Ductile fracture models

A void nucleation and growth fracture model embedded in a general viscoelastic-plastic material model is representative of approaches to ductile dynamic fracture (Davison et al., 1977 Kipp and Stevens, 1976). Other approaches include employing the plastic strain as a damage variable (Johnson and Cook, 1985) so that both spall and large strain-to-failure can be treated. 

Ductile mechanical models. Stress concentrations at the base of corrosion slots or pits increase to the point of ductile formation or fracture. 

Figure 27.2 Fracture surface of semi-ductile fracture (a) PA 11 at room temperature (b) HIPS at -40 C (c) variables considered in semiductile model...

To understand the failure in this model, an approximate criterion for the brittle or ductile fracture was proposed. One considers the sequence of the weakest bonds and asks for the average failure voltage for the nth weakest bond. It is given by... 

The correlation is quite good for the SRI500 resin, while for the more ductile adhesive resin the predictions overestimate the measured failure loads. However, in the latter case an extensive damage zone develops before final failure and the non-linear elastic fracture model is no longer appropriate. It is interesting to note however, that when a fillet is left at the end of the overlap the test values are much closer to the predictions. 

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. 

As indicated in section 8.1, fracture can take place in essentially two ways, either following macroscopic yield, when the fracture is said to be ductile fracture, or without macroscopic yield, when it is called brittle fracture. The present section is concerned with the brittle fracture of polymers. Experimental studies of brittle fracture can be divided broadly into two types, those that are undertaken with a view to understanding the details of what happens during fracture and those that are aimed at providing engineering data about a polymer. Experiments of the former type are often designed to test the predictions of a theoretical model, whereas experiments... 

Samples of unfilled polyetherimide plaques or films were pretreated and metallized with copper. Peel strengths of -170 g/mm were achieved. Both sets of samples failed cohesively within the polymer layer. This failure mode has been discussed previously for filled-polymer resinsS S.H. Fracture patterns on the polymer side of the peel were found to be similar for both materials when viewed at high magnification (20,000 X), Figure 5. The ductile failure model 8 observed for the polyetherimide film was not apparent at low magnifications (300X). 

In every approach one finds a wide range of sophistication. In the continuum approach, the simplest (and most common) models are based on linear elastic fracture mechanics (LEFM), a well developed discipline that requires a linear elastic behaviour and brittle fracture, not always exhibited by fibres. Ductility and the presence of interfaces, not to mention hierarchical structures, make modelling much more involved. The same is true of the atomistic approach fracture models based on bond breaking of perfect crystals, using well established techniques of solid state physics, allow relatively simple predictions of theoretical tensile stresses, but as soon as real crystals, with defects and impurities, are considered, the problem becomes awkward. Nevertheless solutions provided by these simple models — LEFM or ideal crystals — are valuable upper or lower bounds to fibre tensile strength. 

Fig. 1.7 is a schematic plot of stress versus strain, where curve (1) models brittle fracture and curve (2) ductile fracture with large deformation. The two extreme cases... 

Lemaitre J (1985), Continuous Damage Mechanics Model for Ductile Fracture. Journal of Engineering Materials and Technology, 107, 83-89. 

The applied stress may be tensile, compressive, shear, hydrostatic, or torsional (see Fig. 1). Two fracture models are possible, ductile and brittle. In ductile materials fracture is preceded by substantial plastic deformation with high energy absorption. By contrast, there is normally little or no plastic deformation and low energy absorption accompanying a brittle fracture. The ductihty is a function of temperature of the material, the strain rate, and the stress state. Depending on these factors, a material considered ductile material may actually fail in a brittle manner. 

---