Exchange bias and training effect are simulated for IrMn/NiFe bilayers. As a function of the thickness of the antiferromagnet the bias field shows a maximum for a thickness of 22 nm. For decreasing antiferromagnetic thickness the domain wall energy approaches zero. For large thicknesses the high anisotropy energy hinders switching of the antiferromagnetic grains resulting in weak bias. Starting from the field cooled state as initial configuration a bias field of about 8 mT is obtained assuming a antiferromagnetic layer thickness of 20 nm, a ferromagnetic layer thickness of 10 nm, and a grain size of 10 nm. The next hysteresis cycle shows a reduction of the bias field by about 65%. Exchange bias and training effect in fully compensated antiferromagnet/ferromagnet bilayers are explained with a simple micromagnetic model. The model assumes no defects except for grain boundaries, and coupling is due to spin flop at a perfect interface. The simulations show that a weak exchange interaction between randomly oriented antiferromagnetic grains and spin flop coupling at a perfectly compensated interface are sufficient to support exchange bias.