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Extension fractures are typical for the deformation under low or no confining pressure. They can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. In this article, it is shown that the simple extension strain criterion makes unrealistic strength predictions in biaxial compression and tension. To overcome this major limitation, a new extension strain criterion is proposed by adding a weighted principal shear component to the simple criterion. The shear weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting extension failure modes, which are unexpected in the classical understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain leading to dilatancy. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak stress CP. Different from compressive loading, tensile loading requires only a limited number of critical cracks to cause failure. Therefore, for tensile stresses, the failure criteria must be modified somehow, possibly by a cut-off corresponding to the CI stress. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
This paper introduces an inexpensive Wiegand-sensor-based rotary encoder that avoids rotating magnets and is suitable for electrical-drive applications. So far, Wiegand-sensor-based encoders usually include a magnetic pole wheel with rotating permanent magnets. These encoders combine the disadvantages of an increased magnet demand and a limited maximal speed due to the centripetal force acting on the rotating magnets. The proposed approach reduces the total demand of permanent magnets drastically. Moreover, the rotating part is manufacturable from a single piece of steel, which makes it very robust and cheap. This work presents the theoretical operating principle of the proposed approach and validates its benefits on a hardware prototype. The presented proof-of-concept prototype achieves a mechanical resolution of 4.5 ° by using only 4 permanent magnets, 2Wiegand sensors and a rotating steel gear wheel with 20 teeth.