Triaxial Limit and Safety Factor of an Anisotropic Corrosion-Resistant Alloy Tubular Udaya B. Sathuvalli, P. V. (Suri) Suryanarayana, Shaikh Rahman, and Sharat Chandrasekhar, Blade Energy Partners Summary Tubulars made with corrosion-resistant alloys (CRAs) exhibit a moderate degree of transverse anisotropy. This results in lower yield strength in the plane perpendicular to the rolling axis of the tubular. In addition, cold work during mill finishing introduces yield strength asymmetry along the axis. The majority of CRA tubulars are low-d o /t (10–15) production strings. Their design is usually driven by pressure and tension. Given the reduced yield strength in the hoop direction (as compared with axial yield strength), a rigorous method to assess the effect of yield strength anisotropy on the triaxial limits of the pipe is needed. Though there is a substantial body of literature on anisotropy in metals and manufactured composites, anisotropy of tubulars has received minimal attention by tubular designers. In this context, we use Hill’s celebrated criterion (Hill 1950) for the yielding of anisotropic metals to develop an equation for the tri- axial limits of a hollow cylinder and show that the currently used isotropic triaxial ellipse is a special case of the general limit. Also, by recognizing that purely elastic load excursions do not alter the yield surface, we extend the aforementioned triaxial limit to tubulars with tension-compression asymmetry along the tube axis. Finally, on the basis of the notion of a strength utilization factor, we propose a method to determine the triaxial safety factor for anisotropic CRA tubulars. This method is consistent with the definition of the triaxial safety factor for isotropic tubulars. Introduction In working stress design, the mechanical integrity of casings and tubing is characterized by burst, collapse, tension-compression, and tri- axial safety factors. The triaxial safety factor is defined as the ratio of the minimum uniaxial yield stress of the casing steel to the maxi- mum triaxial stress in the casing string. When necessary, the uniaxial yield stress of the casing is adjusted for temperatures above the ambient (usually assumed to be 68  F). The triaxial stress at a given point in the casing is obtained by combining the radial, hoop, axial, and shear stresses (when present) in the well-known formula for the von Mises equivalent stress. It is also customary to represent the mechanical stress state of the entire casing string in a diagram that shows the load lines in relation to the ellipse that defines the triaxial limit of the casing. The triaxial limit of the casing is a 2D representation of the triaxial yield surface for points on the inner surface of the casing. It is determined by applying the Mises criterion to the inner surface of a pressurized cylinder subjected to an arbitrary axial force. Because the majority of oilwell tubulars are made of low-carbon steel (which is a linear elastic isotropic material), the Mises criterion can be used to determine their triaxial limits. However, some special applications require production strings made with CRA. There are significant differences between the material properties of carbon and CRA steels, but the parameters that influence structural design are yield strength anisotropy, axial tension-compression yield strength asymmetry, and the high coefficient of thermal expansion. In an isotropic material, the material properties are independent of direction. Though the raw material used to make CRA tubes is isotropic, cold work during manufacture instills a tangible degree of anisotropy in the tubular. As a result, the material properties of the tubular vary with direction. Further, the Bauschinger effect 1 may create tension-compression asymmetry in the material yield strength, usually along the axial direction of the manufactured tubular. Hence, the compressive and tensile yield strengths of the tubular might differ by as much as 20%. The basis for the triaxial limit of isotropic casings and tubings is well-understood and is widely used in our industry (Greenip 1977; Klementich and Jellison 1986; Lewis and Miller 2009). Though the theoretical foundations of plasticity in anisotropic metals date back to Hill’s classic work in 1948 (Hill 1950), the role of anisotropy and tension-compression asymmetry in the triaxial limits of oilwell tubulars has received little attention. In this light, we present a method to determine the triaxial limit of a ductile anisotropic hollow metal cylinder. Further, we suggest a method to determine the effect of axial yield strength asymmetry on the triaxial limit of the cylinder. Anisotropic Strength Criteria Plastic anisotropy of metals is a mature discipline in mechanical engineering (Chapter 6, Chakrabarty 2010 and references therein). Similarly, anisotropy of fiber-reinforced composites and laminates has been studied extensively (Chapters 3 and 6, Mallick 2007). The basis for yielding in a linear elastic isotropic material that does notexhibit the Bauschinger effect was postulated by von Mises (1913). Though Huber anticipated the same result in 1904 (page 20, Hill 1950), it did not come to fore for nearly 20 years. In 1924, Hencky pointed out that the Mises criterion implies the onset of yielding when the elastic energy of distortion reaches a critical value (page 20, Hill 1950). Therefore, the Mises criterion is also known as the Huber-Mises-Hencky criterion, or the distortional energy criterion. The most widely used criterion to determine the onset of yielding in anisotropic metals is that proposed by Hill (1950). Nevertheless, it is appropriate to mention the criteria proposed by Azzi and Tsai (1965) and Tsai and Wu (1970). The Azzi-Tsai criterion is based on Hill’s criterion and is valid for orthotropic laminae in a state of plane stress. The Tsai-Wu criterion is considered to be the most general anisotropic strength criterion, and is based on the application of tensor algebra to stress states that cause failure in manufactured Copyright V C 2019 Society of Petroleum Engineers This paper (SPE 191032) was accepted for presentation at the IADC/SPE Asia Pacific Drilling Technology Conference and Exhibition, Bangkok, Thailand, 27–29 August 2018, and revised for publication. Original manuscript received for review 11 September 2018. Revised manuscript received for review 14 January 2019. Paper peer approved 29 January 2019. 1 When a plastically deformed specimen is unloaded, it retains residual stresses. If the specimen is loaded in the reverse direction, the residual stresses hasten the onset of yielding in the reverse direction. For example, if a specimen is loaded to a stress higher than yield in tension, unloaded and then loaded in compression, the compressive yield strength is less than the ten- sile yield strength. This effect is known as the Bauschinger effect (pp. 410–414, Timoshenko 1956). 306 September 2019 SPE Drilling & Completion