Ductile fracture mechanics

Linear elastic fracture mechanics studies on toughened brittle plastics at room temperature concentrated on thermosetting resins, which have sufficiently high yield stresses to meet the requirements of Eq. 12.7. There has been increasing emphasis on ductile fracture mechanics in testing the toughened thermoplastics. An alternative approach is to determine the parameter, Jj, which is the quantity corresponding to Gj in linear elastic fracture mechanics, as discussed below. 

Ductile polymers. For ductile polymers, the linear elastic fracture mechanics do not apply. The introduction of the J-integral by Rice(20) has facilitated the application of ductile fracture mechanics for this polymer system.(17) Without detailed discussion, the ductile fracture energy is used instead of in Eq. (5) ... 

Several researchers tried to replace the single-shear plane model by a shear zone model. Lee and Shaffer (1951) provided a slip-line solution by applying the theory of plasticity. In the slip-line model, the metal is assumed to flow along the line of maximum shear lines. The slip-line field solution cannot be applied easily to three-dimensional as well as strain-hardening cases. Sidjanin and Kovac (1997) applied the concept of fracture mechanics in chip formation process. Atkins (2003) demonstrated that the work for creation of new surfaces in metal cutting is significant. He also points out that Shaw (1954) has shown this work to be insignificant. However, when this work is included based on the modem ductile fracture mechanics, even the Merchant analysis provides reasonable results. 

Atkins, A. G. (2003). Modelling metal cutting using modem ductile fracture mechanics quantitative explanations for some longstanding problems. Intemational Journal of Mechanical Science, 43, 373-396. 

Besides, in the same figure the points represent the values for PASF, calculated aceording to the Eq. (5.9) and the plots of Fig. 8.1 slope. As one can see, the dimensions and good correspondence is observed, from which the conclusion can be made, that PASF film samples fiucture by stable crack mechanism is related to ductile fracture mechanism. These results demonstrate clearly, that the value for polymer samples can be predicted, proceeding from the two indicated above factors polymer structure and its fracture mechanism [13]. 

In moie ductile materials the assumptions of linear elastic fracture mechanics (LEFM) are not vahd because the material yields more at the crack tip, so that... 

Fracture Mechanics Methods These have proved very usebd for defining the minimum stress intensity K[scc. t which stress corrosion cracking of high-strength, low-ductihty alloys occurs. They have so far been less successful when apphed to high-ductility alloys, which are extensively used in the chemicm-process industries. 

Since the surface energy term will usually be negligible by comparison with the plastic work term in the stress corrosion of ductile materials, it may be neglected. The remaining terms may be derived from fracture mechanics and conventional electrochemical conditions and, for the various boundary conditions indicated by West result in... 

Dual nickel, 9 820—821 Dual-pressure processes, in nitric acid production, 17 175, 177, 179 Dual-solvent fractional extraction, 10 760 Dual Ziegler catalysts, for LLDPE production, 20 191 Dubinin-Radushkevich adsorption isotherm, 1 626, 627 Dubnium (Db), l 492t Ductile (nodular) iron, 14 522 Ductile brittle transition temperature (DBTT), 13 487 Ductile cast iron, 22 518—519 Ductile fracture, as failure mechanism, 26 983 Ductile iron... 

Most of the technical raw materials used in solid reactions are polycrystalhne, and these - when in solid form - undergo a range of modifications during milling. The first observation is the fracture of the solid into smaller pieces. The fracture mechanics are a topic of discussion, and fracture can be divided into two steps, namely crack formation and crack propagation . Depending on the ability of the material to undergo plastic deformation before fracture, either brittle or ductile fracture can be defined ... 

Crack propagation involving permanent rupture of the chemical bonds binding together the atoms of a substance. The mechanisms are different in ductile and nonductile materials. Ductile fracture occurs in the direction of the primary slip system. 

The above refers primarily to linear elastic fracture mechanics (LEFM) studies related to the onset of brittle fracture as well as fatigue. The states of the sciences of ductile and dynamic fracture, which only became of serious concern in the early 1960s and 1970s, respectively, have not reached a similar level of maturity despite the immense research efforts expended on these topics in recent years. Yet to be resolved in the former is a viable ductile fracture criterion in view of the recently uncovered uncertainties regarding the /-integral as a crack tip parameter.5,6 As for the latter, a reliable dynamic crack propagation criterion is yet to be established, as will become apparent in subsequent sections of this chapter. 

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... 

This conclusion was only partly confirmed by scanning electron microscopy micrographs of RuC>4 stained surfaces taken at the crack tip of deformed specimens at 1ms-1, where the non-nucleated and /3-nucleated materials showed, respectively, a semi-brittle and semi-ductile fracture behavior. While some limited rubber cavitation was visible for both resins, crazes—and consequently matrix shearing—could not develop to a large extent whether in the PP or in the /1-PP matrix (although these structures were somewhat more pronounced in the latter case). Therefore, a question remains open was the rubber cavitation sufficient to boost the development of dissipative mechanisms in these resins ... 

Interestingly, the ductile-brittle transition observed for the MIM system provided an opportunity to assess the material fracture toughness, which was not possible using classical fracture mechanics tests due to the intrinsic brittleness of the MIM system. The measurement of the critical crack length, Lc, in the contact plane at the onset of brittle propagation allows estimation of a fracture toughness K C = a x+JnLc in the order of 0.85 MPa m1/2, i.e. much less than that of a poly(methylmethacrylate) homopolymer (1.20 MPa m1/2). 

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