Rupture, tensile

In Fig. 20 several relations are shown for the breaking stress Ob of an unfilled vulcanizate of SBR as a function of the rate of elongation at different temperatures [61]. A small correction factor T T) has been applied to the measured values to allow for changes in the elastic modulus with temperature. The corrected values are denoted Ob. 

The variation of tensile strength with temperature, like the variation in fracture energy, is thus due primarily to a change in segmental mobility. 

FIGURE 21 Master relations for breaking stress oi, as a function of rate of elongation e, reduced to Tg (-60°C) by means of the WLF relation, Eqs. (18) and (19). (From Smith [61].) 

Rupture of a tensile test piece may be regarded as catastrophic tearing at the tip of a chance flaw. The success of the WLF reduction principle for fracture energy G in tearing thus implies that it will also hold for tensile rupture properties. Indeed, db and may be calculated from the appropriate value of G at each rate and temperature, using relations analogous to Eqs. (6) and (7). The rate of extension at the crack tip will, however, be much greater than the rate of extension of the whole test piece, and this discrepancy in rates must be taken into account [63]. 

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In conventional cutting the blade has to compress the bulk material to allow a gap the width of the blade to pass through and this applies a tensile rupturing force at... 

Figure 12.14 Summary of a large number of tensile rupture data collected from various sources for Si3N4 plotted to verify the Monkman-Grant equation.

It is a review written to analyse opinions concerning the behaviour of carbon black filled elastomers insofar as the carbon black affects the behaviour at or near failure, whether by abrasion, tear or tensile rupture. Behaviour at low or moderate extensions, which has been adequately reviewed, will not be considered unless it can be shown to bear upon reinforcement in the sense of the word implied in any dictionary definition1. It will be seen that a number of phenomena involved require the formulation of a specific model which shall be treated in considerable detail in the second half of this review. 

Yield Yield Tensile Rupture Strain Elastic... 

In order to describe the process of the rupture of tongue tip precisely, a technical term, tensile rupture ratio, is Introduced and defined as a ratio of the rupture length of the tongue tip to the original length of the tongue (Figure 2). Thus,... 

As seen from Equations (3), (5) and (6), the tensile rupture ratio can be roughly considered to be directly proportional to the frictional force and inversely proportional to the tensile strength ... 

There are two independent variables in the characteristic function of unsteady state, i.e., the number of revolutions and the tensile rupture ratio. The effect of the number of revolutions on unsteady-state rate of wear is obvious as seen by Figure 8 ( y. However, the influence of the tensile rupture ratio on wear rate is still not established. 

As seen in Figure 10, the larger the tensile rupture ratio, the larger the value of the characteristic function is, and, the earlier the steady state is reached (Figure 9). It is also supported by the experimental observation that the larger the frictional force, the earlier the ridges appeared. 

Besides, as shown in Figure 9, the slope of the curve is a steep rise along with an increase in the tensile rupture ratio. 

Hence, the fact that the unsteady-state rate of wear of unfilled NBF is much more sensitive to the number of revolutions than that of filled NBR would be ascribed to the difference in tensile strength or in tensile rupture ratio, i.e., the tensile strength of unfilled NBR is less than that of filled NBF, in other words, the tensile rupture ratio of unfilled NBR is much more than that of filled NBR. 

Evidently, the higher the tensile rupture ratio, the lower the value of the state criterion is. Thus, this state criterion can be applied to estimate the wear characteristics of different elastomers under similar running conditions. 

The characteristic function, f (N,6 ), is a characterizing factor of rubber abrasion in unsteady state. Its value increases with an increase in the number of revolutions and tensile rupture ratio. However, it approaches unity as a limit in the unsteady-state process of wear. Hence, a steady state is reached if once 1 (N,6j ) = 1. 

Figure 10. Characteristic function plotted against tensile rupture ratio (A) i = 20 rev (B) i = 40 rev (C) i = 60 rev.

The number of revolutions transformed the wear state from unsteady to steady can be regarded as a state criterion of rubber abrasion to estimate the wear characteristics of rubber under identical r jnning conditions. It was found to be proportional to a negative exponent of the tensile rupture ratio. 

Figure 5 Smooth (glassy) fracture surface of a brittle urea-formaldehyde adhesive layer fractured by stress developed in the adhesive layer as it cured. Note the tensile rupture of the cells at the wood surface (arrow) caused by the cure-shrinkage crack in the adhesive. 

Equation (10.5) is more generally applicable than Eq. (10.6) because it is not restricted to linearly elastic materials. It constitutes a criterion for tensile rupture of a highly elastic material having a cut in one edge of length, /, in terms are of the fracture energy, Gc- Two important examples of test pieces of this type are (1) the ASTM tear test piece for vulcanized rubber (ASTM D624-54) and (2) a typical tensile test piece that has accidental small nicks caused, for example, by imperfections in the surface of the mold or die used to prepare it. 

Internal reinforcement Odagiri et al. (1997) investigated relaxation characteristics of 6 and 7.4 mm (0.24 and 0.29 in) diameter AFRP tendons with anchorages. Overall, the relaxation rates for AFRP rods were found to be approximately 11% at 1000 hours, and 15% at 17,700 hours (two years). Creep rupture, the tensile rupture of a material subjected to sustained high stress levels over a period of time, is another important concern for FRP reinforcing bars. 

Balanced failure - simultaneous FRP tensile rupture and concrete crushing... 

Compression failure - concrete crushing prior to FRP tensile rupture... 

Tension failure - tensile rupture of the FRP prior to concrete crushing. 

Compression failure is the most desirable of the above failure modes. This failure mode is less abrupt than tension failure, and is similar to the failure of an over-reinforced section when using steel reinforcement. Tension failure is less desirable, since tensile rupture of FRP reinforcement will occur with less warning. Tension failure will occur when the reinforcement ratio is below the balanced reinforcement ratio for the section. This failure mode is permissible with certain safeguards. 

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