Xian-Kui Zhu

Theoretical and Numerical Predictions of Burst Pressure of Pipelines

To accurately characterize plastic yield behavior of metals in multiaxial stress states, a new yield theory, i.e., the average shear stress yield (ASSY) theory, is proposed in reference to the classical Tresca and von Mises yield theories for isotropic hardening materials. Based on the ASSY theory, a theoretical solution for predicting the burst pressure of pipelines is obtained as a function of pipe diameter, wall thickness, material hardening exponent, and ultimate tensile strength. This solution is then validated by experimental data for various pipeline steels. According to the ASSY yield theory, four failure criteria are developed for predicting the burst pressure of pipes by the use of commercial finite element softwares such as ABAQUS and ANSYS , where the von Mises yield theory and the associated flow rule are adopted as the classical metal plasticity model for isotropic hardening materials. These failure criteria include the von Mises equivalent stress criterion, the maximum principal stress criterion, the von Mises equivalent strain criterion, and the maximum tensile strain criterion. Applications demonstrate that the proposed failure criteria in conjunction with the ABAQUS or ANSYS numerical analysis can effectively predict the burst pressure of end-capped line pipes.

Influence of Yield-to-Tensile Strength Ratio on Failure Assessment of Corroded Pipelines

This paper investigates the influence of yield to-tensile strength ratio (YIT) on failure pressure of pipelines without and with corrosion defects. Based on deformation instability and finite strain theory, a plastic collapse model for end-capped defect-free pipes is developed. The stress-strain response of materials is characterized by a power-law hardening curve, and the plastic deformation obeys the von Mises yield criterion and the deformation theory of plasticity. Two formulas to estimate the strain hardening exponent n for a specific Y/T are obtained, and a closed-form solution to the limit pressure of pipes is derived as a function of Y/T. This plastic collapse model is then extended to predict the failure pressure of pipelines with corrosion defects. Numerical and experimental comparisons are presented that validate the present models which characterize the influence of Y/T on the failure behavior of pipeline.

Constraint Corrected J-R - Curve and its Application to Fracture Assessment for X80 Pipelines

Single specimen J-R curve testing for X80 pipeline steel was conducted using single edge notched bend (SENB) and single edge notched tension (SENT) specimens with various crack lengths. Test data indicate that the J-R curves for this steel are strongly constraint dependent. To facilitate transferability of experimental J-R curves to those for actual cracked components, this paper develops a constraint corrected J-R curve for X80 steel. A modified J-Q theory that can consider the global bending stress influence is proposed so as to correctly quantify constraint effect on the crack-tip fields and the J-R curves. Results show that the modified J-Q solution can well match numerical crack-tip fields for bending specimens, with Q being a load-independent constraint parameter under large scale yielding. Based on the experimental data and numerical analysis, a constraint corrected J-R curve is formulated as a function of the parameter Q and crack extension Δa for X80 steel. A general procedure to predict J-R curves for actual cracked components is then outlined. Comparison indicates that the predicted J-R curves developed in this paper agree well with the experimental data for both SENB and SENT specimens. To demonstrate its application in failure assessment, the constraint corrected J-R curve for X80 steel is used to determine failure loads for a surface cracked pipeline. Reasonable agreement to available analytic solution is achieved.

CVN and DWTT Energy Methods for Determining Fracture Arrest Toughness of High Strength Pipeline Steels

Battelle two curve model (BTCM) was developed in the 1970s and successfully used for determining arrest toughness for ductile gas transmission pipelines in terms of Charpy vee-notched (CVN) impact energy. Practice has shown that the BTCM is accurate only for pipeline grades up to X65, but not for high strength pipeline grades X70 and above. Different methods to improve the BTCM were proposed over the years. This paper reviews the BTCM and its modified methods in terms of CVN energy or drop weight tear test (DWTT) energy for determining arrest toughness of ductile gas pipeline steels, particularly for high strength pipeline steels X80 and beyond. This includes the often-used Leis correction method, the CSM factor method, Wilkowski DWTT method and others. The CVN and DWTT energy-based methods are evaluated and discussed through the critical analysis and comparison with full-scale experimental data. The objective is to identify reasonable methods to be used for determining the minimum fracture toughness required to arrest a ductile running crack in a modern high strength, high pressure gas pipeline. The results show that available nonlinear models to correlate the standard DWTT and CVN energies are questionable, and the Leis correction method is a viable approach for determining arrest toughness for high strength pipeline steels, but further study is needed for ultra-high pipeline grades. Suggestions for further improving the BTCM are discussed.Copyright

Experimental Determination of J-R Curves Using SENB Specimens and P-CMOD Data

Fracture toughness and J-R curves of ductile materials are often measured under the guidance of ASTM standard E1820 using the single specimen technique and the elastic unloading compliance method. For the standard single-edge notched bend [SENB] specimens, the load, load-line displacement (LLD), and crack-mouth opening displacement (CMOD) are required being measured simultaneously. The load-CMOD data are used to determine the crack extension, and the load-LLD data together with the crack extension are used to determine the J-integral values in a J-R curve test. Experiments have indicated that the CMOD measurement is very accurate, but the LLD measurement is difficult and less accurate in a fracture test on the SENB specimen. If the load-CMOD records is used to determine the crack extension and the J-integral values, experimental accuracies for the J-R curve testing would be increased, and the test costs can be reduced. To this end, this paper develops a simple relationship between LLD and CMOD that is used to convert the measured CMOD record to the corresponding LLD data, and then to calculate the J values for a growing crack in a J-R curve test on the SENB specimen using one single specimen technique. The proposed method is then verified by the experimental data of J-R curves for HY80 steel using the SENB specimens and the load-CMOD data only. The results show that the proposed method is more accurate and more cost-effective for the J-R curve testing.Copyright

Plastic Collapse Assessment Method For Unequal Wall Transition Joints in Transmission Pipelines

This paper investigates plastic collapse failure behavior and analytical assessment methods for unequal wall transition joints in transmission pipelines. The objective is to (i) validate the plastic-collapse -based code requirements that were determined by the early lower-strength pipes and (ii) develop an effective method for assessing plastic collapse failure of unequal wall joints involving modem high-strength pipes. Detailed finite element analysis was conducted to evaluate the failure behavior of transition joints and the effects of geometry, including weld taper angle, mismatched diameter and location, and material parameters, including the steel grade, mechanical property, yield-to-tensile strength (Y/T) ratio, and anisotropy. Numerical results show that the wall-thickness mismatch and tensile-strength mismatch are the two first-order parameters that control the plastic collapse failure behavior of unequal wall transition joints. Based on these first-order parameters, an analytic solution is formulated to predict burst pressure at plastic collapse as a function of the pipe geometry, material tensile and hardening properties for both end-opened and end-capped pipes in reference to the plastic instability and finite strain theory. A plastic collapse criterion and the corresponding plastic collapse assessment diagram (PCAD) are then developed as a function of the wall-thickness mismatch and tensile-strength mismatch conditions to ensure that plastic collapse failure would occur in the thinner wall, with higher strength pipe. General procedures to use PCAD for assessing the plastic collapse failure of unequal wail joints are outlined. Application of PCAD indicates that high-strength pipeline grades with high Y/T ratios can be safely used beyond current code limitations on the wall-thickness mismatch of transition joints for a wide range of strength mismatch.

Application of Constraint Corrected J-R Curves to Fracture Analysis of Pipelines

Fracture properties of API X80 pipeline steel have been developed using a set of single edge notched bend (SENB) and single edge notched tension (SENT) specimens with shallow and deep cracks to generate different crack-tip constraint levels. The test data show that the J-R curves for X80 pipeline steel are strongly constraint dependent. To facilitate transfer of the experimental J-R curves to those for actual cracked components, like flawed pipeline, constraint corrected J-R curves are developed. The two-parameter J-A2 formulation is adopted to quantify constraint effect on the crack-tip fields and the J-R curves. The constraint parameter A2 is extracted by matching the J-A2 solution with finite element results for a specific crack configuration. A constraint corrected J-R curve is then formulated as a function of the constraint parameter A2 and crack extension Δa. A general method and procedure to transfer the experimental J-R curves from laboratory to actual cracked components are proposed. Using the test data of J-R curves for the SENB specimens, a mathematical expression representing a family of the J-R curves is constructed for X80. It is shown that the predicted J-R curves developed in this paper match well with experimental data for both SENB and SENT specimens. To demonstrate its application in assessing flaw instability, a pipeline with an axial surface crack is considered. For a crack depth of 50% of the wall thickness, the predicted J-R curve is found to be higher than that for the SENB specimen with the same crack length to width ratio. From this predicted J-R curve and crack driving force obtained by finite element analysis, the failure pressures of the pipeline at the crack initiation and instability are determined and discussed.Copyright

Effect of Axial Tensile Strain on Yield Load-Carrying Capacity of Pipelines

This paper theoretically investigates the effect of axial tensile strain on the plastic yield load-carrying capacity of pipelines. The elasticity theory and three plastic yield criteria of Tresca criterion, von Mises criterion, and Average Shear Stress Yield (ASSY) criterion are adopted in the analysis. General solutions of elastic stresses and strains are obtained for a thin-walled, end-caped pipe subjected to internal pressure and an axial strain that is used to represent the outside applied force. Based on the three plastic yield criteria, different nonlinear governing equations are obtained for determining the yield pressure, the yield hoop and axial stresses as well as the yield hoop and radial strains for the pipe. The results showed that the pressure, stresses and strains in the pipe at yield are functions of the axial strain, Poisson’s ratio, Young’s modulus, and yield strength of the pipe steel. The tensile strain limits are then obtained for different pipeline grades. It is concluded that the axial tensile strain can significantly reduce the limit load or the regulation-allowed operating pressure, and the tensile strain limits should be considered in strain-based design to prevent pipeline failure.Copyright

Deterministic and Probabilistic Analyses of Pipeline Burst Failure

Deterministic and probabilistic analyses are carried out in this paper to investigate burst failure of defect-free pipelines. Three deterministic models for predicting the burst pressure of pipelines, i.e., the Tresca solution, the Mises solution and a newly developed Average Shear Stress Yield (ASSY) solution are used in statistical evaluation of experimental data of burst pressure, and in probabilistic analysis of pipeline failure. Monte Carlo simulation is adopted and programmed as Excel macros for calculating probability of failure. The results show that the ASSY solution is the best prediction of the experimental data, the Tresca and Mises solutions provide a lower bound and an upper bound, respectively. These three theoretical solutions can significantly affect the possibility of burst failure for pipelines, and the difference can be in several orders of magnitude. Validity of the modified ASME B31G and other criteria to predict the burst failure is examined, and influence of the probability distribution type of random variables on probability of failure for pipelines is also discussed.Copyright

Plastic Collapse Assessment of Unequal Wall Joints in Pipeline Transitions

This paper presents the results of extensive numerical and analytical analyses considering the many differences in the flow properties of today’s steels with a view to determine if the code design basis developed for early steels remains appropriate in light of these changes. These analyses involved parametric study of steel grade, tensile strength, yield-to-tensile (Y/T) strength ratio, and joint geometry, for a range of transitions within as well as beyond current ASME code allowables. The numerical results indicate that the plastic-collapse failure conditions of unequal wall joints are controlled by the pipe or fitting remote to the weld, as would occur for high-quality slightly over-matched welds. Mismatch location, taper angle and anisotropy of unequal wall joints have limited influence on such failures. Based on trends in these results, a closed-form plastic collapse solution to predict internal pressure was developed as the pipe geometry, material hardening and tensile properties for both end opened and end capped pressurized pipes in reference to deformation instability, finite strain theory and deformation theory of plasticity. A plastic collapse criterion and the corresponding plastic collapse assessment diagram (PCAD) were then developed as a function of the wall thickness and tensile strength mismatch conditions to ensure plastic collapse failure in the thinner-wall, higher strength line pipe. General procedures to use the PCAD are outlined in this paper. Application of PCAD indicates that the high yield strength grades with high Y/T can be used within as well as beyond current code limitations on the transition wall-thickness mismatch for a wide range of strength mismatch.Copyright