Notch triaxial stress state

Loading of the material in a triaxial stress state that keeps Mohr s circle small and shifts it to the right in the direction of the cleavage strength. Such a stress state can be found in the notched bar impact bending test [42]. In components, changes in cross section and notches cause such... 

The maximum external force during the test is larger in the notched than in the un-notched case. This is again due to the triaxial stress state and can be explained in the same way as for the onset of yielding above. It has to be kept in mind that the diameter of the un-notched specimen is the same as that of the notched specimen at the notch position. Thus, it should not be assumed that a specimen can be made stronger by notching it. 

Prior to the advent of fracture mechanics as a scientific discipline, impact testing techniques were estabhshed to ascertain the fracture characteristics of materials at high loading rates. It was realized that the results of laboratory tensile tests (at low loading rates) could not be extrapolated to predict fracture behavior. For example, under some circumstances, normally ductile metals fracture abruptly and with very little plastic deformation imder high loading rates. Impact test conditions were chosen to represent those most severe relative to the potential for fracture —namely, (1) deformation at a relatively low temperature, (2) a high strain rate (i.e., rate of deformation), and (3) a triaxial stress state (which may be introduced by the presence of a notch). 

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. 

Correlation of results from one test to another for a given material becomes difficult because of different stress states of the specimen and the associated strain rates in different tests. In the tensile-impact test, the stress state is uniaxial and it measures the tensile property at a high strain rate. In Izod and Charpy tests, the presence of notch gives a triaxial state of stress. The falling-... 

Crazing requires the presence of dUatational component in the stress tensor and may be inhibited by hydrostatic pressure. On the other hand, it is enhanced by the presence of triaxial tensile stress (Kinloch and Young 1983). Unfortunately, such a stress state exists ahead of large flaws or notches in relative thick specimens (plane-strain conditions). Therefore, the presence of sharp cracks, notches, or defects in thick specimens wUl favor craze initiation leading to brittle fracture, which is opposite to a bulk shear yielding mechanism that leads usually to ductile behavior. 

Polyamides 6 and 66 exhibit low notched Izod impaet values of 50 to 60 J/m in the dry as in the molded state and even lower values at lower temperatures. This is due to the fact that under the triaxial stress concentrations encoimtered at the notch or crack tip in thick cross-sections (Scheme 8.1), unmodified polyamides begin to fail like many other plastics... 

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