Sharp notch

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. 

Fig. 2.79 shows the typical variation of impact strength with notch tip radius for several thermoplastics. The first important fact to be noted from this graph is that the use of a sharp notch will rank the plastics materials in a different order to that obtained using a blunt notch. This may be explained by considering the total impact strength as consisting of both crack initiation and crack propagation... 

Graphs such as Fig. 2.79 also give a convenient representation of the notch sensitivity of materials. For example it may be seen that sharp notches are clearly detrimental to all the materials tested and should be avoided in any good design. However, it is also apparent that the benefit derived from using generously rounded comers is much less for ABS than it is for materials such as nylon or PVC. 

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). 

In particular, standard specimens contain a sharp notch so that it is propagation energy rather than initiation energy which is the dominant factor. In general the standard tests are useful for quality control and specification purposes but not... 

In recent years impact testing of plastics has been rationalised to a certain extent by the use of fracture mechanics. The most successful results have been achieved by assuming that LEFM assumptions (bulk linear elastic behaviour and presence of sharp notch) apply during the Izod and Charpy testing of a plastic. 

Fracture is caused by higher stresses around flaws or cracks than in the surrounding material. However, fracture mechanics is much more than the study of stress concentration factors. Such factors are useful in determining the influence of relatively large holes in bodies (see Section 6.3, Holes in Laminates), but are not particularly helpful when the body has sharp notches or crack-like flaws. For composite materials, fracture has a new dimension as opposed to homogeneous isotropic materials because of the presence of two or more constituents. Fracture can be a fracture of the individual constituents or a separation of the interface between the constituents. 

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.

Check slip areas for longitudinal and transverse cracks and sharp notches. Check tool Joints for wear, galls, nicks, washes, fins, fatigue cracks at root of threads, or other items that would affect the pressure holding capacity or stability of the Joint. 

Tests may include tensile elongation, sharp-notch tensile strength (to be compared with unnotched tensile strength), and/or other tests, conducted at or below design minimum temperature. See also para. GR-2.1.3(d). 

Sharp notches or grooves at the edge of the weld where it joins a slanted surface shall be avoided. 

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. 

The analysis by Inglis showed that the local stress at sharp notches or corners of the microcrack can rise to a level several times that of the applied stress. This shows how the microscopic cracks or flaws within the solid might become potential sources of weakness of the solid. 

Usually the radius of curvature p at the sharp notch of the crack is determined by the atomic sizes and is very small. It is immediately evident that the stress concentration at the sharp notches of the microcracks can become extremely large due to the above stress intensity factor, and the fracture should start propagating from there. Although this analysis indicates clearly where the instabilities should occur, it is not sufficient to tell us when the instability does occur and the fracture propagation starts. This requires a detailed energy balance consideration. 

Since crazing represents a cavitational form of plasticity, it is clear that crazes play an important role in the fracture of polymers. Crazing is, generally, involved when PC fails under plane strain conditions, e.g. in fracture mechanics tests on thick samples with sharp notches where high triaxial stresses are built... 

There can be no doubt as to the importance of plane strain conditions for the fracture of plastics especially where sharp notches and thick sections are concerned. Such conditions nearly always lead to brittle or semi-brittle fracture. Vincent has shown that the notch sensitivity in a braod range of amorphous and crystalline polymers is increased as the testing temperature is lowered and the loading rate is increased. Before fracture occurs, amorphous plastics often craze under these conditions. The complex questions of craze initiation, propagation and transformation into a crack have been treated extensively for amorphous polymers in the first three chapters of this book (see also The problem becomes more complicated when... 

The brittle-ductile transition temperature depends on the characteristics of the sample such as thickness, surface defects, and the presence of flaws or notches. Increasing the thickness of the sample favors brittle fracture a typical example is polycarbonate at room temperature. The presence of surface defects (scratches) or the introduction of flaws and notches in the sample increases Tg. A polymer that displays ductile behavior at a particular temperature can break in the brittle mode if a notch is made in it examples are PVC and nylon. This type of behavior is explained by analyzing the distribution of stresses in the zone of the notch. When a sample is subjected to a uniaxial tension, a complex state of stresses is created at the tip of the notch and the yield stress brittle behavior known as notch brittleness. Brittle behavior is favored by sharp notches and thick samples where plane strain deformation prevails over plane stress deformation. 

Fig. 3. Device for machining automatically a sharp notch with a razor blade.

A first notch of 250 micrometers radius at the tip was mill cut with a rotary cutter. In order to prevent heating while machining, specimens were cooled with fresh compressed air during cutting. A sharp notch was further introduced at the tip of the first notch with a razor blade. The displacement of the razor blade was controlled by a micrometric thrust so that slow and careful control of the blade advance could be monitored. Figure 3 shows the device used to machine the sharp notches automatically in order to improve reproducibility. 

Examples of the blunt and sharp notches are shown in Fig.4. From the first blimt notch of 250 pm radius (Fig. 4a), the machined sharp notches for PMMA (Fig. 4b) and for PC (Fig. 4c) are similar and their crack tip is about few micrometers. The comparison between Figs. (4b) and (4c) suggests that some plasticity is induced by the machining in PC and not in PMMA. 

Fig. 5. Photoelasticity of PC for (a) 250 pm notch radius and (b) a sharp notch radius.

Fig. 6. Evolution of toughness versus loading rate for PMMA and PC for the three configurations Pj, Gj and G2 and sharp notches...

Since the blunt-notched specimen undergoes the same viscoelastic deformation as the sharp-notched specimen, but without crack propagation, the crack initiation time can be identified as the time at which the two curves diverge. Determination of the subsequent crack growth is a somewhat more difficult task direct optical observation was not possible, due to the wrapping bag. An indirect method based on compliance analysis was therefore adopted. 

Deformation curves in Fig. 4 clearly show that materials cannot be considered linearly elastic, and therefore Eq. 2 cannot be used directly in this form. However, by subtracting from the sharp-notched specimen curve the flexural and shear deformation contributions given by the blunt-notched specimen curve, a curve accounting for the crack length contribution to the specimen compliance can be derived from the data of Fig. 4. Eq. 2 can then be rewritten as follows ... 

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