Work of rupture

A relation between rupture phenomena and (specific) surface energy 7 was postulated by Dupre 4 almost simultaneously with the hypothesis of Quincke. Let a cylindrical rod be broken in tension. After rupture, two new gas — solid interfaces of vr2 each are present, r being the radius of the rupture surface. Consequently, the work of rupture ought to contain a term 2 nr2 7 . Dupre did not indicate how to separate this term from the main component of the work of rupture, which is the work required to extend the rod to its maximum elongation (or strain). The modern development of Dupre s ideas is reviewed in Section III.3. below. 

Mechanical properties of a material can be used to estimate its ys or, more exactly, 7 . When a tensile stress om is applied to a bar, the latter extends along its whole length. However, to find 7 , only the extension of one interplanar distance from its equilibrium value a to the value a + A a (at which rupture occurs) is needed. The corresponding work of rupture is 2 7 , and... 

As mentioned in the Introduction above, this method originated with Dupre4. The first task of the experimenter is to separate that part of the work of rupture which is spent on the mechanical deformation of the sample from that used up to create a new surface 2,4 (on both sides of the crack together). 

Essential work of fracture measurements clearly show that this efficiency always corresponds to a significant increase in the apparent plastic work, whereas essential work of rupture remains low. This observation suggests that toughening results from an additional process induced by the particles. 

Mechanical tests were carried out in a laboratory where the temperature was maintained at 25°C using a Universal Testing Machine, LR-50 K (LLOYD Instrument, England) at a crosshead speed of 50 mm/min and 98 mm as gauge length. Stress at break, strain at break, work of rupture, and initial modulus were determined as per ASTM standards. Izod notched impact test specimens were... 

Ratner(19) found that there were three stages involved in the formation of a loose wear particle 1) deformation of the surfaces to an area of contact determined by the hardness, H 2) relative motion opposed by a friction force F = pL and 3) rupture of the material at the junctions involving the work of rupture equal to the integral of the stress-strain relationship o e). Hence, the wear volume is... 

Figure 18 Force/clongation curve for illustration of work of rupture.

So for materials having the same tenacity, the work of rupture will be higher if the work factor exceeds 0.5 or lower if the work factor is less than 0.5. 

The breaking force, tenacity, elongation at break, initial modulus, chord modulus, and toughness (i.e.. work of rupture in J g) is calculated for each individual test result and the mean value reported. 

As explained earlier, the work of rupture is represented by the area under the stress-strain curve. However, the proportions and limits of the stress- strain curve, and hence the area it encompasses, will be dependent upon the speed of jaw separation and cross-head load range in the vertical axis, and the chart width and chart recording speed. Also of course, as... 

The elastic modulus can be derived directly from the shape of the stress-strain curve and is equal to its initial, constant slope. Its value equals that of the stress that would be required to double the length of the fiber at the initial conditions it is therefore measured in units of stress or specific stress. The work of rupture, a measure of the toughness of the fiber, is defined as the energy needed to break the fiber and may be represented by the following equation ... 

The units are joules. Since the work of rupture is proportional to the fiber mass per unit length, a specific work to rupture may be defined according to the following equation ... 

From an extensive series of correlations between fiber properties and yarn properties, Mather concluded that the tensile properties of a yarn could be predicted from two measurements only on the raw fiber, namely, the linear density and the ballistic work of rupture of uncarded strands of fiber. 

Quantitatively, Mather concludes that for jutes exported from Bangladesh (or the erstwhile East Pakistan), the range of linear density is about 1.3 2.4 tex, whereas work of rupture ranges from 4.0 to 8.3 g/cm/tex. For kenaf, although work of rupture is little different, the linear density is often higher than for jute, and a survey of H. sabdarijfa grown in Thailand showed a range of 1.9-3.0 tex. 

Wenbang [188] reports on the crystalline structure and optical properties of three different types of ramie fibers and different parts of the fibers. The author finds some variation in crystallinity in different parts of the fiber. He also finds tenacity, breaking elongation, and work of rupture of the fibers somewhat correlated to crystallinity and orientation factors of the fibers. 

Work of Rupture of Acetate and Some Other Common Fibers... 

Yarn Linear density (Tex) Breaking force (cN) Tenacity (cN/Tex) Work of rupture (cN cm) Breaking extension (%) Breaking time (s)... 

HT nylon 6.6 High tenacity, high work of rupture, good elastic recovery Low modulus, low second order temperature ( 45 °C), poor UV resistance and hoses... 

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