Plasma facing components inside future nuclear fusion reactors are subjected to a high heat load and intense irradiation conditions. Using advanced computational material models, several problems can be solved that reflect tungsten monoblocks under fusion relevant loading scenarios. This allows for the identification of the conditions under which material failure is probable. The material model and parameters are identified such that the mechanical behaviour is in accordance with the homogenized behaviour of a previously developed crystal plasticity model on the microscopic scale. The heterogeneous stress field that follows is analysed in order to assess the probability of material failure, which is typically reflected by unstable crack propagation. Since fracture is an inherently multi-scale problem, critical regions are analysed in detail by means of a representative volume element. The resulting analysis reveals that in case the stress relaxation in the monoblock under the applied static heat load is complete, the probability of unstable crack propagation can reach values close to 35%. Finally, the impact of prolonged neutron irradiation is simulated by means of a cluster dynamics model. Although irradiation drastically increases the brittleness of tungsten, its impact on the overall monoblock performance remains limited.