The essential work of fracture (EWF), a tool for characterizing fracture toughness of ductile materials, is becoming popular due to its simplicity and usefulness. On the other hand, this method is still regarded by many as an empirical method without a sound understanding of its physical background. This is mostly because it is extremely difficult to build mathematical models that can precisely describe the post-yielding fracture with the involvement of large-scale plastic deformation. The aim of the present work is to understand the EWF using the bottom-up approach through establishing the correlations between EWF parameters and molecular characteristics of ductile polymers. The results of this work can also provide guidelines for development of new polymers with tailored molecular structures for high toughness.
Two series of amorphous polymers, polyurethanes and copolyesters, are employed. Each of them is constituted of a different network conformation. The polyurethanes synthesized by myself are disclosed to have a homogenous morphology while their network characteristics vary with the hard-to-soft segment ratio and the treatment of gamma-ray irradiation with different dosages. The molecular structure of the copolyesters was modified with the incorporation of stiff moieties into the main chain of poly(ethylene terephthalate). The EWF measurements were carried out under various test conditions. The results revealed that at low deformation rates the specific essential work of fracture, we
, is mostly determined by the properties of the chain segments between entanglements/crosslinks. The longer the segments, the larger is we
. At high deformation rates, due to the influences of deformation restriction and deformation mechanism, we
changes. At T < Tg
, the glass transition temperature of a polymer, we
is nearly insensitive to test temperature. The specific plastic work of fracture, wp
, exhibits the same temperature dependence of the yield stress of polymers, σy
. The wp
ratio was found to be essentially a constant, independent of temperature but dependent on the molecular structure of polymers.
Based on the experimental findings and well-established polymer physics, physical models of the EWF parameters are built at the molecular level for glassy polymers. wp
is proposed to be the energy for fully extending the networks in the plastic zone, which can be predicted by wp
-1), where C∞
is the characteristic ratio defined as the ratio between the mean-square end-to-end distance of an unperturbed coiled real chain and that of a freely jointed chain; while we
is proposed to be the energy for elastically stretching and breaking the skeletal covalent bonds of the highly orientated chains near the fracture plane, which can be predicted by we
= (140 x 10-18
J) x Ne
x Ω , where Ne
is the number of the skeletal bonds in a chain segment between two adjacent entanglement junctions and Ω is the chain density crossing the fracture plane. With these models, the experimental observations of the dependences of the EWF parameters on intrinsic and extrinsic factors can be explained successfully. The theoretically estimated values of the EWF parameters are in good agreement with those from experiments for a variety of glassy polymers published by our team and other researchers.
Through this thesis work, an in-depth physical insight into the EWF is provided for the first time, which lays the basis for appreciation of this toughness determination method. Using the proposed physical models, the toughness of ductile polymers can be predicted by their intrinsic molecular characteristics. This may be used for the design of tougher materials.
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