Three-point beam bending

It has been shown that the tensile strength of roller compacted ribbons is reflected in the density of the compacts (59). A three point beam bending approach (69) was used to determine both tensile strengths and Young s moduli for both ribbons and uniaxial compacted surrogates for ribbons (Fig. 16) (4) which have been used to determine compaction properties when material is limiting. 

Table 4 Elastic moduli and section stiffnesses calculated from simply supported three-point beam bending tests on 203x203x9.5 mm WF-section.

Figure 21.37. Experimental curve (normalized load vs. time) taken by beam bending for a silica geL Inset, typical semp used for a three-point beam bending measurement (see also [94]).

It appears that the first three-point, beam bending tests on structural-grade pultruded GFRP profiles were reported by Sims et al. (1987) and Bank (1989). The purpose of these tests was not to demonstrate directly that linear, first-order shear deformation beam theory could be used to predict the flexural... 

FIGURE 5.9 Schematic representations of nonhomogeneous stressed states pure bend (a) three-point beam bend (b) eccentric compression (c) the loss of elastic resistance (d) indentation by a rigid sphere (e). 

In the deflection temperature under load test (heat distortion temperature test) the temperature is noted at which a bar of material subjected to a three-point bending stress is deformed a specified amount. The load (F) applied to the sample will vary with the thickness (t) and width (tv) of the samples and is determined by the maximum stress specified at the mid-point of the beam (P) which may be either 0.45 MPa (661bf/in ) or 1.82 MPa (264Ibf/in ). 

Flexural strength is determined using beam-shaped specimens that are supported longways between two rollers. The load is then applied by either one or two rollers. These variants are called the three-point bend test and the four-point bend test, respectively. The stresses set up in the beam are complex and include compressive, shear and tensile forces. However, at the convex surface of the beam, where maximum tension exists, the material is in a state of pure tension (Berenbaum Brodie, 1959). The disadvantage of the method appears to be one of sensitivity to the condition of the surface, which is not surprising since the maximum tensile forces occur in the convex surface layer. 

We perform flexural testing on polymer rods or beams in the same basic apparatus that we use for tensile or compressive testing. Figure 8.6 illustrates two of the most common flexural testing configurations. In two-point bending, shown in Fig. 8,6 a), we clamp the sample by one end and apply a flexural load to the other. In three-point bending, shown in Fig. 8.6 b), we place the sample across two parallel supports and apply a flexural load to its center. 

We use a variant of flexural testing to measure a sample s heat distortion temperature. In this test, we place the sample in a three point bending fixture, as shown in Fig. 8.6 b), and apply a load sufficient to generate a standard stress within it. We then ramp the temperature of the sample at a fixed rate and note the temperature at which the beam deflects by a specified amount. This test is very useful when selecting polymers for engineering applications that are used under severe conditions, such as under the hoods of automobiles or as gears in many small appliances or inside power tools where heat tends to accumulate. 

The short beam shear test designated in ASTM D 2344 (1989) involves loading a beam fabricated from unidirectional laminate composites in three-point bending as... 

Fig. 3.18. (a) Shear stress eontours and (b) shear stress distributions aeross the thickness of a three-point bending specimen in a short beam shear test. After Cui and Wisnom (1992). Reproduced by permission of... 

Cui, W.C. and Wisnom, M.R. (1992). Contact finite element analysis of three- and four-point short beam bending of unidirectional composites. Composites Sci. Technol. 45, 323-334. 

This is discussed in standard tests on elasticity, and the anisotropic case in Lekhnitskii171. The simplest assumption is that of the Bernoulli-Euler theory in which plane sections remain plane and Poisson contraction is ignored. Young s modulus measured by the deflection of a simply supported beam under three point bending is given by... 

Another important large deformation measurement is the three point bending test (Figure 17.19). Here a mold of the solid fat is plaeed on two beams and a third beam applies an external force between the other two beams. The Young s modulus ( ) and yield force may be determined depending on the cross-section as (rectangular Equation (17.18) or circular Equation (17.19)) ... 

Figure 11 Dynamic load thermomechanical analysis of a carbon fibre/epoxy resin beam measured in three point bending mode. The force steps between 0.5 and 1.5 N and hack every 12 s. Heating rate 5°C min in air...

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