Load-deformation-failure

Note that the lamina failure criterion was not mentioned explicitly in the discussion of Figure 4-36. The entire procedure for strength analysis is independent of the actual lamina failure criterion, but the results of the procedure, the maximum loads and deformations, do depend on the specific lamina failure criterion. Also, the load-deformation behavior is piecewise linear because of the restriction to linear elastic behavior of each lamina. The laminate behavior would be piecewise nonlinear if the laminae behaved in a nonlinear elastic manner. At any rate, the overall behavior of the laminate is nonlinear if one or more laminae fail prior to gross failure of the laminate. In Section 2.9, the Tsai-Hill lamina failure criterion was determined to be the best practical representation of failure... 

For cross-ply laminates, a knee in the load-deformation cun/e occurs after the mechanical and thermal interactions between layers uncouple because of failure (which might be only degradation, not necessarily fracture) of a lamina. The mechanical interactions are caused by Poisson effects and/or shear-extension coupling. The thermal interactions are caused by different coefficients of thermal expansion in different layers because of different angular orientations of the layers (even though the orthotropic materials in each lamina are the same). The interactions are disrupted if the layers in a laminate separate. 

For angle-ply laminates, no such knee or change in slope occurs in the load-deformation behavior. Simultaneous failure (fracture) of all layers occurs. 

The maximum in the curve denotes the stress at yield av and the elongation at yield v. The end of the curve denotes the failure of the material, which is characterized by the tensile strength a and the ultimate strain or elon gation to break. These values are determined from a stress-strain curve while the actual experimental values are generally reported as load-deformation curves. Thus (he experimental curves require a transformation of scales to obtain the desired stress-strain curves. This is accomplished by the following definitions. For tensile tests ... 

A survey of the load-deformation curves for linear polymers at different temperatures is given in Fig. 25.1A. Each mechanism is further illustrated by a schematic diagram (Figs. 25.1B-E). The mathematical equations for the different mechanisms were given in the Chaps. 13-15. Based on the respective equations Ahmad and Ashby designed Failure Mechanism Maps. The most important of these are reproduced here as Fig. 25.2A-D. 

Fatigue Wear (Hailing, 1975) Hailing model Wf, = K 4 Fn Wf3 = wear rate j] = line distribution of asperities 7 = constant defining particle size ej = strain to failure in one loading cycle H = hardness of the softer material K = wear coefficient Incorporates the concept of fatigue failure as well as simple plastic deformation failure. 

Fig. 6.2 Typical load-deformation relationship of the ACL and the definition of structural properties (stiffness, load at failure, and maximum deformation). Numerical data of the load at failure and stiffness are referred from the original work [33] while numerical datum of the maximum deformation is an approximate number...

It has been our practice to preload the tensile specimens at a crosshead speed of 0.00004 cm/s to a 455-kg (1000 lbs) load to allow the copper collets to deform around the root radius of the buttonhead. After seating for 5 minutes the specimen is loaded to failure using a crosshead speed of 0.004 cm/s. For elevated temperature strength measurements the heated furnace is placed around the preloaded specimen, which is allowed to reach the test temperature ( 15 minute soak time), and then fast-loaded to failure. During the initial testing at 1400°C the first three PY6 specimens failed under preload (455 kg -140 MPa) during the 15-minute soak time. To prevent premature... 

An idea of the impact energy associated with these types of failure can be ascertained by consideration of a typical load-deformation curve. This in general will be of the form shown in Figure 18.26. From the definitions given previously a brittle-type failure will occur on the initial, essentially linear part of the curve, prior to the yield point. A... 

If this ve el had been fabricated from SA-283, Grade C steel, two of the stresses in the shell, /axiai combined and / circumferential combined, would be above the minimum yield point of 30,000 psi for this material. This indicates that mme plastic deformation will occur and that these computed theoretical stresses will not be reached since- they will be relievetl by plastic defonnation. If this vessel was operateti under cyclic loading conditions, failure might have occurred by brittle fracture if the stress range had ext eeded twice the yield point. (See Chapter 2.)... 

The effective strength of plastics is influenced by time, temperature, and environment. For example, the breaking point for a thermoplastic material under short-term tensile testing is reached only after considerable material deformation has taken place, at least 10 percent, and in some cases over 100 percent (the ultimate elongation for reinforced thermosets is lower than for thermoplastics). Under long-term continuous loading, material failure (or an unacceptable level of material damage) will occur at much lower deformations than in tensile test-... 

Force and/or temperature-induced elastic deformation failure occurs whenever the elastic (recoverable) deformation in a product, brought about by the imposed operational loads or temperatures, becomes large enough to interfere witli its ability to perform its intended function satisfactorily. 

In addition to load distribution, failure of the diaphragm is also important to model apart from failure of arch-supported diaphragms that tend to be sensitive to relative in-plane deformations of... 

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