Strain-softening

It is instructive to describe elastic-plastic responses in terms of idealized behaviors. Generally, elastic-deformation models describe the solid as either linearly or nonlinearly elastic. The plastic deformation material models describe rate-independent behaviors in terms of either ideal plasticity, strainhardening plasticity, strain-softening plasticity, or as stress-history dependent, e.g. the Bauschinger effect [64J01, 91S01]. Rate-dependent descriptions are more physically realistic and are the basis for viscoplastic models. The degree of flexibility afforded elastic-plastic model development has typically led to descriptions of materials response that contain more adjustable parameters than can be independently verified. 

Usually, the molecular strands are coiled in the glassy polymer. They become stretched when a crack arrives and starts to build up the deformation zone. Presumably, strain softened polymer molecules from the bulk material are drawn into the deformation zone. This microscopic surface drawing mechanism may be considered to be analogous to that observed in lateral craze growth or in necking of thermoplastics. Chan, Donald and Kramer [87] observed by transmission electron microscopy how polymer chains were drawn into the fibrils at the craze-matrix-interface in PS films [92]. One explanation, the hypothesis of devitrification by Gent and Thomas [89] was set forth as early as 1972. 

The fracture behavior can be attributed to strain softening [91] in the deformation zone [92, 93] or to stress-activated devitrification [89, 96]. The strands are comparatively free to move in the strain softened regions of the deformation zone. The van der Waals interaction between adjacent strands is greatly reduced and the clearence between molecular segments is enlarged. 

The behavior of the strain softened material resembles the behavior of rubberlike polymers. For instance, the Poisson s ratio of an ideally plastic material is also close to 0.5 [94, 95], Proper understanding of crack propagation involves the microscopic level. Apparently, the load is transmitted by the molecular strands [97] from one crosslink to the next crosslink, exactly, as it is in rubberlike materials. However, two things are different in strain softened polymers as compared to rubberlike materials ... 

The inability of the strain softened molecules to recover their random coil conformation when unloaded. 

At high stresses and strains, non-linearity is observed. Strain hardening (an increasing modulus with increasing strain up to fracture) is normally observed with polymeric networks. Strain softening is observed with some metals and colloids until yield is observed. 

Strain rate, test temperature and the thermal history of the specimen all affect the appearance of shear bands in a particular glassy polymer [119]. The differences in morphology of shear bands was proposed to be due to different rates of strain softening and the rate sensitivity of the yield stress. Microshear bands tend to develop in polymers with a small deformation rate sensitivity of Oy and when relatively large inhomogeneities exist in the specimen before loading. This is sometimes characterized by a factor e j, introduced by Bowden in the form [119] ... 

The properties of a material must dictate the applications in which it will best perform its intended use. All materials made to date with polymerized sulphur show time-dependent stress-strain behaviour. The reversion to the brittle behaviour of orthorhombic sulphur is inevitable as the sulphur transforms from the metastable polymeric forms to the thermodynamically stable crystalline structure. The time-span involved of at most 15 months (to date) would indicate that no such materials should be used in applications dependent on the strain softening behaviour. Design should not be based on the stress-strain relationships observed at an age of a few days. Since the strength of these materials is maintained, however, uses based on strength as the only mechanical criterion would be reasonable. 

It is worth noting that the cooperativity of p transition motions, observed in PMMA and MGIMx copolymers, is intramolecular, unlike the case of bisphenol A polycarbonate where intra- and intermolecular cooperativi-ties exist. The consequences of such a difference on the mechanical properties (in particular the strain softening) of these two types of polymers are investigated in a second paper [1]. 

Fig. 2 Typical stress-strain curves for amorphous polymers, a Elastic, anelastic, strain softening, and plastic flow regions can be seen, b Plastic flow occurs at the same stress level as required for yielding so strain softening does not exist, c Strain hardening occurs very close to yielding, suppressing both strain softening and plastic flow behaviour...

Straining the specimen beyond ey, a decrease of true stress is observed this is the strain softening behaviour. 

The strain softening effect can be characterised by its amplitude, SSA, defined as ... 

However, when considering temperature or strain dependencies of strain softening, the absolute stress difference (ay - apf) does not allow one to discriminate between a change of the absolute values of ay and crpf and an intrinsic effect on the strain softening behaviour. 

To overcome this ambiguity and focus on the intrinsic change of strain softening, another descriptor is more appropriate, consisting in normalising SSA by Opf ... 

Though SSA was used in our previous papers on this topic, hereafter the strain softening behaviour will be discussed in considering preferentially nSSA as descriptor. 

At the craze tip, the advance mechanism would be by a Taylor meniscus instability leading to a series of void fingers occurring in the plastically deformed and strain-softened polymer formed at the craze tip. As the finger-like craze tip propagates, fibrils develop. 

First, it is important to notice that the stress-strain curves and, consequently, the derived characteristics (yield stress, cry, plastic flow stress, crpf, and strain softening) have been studied in a temperature range extending to, typically, Ta - 20 K. Indeed, for temperatures closer to Ta, the experimental results are less reliable, as some creep behaviour can occur. 

The compression stress-strain curves obtained over quite a broad temperature range are shown in Fig. 15 [33]. It appears that the strain softening, weak and slightly temperature-dependent in the temperature range from 40 to 100 °C, increases when lower temperatures are considered. 

Fig. 17 Temperature and strain rate dependencies of the stress-strain curve shapes of PMMA small (less than 10 MPa) and larger strain softening (From [33])...

As above described, depending on temperature and strain rate, the stress-strain curves present a strain softening of variable amplitude. 

Fig. 23 Temperature dependence of strain softening amplitude (SSA) of PMMA at a strain rate of 2 x KT3 s 1...

The strain softening amplitude, SSA, used in our previous papers, is shown for PMMA in Fig. 23. It is clear that SSA values are quite small and constant above 50 °C and sharply increase at temperatures lower than 0 °C. This feature was already pointed out when comparing aY and crpf versus temperature (Fig. 18). 

Fig. 25 Pressure dependence of yield stress and strain softening of PMMA (From [36])...

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