Plastic constraint factor

Mean-square length of a statistical unit of the chain Mv Molecular mass of a statistical skeletal unit nip Plastic constraint factor... 

The plastic constraint factor macroscopic yield stresses [32] ... 

FIGURE 5.7 The dependence of plastic constraint factor on defomiation energy release critical rate attesting temperature 293 (1), 313 (2), 333 (3) and 353 K (4) for HDPE [32]. 

Hence, the stated above results have shown that plastic constraint factor is dependent on structiual eharaeteristics of polymer and their change in deformation process and influenees essentially on its meehanical properties in impact tests. Growth k results to reduction of both plasticity and strength of polymer samples [32]. 

Kozlov, G. V., Novikov, V. U. (1997). The Physical Significance of Dissipation Processes in Impact Tests of Semicrystalline Polymers. Prikladnaya Fizika, 1,77-84. Kozlov, G. V., Serdyuk, V. D., Beloshenko, V. A. (1994). Plastic Constraint Factor and Mechanical Properties of High Density Polyethylene at Impact Loading. Mekhanika... 

As explained above, the existence of a sharp notch can strengthen the ductile metal due to the triaxiality of stress. The ratio of notched-to-unnotched yield stress is referred to as the plastic constraint factor, q. In contrast to the elastic stress concentration factor that can reach values in excess of 10, the value of q does not exceed 2.57 (Orowan, 1945). However, brittle metals could prematurely fail due to stress increase at the notch before plastic yielding occurs. 

Hardness values are related to flow stress by a constraint factor. It is easy to visualize this by considering a simple compression test because in such a test the whole specimen goes plastic due to the fact that there is no resistance to side flow with the specimen being only surrounded by air. In the indentation test the part of the specimen that flows is surrounded by elastic material and so side flow is restricted. Therefore a greater mean stress is required to cause plastic flow in hardness tests than in simple compression tests. In equation (1.9) C is called the constraint factor, approximating to 3 for Brinell, Vickers, and Knoop hardness. 

Microindentation hardness normally is measured by static penetration of the specimen with a standard indenter at a known force. After loading with a sharp indenter a residual surface impression is left on the flat test specimen. An adequate measure of the material hardness may be computed by dividing the peak contact load, P, by the projected area of impression1. The hardness, so defined, may be considered as an indicator of the irreversible deformation processes which characterize the material. The strain boundaries for plastic deformation, below the indenter are sensibly dependent, as we shall show below, on microstructural factors (crystal size and perfection, degree of crystallinity, etc). Indentation during a hardness test deforms only a small volumen element of the specimen (V 1011 nm3) (non destructive test). The rest acts as a constraint. Thus the contact stress between the indenter and the specimen is much greater than the compressive yield stress of the specimen (a factor of 3 higher). 

Because of the constraint imposed under plane strain conditions, yielding (onset of plastic deformation) would occur at a higher stress level. A number of estimates were made with different assumed constraint and yielding criteria [9]. But, because of the approximate nature of these estimates, the plastic zone correction factor for plane strain is taken to be that given by Eqn. (3.50). 

The key points to be gleaned from this exercise are that the plastic zone size depends on the state of stress (or constraint) and is proportional to (Ki/oys). Its size is expected to vary through the thickness of a plate, and it would increase with increasing stress intensity factor Kj and decreasing yield strength ays. The consequence of plastic deformation on fracture behavior and fracture toughness measurements is considered briefly in the next section. 

If the specimen is very thick i.e., with thickness B much greater than the plastic zone size, or Kic/oysY), the constraint condition along the crack front in the midthickness region is that of plane strain and is barely affected by plastic deformation near the surfaces. Abrupt fracture crack growth) will occur when the crack-tip stress intensity factor reaches the plane strain fracture toughness Kjc. The load-displacement record, similar to that of the penny-shaped crack, is depicted by Fig. 4.7a. 

The mechanical strength of hard materials is critical for load-bearing, structural applications. These brittle materials only deform plastically at high temperatures, or under severe hydrostatic constraint, since the Peierls stress for dislocation movement is high. Failure is usually by unstable crack propagation under a tensile stress that exceeds the tensile strength of the material. In terms of fracture mechanics, brittle failure occurs when the Mode I stress intensity factor Kj reaches the fracture toughness of the material, Kic (see below). 

Trachte and DiBenedetto, 1971 Wambach et ai, 1968). Since PPO is much more ductile at 25 C than the epoxy resins mentioned, the effects of filler and adhesion promoter on PPO should tend to resemble the effects on an epoxy resin in a ductile state (e.g., at 130°C). Indeed this is the case. The point is that a filler tends to increase surface roughness and hence y in an otherwise brittle matrix, especially if the filler-matrix adhesion is poor, but tends to inhibit plastic deformation (by constraints or by simple volume replacement) in an otherwise ductile matrix. Such effects are not accounted for in Nielsen s simple treatment (Section 12.1.2.3) and conceivably may occur as competitive mechanisms (see Figure 12.20). A useful summary of such competitive factors is given in Table 12.3 for the glass-bead-epoxy systems (DiBenedetto and Wambach, 1972) the discussion should be relevant to other cases as well. 

The crucial practical consequence of constraint at the crack tip (under the imposed plane-strain conditions) is that it inhibits crack tip plastic deformation, and consequently reduces the critical strain energy release rate to a value below G. Similarly, the critical stress intensity factor falls below K. ... 

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