The Rupture Work of Crosslinked Polymers
The work “γ” of fracture was identified by Dupré and Griffith with the surface energy of solids. In reality work is spent on the deformation leading to rupture rather than on the break itself. In simple instances it is equal to the work needed to extend a column of material (of unit cross-section) in front of the growing crack until the column snaps. This extension may be purely elastic. The new concept, contrary to the old, (a) indicates the analogy between the breaks of a liquid and a solid, (b) accounts for the absolute value of “γ,” (c) agrees with the effect of cross-linking on “γ,” (d) is compatible with the rate dependence of “γ,” and (e) explains the liberation of heat during fracture. The absence of any clear effect of macroscopical plasticity on “γ” contradicts the hypothesis attributing the high values of “γ” to plastic deformation.
If a Hookean cylindrical bar of length 10 and radius r is extended to the length 1m and then breaks, and if the tensile force F at every moment is only insignificantly greater than the elastic resistance of the bar, then the work (which has achieved rupture) is 0.5 Fm(1m− 10), if Fm is the highest value of F (i.e., in the moment of fracture). This product obviously has no fundamental importance and is not a material constant as it depends on the absolute extension 1m− 10 which is greater the greater the initial length 10. It also depends on the value of r but this complication usually can be successfully avoided by substituting the external (average) stress fm( = Fm/πr2) for Fm and referring the work of rupture to unit cross-section.
Three attempts are known to define, and to account for, a work of rupture which is independent of the sample dimensions and thus may represent a property of the material studied. The most common mode of rupturing a solid involves the growth of a crack. In many instances it is possible, more or less convincingly, to separate the work W (ergs or joules) necessary for this growth from the work done on the simultaneous gross deformation of the test sample (and the instrument employed). Usually it is found that this W is proportional to the area A of the new crack surfaces, so that W/A ≠ “γ“(g/sec2 or kg/sec2) remains constant when the crack expands; it is moreover independent of the initial length 10. The physical meaning of the quantity ”γ” is the subject of the present discussion.
KeywordsSurface Energy Free Surface Energy Maximum Strain CROSSLINKED Polymer Phthalic Anhydride
Unable to display preview. Download preview PDF.