Sharp notch failure

In the laboratory the impact behaviour of a material could be examined by testing plain samples, but since brittle failures are of particular interest it is more useful to ensure that the stress system is triaxial. This may be achieved most conveniently by means of a notch in the sample. The choice of notch depth and tip radius will affect the impact strengths observed. A sharp notch is usually taken as 0.25 mm radius and a blunt notch as 2 mm radius. 

It may be seen from Fig. 2.80 that some plastics experience the change from ductile to brittle behaviour over a relatively narrow temperature range. This permits a tough/brittle transition temperature to be quoted. In other plastics this transition is much more gradual so that it is not possible to attribute it to a single value of temperature. In these circumstances it is common to quote a Brittleness Temperature, rg(l/4). This temperature is defined as the value at which the impact strength of the material with a sharp notch (1/4 mm tip radius) equals 10 kJ/m. This temperature, when quoted, gives an indication of the temperature above which there should be no problems with impact failures. It does not mean that the material should never be used below Tb(1/4) because by definition it refers only to the sharp notch case. When the material has a blunt notch or is un-notched its behaviour may still be satisfactory well below Tb(1/4). 

Figure 17 Correlation of failure time and melt flow rate MFR 190/5 of sharp notched bars under stress for unimodal homopolymer and copolymers, and bimodal copolymers. Source Ref. 130.

The stresses near the root of a notch are extremely complex and the stress analysis becomes exceedingly difficult when the strain is large, as is the case when yield or failure is imminent. A sharp notch causes constraints and introduces a state of triaxial tension behind the root of the notch (5). This state of stress is consistent with LeGrand s observation of the growth of a flaw behind a notch in a bar of polycarbonate (4). A blunt notch causes constraints when the thickness of the specimen is large. Such a notch can also introduce a state of triaxial tension. While it is desirable to investigate the behavior of polymers in a well-defined state of triaxial tension, it is difficult to accomplish experimentally. However, as we demonstate below, a state of plane strain is relatively easy to produce. The relationship between plane strain and brittleness of plastics is the subject of our investigation. 

By the first decade of this century it was established that material failures occur at such low stress levels, because real materials do not usually have a perfect crystalline structure and almost always some vacancies, interstitials, dislocations and different sizes of thin microcracks (having linear structure and sharp edges) are present within the sample. Since the local stress near a sharp notch may rise to a level several orders of magnitude higher than that of the applied stress, the thin cracks in solids reduce the theoretical strength of materials by similar orders, and cause the material to break at low stress levels. The failure of such (brittle or ductile) materials was first identified by Inglis (1913) to be the stress concentrations occurring near the tips of the microcracks present within the sample. 

In several polymers, it is possible to induce brittle failures in impact with quite blunt notches and it is possible to give an apparent Gic, for these cases. Rigorously, of course, the use of Ki is not valid for anything other than a sharp notch. However, if ATjc is interpreted as a critical stress at a critical distance C we may write > ... 

When the part is being designed, stress concentrators should be avoided. These are items such as sharp notches, internal comers, and sharply angled wall sections. Surface interruptions such as holes and inserts can significantly reduce the strength of plastic parts and induce failure. When parts are designed for performance, certain questions should be asked ... 

The test results suggest that the observed variation in failure stress with bond area could be correlated using just the associated with the stronger singularity. As an aside, Dunn and his colleagues have also used a ATa-based approach to successfully predict the fracture of homogeneous materials containing a sharp notch when the material is isotropic [69,70] and when the material is anisotropic [71,72],... 

Finally, the presence of sharp notches or cracks can give rise to a reduction in strength of a polymer compared with that of an uncracked specimen as shown in Figure 10 for PMMA. The cracks and notches give rise to stress concentrations and failure at relatively low stresses, especially for brittle polymers. Recent improvements in the mechanical properties of polymers have led to tougher materials with improved resistance to brittle fracture. These are discribed next. 

Instron Three-Point Bending Failure. Three-point bending tests have also been conducted on notched Izod specimens at crosshead rates of 0.02-20 inches/min (Figure 5). Plots of work to break obtained from the areas under the Instron force-displacement traces show abrupt ductile-brittle transitions these are displaced to lower temperatures as the test rate is decreased. However the temperature interval between ductile-brittle transitions of the two materials remains about the same. The force-displacement trace for each specimen shows a yield point with a ductile failure but a sharp termination when the sample breaks in a brittle fashion. 

The objective of this test method is to measure the cohesive stress and the time to failure of a crystalline polymer craze layer under rapid, uniform extension. The method is an impact variant of the Full Notch Creep test used by Fleissner [12], Duan and Williams [13], Pandya and Williams [14] and others. The specimen (Fig. 2), a square-section tensile bar, is injection moulded. At the mid-plane of the gauge length a sharp, deep circumferential notch reduces the cross-section to about one fifth of its original area. This notch plane is formed by a moulded-in, hardened steel washer. Specimens were injection moulded at 210°C into a warm (100°C) mould and air cooled to 40 C using a hold pressure of 45-50 bar. 

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