Tensile strength distribution

Several additional, non-microstructural, inputs are required for the fracture model (i) Particle critical stress intensity factor, KIc. Here, the value determined in a previous study (Klc = 0.285 MPa in )[3] was adopted for all four graphites studied. This value is significantly less than the bulk Klc of graphites (typically -0.8-1.2 MPa rn). However, as discussed in the previous section, when considering fracture occurring in volumes commensurate in size with the process zone a reduced value of Klc is appropriate (ii) the specimen volume, taken to be the stressed volume of the ASTM tensile test specimens specimen used to determine the tensile strength distributions and (iii) the specimen breadth, b, of a square section specimen. For cylindrical specimens, such as those used here, an equivalent breadth is calculated such that the specimen cross sectional area is identical, i.e.,... 

Figure 10. Weibull plots of tensile-strength distribution for kilometer lengths of fibers tested in 20-m gauge lengths. In each case one variable was intentionally altered and all others were optimized. (Reproduced with permission from Ref. 6. Copyright 1980 IEEE.)...

Because of the difficulties in producing defect-free CNTs, CNT tensile strength is not a single-valued quantity, and has to be described on the basis of probability approach. However, report on the distribution of CNT tensile strength is still absent to date. Here we present die results of a study on direct tensile tests of SWNT bundle and use a two-parameter Weibull distribution to describe its tensile strength distribution. 

Content of Ot-Olefin. An increase in the a-olefin content of a copolymer results in a decrease of both crystallinity and density, accompanied by a significant reduction of the polymer mechanical modulus (stiffness). Eor example, the modulus values of ethylene—1-butene copolymers with a nonuniform compositional distribution decrease as shown in Table 2 (6). A similar dependence exists for ethylene—1-octene copolymers with uniform branching distribution (7), even though all such materials are, in general, much more elastic (see Table 2). An increase in the a-olefin content in the copolymers also results in a decrease of their tensile strength but a small increase in the elongation at break (8). These two dependencies, however, are not as pronounced as that for the resin modulus. 

Desirable properties of elastomers include elasticity, abrasion resistance, tensile strength, elongation, modulus, and processibiUty. These properties are related to and dependent on the average molecular weight and mol wt distribution, polymer macro- and microstmcture, branching, gel (cross-linking), and... 

HDPE melts at about 135°C, is over 90% crystalline, and is quite linear, with more than 100 ethylene units per side chain. It is harder and more rigid than low density polyethylene and has a higher melting point, tensile strength, and heat-defiection temperature. The molecular weight distribution can be varied considerably with consequent changes in properties. Typically, polymers of high density polyethylene are more difficult to process than those of low density polyethylene. 

Polyphase Alloys. The two-phase alloys have a rather wide range of properties resulting from variations within the stmcture. If the second phase is distributed in critical depression, the hardness and strength are at a maximum and the ductility is at a moderate level. Tensile strength may be 415—825 MPa (60,000—120,000 psi) yield strength, 170—585 MPa (25,000—85,000 psi) and elongation, 10—40%. 

In reference to the tensile-strength table, consider the summary statistics X and. s by days. For each day, the t statistic could be computed. If this were repeated over an extensive simulation and the resultant t quantities plotted in a frequency distribution, they would match the corresponding distribution oft values summarized in Table 3-5. 

In terms of the tensile-strength table previously given, the respective chi-square sample values for the daily, weekly, and monthly figures couldbe computed. The corresponding df woiJdbe 4, 24, and 99 respec tively. These numbers would represent sample values from the respec tive distributions which are summarized in Table 3-6. 

F Distribution In reference to the tensile-strength table, the successive pairs of daily standard deviations could be ratioed and squared. These ratios of variance would represent a sample from a distribution called the F distribution or F ratio. In general, the F ratio is defined by the identity... 

The low tensile strength of cement paste is, as we have seen, a result of low fracture toughness (0.3 MPa m ) and a distribution of large inherent flaws. The scale of the flaws can be greatly reduced by four steps ... 

---