Digital Twins are complex digital representations of assets that are used by a variety of organizations across the Industry 4.0 value chain. As the digitization of industrial processes advances, Digital Twins will become widespread. As a result, there is a need to develop new secure data sharing models for a complex ecosystem of interacting Digital Twins and lifecycle parties. Decentralized Applications are uniquely suited to address these sharing challenges while ensuring availability, integrity and confidentiality. They rely on distributed ledgers and decentralized databases for data storage and processing, avoiding single points of trust. To tackle the need for decentralized sharing of Digital Twin data, this work proposes an owner-centric decentralized sharing model. A formal access control model addresses integrity and confidentiality aspects based on Digital Twin components and lifecycle requirements. With our prototypical implementation EtherTwin we show how to overcome the numerous implementation challenges associated with fully decentralized data sharing, enabling management of Digital Twin components and their associated information. For validation, the prototype is evaluated based on an industry use case and semi-structured expert interviews.