Span-to-depth ratio

This test has an inherent problem associated with the stress concentration and the non-linear plastic deformation induced by the loading nose of small diameter. This is schematically illustrated in Fig 3.17, where the effects of stress concentration in a thin specimen are compared with those in a thick specimen. Both specimens have the same span-to-depth ratio (SDR). The stress state is much more complex than the pure shear stress state predicted by the simple beam theory (Berg et al., 1972 ... 

Boukhili, B., Hubert, P. and Gauvin, R. (1991). Loading rate effect as a function of the span-to-depth ratio in three-point bend testing of unidirectional pultruded composites. Composites 22, 39-45. 

Fisher, S., Rosensaft, M. and Marom, G. (1986). Dependence of the interlaminar shear strength on the loading span-to-depth ratio in aramid fiber-reinforced beams. Composites Sci. Technol. 25, 69-73. 

As with tensile properties, both compressive strength and modulus depend on the fiber content and hber orientation (see Table 5.8). The interlaminar shear strength reported in Table 5.8 is a measure of the shear strength in the thickness direction of the SMC sheet. It is determined by three-point flexural testing of beams with short span-to-depth ratios and is considered to be a quality-control test for molded composites. 

The miniature test bars were evaluated by a modified ASTM flexural test procedure using 3-point loading at a crosshead speed of 2 cm/min. The span-to-depth ratio was normalized at 6.62 so that the values of breaking load could be compared. Both the maximum load to fracture and the total strain energy were recorded. In most experiments an average of five measurements was determined for each condition. 

The ASTM procedure indicates that a support span-to-depth ratio should be 16 1. Decreasing the ratio much below 16 1 would move the test from a flexural mode to a shear mode and would effectively increase the apparent flexural strength of the material to very high values. The procedure does not recommend to use the ratio below 14 1. However, for some highly anisotropic composites, the procedure recommends to avoid shear effects as much as possible, particularly when flexural modulus data are required, and increase the span-to-depth ratio to 20 1, 32 1,40 1, and even to 60 1. 

Note of the author ASTM D 6109 does not mention the effect of some anisotropic composites on flexnral modnlus (and flexural strength, but in a lesser degree) at a reduced span-to-depth ratio (less than 16 1, and particularly less than 10 1). Examples are given below, in the next section. In order to avoid shear effects as much as possible, particularly when flexnral modnlns data are required, an increased span-to-depth ratio (eqnal or higher than 16 1) should be considered. 

The second value of flexural strength, at a higher span-to-depth ratio (average... 

TABLE 7.11 Flexural strength for GeoDeck composite material (cut from a deck board) at two different span-to-depth ratios for third-point load ... 

Width (in.) Depth (in.) Span (in.) Span-to-depth ratio Ultimate load (lb) Flex strength (psi)... 

Flexural strength appears to be higher when tested at span-to-depth ratio lower than 16 1 and particularly when lower than 10 1. 

The flex strength values in Table 7.17 differ by 27%. Apparently, such a difference is a result of a different span-to-depth ratio in these two tests. The ratio was 12.8 for Traditional board and only 10.4 for Heavy Duty board, which was a signihcant... 

One can see that three different test data for Trex boards (Tables 7.29-7.31) obtained with samples of three different sizes (with 1.04", 1.16" and 5.5"), different support spans (6", 14", and 20"), and using two different load apphcations (third-point load and center-point load) gave flex modulus values that differed by only 12% from the average (191,200 23,750 psi). This might be explained that span-to-depth ratio, to which flex modulus is very sensitive, was not too much different in the three tests, that is, 12,15, and 16. 

It was mentioned earlier that if the support span-to-depth ratio is noticeably less than 16 1, this would move the test from a flexural mode to a shear mode and would effectively decrease the apparent flexural modulus of the material to much lower values. Data in Table 27 show, though, that for this effect to be quite noticeable, the span-to-depth ratio should not necessarily be much lower than 16 1. Even a move of the ratio from 16 1 to 11.2 1 results in 28% (on average) decrease of flexural modulus, such as from 300,000 to 234,000 psi, as an example. 

Support span-to-depth ratio, 236 Surface burning characteristics, ASTM standard, 480 Surface defects, 660 Surface roughness, 617 Surface rupture, 644 Surface tearing, 656, 667 Surface temperature of boards, 358 Surface temperature, 550 Susceptibility to microbial degradation, 414 Swagging extrudate, 660 Swell, 26, 209, 643... 

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. 

After 12-18 months, the three-point bend flexural strength (with a span-to-depth ratio of 10) of the polyester laminate was reduced by up to 20%, although this reduction occurred mainly in the flrst few (3-9) months of exposure. The polyester suffered large reductions in impact strength (50-70%, with a high level of scatter) after 6-9 months exposure, after which the values stabilized. The flexural strength of the epoxy was less severely de-... 

Allowable span to depth ratio Actual span to... 

ASTM D790-99 (support span-to-depth ratio < 16 1) S = 3PyL/2bd E = L V4bd rods use ASTM D4476-97... 

ASTM D790 Method I Procedure-A Procedure-B Test specimen dimensitms and rate of cross-head motirai are to be selected based on support span-to-depth ratios (1/d = 16 to 1, 32 to 1,40 to 1 or 60 to 1) that hacture at small deflections... 

Method II Procedure A Procedure B Four-point loading system. Recommended test specimen dimensions and rate of crosshead motion are given based on support span-to depth ratios Procedure-B is fra materials that undergo large deflections... 

The flexural properties of the composites were determined using a span to depth ratio of 32 1. All samples had a width of 0.5 in. and a cross-head speed of 0.1 in./min was used (ASTM D 790-70) ... 

Interlaminar shear strength was determined according to ASTM D 2344-76, A span-to-depth ratio of 5 1, cross-head speed of 0.05 in./min, and sample width of 0.498 in. were used. 

For the SEPB test specimen, good SIFC s are available for configuration similar to those used in testing of metallic materials. However, ceramics are frequently tested in shorter sections that alter the span-to-depth ratio and thereby affect the SIFC. In order to allow a wider range of span-to depth ratios, previously unpublished solutions generated at the Materials Technology Laboratory, Watertown, Massachusetts [27] were reviewed and added to C 1421. 

CerUunly, this will minimize any confusion when reading future data sheets. No longer will one have to question how the material was tested, which span to depth ratio was used, nor guess the testing speed. However, the question of which modulus should be reported still lingers. 

Flexural tests were following the ASTM D790 method with a span-to-depth ratio of 40 and crosshead speed of l.Omm/min. The dimensions of samples were... 

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