One of the missions of the WEST tokamak is to test in a realistic tokamak environment, the ITER-like divertor plasma facing components made with tungsten. On exposed leading edges of monoblocks, poloidally-distributed cracks having an average spacing of 0.4 mm, running perpendicular to the cooling tube axis, were observed following the experimental campaigns in 2018. Damage may be induced by different processes which can lead to: brittle fracture below the Ductile to Brittle Transition temperature or ductile failure for which softening (recovery / recrystallization) process plays a major role. To improve our understanding about the leading edge damage process, numerical simulations were run here. The following results are specially studied: (i) the thermal gradients; (ii) the softening fraction gradient and (iii) the stress and strain distributions taking into account the mechanical properties of tungsten (elastic-viscoplastic) and the softening phenomenon. This paper describes the results obtained for a range of WEST steady state parallel heat flux (from 45 MW/m² to 70 MW/m²) and disruption (600 MW/m²) heat loading on the leading edge. Estimated results related to the plastic strain accumulation, give an interpretation of the premature cracking of the monoblock leading edge but do not explain the poloidal distribution. According to the numerical results, brittle fracture are expected under disruption as estimated normal stresses are beyond the material yield stress, along 88% of the leading edge.