One of the main reasons why Byzantine fault-tolerant (BFT) systems are not widely used lies in their high resource consumption: 3f + 1 replicas are necessary to tolerate only f faults. Recent works have been able to reduce the minimum number of replicas to 2f + 1 by relying on a trusted subsystem that prevents a replica from making conflicting statements to other replicas without being detected. Nevertheless, having been designed with the focus on fault handling, these systems still employ a majority of replicas during normalcase operation for seemingly redundant work. Furthermore, the trusted subsystems available trade off performance for security; that is, they either achieve high throughput or they come with a small trusted computing base. This paper presents CheapBFT, a BFT system that, for the first time, tolerates that all but one of the replicas active in normal-case operation become faulty. CheapBFT runs a composite agreement protocol and exploits passive replication to save resources; in the absence of faults, it requires that only f + 1 replicas actively agree on client requests and execute them. In case of suspected faulty behavior, CheapBFT triggers a transition protocol that activates f extra passive replicas and brings all non-faulty replicas into a consistent state again. This approach, for example, allows the system to safely switch to another, more resilient agreement protocol. CheapBFT relies on an FPGA-based trusted subsystem for the authentication of protocol messages that provides high performance and comprises a small trusted computing base.

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In this article, an advanced analytical formulation is developed to predict thickness change of an aluminum/copper clad sheet. Springback analytical formulation is also introduced using the combination of advanced and primary bending theories in air bending process. Experiments were performed to verify analytical results and to investigate the effect of different geometrical parameters such as punch stroke, die opening, punch radius and setting condition on the springback. It was observed that die opening had the most striking effect, while setting condition had a negligible effect on springback. On the other hand, setting condition played a crucial role on thickness change in bent clad sheets. Clad sheet thickened in the Al/Cu setting condition, while in the Cu/Al setting it thinned. Finite element method simulation was also applied to verify analytical predictions of the thickness change and study stress distribution in the layers of the clad sheet. Good correlation was observed between analytical and numerical results.

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