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The ductile fracture behaviour of an undermatched aluminium weld is investigated experimentally and simulated numerically by two different models of ductile damage, namely the microstructure-based Gurson-Tvergaard-Needleman model and a phenomenological cohesive model. The model parameters for the different material zones are determined by a hybrid approach combining microstructural analyses, mechanical testing and numerical simulations. Particular emphasis is placed on a configuration where the initial crack is located in the heat affected zone and extends into the softer fusion zone. A simplified model of a bi-material system with a crack at the interface is used to simulate crack path deviation.