Bending four-point

ROR = ring-on-ring bending FP = four-point bending TT = tensile test and TP = three-point bending. 

Fig. 3. Load—deflection curve for a SiC—C—SiC composite in four-point bending. Note the extreme change in behavior fora composite fabricated with a 0.17-p.m carbon layer between the SiC fiber and the SiC matrix as compared with a composite with no interfacial layer (28).

Note that these stress, strain and modulus equations are given for illustration purposes. They apply to three-point bending as shown in Fig. 2.3. Other types of bending can occur (e.g. four-point bending, cantilever, etc.) and different equations will apply. Some of these are illustrated in the Worked Examples later in this chapter and the reader is referred to Benham et al. for a greater variety of bending equations. 

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. 

Double torsion test specimens take the form of rectangular plates with a sharp groove cut down the centre to eliminate crack shape corrections. An initiating notch is cut into one end of each specimen (Hill Wilson, 1988) and the specimen is then tested on two parallel rollers. A load is applied at a constant rate across the slot by two small balls. In essence the test piece is subjected to a four-point bend test and the crack is propagated along the groove. The crack front is found to be curved. 

Slight modification was also made to the loading fixture (Slepetz et al., 1978), leading to the so-called asymmetrical four-point bending (AFPB) test as illustrated in Fig 3.20(b), which requires the use of fixture dimensions in calculating the shear stress... 

Shih, G.C. and Ebert, L.J. (1986). Interface strength effects on the compressive-flexure/shear failure mode transition of composites subjected to four-point bending. J. Mater. Sci. 21, 3957-3%5. 

Spigel, B.S.. Sawyer, J.W. and Prabhakaran, P. (1985). An investigation of the losipescu and asymmetric four-point bend tests for composite materials. In Proc. 1985 SEM Spring Conf. Experimental Mechanics, Society of Experimental Mechanics, pp. 833-843. 

The flexural strength will depend on sample size, since with increasing size there is an increase in the probability of the existence of a crack-producing flaw, along with a corresponding decrease in the flexural strength. This test, and others like it such as the four-point bend, are common for brittle materials such as ceramics, which we... 

A calculation example of a four point bending test ... 

The E modulus of the material can also be determined with the three or four point bending test. The following formulas apply... 

Most ceramic materials exhibit elastic deformations with slight elongations, followed by fracture. In chapter 9 we discussed E-modulus measurements on ceramic materials. This can e.g. be done by means of three or four point bending tests or by measuring the speed at which a sound wave passes through a material. 

High-temperature four-point bending tests of Si3N4 and Si3N4/20%SiC(w) composites prepared with no external sintering aids by hot isostatic pressing... 

Although superplasticity is defined as the ability of a polycrystalline material to exhibit large elongations, in many ceramics-related materials and ceramic composites superplasticity is also said to occur even though the polycrystal is deformed in compression, or in three- or four-point bending conditions, as long as GBS is the primary deformation process.4-7... 

D. Munz, R. T. Bubsey, and J. L. Shannon, Jr., Fracture Toughness Determination of A1203 using Four-Point-Bend Specimens with Straight-Through and Chevron Notches, Journal of the American Ceramic Society, 63[5—6], 300-305 (1980). 

For the four-point bend geometry used in the present experiments and under plane strain conditions, the C integral is given by 30... 

Fig. 7.3 Examples of crack profiles in AI2O3/33 vol.% SiC whisker composite subjected to static and cyclic tensile loads (in a four-point bend configuration) in 1400°C air. From Ref. 22. Crack growth direction is from right to left, (a) Static crack growth at K 4-5 MPaVnT (b) Cyclic crack growth at R = 0.15 and vc = 0.1 Hz in the AK range 3.5-5 MPaVfiT...

Microcracks are also known to occur in the elevated temperature creep of alumina with little or no preexisting glass phase. For example, the development of microcracks during creep fracture of two hot-pressed aluminas, which were free of grain boundary glass films, was studied by Wilkinson et al.52 who employed tensile and four-point bend specimens. They found that the concentrations and morphology of the cavities and microcracks were strongly... 

Fig. 12.8 Schematic of four-point bend test fixture as per ASTM 0161.

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