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Data replication is an important technique for improving the accessibility, availability, and reliability of distributed data storage systems. Secret sharing or erasure coding based data fragmentation techniques can be integrated into these systems to improve the system security and survivability. In this paper, a two-tier distributed system is modeled to provide secure data object replication using the integration of data replication and fragmentation approaches. We study the secure replica placement problem in the system with the presence of rational but selfish data owners. Multiple agents place replicas of data objects in the system in order to maximize their own profits while satisfying their security requirements. Algorithmic mechanism design theory is applied to design a direct revelation mechanism to motivate the truth telling of data owners and to approximate the local optimal replica placement. Comparative experiments have been conducted to evaluate the performance of the mechanism.