Experimental and numerical characterisation and modelling of viscoelastic/viscoplastic crack growth in adhesive joints

Adhesive bonding is a widely used technique in the aerospace and automotive industry, whose advantages with respect to more conventional connections of structural components include the great reduction of stress concentration and weight. Debonding of joints can be effectively simulated using cohesive-zone models (CZMs), which define a nonlinear `traction-separation’ law (TSL) between the displacement jump and the associated interface traction [1] or more traditional methods based on linear and non-linear fracture mechanics. In fracture-mechanics-based methods, one parameter only is normally considered, that is the critical energy release rate, Gc, in linear elastic fracture mechanics (LEFM) or the critical value of the J integral, Jc, in nonlinear fracture mechanics (NLFM). More parameters are needed to characterise a CZM, but in most cases the area under the TSL, that is the ‘work of separation’, is the most important. The relationship between Gc, Jc and the work of separation used in a CZM has been thoroughly investigated by the proposed supervisor of this project and his co-workers [2]. For many important engineering problems the rate-dependence of the adhesive joint structural response, that is the effect of the speed with which loading actions are applied, is of great importance. For example, the adhesive joint response can be very different in the case of loads applied at relatively slow speed or in the case of impact. Rate dependence is therefore of great importance for the assessment of crashworthiness of vehicles. Although a number of models that account for rate dependence have been proposed [3-5], the extent to which rate dependence is due to viscoelastic or viscoplastic material behaviour is not well understood. Recent (not yet published) experimental tests conducted by the proposed supervisor suggest that both types of behaviour occur simultaneously. Therefore, this project will investigate the roles played by visco-plasticity and visco-elasticity in mode-I (opening) crack propagation in adhesive joints, by conducting experimental testing and numerical simulations of double cantilever beams (DCBs), made of aluminium plates bonded with polymer adhesives. The numerical modelling part of the project will include the development of novel CZMs that combine both visco-elastic and visco-plastic adhesive behaviour with interface damage and fracture. This project is suitable for candidates who have a good first degree in Mechanical, Aerospace, Civil Engineering, Applied Mathematics or related subjects, with good background in solid body mechanics and mathematical modelling. Knowledge of and experience in finite-element analysis and programming is desirable but not essential. References [1] G. Alfano, M.A. Crisfield (2001). Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. International Journal for Numerical Methods in Engineering, 50(7): 1701-1736. [2] L. Škec, G. Alfano, G. Jelenić (2018). On Gc, Jc and the characterisation of the mode-I fracture resistance in delamination or adhesive debonding. International Journal of Solids and Structures 144-145:100-122. [3] G. Alfano, M. Musto (2017). Thermodynamic derivation and damage evolution for a fractional cohesive-zone model. Journal of Engineering Mechanics 143(7):D4017001. [4] C. Xu, T. Siegmund, K. Raman (2003). Rate-dependent crack growth in adhesives I. Modelling approach. International Journal of Adhesion and Adhesives 23:9-13. [5] G. London, G.H. Paulino, W.G. Buttlar (2019). Fractional calculus derivation of a rate-dependent PPR-based cohesive fracture model: theory, implementation, and numerical results. International Journal of Fracture. In Press.

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