This study extensively investigates the effects of trivalent Dy/Bi partial substitution in the Bi2.1−xDyxSr2.0Ca1.1Cu2.0Oy ceramic matrix (0.00 ≤ x ≤ 0.10) on mechanical performance properties and load-independent Vickers hardness in the plateau limit (PL) regions by means of the microhardness (Hv) measurements and semi-empirical modeling approaches. According to the Hv findings, Dy3+ ions are confirmed to successfully substitute for Bi sites within the ceramic matrix. Notably, the substitution ratio of x = 0.01 is identified as the optimal level for enhancing mechanical performance features, critical performance indicators, and related mechanical performance features. The formation of further cracks and deformations is constrained by the saturation of available slip systems and hence the elastic recovery mechanism is dominant. In this respect, the Bi2.09Dy0.01Sr2.0Ca1.1Cu2.0Oy structure is the least sensitive to indentation forces and load-induced deformations. Numerically, the compound exhibits the highest Hv parameter of 0.5556 GPa at 0.295 N. On the other hand, especially after the Dy/Bi level of x = 0.03, the fundamental mechanical performances degrade harshly as a consequence of rapid increase in the deformation degree, stored internal strain energy, and microscopic crystallinity problems. Thus, stress-induced phase transformation is more dominant in the ceramic structure. To sum up, the research successfully indicates the intricacies of load-independent microhardness values, elastic/plastic deformation behavior, and phase stability. Each model supports totally our experimental results. The largest AMeyer and AHK constants are approximately 3.696 × 10–6 N/μm2 and 2.72 × 10–4 N/μm2 calculated in Hays–Kendall and Meyer’s law approaches for the Bi2.09Dy0.01Sr2.0Ca1.1Cu2.0Oy structure. The consistent results across different models show the strength of the mechanical analysis. The modified proportional sample resistance (MPSR) model is especially effective to examine both elastic and plastic deformation and reliably estimate load-independent Hv values (0.5086–0.5110 GPa) within the experimental range in the PL regions. This study also presents a comprehensive analysis of the underlying mechanisms that simultaneously govern the electrical, superconducting, and mechanical properties within the crystal structures of ceramic materials. These findings are substantiated through a combination of experimental data, theoretical modeling, and scientifically grounded interpretations. Hence, this work shows a careful approach and a clear understanding of how mechanical properties affect material performance, providing a strong basis for future research.

Evaluation of load-independent microhardness in Dy-substituted Bi-2212 ceramics using semi-empirical mechanical models: correlations with electrical-superconducting and crystallographic properties

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发表日期：

2025年8月22日

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B. Akkurt,
A. S. Erturk,
U. Erdem,
G. Kurtul,
G. Yildirim

摘要

This study extensively investigates the effects of trivalent Dy/Bi partial substitution in the Bi_2.1−xDy_xSr_2.0Ca_1.1Cu_2.0O_y ceramic matrix (0.00 ≤ x ≤ 0.10) on mechanical performance properties and load-independent Vickers hardness in the plateau limit (PL) regions by means of the microhardness (H_v) measurements and semi-empirical modeling approaches. According to the H_v findings, Dy³⁺ ions are confirmed to successfully substitute for Bi sites within the ceramic matrix. Notably, the substitution ratio of x = 0.01 is identified as the optimal level for enhancing mechanical performance features, critical performance indicators, and related mechanical performance features. The formation of further cracks and deformations is constrained by the saturation of available slip systems and hence the elastic recovery mechanism is dominant. In this respect, the Bi_2.09Dy_0.01Sr_2.0Ca_1.1Cu_2.0O_y structure is the least sensitive to indentation forces and load-induced deformations. Numerically, the compound exhibits the highest H_v parameter of 0.5556 GPa at 0.295 N. On the other hand, especially after the Dy/Bi level of x = 0.03, the fundamental mechanical performances degrade harshly as a consequence of rapid increase in the deformation degree, stored internal strain energy, and microscopic crystallinity problems. Thus, stress-induced phase transformation is more dominant in the ceramic structure. To sum up, the research successfully indicates the intricacies of load-independent microhardness values, elastic/plastic deformation behavior, and phase stability. Each model supports totally our experimental results. The largest A_Meyer and A_HK constants are approximately 3.696 × 10^–6 N/μm² and 2.72 × 10^–4 N/μm² calculated in Hays–Kendall and Meyer’s law approaches for the Bi_2.09Dy_0.01Sr_2.0Ca_1.1Cu_2.0O_y structure. The consistent results across different models show the strength of the mechanical analysis. The modified proportional sample resistance (MPSR) model is especially effective to examine both elastic and plastic deformation and reliably estimate load-independent H_v values (0.5086–0.5110 GPa) within the experimental range in the PL regions. This study also presents a comprehensive analysis of the underlying mechanisms that simultaneously govern the electrical, superconducting, and mechanical properties within the crystal structures of ceramic materials. These findings are substantiated through a combination of experimental data, theoretical modeling, and scientifically grounded interpretations. Hence, this work shows a careful approach and a clear understanding of how mechanical properties affect material performance, providing a strong basis for future research.