A virtual laboratory is presented, capable of calculating virtual loads using the spectral solver in the DAMASK software for crystal plasticity simulations in desired stress directions. Calculations are used for the calibration of yield surfaces. The required spatial resolution is assessed based on a comparison with the previously published crystal plasticity finite element method (CPFEM) and experimental results for three different aluminium alloys (AA1050, AA3103-O, and AA3103H18) with 1000 and 2500 grains in a representative volume element. The results of the crystal plasticity fast Fourier transform (CPFFT) method agree well with CPFEM. The elongated grain morphology of the AA3103H18 alloy was found to have a negligible effect on predicted anisotropy. Also, the virtual laboratory is used to analyse the impact of hard particles inside the aluminum matrix. Different volume fractions of elastic particles are examined, and their influence on the anisotropy of yield surfaces is studied. Also, a spatial resolution investigation is made, and the minimum required resolution is specified.