Mathematical modeling of the effect of hydrogen on the mechanical behavior of metals: assessing the maximum defect size in pipelines
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The presence of hydrogen in metals can lead to a significant degradation of their mechanical properties, a phenomenon known as hydrogen embrittlement. This work presents a mathematical modeling approach to describe the influence of hydrogen on the mechanical behavior of metals, from fracture surface analysis to the formulation of a modified hardening rule. The modeling considers mechanisms such as stress-assisted diffusion, hydrogen interaction with dislocations, and the formation of microcracks, which affect the material’s ductility and strength. To describe the mechanical behavior, a formulation based on Gao’s model is proposed, considering the effect of hydrostatic pressure. A constitutive equation is introduced to incorporate the influence of hydrogen on the evolution of hardening, enabling more accurate predictions of the service life and failure of metallic components. Thus, hydrogen concentration is coupled with the material's hardening rule. The model calibration for determining the expected plastic strain at fracture is conducted using three mechanical tests: smooth cylindrical tensile testing in air, notched cylindrical tensile testing in air, and smooth cylindrical tensile testing in a hydrogen environment. The modeling results are validated by comparison with experimental data, demonstrating the approach's reliability and relevance for industrial applications and structural engineering. This study focuses on analyzing the maximum defect size in natural gas transport pipelines during the transition to hydrogen transport, thereby mitigating the risk of catastrophic failures.
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