Ultrasonic measurement of contact stress at metal-to-metal interface based on a real rough profile through modeling and experiment

[Display omitted] •Ultrasonic quantification method is used to predict the metal-to-metal interface contact stress.•A two-dimensional ultrasonic propagation model of the rough contact interface is developed based on an actual rough profile.•The size and distribution of the contact area affect the reflection coefficient.•An empirical formula for ultrasonic prediction of contact stress at rough interface under elastic contact considering lubricant is established.•Accuracy of ultrasonic quantitative characterization of contact stress is verified by experiments. Metal-to-metal seals are widely used in tubing and casing connections in oil and gas wells; therefore, the integrity of sealing is crucial. As the quality of seals is directly influenced by the metal-to-metal contact stress, this study investigates the measurement and evaluation of contact stress at rough interfaces numerically and experimentally using an ultrasonic quantitative method. A two-dimensional ultrasonic propagation model of the rough contact interface is developed based on an actual rough profile. The reflection coefficient decreases gradually as the normal deformation and contact rate increase, and a relationship between the reflection coefficient and the contact rate is established. The reflection coefficient reduces exponentially to approximately zero when the contact rate is less than 0.5. Combined with the contact mechanics theory, for an elastic contact, an empirical fitting formula for the interface reflection coefficient, contact stress, root mean square deviation (Rq), and mean width of the profile elements (RSm) is established. Note that at the same contact rate, the reflection coefficient decreases as the interface lubricant parameter ρc2 increases. Therefore, ρc2 is introduced to optimize the empirical fitting formula. Accuracy of the empirical fitting formula is verified using experimental results, that is, through the ultrasonic measurement of the contact stress at the loaded metal-to-metal interface. Thus, this study serves as a reference for measuring and quantifying the metal-to-metal contact stress.