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About the critical opening value in cohesive models

Good mourning Imechanica residents :D,

I have a question about the order of the critical value of the opening in the cohesive models, since the crack initiate after a developement of a process zone which is modeled by a cohesive law mainly  a traction separation law, the new crack surface is created after a critical opening value is reached, then the cohesive Traction value drops to zero and a new free surface is develped ahead of the previous crack tip, so the question adressed to those who tried to measure this critical opening experimentaly in metals and alloys, this value is in the order of what (millimeter, micrometer) if it is possible give us some referance Guys. Thanks

  

Comments

Good evening Brick, :)

Roughly speaking, the value of critical opening is in the order of Gc/sigma_yield (material toughness divided by its yield strength).

Hope it helps,

Thank you So much

  

Bent F. Sørensen's picture

Hi Brick,

I don't know about critical separation for metals, but based on my experience it is very material system dependent so that it is difficult to make general conclusions regarding the magnitude of the critical separation. You need to measure it for the material in question.

We have measured the critical separation a number of ways. Probably the most accurate way is in-situ observations of the crack tip by microscopy. We have conducted fracture mechanical tests using DCB specimens loaded with pure bending moments in an environmental scanning electron microscope - this provides stable crack growth and thus facilitates in-situ observations. For brittle materials (e.g. brittle adhesives) it appears that the critical separation is in the order of one micron Goutianos and Drews (2007). For composite materials we often find that the fracture process consists of a crack tip region (where the critical separation is about one micron), and a bridging zone where the critical separation can be much larger, e.g. in the order of 150 micron, see Goutianos et al. (2014).

We can also obtain the critical separation from macroscopic experiments where the crack tip opening displacement is measured e.g. by an extensometer mounted across the crack faces at the end of the cohesive zone. For a "ductile" polyurethane/steel interface we found the critical separation to be in the range of 1.7 - 3.3 mm, highest for the highest opening rate (Sørensen, 2002). For an ("brittle") epoxy/steel interface we found that the critical separation in the order of 0.1 mm (Högberg et al., 2007). For crack growth parallel to the fibre direction in unidirectional fibre composite (intralaminar cracking or delamination) fibre composites can develop large-scale crack bridging by long fibres. Then we found the critical separation under Mode I to be in the order of 3 mm (Sørensen and Jacobsen, 1998; Sørensen and Jacobsen, 2009). 

Best regards, Bent

Goutianos, S & Drews, JM 2007, 'Estimation of interface cohesive laws by digital image correlation'. in BF Sørensen, LP Mikkelsen, H Lilholt, S Goutianos & FS Abdul-Mahdi (eds), Interface design of polymer matrix composites - mechanics, chemistry, modelling and manufacturing. Proceedings. Risø National Laboratory, Roskilde, pp. 181-190.

Goutianos, S, Arévalo, R, Sørensen, BF & Peijs, T 2014, 'Effect of Processing Conditions on Fracture Resistance and Cohesive Laws of Binderfree All-Cellulose Composites' Applied Composite Materials, vol 21, no. 6, pp. 805-825., 10.1007/s10443-013-9381-0

Högberg, J. L., Sørensen, B. F., and Stigh, U., 2007, "Constitutive behaviour of mixed mode loaded adhesive layer", International Journal of Solids and Structures, Vol. 44, pp. 8335-54.

Sørensen, B. F., 2002, "Cohesive law and notch sensitivity of adhesive joints", Acta Mater., Vol. 50, pp. 1053-61

Sørensen, B. F. and Jacobsen, T. K., 1998, "Large scale bridging in composites: R-curve and bridging laws", Composites part A, vol. 29A, pp. 1443-51.

Sørensen, B. F., and Jacobsen, T. K., 2009, "Delamination of fibre composites: determination of mixed mode cohesive laws", Composite Science and Technology, Vol. 69, pp. 445-56.

 

It very intressting and helpfull response from you Mr Bent, we've been thinking about in-situ observations by microsopy since this is available, but to do that we need to built a little tensile machine but this is very intressting. According to some works it is possible to consider two parameters that we can determine experimentaly the fracture energy and the critical stress and we wonder if this is possible to build the corresponding cohesive low for that particular case of material. thanks too much 

  

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