain the time dependence of the shear strain under the shear stress history indicated in Figure 5.13. In this case a = and H t — 0)ci = 0. The shear strain at t = 0 will be... [Pg.208]

This is the Boltzmann superposition principle for creep experiments expressed in continuous form. If the stress is a continuous function of time in the interval —oo < < 8i, constant in the interval 0i < / < 02, and again a continuous function for t > 02 (see Fig. 5.14), then Eq. (5.35) cannot be used to obtain e because the contribution of the stress to the strain in the interval 0i < t < 02 would be zero. The response for this stress history is given by... [Pg.211]

Figure 5.16 Schematic sketch showing fading memory for an arbitrary shear stress history. Figure 5.16 Schematic sketch showing fading memory for an arbitrary shear stress history.
For a stress history ct = CToFT(0 the Laplace transform of Eq. (10.27) gives... [Pg.401]

Figure 1.5. Axial stress history at various depths (every 50 pm) within a calcite sample shocked with the electric discharge gun. The shock wave is induced by the unpact of a 50 pm Mylar plus a 50 pm Al foil onto the bulk calcite target. Figure 1.5. Axial stress history at various depths (every 50 pm) within a calcite sample shocked with the electric discharge gun. The shock wave is induced by the unpact of a 50 pm Mylar plus a 50 pm Al foil onto the bulk calcite target.

See other pages where Stress history is mentioned: [Pg.116]    [Pg.128]    [Pg.362]    [Pg.202]    [Pg.123]    [Pg.98]    [Pg.99]    [Pg.375]    [Pg.137]    [Pg.185]    [Pg.108]    [Pg.9]    [Pg.324]    [Pg.19]    [Pg.100]    [Pg.100]    [Pg.115]    [Pg.210]    [Pg.212]    [Pg.213]    [Pg.231]    [Pg.698]    [Pg.13]    [Pg.226]   
See also in sourсe #XX -- [ Pg.158 , Pg.160 ]

See also in sourсe #XX -- [ Pg.153 ]

See also in sourсe #XX -- [ Pg.375 ]




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