The glasses currently used for nuclear waste containment can incorporate fission products and minor actinides up to 18.5% by mass. The glass-ceramic materials envisaged for this application would be an interesting alternative, making it possible to reduce package volume by increasing this loading rate. However, during storage, the crystalline phase inclusions, rich in fission products, would be subjected to $\alpha$ self-radiation, causing swelling that could lead to cracking of the glass matrix [1]. With this application in mind, we study crack nucleation in composite materials with swelling inclusions. We use a gradient-damage model, that can be interpreted as a phase-field approach to fracture [2]. Hence, we leverage the massive parallel FFT code AMITEX_FFTP [3] for solving numerically the full-field problem for the heterogenous material. In this contribution, we discuss the influence of the choice of the phase-field parameters, the fracture toughness $G_c$ and the internal length $\ell_0$, on the crack nucleation threashold. We consider the case of swelling elastic inclusions in a brittle matrix. Unfortunately, the choice of model parameters ($G_c$,$\ell_0$) to reproduce both initiation and propagation conditions proves tricky. This choice is limited not only by the size of the heterogeneities, but also by the resolution of the computational support. The solution envisaged for this application consists in choosing an internal length $\ell_0$ that is reasonable in terms of spatial discretization, and adapting $G_c$ to meet an initiation criterion set by the "experiments" [4]. We present different simplified approaches for estimating the nucleation threshold of the first cracks and compare thel to full-field FF simulations. We will also discuss the effect of the distance between inclusions and the crack nucleation threshold observed in large cells with a random distribution of inclusions.