Flexural geometry

Figure 2. Schematic of asymmetric four point flexure geometry with accompanying shear force and bending moment diagrams.

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

In any particular material, the flexural stiffness will be defined by the second moment of area, /, for the cross-section. As with a property such as area, the second moment of area is independent of the material - it is purely a function of geometry. If we consider a variety of cross-sections as follows, we can easily see the benefits of choosing carefully the cross-sectional geometry of a moulded plastic component. 

El theory In each case displacing material from the neutral plane makes the improvement in flexural stiffness. This increases the El product that is the geometry material index that determines resistance to flexure. The El theory applies to all materials (plastics, metals, wood, etc.). It is the elementary mechanical engineering theory that demonstrates some shapes resist deformation from external loads. 

The mechanical properties of rapidly polymerizing acrylic dispersions, in simulated bioconditions, were directly related to microstructural characteristics. The volume fraction of matrix, the crosslinker volume in the matrix, the particle size distribution of the dispersed phase, and polymeric additives in the matrix or dispersed phase were important microstructural factors. The mechanical properties were most sensitive to volume fraction of crosslinker. Ten percent (vol) of ethylene dimethacrylate produced a significant improvement in flexural strength and impact resistance. Qualitative dynamic impact studies provided some insight into the fracture mechanics of the system. A time scale for the elastic, plastic, and failure phenomena in Izod impact specimens was qualitatively established. The time scale and rate sensitivity of the phenomena were correlated with the fracture surface topography and fracture geometry in impact and flexural samples. 

For a rectangular or square beam in bending under centerpoint loading, the flexure formula is varied to reflect loading conditions and beam geometry... 

Thermomechanical analysis methods are used in geometries more commonly associated with traditional mechanical testing to increase sensitivity or to mimic other tests. The most common of these are the flexural and penetration modes. Flexure studies involve loading a thin beam, often a splinter of material, with a constant load of lOOmN or more and heating until... 

Flexural Strength - The maximum stress in the extreme fiber of a specimen loaded to failure in bending. Note Flexural strength is calculated as a function of load, support span, and specimen geometry. Also csAXeAmodulus of rupture, bending strength. 

Standard methods use rectangular beam test pieces. The geometry of the beam is chosen to make shear stresses and flexure across the width unimportant. For three-point loading a span-to-depth ratio of 16 is generally satisfactory but does vary with the material characteristics. The quite different situation of deliberately introducing shear forces to measure interlaminar strength was discussed in Section 5. 

Fracture toughness tests for isotropic materials normally use edge-notched flexure beams and compact tension specimens. These methods are. as for the impact tests, only suitable for the injected or compression molded materials, which do not have a strongly laminated structure. Laminated composite materials have their primary failure path between the layers, and a new set of test geometries has been developed. 

Figure 9.7 Schematic illustration of relation between strain energy release rate G and delamination crack growth rates as established via tests on standard geometry double cantilever bend and edge notched flexure samples, showing threshold for growth at G and static fracture at G = Gic-...

Loads on a fabricated product can produce different t3q>es of stresses within the material. There are basically static loads (tensile, modulus, flexural, compression, shear, etc.) and dynamic loads (creep, fatigue torsion, rapid loading, etc.). The magnitude of these stresses depends on many factors such as applied forces/loads, angle of loads, rate and point of application of each load, geometry of the structure, manner in which the structure is supported, and time at temperature. The behavior of the material in response to these induced stresses determines the performance of the structure. 

The maximum deflection Y occurs at x=L, i.e., Y =FVI2> El nd this equation could be used to determine E from the beam deflection. If one inspects Fig. 4.5, the three-point geometry can be viewed as two attached cantilever beams. Replacing Fhy FI2 and L by Ul in the cantilever beam deflection formula, the maximum deflection in three-point bending can be determined, i.e., Tp=FZ,V48 /. The resistance of a beam to bending depends on El (Eq. (4.9)), which is termed the flexural rigidity. 

As mentioned in Section 3.8, use can be made of composite beams. In a sandwich beam, such as that shown in Fig. 3.26, the core usually has lower values of Young s and shear modulus than the thin faces. The Young s modulus of the faces and core will be denoted by and E, respectively. One approach to stress analysis in these sandwich beams, is to transform the cross-section into a geometry with an equivalent flexural rigidity but consisting of a single material. This transformation is shown in Fig. 4.10 in which the core is replaced by the same material as the faceplates but with a width bE IE ). In sandwich beams, the faces are usually much thinner than the cores and the equivalent flexural rigidity can be written approximately as... 

It is not immediately clear which type of testing geometry should be associated with the strength value but the biaxial nature of the stress field would suggest that biaxial flexure values might be the most appropriate estimate. 

S. R. Choi and J. P. Gyekenyesi, Specimen geometry effect on the determination of slow crack growth parameters of advanced ceramics in constant flexural stress-rate testing at elevated temperatures, Ceram. Eng. Sci. Proc., 20 [3] 525-534 (1999). 

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