Force-deflection curves

For the standard test pieces, force/deflection is recorded up to 25% at 10 mm/min, four cycles being made and from the fourth the secant moduli at 10% and 20% strain are obtained. The importance of mechanical conditioning has been discussed in Chapter 5 and this standard is one of the rare examples of where such a procedure is specified. Quite illogically, the test for products is normally done without mechanical conditioning and the force deflection curve is obtained to 30% so that the stiffness at 25% can be used as the result. Sensibly, provision would be made for the strain and the conditioning to be chosen to suit the particular application. 

The CFD (compression force deflection) as well as IFD (indentation force deflection) curves of these foams are relatively linear in comparison with slabstock foams, as shown in Figures 10 and 11. 

The growth of fracture mechanics has placed greater emphasis on tests that use sharply notched specimens. These results were found to provide more fundamental information. Instrumented impact testing is a recent development that provides information on force-deflection curves. In addition to these notched bar tests, extensive use of falling dart tests is also being made. However, interpretation of the data from the latter is far from straight... 

One term unique to the flexural test is the stress at the conventional deflection. Generally with ductile materials the test piece does not reach a point of fracture but simply keeps bending until eventually it slips from the outer supports. The conventional deflection is defined as 1.5 times the test piece thickness, which for the standard span of 16 times the thickness equates to a strain of 3.5%. The stress at this point forms a useful, if arbitrary, charaeteristic for duetile materials, which occurs before the peak in the force-deflection curve is reached. 

FIGURE 2.10.3 Force-deflection curves for multiple probes of a single bovine Hver. The curves are truncated at the deflection where puncture occurs. Different curves indicate differences in blood vessel locations as well as other tissue inhomogeneities. (From Okamura, A.M. et al., IEEE Tram. Biomed. Eng., 51,1707,2004. With permission.)... 

Figure 14.14 Force-deflection curves predicted for a bicycle helmet impacting flat, kerbstone and hemispherical anvils.

In Fig. 14.15, the energy under the force-deflection curve is equal to the energy input . Calculations will be made for E = 100 J. If the force just reaches lOkN, when the head-form decelerates to a momentary halt at deflection... 

In the discussion so far we have considered onfy linear elastic firacture mechanics (LEFM) the term linear elastic means that the cracked specimen ob Hooke s law to a good approximation. In the context of fracture mechanics, the requirement is that the extent of yielding in the neighbourhood of the crack tip is negligible, so that the force-deflection curves for... 

Figure 24.15 Comparison of force-deflection curves recorded in interlaminar shear strength tests between composites made with commercial glass fibers (as received) and fibers coated with the Pyre...

FIGURE W-5—Determination of energy area under force deflection curve for all types of ROPS equipment defined in 1926.1001... 

In the discussion so far we have considered only linear elastic fracture mechanics (LEFM) the term linear elastic means that the cracked specimen obeys Hooke s law to a good approximation. In the context of fracture mechanics, the requirement is that the extent of yielding in the neighbourhood of the crack tip is negligible, so that the force-deflection curves for test specimens are linear. In addition, the value of B must be sufficiently high that the deformation at the crack tip occurs under plane-strain conditions. It is found experimentally that these conditions are met if B, (IV — a), and a are all greater than 2.5(K,c/ffy). Provided these conditions are met, the spatial extent of the plastically deformed zone at the crack tip is less than 2 % of the above dimensions, the specimen fractures in plane-strain and the measured is a true material property. 

All these tests lead to the apparently justified conclusions that before is reached the preceding linear part of the force-deflection curve corresponds to elastic shear bond, and that the debonding processes start just at the maximum pull-out force Such a simple image was completed by observations published already by Pinchin and Tabor (1975) who have shown that the debonding crack appears along the pulled fibre at a certain distance of a few micrometers from its surface. These observations in the fibre-matrix interface after the pull-out test corroborated well with the measurements of micro-hardness of the interface, which have shown that the weakest layer was situated at a distance from the fibre surface (cf. Chapter 7). 

The value of is evaluated from the (nonlinear) force-deflection curve of the specimen at the moment of crack propagation and 2T is therefore determined without appeal to either linearity or finite-strain limitations. There is, however, an implicit appeal to elastic behavior, that is, to the assumption that no energy is dissipated in the recovery of strain in the shaded area of Figure 1. Since this is not in general a valid assumption, the fracture parameter 2T contains contributions from energy dissipated remote from the crack itself. A further consequence of this is that 2T may cease to be independent of the specimen configuration (size and shape). This problem is of course present with LEFM also. 

Many isolators, notably helical coil springs of steel, have straight-line force-deflection curves in their rated load range. For such isolators the slope of the force-deflection curve is equal to the stiffness and the stiffness is simply related to the static deflection s that the isolator experiences due to the load it supports. The static deflection needed to obtain a given transmissibihty may be estimated from... 

Carman et al. [ 18] developed a test called the meso-indentation test which used a hard spherical ball indenter to apply a compressive force to a surface of the composite perpendicular to the fiber axis. The indenter was much larger than the diameter of a single fiber therefore, when the ball was forced into the end of the composite, it made a permanent depression in the material. From the size of the depression and the force-deflection curve, they calculated a mean hardness pressure as a function of strain in the coupon. Qualitative differences have been reported in tests conducted on carbon fiber-epoxy composites where the fiber-matrix adhesion had been varied systematically. 

Chose an equally-spaced increasing sequence of stress Oj = /Ao (i = 1, 2, 3,...) and denote the associated static and creep time to failure fs(f) = fs(Oi) and t (i) = 4(0i), respectively. During static tests, the strain rates are kept constant and the force deflection curves are considered linear until failure is reached. Therefore, the stress increase is assumed to be linear during the static test. The linear stress gradient is approximated by a staircase function with the steps o O3,05,..., shown in Figure 6.15. This means that the overall degradation in a CSR test can be considered as series of creep loads. From Eq. 6.9 it follows ... 

Next we examined the expected error when mixing the material models inappropriately. Eigure 6 shows the non-cyclic material model and the cyclic material model in comparison to the first cycle data. As expected, the first cycle material model provides a better prediction of the response. This is especially noticeable at higher displacements where the first cycle FEA prediction is much closer to the experimental data. We then looked at the two material models versus the 5 cycle experiment, Eigure 7, and we see that the cycled material model provides a superior prediction of the force/deflection curve. The cycled FEA, MR 15c, captures the cyclic softened response of the fifth cycle. One caveat is at maximum deflection, comparing the fifth cycle experimental data versus the FEA will show a divergence due to the experiment approaching the maximum strain previously seen. 

---