Fracture transitions

The fracture transition from compressive to tensile type occurred at a fixed size ratio—at a critical size ratio (b/h)c at constant temperature... 

Irwin, G. R., Linear Fracture Mechanics, Fracture Transition and Fracture Control, Journal of Engineering Fracture Mechanics, 1 (1968), 241-257. 

The w can be obtained if 1/t ratio is large enough to ensure plane-stress condition in the ligament area and it is proved to be a material constant for a given sheet thickness [Mai and Cotterell, 1986 Mai et al., 1987 Mai and Powell, 1991]. With a reduction of 17t ratio, plastic constraint increases and the plane-stress/plane-strain fracture transition may occur at a certain 1/t ratio. Theoretical analysis shows that the specihc essential work of fracture method is equivalent to the J-integral method for all three fracture modes [Mai and Powell, 1991 Mai, 1993]. 

The intersection of the crack arrest curve with the yield curve (Curve B) is called the fracture transition elastic (FTE) point. The temperature corresponding to this point is normally about 60°F above the NDT temperature. This temperature is also known as the Reference Temperature - Nil-ductility Transition (RTj dt) is determined in accordance with ASME Section III (1974 edition), NB 2300. The FTE is the temperature above which plastic deformation accompanies all fractures or the highest temperature at which fracture propagation can occur under purely elastic loads. The intersection of the crack arrest curve (Curve D) and the tensile strength or ultimate strength, curve (Curve A) is called the fracture transition plastic (FTP) point. The temperature corresponding with this point is normally about 120°F above the NDT temperature. Above this temperature, only ductile fractures occur. 

Here Kq is the value of the stress intensity factor at the instant of the crack onset, Kc is the stress intensity factor critical value corresponding to the fracture transition into the stage of unstable crack propagation, while the difference Kq — Kq characterizes the residual strength of a specimen with a propagating crack. 

A Theory of Brittle-Ductile Transitions Consistent with Fracture Mechanics Fracture Transitions... 

We therefore see that the most acceptable approach to brittle-ductile transitions or plane strain-qtlane stress transitions, i.e. all types of fracture transition, is to regard each test as relating to a characteristic length in a particular test. The transition is then characterised by a critical length xoc, where xoc = aGcE jay and a is a numerical constant whose value is determined by the stress field in the test. 

To summarise, the choice of the particular fracture test determines a, and defines a critical length, for example the width of the beam in the double cantilever beam test piece or the plastic zone size at general yield of a notched bar. The fracture transition then occurs... 

Figure 1337 Schematic comparison of the brittle-ductile temperature transition in four different tests ( ) Hertzian indentation (lower transition), (2) plastic-elastic indentation (upper transition), (3) Double cantilever beam (lower transition) and (4) notched bar (upper transition). (Reproduced from Puttick, K.E. (1980) The correlation of fracture transitions. ). Phys. D, 13, 2249. Copyright (1980) Institute of Physics.)...

Figure 10.1 reprinted fr om Advanced Materials, Vol. 18,2006, Authors Barber B A, Cohen S R, Eitan A, Schadler L S and Wagner H D, Title Fracture transitions at a carbon nanotube/polymer interface, pp. 83-87, Copyright (2007), with permission from Wiley-VCH. 

Other synthetic fibers, as well as natural fibers, were employed in epoxy-based multicomponent systems. Thus, a comparative study between polymeric fibers reinforced epoxy resins and natural fibers reinforced ones, all obtained by UV curing, was performed [186]. Isotactic PP (iPP) fibers modified with 20 wt% EVA and hemp fibers were employed, while the matrices used were epoxy acrylate and epoxy methacrylate. Data indicated that relatively regular distribution of fibers was achieved the addition of fibers caused an increase in Shore hardness of the epoxy methacrylate based composites the epoxy acrylated composites showed a decrease in hardness when EVA-modified iPP fibers were used, whereas hemp fibers caused an opposite effect. Even more, the iPP fibers reinforced photocurable composites displayed a brittle to ductile fracture transition. 

Nickel/gold component terminations and solder pad surface finishes are the source for Au in solder joints where Sn Au intermetallics are formed. The formation of a brittle intermetallic compound (Au,Ni)Sn4 is a characteristic feature of these Pb-free alloys. The boundary between Ni3Sn4 and (Au,Ni)Sn4 is weak, and hence provides a low-energy path for crack propagation and the opportunity for the ductile-to-brittle fracture transition to occur. Subsequent aging indicates transgranular cracks at the (Au,Ni)Su4 layer [13]. Increasing the solder volume or solder joint size... 

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