Elastic-plastic behaviour

Load-extension curves for non-elastic (plastic) behaviour... 

The same test can also be used for the determination of the elastic/plastic behaviour of materials for example, the yield strength. For this purpose, computer programs necessary to correlate the characteristics and behaviour of materials with the detonation parameters of explosives have been developed. 

Comas-Cardona S, Le Grognec P, Binetruy C, Krawczak P. Unidirectional compression of fibre reinforcements. Part 1 A non-linear elastic-plastic behaviour. Composites Science andTechnology,20017,67(3-4) 507—514. EX)I http //dx.doi. org/10.1016/j.compsci tech.2006.08.017. 

The elastic-plastic behaviour of materials is frequently described by stress-strain curves measured in tensile tests. Tensile tests are used to determine material parameters that are then listed in tables, for example in ISO standards. These parameters are used in selecting materials and in component design. Even if the shape of the component is complex and the stress state multiaxial, criteria can be used that allow to employ the parameters determined in tensile tests. We will see in section 3.3 how this is done in the case of plasticity. 

A. C. Fischer Cripps, Elastic plastic behaviour in materials loaded with a spherical indenter, J. Mat. Sci. 32, 727 36 (1997). 

Figure 3 shows the load (P) - load line displacement (5) records obtained from fracture tests at room temperature and at quasi-static conditions (low loading rates) of propylene homopolymer, PPO, and thee controlled-rheology PPs. The mechanical response for all the materials presented clearly elastic-plastic behaviour and this justifies the use of the EPFM multiple specimen method to evaluate the fracture behaviour. In addition, all the curves deviated from linearity and at a certain deflection level, sudden instability occurred and the specimen broke in two halves. The difference in stiffness is due to the different initial crack lengths. 

As clearly discussed, the mechanical behaviour of polymers changes rapidly as the temperature is reduced or the strain rate increased. Brooks et al. have shown that for polyethylene there is a sudden transition in the yield strain at temperatures below ambient, the exact temperature depending on the sample morphology. Figure 12.31 shows results for linear PE. It was also found that this temperature marks the change from classical elastic-plastic behaviour to time-dependent viscoelastic behaviour where the yielded samples show... 

Figure 6.17 Elastic-plastic behaviour of the adhesive, (a) Models of the elastic-plastic shear stress versus strain curve of the adhesive for use in stress analysis calculations (i) the dashed line is the representation suggested by Hart-Smith [4,55] i.e. perfect elastic-plastic behaviour, (ii) representation suggested by ESDU [64,67]. (b) Schematic representation of the effect of elastic-plastic, as opposed to solely elastic, behaviour of the adhesive on the stress distribution in a single lap joint.

The depth of the print, created during nanoindentation test, hereafter called residual displacement, e is a function of the applied load W, and of the local elastic plastic behaviour of the material, that can be represented by the value of Xe, E and v. Therefore, since the load is known and the elastic parameters are constant in die depth of the nitrided layer (E=210 GPa, v = 0.3 [8]), there is a direct relation between e, and Xe. To measure the depth of the print, the indentation head is loaded and unloaded at increasing maximum load, following the procedure shown in figure 3. The displacement is recorded at the same time. The residual displacement is calculated as the difference between displacement for a low load after unloading and before the first load. In a single test, 0, is then determined for several loads W and for the same local elastic plastic behaviour. 

This process has been applied to the measurement of the elastic plastic behaviour of the nitrided layer of 32CrMoV13 steel. Nano-indentation tests have been made at different depth of the nitrided layer, on a cut perpendicular to the nitrided surface. 

The endurance limit HIM has also been determined for dents created on M50. The elastic plastic behaviour of M50 has been determined by Lamagn e et al. [5]. Results are compared for both steels in figure 16 and 17, for dents made with the indenter of radii Rp=200 and 400 pm at different loads Wj. For all dents, HIM is equal or higher for nitrided 32CrMoV13 than for M50, as it is observed experimentally. In addition it can be noted that Rp=400 pm indenter (figure 17) is more efficient to discriminate materials than Rp=200 pm indenter (figure 16). 

Recommendations for design, testing and evaluation of such composites were developed in France [45]. Using these recommendations, Chanvillard and Rigaud [46] evaluated the tensile and flexural properties of DUCTAL using notched specimens. Elastic-plastic behaviour in tension was observed, up to crack widths... 

Historically, the modulus problem has been dealt with on a purely empirical basis and it is only recently that advances in mathematical modelling have given an insight into what is really required — the modification of the elastic/plastic behaviour of adhesives (shown schematically in Fig. 7.5 where the two extreme curves bracket the possibilities generated by the manipulation of the intermediate example). 

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