Failure theories viscoelastic

At this juncture it is appropriate to recall the failure envelope given in Chapter 2, Fig. 2.21 that displays a comparison of failure stresses for both metals and polymers to the three failure theories mentioned therein. The data provided for both polymers and metals were developed without regard to possible rate and/or viscoelastic effects. In Fig. 11.11 and in Fig. 11.12 it has been demonstrated that yielding of polycarbonate is both rate and time dependent. The same is true for most ductile polymers and, as a result, the yield (or failure) surface for polymers should be understood to... 

As mentioned already, the main consideration In this work will be the failure occurring as a result of necking during the uniaxial creep of polyethylene at relatively high loadings. Recently, Bernstein and Zapas [2] have extended the work of Erlcksen [3] on the instability of elastic bars to the case of viscoelastic materials, more specifically to the class of materials which behave according to the BKZ theory [4]. 

Adolf et al [27] developed a physically realistic continuum-scale constitutive equation-based theory which they implemented in a finite element scheme. An especially interesting recent publication from this team [175] investigates cohesive failure in partially cured epoxies. KIc was measured with notched three-point bend fracture specimens at a constant (T-Tg) value (thereby normalizing the viscoelastic relaxations) and was shown to manifest a strong dependence on the crosslink density. It increased by more than an order of... 

The accurate applicability of linear viscoelasticity is limited to certain restricted situations amorphous polymers, temperatures near or above the glass temperature, homogeneous, isotropic materials, small strains, and absence of mechanical failure phenomena. Thus, the theory of linear viscoelasticity is of limited direct applicability to the problems encounted in the fabrication and end use of polymeric materials (since most of these problems involve either large strains, crystalline polymers, amorphous polymers in a glass state failure phenomena, or some combination of these disqualifying features). Even so, linear viscoelasticity is a most important subject in polymer materials science—directly applicable in a minority of practical problems, but indirectly useful (as a point of reference) in a much wider range of problems. 

Analysis of Failure Failure of "Flawless" Materials Fracture Mechanics Griffith Theory Stress Intensity Factors Fracture Energy Viscoelastic Effects Examples Fatigue Conclusion... 

Bueche and Halpin 126, 203, 215-217) have developed a fracture theory for amorphous rubbers. Their model pictures rupture as the result of the propagation of tears or cracks within the material. The growth of a tear is viewed as a process in which molecular chains at the tip of the tear stretch viscoelastically, under the influence of a high stress concentration, until they rupture. The failure process is a non-equilibrium one, developing with time and involving consecutive rupture of molecular chains. The principal result of the theory is embodied in the equation... 

The validity of the viscoelastic model (5.32) has been tested against experimental and molecular dynamics simulation results [26, 27, 28]. The detailed comparison has established that the viscoelastic model works remarkably well for wavenumbers k km, where km denotes the first peak position of the static structure factor S k). However, it has also been found that the situation is not so satisfactory for smaller wavenumbers, where the viscoelastic model is shown in some circumstances to yield even qualitatively incorrect results. This failure was attributed to the fact that the single relaxation time model (5.31) cannot describe both the short-time behavior of the memory function, dominated by the so-called binary collisions, and in particular the intermediate and long-time behavior where in the liquid range additional slow processes play an important role (see the next subsection). It is obvious that these conclusions demand a more rigorous consideration of the memory function, which lead to the development of the modern version of the kinetic theory. Nevertheless, the viscoelastic model provides a rather satisfactory account of the main features of microscopic collective density fluctuations in simple liquids at relatively large wavenumbers, and its value should not be undervalued. 

The Doi-Edwards theory of linear viscoelasticity predicts 1.2 for JeG, where is the plateau shear modulus. This value is significantly lower than typical experimental values found in the range 2—4 [3, 71]. This defect of the Doi-Edwards theory, along with its failure of predicting the 3.4 power law for viscosity, has been pointed out by Osaki and Doi [72]. It is associated with the fact that the Doi-Edwards theory yields a relaxation time distribution which is too narrow compared with observed ones [69]. Modifications of the Doi-Edwards theory have been made so as to bring JeG closer to measured values, but no remarkable success has as yet been achieved. 

Time-dependent creep can be accurately modelled using the viscoelastic theory, which inherently assumes that all deformation is eventually recovered. However, when considering the long-term deformational behaviour of polymers it is important to realise that all polymers are subject to physical ageing, which not only affects the polymer s stiffness but has a profound influence on its creep deformation. Physical ageing of the matrix material should therefore be considered in order to make the investigation of the delayed failure of the composite meaningful. 

The Nagdi and Murch theory of viscoelastic-plasticity contains many of the same caveats as in plasticity theory and, in fact, reduces to the two limiting cases of plasticity for non-viscoelastic materials and linear viscoelasticity for non-yielded materials. The only portions needed here are the linear viscoelastic constitutive equations given in Chapter 6 and a generic failure law given by,... 

The Larson-Miller and other similar methods have been widely used for metals but here it is important to note that difficulties arise for fiber reinforced composite laminates because the constants are only valid for one configuration of the plies and a more general approach is needed. Dillard (1981) developed an incremental viscoelastic time dependent lamination theory approach that included the Tsai-Hill failure law modified to account for delayed failures using the Zhurkov time dependent failure model that will be discussed in the next section. The advantage of the Dillard approach is that information on the viscoelastic behavior as well as the delayed failure behavior of 0°, 10° and 90° plies can be used to predict the behavior of general laminate configurations. 

Earlier authors proposed theories which predict the speed of viscoelastic crack propagation, by assigning a detailed structure to the crack tip, both under unstable and subcritical or fatigue failure. We mention Knauss (1970, 1974), Knauss and Dietmann (1970), Mueller and Knauss (1971) and a review by Knauss (1973) also the work of Wnuk (1971-73b). Later, there was the work of Schapery (1974-79), McCartney (1977-79) and Golden and Graham (1984). See also Kanninen and Popelar (1985). Majidzadeh et al. (1976) discuss various models in the context of application to pavement design. McCartney (1987) is concerned with crack extension criteria for fibre-reinforced composites. 

In this chapter an overview of conceptually different fracture theories is presented which have in common that they do not make explicite reference to the characteristic properties of the molecular chains, their configurational and super-molecular order and their thermal and mechanical interaction. This will be seen to apply to the classical failure criteria and general continuum mechanical models. Rate process fracture theories take into consideration the viscoelastic behavior of polymeric materials but do not derive their fracture criteria from detailed morphological analysis. These basic theories are invaluable, however, to elucidate statistical, non-morphological, or continuum mechanical aspects of the fracture process. 

In order to predict the creep behavior and possibly the ensuing failure a number of approaches have been proposed. These are based respectively on the theory of viscoelasticity — including the concept of free volume — or on empirical representations of e(t) or of the creep modulus E(t) = ao/e(t). The framework of the linear theory of viscoelasticity permits the calculation of viscoelastic moduli from relaxation time spectra and their inter conversion. The reduction of stresses and time periods according to the time-temperature superposition principle frequently allows establishment of master-curves and thus the extrapolation to large values of t (cf. Chapter 2). The strain levels presently utilized in load bearing polymers, however, are generally in the non-linear range of viscoelasticity. This restricts the use of otherwise known relaxation time spectra or viscoelastic moduli in the derivation of e (t) or E (t). 

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