Elastic-Plastic Fracture Mechanics Assessment of Test Data for Circumferential Cracked Pipes

2003 ◽  
Author(s):  
Nam-Su Huh ◽  
Do-Jun Shim ◽  
Yun-Jae Kim ◽  
Young-Jin Kim
Keyword(s):  
Test Data ◽  
Experimental Validation ◽  
Limit Load ◽  
Maximum Load ◽  
The Other ◽  
Surface Cracks ◽  
Plastic Limit ◽  
Load Range ◽  
Reference Stress ◽  
Plastic Limit Load

This paper presents experimental validation of two reference stress based methods for circumferential cracked pipes. One is the R6 method where the reference stress is defined by the plastic limit load. The other is the enhanced reference stress method, recently proposed by the authors, where the reference stress is defined by the optimized reference load. Using thirty-eight published pipe test data, the predicted maximum instability loads according to both methods are compared with the experimental ones for pipes with circumferential through-thickness cracks and with part circumferential surface cracks. It is found that the R6 method gives conservative estimates of the maximum loads for all cases. Ratios of the experimental maximum load to the predicted load range from 0.54 to 0.98. On the other hand, the proposed method gives overall closer maximum loads than R6, compared to the experimental data. However, for part through-thickness surface cracks, the estimated loads were slightly non-conservative for four cases, and possible reasons were fully discussed.

The Effects of Classification of Misalignment-Induced Stresses in Engineering Critical Assessments of Welded Joints With Some Misalignment

2010 ◽  
Author(s):  
Liwu Wei
Keyword(s):  
Welded Joints ◽  
Driving Force ◽  
Limit Load ◽  
Surface Cracks ◽  
Plastic Limit ◽  
Secondary Stress ◽  
Butt Weld ◽  
Crack Driving Force ◽  
Plastic Limit Load

In the ECA of a structure or component such as a pipeline girth weld, the bending stress component arising from misalignment across the weld is often classified as primary, partly because standards such as BS 7910 and API 579-1/ASME FFS-1 do not give definitive guidance on this subject. This approach may be over-conservative as the σmis is localised. In order to obtain a more realistic assessment of the structural integrity of structures containing misalignment, it is necessary to understand the conservatism or non-conservatism in an ECA associated with the classification of σmis. To address the above concerns, systematic investigations were carried out of surface cracks in a plate butt-weld including some misalignment, external circumferential surface cracks and external fully circumferential cracks in a misaligned pipe connection. FEA of these cracked welded joints with some misalignment (typically from 1mm to 2mm) was performed to calculate crack driving force and plastic limit load. The results from FEA were compared with the existing solutions of KI and σref in BS 7910 generated by assuming three options of treating the σmis. The three options were: (1) classification of σmis wholly as primary stress; (2) 15% of σmis as primary and 85% of σmis as secondary stress; and (3) classification of σmis wholly as secondary stress. Variations in parameters (eg misalignment, crack size, loading, weld overmatch and base material properties) were taken into account in order to determine the effects of these parameters on plastic limit load and crack driving force. The implication of different classifications of σmis in terms of ECAs of misaligned welded joints was revealed by conducting BS 7910 Level 2B assessments with the use of a FAD. It was found in this work that for the cases examined, use of the σmis as entirely primary bending in an ECA was over-conservative, and even treatment of σmis as entirely secondary bending was generally shown to be still conservative, when compared with the assessments based on FEA solutions. Furthermore, caution should be exercised in using the solutions of KI and σref given in the existing BS 7910 for crack-containing structures subjected to a bi-axial or tri-axial stress state. A non-conservative estimate may result from the use of these solutions which have been derived based on a uniaxial stress condition.

Plastic Limit Loads for Slanted Through-Wall Cracks in Cylinder and Plate Based on Finite Element Limit Analyses

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Doo-Ho Cho ◽  
Young-Hwan Choi ◽  
Nam-Su Huh ◽  
Do-Jun Shim ◽  
Jae-Boong Choi
Keyword(s):  
Finite Element ◽  
Crack Opening ◽  
Limit Load ◽  
Correction Factors ◽  
Plastic Limit ◽  
Opening Displacement ◽  
Limit Loads ◽  
Axial Tension ◽  
Reference Stress ◽  
Plastic Limit Load

The plastic limit load solutions for cylinder and plate with slanted through-wall cracks (TWCs) are developed based on the systematic three-dimensional (3D) finite element (FE) limit analyses. As for loading conditions, axial tension, global bending, and internal pressure are considered for a cylinder with slanted circumferential TWC, whereas, axial tension and internal pressure are considered for a plate and a cylinder with slanted axial TWC. Then, the verification of FE model and analysis procedure employed in the present numerical work was confirmed by employing the existing solutions for both cylinder and plate with idealized TWC. Also, the geometric variables of slanted TWC which can affect plastic limit loads were considered. Based on the systematic FE limit analysis results, the slant correction factors which represent the effect of slanted TWC on plastic limit load were provided as tabulated solutions. By adopting these slant correction factors, the plastic limit loads of slanted TWC can be directly estimated from existing solutions for idealized TWC. Furthermore, the modified engineering estimations of plastic limit loads for slanted TWC are proposed based on equilibrium equation and von Mises yield criterion. The present results can be applied either to diverse structural integrity assessments or for accurate estimation of fracture mechanics parameters such as J-integral, plastic crack opening displacement (COD) and C*-integral for slanted TWC based on the reference stress concept (Kim, et al., 2002, “Plastic Limit Pressure for Cracked Pipes Using Finite Element Limit Analyse,” Int. J. Pressure Vessels Piping, 79, pp. 321–330; Kim, et al., 2001, “Enhanced Reference Stress-Based J and Crack Opening Displacement Estimation Method for Leak-Before-Break Analysis and Comparison With GE/EPRI Method,” Fatigue Fract. Eng. Mater. Struct., 24, pp. 243–254; Kim, et al., 2002, “Non-Linear Fracture Mechanics Analyses of Part Circumferential Surface Cracked Pipes,” Int. J. Fract., 116, pp. 347–375.)

Estimates of Plastic Limit Loads of Thick-Walled Cylinders With Non-Idealzied Through-Wall Cracks

2013 ◽  
Author(s):  
Tae-Song Han ◽  
Nam-Su Huh ◽  
Do-Jun Shim
Keyword(s):  
Fracture Mechanics ◽  
Structural Integrity ◽  
Limit Load ◽  
Ductile Material ◽  
J Integral ◽  
Plastic Limit ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Reference Stress ◽  
Plastic Limit Load

In order to assess a structural integrity of cracked components made of highly ductile material based on fully plastic fracture mechanics concept, an accurate plastic limit load of components of interest is crucial element. Such a plastic limit load can also be applied to estimate elastic-plastic J-integral based on the reference stress concept. In this context, during last several decades, many efforts have been made to suggest plastic limit load solutions of cracked cylinder. Recent works for evaluating rupture probabilities of nuclear piping indicate that the only use of idealized circumferential through-wall crack leads to very conservative results which in turn gives higher rupture probabilities of nuclear piping, thus the considerations of more realistic crack shape during crack growth due to primary water stress corrosion cracking (PWSCC) and fatigue and axial through-wall crack were recommended to come up with more realistic rupture probabilities of nuclear piping. Then, the needs of fracture mechanics parameters of non-idealized through-wall cracks both in axial and circumferential directions have been raised. In the present work, the plastic limit loads of thick-walled cylinder with non-idealized axial and circumferential through-wall cracks are proposed based on detailed 3-dimensional finite element analyses. The present results can be applied either to assess structural integrity of thick-walled nuclear piping with non-idealized through-wall cracks or to calculate elastic-plastic J-integral using the reference stress concept.

Plastic Limit Analysis Using the Simplified Theory of Plastic Zones

2021 ◽  
Vol 143 (2) ◽  
Author(s):  
Hartwig Hübel
Keyword(s):  
Limit Analysis ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Maximum Load ◽  
Load Level ◽  
Material Behavior ◽  
Plastic Limit ◽  
Plastic Limit Load ◽  
Plastic Zones

Abstract The simplified theory of plastic zones (STPZ) was mainly developed to determine strain ranges and accumulated strains in the state of shakedown at cyclic loading between prescribed levels of loading. Kinematic hardening is an indispensable feature of the STPZ. The plastic limit load, however, is defined for monotonic loading and elastic–plastic material behavior without hardening. Simply assigning a zero value or a numerically very low value of the tangent modulus when applying the STPZ is generally not possible due to arising numerical instabilities. It is, therefore, not immediately obvious how the STPZ can be used to determine the maximum load level that can be applied to a structure without developing a kinematic mechanism. This paper describes the theory and the analysis steps required and provides some illustrative examples. Typically, between one and three linear elastic analyses and some local calculations are required to provide either the exact value or at least a reasonable estimate of a range of the plastic limit load, as well as of the associated stress and strain fields and displacements that are not provided by classical limit analysis.

The Effect of Bi-Axial Stress on Limit Loads of Structures Containing Surface-Breaking Flaws and its Influence on Structural Integrity Assessments

2012 ◽  
Author(s):  
Liwu Wei ◽  
Isabel Hadley
Keyword(s):  
Surface Crack ◽  
Structural Integrity ◽  
Axial Loading ◽  
Limit Load ◽  
Plastic Limit ◽  
Integrity Assessment ◽  
Reference Stress ◽  
Fracture Assessment ◽  
Plastic Limit Load ◽  
Assessment Procedures

Fracture assessment diagram (FAD) based fracture assessment procedures are universally adopted by standards/documents including BS7910, R6, API579-1/ASME FFS-1 and FITNET. In the use of a FAD for structural integrity assessment, one important consideration is to determine the load ratio (Lr) which is defined by two equivalent definitions: Lr is either defined as the ratio of reference stress (σref) to yield strength (σY) as in BS7910, or as the ratio of applied load to plastic limit load as in R6. The solutions of reference stress or limit load are given in the assessment procedures for commonly encountered flawed structures such as a plate containing a surface crack and a cylinder containing an external surface crack. Although the solutions given in the various standards are not all the same, they were invariably derived on the basis of analysis of the force and moment equilibrium with regard to a flawed section and none of them has taken into account the effects of bi-axial stressing on a flawed section, thus leading to the likelihood of an overly conservative assessment. In this work, finite element analysis (FEA) of various flawed geometries (plate and cylinder containing surface cracks) was performed to compute plastic limit load, with the focus on understanding the effects of bi-axial stressing on plastic limit load. The geometries assessed include a plate with a surface crack subjected to both uni-axial and bi-axial loading, and a cylinder with circumferentially internal and external surface cracks sustaining a combination of axial loading and internal pressure. The investigation of these cases has demonstrated a significant increase in plastic limit load arising from bi-axial stressing. Comparison of the results of plastic limit load obtained from FEA with those derived from BS 7910 reference stress solutions was carried out to assess the extent of conservatism when the standard solutions are used in the applications containing bi-axial stresses. The implication for structural integrity assessment due to bi-axial stressing was also addressed. A comparison between BS 7910 Level 2B (material-specific FAD) and Level 3C (based on a FAD generated with FEA) procedures was also made and it was shown that whether the Level 3C procedure can reduce the conservatism in an assessment is dependent on individual cases.

The Numerical Investigation of Plastic Collapse Loads in Cylinders Containing Circumferential Flaws Under a Combined Loading of Internal Pressure, Tension and Bending Moment

2013 ◽  
Author(s):  
Liwu Wei
Keyword(s):  
Surface Crack ◽  
Bending Moment ◽  
Limit Load ◽  
Plastic Collapse ◽  
Plastic Limit ◽  
Integrity Assessment ◽  
Reference Stress ◽  
Fracture Assessment ◽  
Plastic Limit Load ◽  
Assessment Procedures

Fracture assessment diagram (FAD) based fracture assessment procedures are universally adopted by standards/documents including BS7910, R6, API579-1/ASME FFS-1 and FITNET. In the use of a FAD for structural integrity assessment, one important consideration is to determine the load ratio (Lr) which is defined by two equivalent definitions: Lr is either defined as the ratio of reference stress (σref) to yield strength (σY) as in BS7910, or as the ratio of applied load to plastic limit load as in R6. The solutions of reference stress or limit load are given in the assessment procedures for commonly encountered flawed structures such as a plate containing a surface crack and a cylinder containing an external surface crack. Although the solutions given in the various standards are not all the same, they were invariably derived on the basis of analysis of the force and moment equilibrium with regard to a flawed section and few of them has taken into account the effects of bi-axial stressing on a flawed section, thus remaining a question whether these solutions are still valid in situations involving bi-axial loading such as the presence of pressure in a cylinder in addition to axial tension and bending. In this work, finite element analysis (FEA) of plastic collapse was systematically performed on circumferential internal surface cracks in a cylinder subjected to various combined loads, including combined tension and pressure, combined bending moment and pressure, and combined tension, bending moment and pressure. The focus was on understanding the effects of bi-axial stressing due to pressure on plastic limit load. The investigation of these cases has demonstrated a significant effect in plastic limit load arising from the application of pressure introducing a state of bi-axial stressing. Comparison of the results of plastic limit load obtained from FEA with those derived from BS 7910 reference stress solutions was carried out to assess the applicability when the standard solutions of plastic collapse are used in the applications containing bi-axial stresses.

Shakedown and Limit Analysis of Kinematic Hardening Piping Elbows Under Internal Pressure and Bending Moments

2021 ◽  
Author(s):  
Heng Peng ◽  
Yinghua Liu
Keyword(s):  
Yield Strength ◽  
Internal Pressure ◽  
Limit Analysis ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Bending Moments ◽  
Plastic Limit ◽  
Plastic Limit Load ◽  
Interaction Curves ◽  
Shakedown Limit

Abstract In this paper, the Stress Compensation Method (SCM) adopting an elastic-perfectly-plastic (EPP) material is further extended to account for limited kinematic hardening (KH) material model based on the extended Melan's static shakedown theorem using a two-surface model defined by two hardening parameters, namely the initial yield strength and the ultimate yield strength. Numerical analysis of a cylindrical pipe is performed to validate the outcomes of the extended SCM. The results agree well with ones from literature. Then the extended SCM is applied to the shakedown and limit analysis of KH piping elbows subjected to internal pressure and cyclic bending moments. Various loading combinations are investigated to generate the shakedown limit and the plastic limit load interaction curves. The effects of material hardening, elbow angle and loading conditions on the shakedown limit and the plastic limit load interaction curves are presented and analysed. The present method is incorporated in the commercial finite element simulation software and can be considered as a general computational tool for shakedown analysis of KH engineering structures. The obtained results provide a useful information for the structural design and integrity assessment of practical piping elbows.

Development of Z-Factor for Circumferential Part-Through Surface Cracks in Dissimilar Metal Welds

2008 ◽  
Author(s):  
D.-J. Shim ◽  
G. M. Wilkowski ◽  
D. L. Rudland ◽  
F. W. Brust ◽  
Kazuo Ogawa
Keyword(s):  
Correction Factor ◽  
Carrying Capacity ◽  
Limit Load ◽  
Maximum Load ◽  
Load Carrying Capacity ◽  
Surface Cracks ◽  
Crack Driving Force ◽  
Dissimilar Metal ◽  
Load Carrying ◽  
J Estimation

Section XI of the ASME Code allows the users to conduct flaw evaluation analyses by using limit-load equations with a simple correction factor to account elastic-plastic fracture conditions. This correction factor is called a Z-factor, and is simply the ratio of the limit-load to elastic-plastic fracture mechanics (EPFM) maximum-load predictions for a flaw in a pipe. The past ASME Section XI Z-factors were based on a circumferential through-wall crack in a pipe rather than a surface crack. Past analyses and pipe tests with circumferential through-wall cracks in monolithic welds showed that the simplified EPFM analyses (called J-estimation schemes) could give good predictions by using the toughness, i.e., J-R curve, of the weld metal and the strength of the base metal. The determination of the Z-factor for a dissimilar metal weld (DMW) is more complicated because of the different strength base metals on either side of the weld. This strength difference can affect the maximum load-carrying capacity of the flawed pipe by more than the weld toughness. Recent work by the authors for circumferential through-wall cracks in DMWs has shown that an equivalent stress-strain curve is needed in order for the typical J-estimation schemes to correctly predict the load carrying capacity in a cracked DMW. In this paper, the Z-factors for circumferential surface cracks in DMW were determined. For this purpose, a material property correction factor was determined by comparing the crack driving force calculated from the J-estimation schemes to detailed finite element (FE) analyses. The effect of crack size and pipe geometry on the material correction factor was investigated. Using the determined crack-driving force and the appropriate toughness of the weld metal, the Z-factors were calculated for various crack sizes and pipe geometries. In these calculations, a ‘reference’ limit-load was determined by using the lower strength base metal flow stress. Furthermore, the effect of J-R curve on the Z-factor was investigated. Finally, the Z-factors developed in the present work were compared to those developed earlier for through-wall cracks in DMWs.

J-Integral Analysis of Surface Cracks in Round Bars under Bending Moments

2011 ◽  
Vol 52-54 ◽  
pp. 43-48 ◽  
Author(s):  
Al Emran Ismail ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali ◽  
Ruslizam Daud
Keyword(s):  
Finite Element ◽  
Crack Depth ◽  
Crack Tip ◽  
Bending Moment ◽  
Limit Load ◽  
Fe Model ◽  
Surface Cracks ◽  
Element Analysis ◽  
Reference Stress ◽  
Proposed Model

This paper presents a non-linear numerical investigation of surface cracks in round bars under bending moment by using ANSYS finite element analysis (FEA). Due to the symmetrical analysis, only quarter finite element (FE) model was constructed and special attention was given at the crack tip of the cracks. The surface cracks were characterized by the dimensionless crack aspect ratio, a/b = 0.6, 0.8, 1.0 and 1.2, while the dimensionless relative crack depth, a/D = 0.1, 0.2 and 0.3. The square-root singularity of stresses and strains was modeled by shifting the mid-point nodes to the quarter-point locations close to the crack tip. The proposed model was validated with the existing model before any further analysis. The elastic-plastic analysis under remotely applied bending moment was assumed to follow the Ramberg-Osgood relation with n = 5 and 10. J values were determined for all positions along the crack front and then, the limit load was predicted using the J values obtained from FEA through the reference stress method.

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