Traction-separation

EFFECTS OF CONSTRAINT ON THE TRACTION-SEPARATION BEHAVIOUR OFPOLYETHYLENE... 

The present experiments were designed to measure in-situ the development of the damage zone (craze) under different constraint conditions over a wide range of loading speeds. Here, the localised fracture process is represented in terms of a traction separation relation on the plane of fracture. The aim was to show that the formation and subsequent failure of the damage zone was dependent on the constraint level, in addition to the applied rate. 

Effects of Constraint on the Traction-Separation Behaviour of Poiyethyiene 145... 

Motivated by the Kramer and Berger [3] description of the crazing process, Tijssens et al. [9] proposed a viscoplastic crazing model within the fiamework of a cohesive zone methodology. The traction-separation law proposed in [9] comprises three parts corresponding to initiation, thickening and breakdown of the craze. 

The cohesive zone approach to fracture mechanics reduces the fracture resistance properties of a material to a traction-separation law. This Taw relates, o, the normal cohesive stress which resists the parallel separation of two internal planes which were initially very close together, to the current increase r] in their separation. The fracture resistance (and hence the fracture toughness K,.) is simply given by the area under the o,. ri) curve up to 6,.. The simplest form of traction separation law assumes 0 (77) to be constant up to a critical maximum separation 4. and this was developed analytically into a fracture model by Dugdale... 

To obtain fracture properties of HDPE conventional essential work of ifacture tests are performed. Two grades of blow-moulded HDPE are tested at different test speeds. The main aim of these tests is to estimate traction-separation (cohesive zone) properties of the materials. In future work, these will be combined with the fluid-structure interaction model to provide a powerful tool for predicting the complex behaviour and potential failure of fluid-filled containers imder drop impact. 

The procedure presented the skeleton for the development of a general, predictive fluid-structure-fracture procedure that will be applied to predict failures of fluid-filled containers under drop Impact. The missing constituent required by the model is the traction-separation data for the materials considered. In order to calibrate the CZM parameters, combined experimental/numerical work employing the essential work of fracture and FV simulations has been conducted. 

Fig. 3 (a) Schematic of the FV CZ model (b) Dugdale traction-separation curve used in the analysis. 

Figure 8.4 A typical nonlinear interfacial traction-separation law. Source [66] Reproduced with permission from Elsevier...

Similar to the Mode I fracture test, the energy release rate /jj can be experimentally determined as a function of the crack tip slip Sq and the global shear force gj. Once the experimental /n o curves are obtained according to Equation (8.13), the Mode 11 interfacial traction-separation law t = t(Sq) can be experimentally determined as foUows ... 

Figure 8.14 Typical shapes of the interfacial traction-separation laws at different adhesive layer thicknesses ha- Source [63] Reproduced with permission from Springer...

Finally, Figure 8.18 shows the overall mixed mode traction-separation laws with various adhesive thicknesses. It is seen that the area under the T-cp curves increase as the thickness of the adhesive layer increases, which suggests that the energy release rate increases, as also does the fracture toughness. It is interesting to note that the peak traction is almost constant as the adhesive layer thickness increases. This is understandable because the peak traction represents the strength of the material under the complex stress condition. 

Zhu, Y., Liechti, K.M., and Ravi-Chandar, K. (2009) Direct extraction of rate-dependent traction-separation laws for polyurea/steel interfaces. International Journal of Solids and Structures, 46, 31-51. 

Figure 17.10 Implementation of the Cohesive Zone Model (CZM) (a) the Traction Separation Law (TSL), (b) Intrinsic TSL and (c) Extrinsic TSL. The cohesive laws are characterized by the strength, the critical opening and the critical energy release rate [145].

FEA has also been used to study interface adhesion between thin film and substrate under indentation. Liu et al. (2007) examined the interface delamination and buckling of thin film subjected to microwedge indentation. In their model, the interface adjoining the thin film and substrate is assumed to be the only site where cracking can occur. A traction—separation law with interface strength and interface energy as two major parameters was introduced to simulate the adhesive and failure behaviors of the interface between the film and the substrate. 

As discussed earlier, the area under the traction-separation curve Fi and Fiio) and the peak stress (a and f) are the important parameters that describe the cohesive tractions. The precise shape of the traction-separation law does not strongly influence the behavior of the system. For example, one generally useful form of a mode-I traction-separation law is shown schematically in Fig. 4. It should be appreciated that while the area and peak stress are the two important parameters from a mechanics point-of-view, they may not necessarily represent the fundamental parameters from a materials perspective. In some ways, the peak... 

Fig. 4. Schematic mode-1 traction-separation law that is generally useful in cohesive-zone models.

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