Ductile material, crazes

The criteria (Eqs. 11 and 12) are similar and are derived from studies on materials that are elastic at initiation of crazing, while more ductile materials like polycarbonate show a more pronounced sensitivity to the hydrostatic tension. This has been found experimentally by Ishikawa and coworkers [1, 27] for notched specimens of polycarbonate. Crazing appears ahead of the notch root, at the intersection of well-developed shear bands. From a slip fine field analysis, the tip of the plastic zone corresponds to the location of the maximum hydrostatic stress. This has been confirmed by Lai and Van der Giessen [8] with a more realistic material constitutive law. Therefore, Ishikawa and coworkers [1,27] suggested the use of a criterion for initiation based on a critical hydrostatic stress. Such a stress state condition can be expressed by Eq. 11 with erg = 0 and I r = B°/A°. Thus, the criterion (Eq. 11) can be considered general enough to describe craze initiation in many glassy polymers. For the case of polycarbonate, a similar criterion is proposed in [28] as... 

Craze stress The craze grows (at least partially) by drawing new material out of the bulk. This mechanism requires a certain stress at the junction between craze fibril and bulk. It is sometimes compared to the propagation of a neck in a tensile test on ductile material. In the constant stress assumption , the value of craze stress calculated is actually a mean value over the whole interface between craze and bulk, neglecting the fact that the sum of the fibrils cross section area is smaller than the craze boundary surface. 

This work is a contribution to the definition of an experimental protocol which aims in identifying the parameters involved in a description of crazing within a cohesive surface methodology. The results obtained for PMMA are valuable for the calibration to perform in connection to the numerical work of Estevez et al. [2]. The method of preparation needs to be improved for more ductile material in order to characterize the failure by crazing only. 

By fitting Eq. (23) to experimental data for strong interfaces where Ojihril = 2fb we can obtain a reasonable estimate of <5 and of Q, provided that the crazing stress of the more ductile material is known. These constants can then be used to predict the value of o 6n /ac for more complicated cases where either the actual areal density of effective connecting chains or the force to break a connector is not precisely known. 

The crazing agent thus acts through its presence within the polymer matrix. In increasing the chain mobility (lowering Tg) it facilitates the primary and secondary steps of craze initiation nucleation and stabilization of a craze. This leads to the lowering of 0 and ej in brittle polymers such as PS. Easier nucleation and stabilization even cause the appearance of crazes in otherwise ductile materials such as PPO, PSU, PVC, or PC. 

However, at lower constant loads the rate of crystal plastic deformation decreases and (at 80 °C) disentanglement becomes competitive leading to the development of isolated planar craze-like defects extending perpendicular to the tensile axis (Fig. 15). The ensuing concentration of stress will further localize most of the sample deformation in such creep crazes and lead to a macroscopic ductile-brittle transition—in this material observed at 20 MPa (Fig. 14 [67]). 

The fracture energy cannot be related to the failure of chemical bonds which may contribute only with a few Jm-2. Furthermore, the possibility of crazing is not allowed in thermosets because fibrils cannot exist due to the high crosslink density. So, in the case of high-Tg cross-linked materials the main source of energy absorption before failure is the yielding of the network. This assumption is obviously valid only above the ductile-brittle transition temperature (Fig. 12.5), where yielding is temperature-dependent. ... 

Morphological explanations for the improved ductility of the fl nucleated materials have focussed on the lamellar texture. That crazes in a iPP are more localised and better defined than in /3 iPP may reflect both the influence of the cross-hatched structure on lamellar slip described in the previous section, and the strong correlation between deformation in ft iPP and the local orientation of the lamellae with respect to the tensile axis. Indeed, the trend towards more localised deformation in a spherulites may simply reflect the relatively homogeneous lamellar textures of these latter [24]. 

This conclusion was only partly confirmed by scanning electron microscopy micrographs of RuC>4 stained surfaces taken at the crack tip of deformed specimens at 1ms-1, where the non-nucleated and /3-nucleated materials showed, respectively, a semi-brittle and semi-ductile fracture behavior. While some limited rubber cavitation was visible for both resins, crazes—and consequently matrix shearing—could not develop to a large extent whether in the PP or in the /1-PP matrix (although these structures were somewhat more pronounced in the latter case). Therefore, a question remains open was the rubber cavitation sufficient to boost the development of dissipative mechanisms in these resins ... 

A shortening in relaxation time in the critically strained region makes some materials tough. The shift of relaxation time is attributed to strain-induced dilatation and can reach as much as five decades. Thermal history, on the other hand, dictates the initial state from which this dilatation starts and may be expressed in terms of excess entropy and enthalpy. The excess enthalpy at Tg is measurable by differential scanning calorimetry. Brittle to ductile transition behavior is determined by the strain-induced reduction in relaxation time, the initial amount of excess entropy, and the maximum elastic strain that the material can undergo without fracturing or crazing. 

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