Stress-strain behavior nonlinear

Robert M. Jones ar Harold S. Morgan, Analysis of Nonlinear Stress-Strain Behavior of Fiber-Reinforced Composite Materials, AIAA Journal, December 1977, pp. 1669-1676. 

Harold S. Morgan and Robert M. Jones, Analysis of Nonlinear Stress-Strain Behavior of Laminated Fiber-Reinforced Composite Materials, Proceedings of the 1978 International Conference on Composite Materials, Bryan R. Noton, Robert A. Signorelli, Kenneth N. Street, and Leslie N. Phillips (Editors), Toronto, Canada, 16-20 April 1978, American Institute of Mining, Metallurgical a Petroleum Engineers, New York, 1978, pp. 337-352. 

Harold S. Morgan and Robert M. Jones, Buckling of Rectangular Cross-Ply Laminated Plates with Nonlinear Stress-Strain Behavior, Journal of Applied Mechanics, September 1979, pp. 637-643. 

Let s address the issue of nonlinear material behavior, i.e., nonlinear stress-strain behavior. Where does this nonlinear material behavior come from Generally, any of the matrix-dominated properties will exhibit some degree of material nonlinearity because a matrix material is generally a plastic material, such as a resin or even a metal in a metal-matrix composite. For example, in a boron-aluminum composite material, recognize that the aluminum matrix is a metal with an inherently nonlinear stress-strain curve. Thus, the matrix-dominated properties, 3 and Gj2i generally have some level of nonlinear stress-strain curve. 

For optimum cross-linking efficiency, a combination of accelerators is used. Table 6 shows the increase in load-bearing capability of vulcanizates based on different rubbers as the ratio of two accelerators is changed (14). The term 300% modulus represents the strain at 300% stress and is not a true modulus because rubber gives nonlinear stress—strain behavior. For polymers with primary allylic carbon atoms, the use of two accelerators gives significandy higher 300% modulus than either accelerator used alone. When the mbber polymer consists of secondary allylic carbon atoms, the modulus is level until the sulfenamide OBTS becomes the principle accelerator. 

Several typically negligible effects have been neglected in the derivation of Eq. 3.83, including (1) interactions between the interstitials, (2) effects of the interstitials on the local elastic constants, (3) quadratic terms in the elastic energy, and (4) nonlinear stress-strain behavior. A more complete treatment, applicable to the present problem, takes into account many of these effects and has been presented by Larche and Cahn [21]. 

Generally, when testing materials with a nonlinear stress-strain behavior, the tests should be conducted under uniform stress fields, such that the associated damage evolution is also uniform over the gauge section where the material s response is measured. Because the stress field varies with distance from the neutral axis in bending tests, uniaxial tension or compression tests are preferred when characterizing the strength and failure behavior of fiber-reinforced composites. 

Polymers which yield extensively under stress exhibit nonlinear stress-strain behavior. This invalidates the application of linear elastic fracture mechanics. It is usually assumed that the LEFM approach can be used if the size of the plastic zone is small compared to the dimensions of the object. Alternative concepts have been proposed for rating the fracture resistance of tougher polymers, like polyolelins, but empirical pendulum impact or dart drop tests are deeply entrenched forjudging such behavior. 

The model couples the effects of stress and flow and accounts for varying permeability and compressibility of the pore fluid and nonlinear stress-strain behavior of the reservoir rock. The major factor responsible for fluid production is the compressibility attained by the pore fluid as a result of gas evolution. Transient flow rate is a function of the reservoir... 

The latter requires the torque to be constantly adjusted and so is more inconvenient to apply, but it keeps the strain in the test piece much more constant, and therefore the nonlinear stress strain behavior of the material causes less interference in the estimation of the temperature effect. 

Fig. 8. (a) Stress-strain plot for a generalized Maxwell model to different strain rates, as depicted in figure. Plot shows nonlinear stress-strain behavior in spite of material model (Maxwell) following laws of linear viscoelasticity (see text), (b) Stress and strain data from different strain rates given in (a) divided by strain rate dy/dt, demonstrating that material model follows linear viscoelasticity (see text). 

As mentioned earlier, there have been many attempts to develop mathematical models that would accurately represent the nonlinear stress-strain behavior of viscoelastic materials. This section will review a few of these but it is appropriate to note that those discussed are not all inclusive. For example, numerical approaches are most often the method of choice for all nonlinear problems involving viscoelastic materials but these are beyond the scope of this text. In addition, this chapter does not include circumstances of nonlinear behavior involving gross yielding such as the Luder s bands seen in polycarbonate in Fig. 3.7. An effort is made in Chapter 11 to discuss such cases in connection with viscoelastic-plasticity and/or viscoplasticity effects. The nonlinear models discussed here are restricted to a subset of small strain approaches, with an emphasis on the single integral approach developed by Schapery. 

The addition of continuous fibers to a ceramic matrix can significantly change the failure mode. Monolithic ceramics have linear stress-strain curves and fail catastrophically at low strain levels. However, CMCs display nonlinear stress-strain behavior with much more area under the curve, indicating that more energy is absorbed during failure and that the material has a less catastrophic failure mode. 

Bounding surface plasticity models may be used to simulate nonlinear stress-strain behavior in one dimension. Example of such models and their application in site response analysis can be found in Borja et al. (2002). 

Figure 8 shows the temperature contour lines for the steady-state thermal analysis. Note the brick half-section was modeled with an element mesh of 9 elements across the width and 18 elements along the length. The element mesh chosen is typically based on the expected nonlinear stress-strain behavior of the refractory and the nonlinear compression-only behavior of the brick joint. In the case of castable systems, the circumferential width of the model is selected by trial solutions to determine the estimated maximum circumferential tensile stress that could be developed by the castable lining. Figure 8 is a line contour plot in which the letters on the contours represent a temperature at that location. Color contour plots are also available from most programs and provide a much better visualization of the temperature distribution, especially for more complicated temperature distributions. 

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