Modern experimental astroparticle physics features large-scale setups measuring different messengers, namely high-energy particles generated by cosmic accelerators (e.g. supernova remnants, active galactic nuclei, etc): cosmic and gamma rays, neutrinos and recently discovered gravitational waves. Ongoing and future experiments are distributed over the Earth including ground, underground/underwater setups as well as balloon payloads and spacecrafts. The data acquired by these experiments have different formats, storage concepts and publication policies. Such differences are a crucial issue in the era of big data and of multi-messenger analysis strategies in astroparticle physics. We propose a service ASTROPARTICLE.ONLINE in the frame of which we develop an open science system which enables to publish, store, search, select and analyse astroparticle physics data. The cosmic-ray experiments KASCADE-Grande and TAIGA were chosen as pilot experiments to be included in this framework. In the first step of our initiative we will develop and test the following components of the full data life cycle concept: (i) describing, storing and reusing of astroparticle data; (ii) software for performing multi-experiment and multi-messenger analyses like deep-learning methods; (iii) outreach including example applications and tutorial for students and scientists outside the specific research field. In the present paper we describe the concepts of our initiative, and in particular the plans toward a common, federated astroparticle data storage.