Growing interest has emerged to understand the coupled awareness-epidemic dynamics in multiplex network. However, most previous studies usually assume that all the infected nodes have the same influence on the susceptible neighbors, without considering node’s heterogeneity. In this paper, with the similarity between epidemic spreading and risk propagation, we apply the UAU-SIS model to investigate the interplay between awareness and risk propagation in R&D networks considering firms’ heterogeneity. Here, the risk triggering probabilities are heterogenous and depend on two factors: cooperation intensity and local risk prevalence. The results reveal that the cooperation intensity can increase the risk propagation prevalence and decrease the risk propagation threshold, while the local risk prevalence can only increase the risk propagation prevalence. Moreover, we find that the risk propagation threshold undergoes an abrupt transition with a certain point of the local awareness ratio (the global awareness ratio) ignoring the global awareness (the local awareness ratio), which includes two-stage effects on risk propagation threshold. Furthermore, threshold lies in three different areas when considering both the global and local awareness. These results could provide a basis for managerial professionals to improve the robustness of interdependent R&D networks under risk propagation by taking effective measures.