Stress-strain-deformation analysis

For URPs, the emphasis is somewhat different. Due to their relatively low stiffness, component deformations under load may be much higher than for metals and the design criteria in step (b) are often defined in terms of maximum acceptable deflections. Thus, for example, a metal panel subjected to a transverse load may be limited by the stresses leading to yield and to a permanent dent. Whereas a URPs panel may be limited by a maximum acceptable transverse deflection even though the panel may recover without permanent damage upon removal of the loads. Even when the design is limited by material failure it is usual to specify the materials criterion in terms of a critical failure strain rather than a failure stress. Thus, it is evident that strain and deformation play a much more important role for URP than they do for metals. As a consequence, step (a) is usually required to provide a full stress/strain/ deformation analysis and, because of the viscoelastic nature of plastics, this can pose a more difficult problem than for metals. 

In summary, it can be seen that plastics and RPs design analysis follows the same three steps (a) to (c) as that for metals, but there are some differences of emphasis and difficulty. In particular, step (a) is usually more substantial for the newer materials, partly because a full stress/strain/deformation analysis is required and partly because of the need to take account of viscoelasticity, inhomogeneity, and/or anisotropy. For long fiber materials, the component design analysis may need to contain the associated material design analysis. 

Leis, B.N., Gowda, C.V.B., Topper, T.H. Cyclic inelastic deformation and the fatigue notch factor. Cyclic stress-strain behavior—analysis, experimentation and failure prediction. Am. Soc. Test. Mater., ASTM STP 519, 133-159 (1973)... 

Shear-stress-shear-strain curves typical of fiber-reinforced epoxy resins are quite nonlinear, but all other stress-strain curves are essentially linear. Hahn and Tsai [6-48] analyzed lamina behavior with this nonlinear deformation behavior. Hahn [6-49] extended the analysis to laminate behavior. Inelastic effects in micromechanics analyses were examined by Adams [6-50]. Jones and Morgan [6-51] developed an approach to treat nonlinearities in all stress-strain curves for a lamina of a metal-matrix or carbon-carbon composite material. Morgan and Jones extended the lamina analysis to laminate deformation analysis [6-52] and then to buckling of laminated plates [6-53]. 

This consists of experimental measurements of stress-strain relations and analysis of the data in terms of the mathematical theory of elastic continua. Rivlin7-10 was the first to pply the finite (or large) deformation theory to the phenomenologic analysis of rubber elasticity. He correctly pointed out the above-mentioned restrictions on W, and proposed an empirical form... 

True Tensile Stress-Strain. As indicated above, analysis of high speed motion pictures of material deformation during tensile testing provides a measure of maximum strain change in cross-sectional area and... 

As shown above, the ZrO/Ni composites examined by disk-bend testing are found to deform in a nonlinear manner, so that composition-dependent fracture strengths cannot be obtained directly from the stress-strain diagram in Fig. 3. Under the circumstances, we now make a micromechanical analysis to estimate actual stresses to be developed by plastic deformation of the ductile constituent on the basis of an established "mean-field" model [12]. In the following, the macrostress a) is related to the microstresses and (o) such... 

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