Toughness fracture mechanics

Short fibre composites, fibre orientation, fracture toughness, fracture mechanisms, fibre pullout, fibre debonding, critical fibre angle. 

The elastic stress cannot exceed the yield stress of the material, implying a region of local yielding at the crack tip. Nevertheless, to apply the simple framework of hnear elastic fracture mechanics, Irwin [J. Applied Mechanics, 24, 361 (1957)] proposed that this process zone size / be treated as an effective increase in crack length be. Fracture toughness is then given by... 

Marshall, G.P. Design for toughness in polymers - Fracture Mechanics, Plastics and Rubber Proc. and Appl. 2(1982) p 169-182. 

T. Kobayashi, H. Toda. Toughness enhancement based on fracture mechanical simulation of Al-SiC composite. Mater Sci Forum 242 193, 1997. 

The large region of yield in materials that fail by tough fracture arises as the molecules of the polymer rearrange themselves in response to the applied stress. This is different from the mechanism of yield in metals, where planes of metal atoms slide over one another. In polymers, the molecular movement... 

The above results are derived from linear elastic fracture mechanics and are strictly valid for ideally brittle materials with the limit of the process zone size going to zero. In order to apply this simple framework of results, Irwin (1957) proposed that the process zone, r be treated as an effective increase in crack length, Sc. With this modification, the fracture toughness becomes... 

The interface debond criterion used in this analysis is based on the concept of fracture mechanics where the strain energy release rate against the incremental debond length is equated to the interface fracture toughness, Gk, which is considered to be a material constant... 

The term fracture toughness or toughness with a symbol, R or Gc, used throughout this chapter refers to the work dissipated in creating new fracture surfaces of a unit nominal cross-sectional area, or the critical potential energy release rate, of a composite specimen with a unit kJ/m. Fracture toughness is also often measured in terms of the critical stress intensity factor, with a unit MPay/m, based on linear elastic fracture mechanics (LEFM) principle. The various micro-failure mechanisms that make up the total specific work of fracture or fracture toughness are discussed in this section. 

Mai (1985) has also given a review of the fracture mechanisms in cementitious fiber composites. The total fracture toughness, / i, is given by the sum of the work dissipation due to fiber pull-out, fiber and matrix fraetures, fiber-matrix interfacial debonding and stress redistribution, i.e.. 

Gershon B. and Marom G. (1975). Fracture toughness and mechanical properties of glass fiber-epoxy composites. J. Mater. Sci. 10, 1549-1556. 

Bradley, W.L. (1989b). Relationship of matrix toughness to interlaminar fraeturc toughness. In Application of Fracture Mechanics to Composite Materials (K. Fricdrieh ed.), Elsevier Seienec Pub., New York, Ch, 5, pp, 159-187. 

Hibbs, M.F., Tse, M.K. Bradley, W.L. (1987). Interlaminar fracture toughness and real time fracture mechanisms of some toughened graphite/epoxy composite. In Toughened Composites, ASTM STP 937 (N.J. Johnston ed,), ASTM, Philadelphia, PA, pp. 115-130. 

In general, the use of FE signals accompanying the deformation and fracture of composites offer elucidation of failure mechanisms and details of the sequence of events leading upto catastrophic failure. The extent of interfacial failure and fiber pull-out are also potential parameters that can be determined. FE can assist in the interpretation of AE and also provide an independent probe of the micro-events occurring prior to failure. FE has been shown to be sensitive to the locus of fracture and efforts are underway to relate emission intensity to fracture mechanics parameters such as fracture toughness (Gjp). Considerable work still remains to fully utilize FE to study the early stages or fracture and failure modes in composites. 

Fracture mechanics deal with the behaviour of materials which break easily. A measure for their strength is the fracture toughness, the maximum stress which can be applied to an object without breaking, i.e. the stress which the object with all its cracks can still withstand. This fracture toughness can be measured in a tensile test test samples are provided with cracks of known dimensions and forms (figure 9.31). 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

By metallurgists in terms of the mechanical properties, such as modulus, fracture toughness, ultimate tensile strength. And they came up with a theory that deals with dislocation, fracture mechanic and continuum mechanics. 

---