Stress intensity factor, plastics mechanical

A third method which recently provided considerable insight into the role of crazes in deformation and fracture of amorphous polymers is the optical interference measurement of crazes (preceding a crack). Since the pioneer work of Kambour, this method has been widely used to determine characteristic craze dimensions and critical displacements. W. Doll gives an overview on recent results and on their interpretation in terms of fracture mechanics parameters (stress intensity factor, plastic zone sizes, fracture surface morphology, fracture energy). 

Mechanical Behaviour of Plastics Solution The stress intensity factor for this configuration is... 

Karger-Kocsis recorded the different fracture behaviors of non-nucleated and -modified PP (MFR 0.8 dg min 1) tested in a three-point bending configuration at 1 ms-1 at 23 °C, a-PP was semi-ductile and /3-PP ductile with a plastic hinge at - 40 °C a-PP was brittle, /i-PP ductile [72], The descriptors from the linear elastic fracture mechanics (LEFM), Kq, the stress intensity factor, and Gc, the energy release rate, used to quantify the toughness correlated well with the fracture picture. This conclusion is also valid for... 

It must be noted that the fracture mechanics framework described above only applies when plastic deformation of the material is limited. Substantial plastic deformation may accompany propagation of existing defects in structures fabricated from relatively low-strength materials, e.g., carbon steels. In these cases, the linear elastic stress intensity factor, K, does not accurately apply in structural design. Alternately, elastic-plastic fracture mechanics methods may apply. ... 

When the stress intensity increases it will finally reach a critical value Kc above which the crack propagates. If the load and crack orientation is like that shown in Figure 7.57, the actual and the critical stress intensity factor are denoted by Ki and Kic, respectively. Kic is also called the fracture toughness of the material. A necessary condition for the applicability of linear elastic fracture mechanics is that the plastic zone ahead of the crack tip is small compared with the thickness of the component and with the crack length. To satisfy this condition we must have... 

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). 

Above a critical yield stress (Tq the singular mode I stresses around sharp cracks are truncated at the yield stress in a plastic zone of extent ( ahead of the crack, which increases with increasing applied stress or stress-intensity factor K. This results in important alterations of the crack-tip stresses. The level of pervasiveness of the plastic zone in parts of finite size governs the nature and extent of the alterations of the crack-tip stresses and strains from those presented in Section 12.2.2 for elastic response only. As the stresses are radically altered around the crack tip in the plastic zone and lose their singularity, the strains become more concentrated. Depending on the different levels of pervasiveness of the plastic zone across the cross section, there occur different forms of alteration of stress and strain fields that govern the eventual forms and mechanisms of crack growth and fracture. 

ISO CD 13586, Plastic—Determination of energy per unit area of crack (Gc) and the critical stress intensity factor (Kc), linear elastic fracture mechanics approach, 2000. 

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