To investigate the performance of graded structure materials under steady-state heat load, six-layered W/Cu functionally gradient materials with full compositional distributions (from 0% to 100%) fabricated by resistance sintering under ultrahigh-pressure method were tested under the electron beam material testing scenario using the fusion relevant quasi-steady-state heat load in the range of 6.5-9.8 MW/m(2) and compared to the W/Cu samples with sharp joint. The specimens were loaded for about 5 s, and then indirectly cooled for 30 s. It is identified that the graded transition layers can really ameliorate the thermal mismatch, and thus prolong the fatigue lifetime. These results were examined by the thermal-stress analysis using finite element method. Moreover, the inserting of graded interlayers may suppress the formation of center vertical cracks of W layer. However, the copper melt exudation within gradient layers occurred under extreme high heat loads of 9.8 MW/m(2), which should be avoided by essential thermal analysis and proper structure design.