Force-displacement diagram

FIGURE 17 Force-displacement diagram for energy analysis [104-108]. 

Repair of damaged SBR concrete specimens using of epoxy resin and of the hard flexible polymer PT. According to the first approach, three pairs of specimens from each group of modified concrete (C5% le and C5% lpt, C10% 2e and C10% 2pt, C20% 3e and C20% 3pt) were tested up to damage with measurements of force and vertical displacement (deflection). Obtained results are presented in form of force-displacement diagrams in Fig. 12a,b,c. Specimens repaired in each pair with the epoxy resin (e5 l, e5 2, e5 3) and the polymer PT (pt5 l, pt5 2, pt5 3) were tested also up to damage. Obtained results are presented as comparison in Fig. 12a,b,c. Every specimen was broken in concrete in a certain distance from the repair joint (Fig. 13a,b). 

Masonry Modeling, Fig. 5 Results obtained with interface cyclic loading model for shear walls, in terms of force-displacement diagram and failure mode (a) wall failing in shear (b) wall failing in bending... 

Rubber Shock Absorbers as a Mitigation Technique for Earthquake-induced Pounding, Fig. 6 Force-displacement diagram of the non-linear impact model with hysteretic damping... 

The force-time and force-displacement diagrams of the proposed nonlinear model for simulating the response of rubber bumpers under impact loading are shown in Fig. 6. Figure 7 demonstrates the same diagrams in the case of exceeding the ultimate compressive capacity of the bumper for three different values of the coefficient of restitution. 

Figure 3. IS A simplified pull-out force-displacement diagram (after Bartos [I]).

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

Other authors tried similar attempts [110, 111] and the developed methods were regarded to be very useful [27, 112-115], Antikainen and Yliruusi [116] more recently tried to derive further parameters from the diagrams to enable a more complete characterization. An overview on the possibilities for force-displacement analysis is given by Ragnarson [117]. 

As described earlier, diagrams of transducer output against time enable parameters such as contact time and dwell time to be defined Fig. 8. Also the slope of the displacement-time diagram equals the speed of the punch and the slope of the force-time diagram is the rate of change of the force. If the operating speed of the press is altered, there is a proportional change in all of these. 

The mechanical behavior of polymers is well recognized to be rate dependent. Transitions from ductile to brittle mode can be induced by increasing the test speed. The isotactic PP homopolymer with high molecular weight is ductile at low speed tensile tests. It is brittle at tension under high test speeds at room temperature. Grein et al. (62) determined the variation of Kiq with test speed for the a-PP CT samples (Fig. 11.22). The force-displacement (F-J) curves and the schematic diagrams of the fracture surfaces of CT samples are presented in Fig. 11.23. At a very low test speed of 1 mm s , the F-d curve exhibits a typical ductile behavior as expected. At 10 mm s, the F-d curve stiU displays some nonlinearity before the load reaches its maximum value, but this is substantially suppressed as test speeds increase further. The samples fail in brittle mode at test speeds >500 mm s . From Fig. 11.22, the Kiq values maintain at 3.2 MPam at test velocities from 1 to... 

Figure 14. Idealized force-displacement curve resulting from a fracture experiment using a uniform double cantilever beam specimen. Load is applied to a certain displacement until the crack propagates, at which point the load and crack length are measured. The diagram shows the results of an experiment in which the sample is unloaded prior to reloading. The change in slope with each reloading is due to the change in compliance of the specimen which is a function of crack length.

In these tests the coefficients were proposed as follows A = 3.5, B = 3.38, 3 = 0.92 for s = 40 pm and ( = 21.3 mm. The equation (8.13) may be represented by a 3D diagram shown in Figure 8.16. This image of the pull-out test is less simple than the previously accepted force-displacement curve, but it reflects a real process in which the equation t = f(s) varies with the coordinate along the embedment zone. 

Figure 13. Force versus displacement diagram for the system with parameters, (b) non-optimal parameters.

Figure 9 demonstrates the load-displacement diagrams for the two cases of the impact velocity and for both cases of with and without the use of the rubber bumper. The results show that the indentation, which represents the local deformation at the vicinity of an impact, is much larger in the case of having the rubber shock absorber due to the reduced impact stiffness. Furthermore, in the case of the relatively high impact velocity of 1.0 m/s, the deformation exceeds the maximum compressive capacity of the 5 cm thick rubber bumper, and the impact force begins to rise rapidly, since the postyield linear impact stiffness is used. 

Fig. 1. Schematic diagram illustrating the mechanical instability for (a) a weak spring (spring constant k) a distance D from the surface, experiencing an arbitrary surface force (after [19]) and (b) the experimentally observed force-distance curve relative to the AFM sample position (piezo displacement) for the same interaction.

Figure 1. Schematic diagram of sample strip chart recording of the peel force vs. displacement.

One method to analyze tableting data is the use of force-time or pressure-time diagrams. They are easily recordable since displacement measurement is not necessary. 

Fig. 5-5. Schematic one-dimensional relative enthalpy diagram for the exothermic bimolecular displacement reaction HO + CH3—Br —> HO—CH3 + Br in the gas phase and at various degrees of hydration of the hydroxide ion [485]. Ordinate standard molar enthalpies of (a) the reactants, (b, d) loose ion-molecule clusters held together by ion-dipole and ion-induced dipole forces, (c) the activated complex, and (e) the products. Abscissa not defined, expresses only the sequence of (a). .. (e) as they occur in the chemical reaction. The barrier heights ascribed to the activated complex at intermediate degrees of hydration were chosen to be qualitatively consistent with the experimental rate measurements cf. Table 5-3 [485]. Possible hydration of the neutral reactant and product molecules, CH3—Br and HO—CH3, is ignored. The barrier height ascribed to the activated complex in aqueous solution corresponds to the measured Arrhenius activation energy. A somewhat different picture of this Sn2 reaction in the gas phase, which calls into question the simultaneous solvent-transfer from HO to Br , is given in reference [487].

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