Keywords: dynamic loading, ductile fracture, cohesive zone model, rate dependency, triaxiality, Gurson type model, centre cracked specimen, aluminium alloy, finite element method.

The rate of loading affects the mechanical response of ductile materials. Depending on the loading speed and material properties, structural resistance to dynamic loading is influenced by inertia, stress waves, rate sensitivity and adiabatic heating. These parameters need to be considered more carefully when a structure contains cracks. Different approaches can be applied for crack propagation and failure analysis, one of which is a local approach named "cohesive zone modeling". The approach is based on the models introduced by Dugdale [1] and Barenblatt [2] called strip-yield models and later applied to finite element method by different authors, e.g. [3,4]. In this approach, crack growth is modelled by introducing a process zone ahead of a crack tip which accounts for traction and separation of material in the damage-free surrounding. The application of the cohesive zone model allows for dividing the dissipated energy into global plastic strain energy and local separation energy. In the context of the finite element method, the surrounding material is modelled using continuum elements and the crack growth is simulated by introducing interface elements that are embedded between the continuum ones. The cohesive properties, which are known as "traction separation law (TSL)" affect the macroscopic stresses and strains and consequently the response of a structure. Because ductile crack growth is the consequence of void nucleation, growth and coalescence, it is wise to obtain the TSL based on the mechanical behavior of voided cells, e.g. Gurson type model [5,6].

The effect of different parameters on the mechanical response of an aluminium specimen during crack propagation analyses has been considered. The analyses containing static and dynamic loading are performed using cohesive zone approach. A single plane strain element, which obeys constitutive equation of Gurson type model, has been used to obtain the shape and the related parameters of the traction separation law (TSL) for cohesive elements at different strain rates and triaxiality values. Quasi-static and dynamic tests have already been performed on an aluminium round bar to obtain Gurson parameters, hardening and rate sensitivity of the aluminium alloy. The respective TSLs are fitted to the stress displacement values obtained from single element analysis to represent the effect of strain rate and triaxiality on the corresponding TSL strength and energy. The cohesive strength and energy curves obtained are used to analyse a centre-cracked plane strain aluminium panel under quasi-static and dynamic loadings. The load-displacement curves are obtained in different cases. The rate sensitivity and triaxiality dependency of cohesive elements and/or continuous elements and also inertia and stress wave effects are considered.

In the paper, it is shown that cohesive elements have the potential of doing ductile crack growth simulation not only in static cases, but also in high speed dynamic loading. The cohesive model presented can be used for both small and large scale yielding and takes effects of different strain rates and triaxialities into account. Unloading at the crack tip, which happens because of stress waves, has been implemented by irreversible separation behaviour. The results of the analysis show that generally, ignoring constraint or local strain rate on TSL makes the analysis underestimate the toughness. The toughness of the structure increases under dynamic loading because of the inertia. Ignoring rate sensitivity of material in high speed loadings can lead to quite high energy absorption predictions. Depending on the load speed, material properties, the structure dimensions and the crack length, the effect of phenomena like elastic waves, strain rate, adiabatic heating and inertia forces might be different.

1

Dugdale, D.S., "Yielding of steel sheets containing slits", Journal of Mechnics and Physics of Solids, 8, 100-104, 1960. doi:10.1016/0022-5096(60)90013-2

2

Barenblatt, G.I., "The mathematical theory of equilibrium cracks in brittle fracture", Advances in Applied Mechanics, 7, 55-129, 1962. doi:10.1016/S0065-2156(08)70121-2

3

Needleman, A., "A continuum model for void nucleation by inclusion debonding", Journal of Applied Mechanics, 54, 525-531, 1987.

4

Scheider, I., Brocks, W., "Simulation of cup-cone fracture using the cohesive model", Engineering Fracture Mechanics, 70, 1943-1961, 2003. doi:10.1016/S0013-7944(03)00133-4

5

Gurson, J., "Continuum theory of ductile rupture by void nucleation and growth. Part I-Yield criteria and flow rules for porous ductile media", Journal of Engineering and Materials Technology, 99, 2-15, 1977.

6

Zhang, Z.L., Thaulow, C., Odegard, J., "A complete Gurson model approach for ductile fracture", Engineering Fracture Mechanics, 67, 155-168, 2000. doi:10.1016/S0013-7944(00)00055-2

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