Creep Analysis and Constraint Effect in a Center-Cracked Plate Under Biaxial Loading

2014 ◽  
Author(s):  
Zhongxian Wang ◽  
Yan-qing Zhang ◽  
Poh-Sang Lam ◽  
Yuh J. Chao
Keyword(s):  
Biaxial Loading ◽  
Crack Tip ◽  
Pressure Vessels ◽  
Contour Integral ◽  
Small Scale ◽  
Crack Tip Field ◽  
Cracked Plate ◽  
Creep Analysis ◽  
Creep Time ◽  
Crack Tip Constraint

Typical pressure vessels are subject to biaxial loading. Creep analysis was conducted with two-dimensional finite element method for a center-cracked plate under a range of biaxial loading ratios (λ = −1, 0, and 0.5). The effects of crack size and the biaxial loading ratio on the crack tip field are reported. In addition, based on a two-parameter fracture theory, C(t)−A2(t), where C is a contour integral and is path-independent when the steady state creep is reached (denoted by C*), and A2 is a time dependent crack tip constraint parameter. The crack tip stress field calculated from the C(t)−A2(t) theory is shown to be more accurate than the Hutchinson–Rice–Rosengren (HRR) singularity solution, especially in the case of λ = 0.5. The loading level appears to have little effects on the constraint parameter A2(t). As creep time increases, the creep zone (based on the equivalent creep strain) increases rapidly but the yield zone (with respect to a reference stress) decreases. Meanwhile, the crack tip constraint is increasing with creep time, particularly for the small cracks. It was also found that the normalized relationship between the contour integral C(t)/C* and the creep time t/tT (where tT is the characteristic time for transition from small-scale creep to extensive creep) is insensitive to the biaxial loading. Therefore, the relationship previously provided for uniaxial loading can be used for biaxial loading.

Features Testing of Stud Material Under Low Constraint Ductile Tearing

2017 ◽  
Author(s):  
P. James ◽  
M. Jackson ◽  
P. Birkett ◽  
C. Madew
Keyword(s):  
Structural Integrity ◽  
High Stress ◽  
Crack Tip ◽  
Pressure Vessels ◽  
Materials Testing ◽  
Screw Thread ◽  
Surface Point ◽  
Defect Tolerance ◽  
Material Response ◽  
Crack Tip Constraint

Defect tolerance assessments are carried out to support the demonstration of structural integrity for high integrity components such as nuclear reactor pressure vessels. These assessments often consider surface-breaking defects and assess Stress Intensity Factors (SIFs) at both the surface and deepest points. This can be problematic when there is a high stress at the surface, for example due to the stress concentration at the root of a screw thread. In the past this has led to the development of complex and costly 3D finite element analyses to calculate more accurate SIFs, and still resulting in small apparent limiting defect sizes based on initiation at the surface point. Analysis has been carried out along with supporting materials testing, to demonstrate that the increased SIF at the surface point is offset by a reduction in crack-tip constraint, such that the material exhibits a higher apparent fracture toughness. This enables a more simplistic assessment which reduces the effective SIF at the surface such that only the SIF at the deepest point needs to be considered. This then leads to larger calculated limiting defect sizes. This in turn leads to a more robust demonstration of structural integrity, as the limiting defect sizes are consistent with the capability of non-destructive examination techniques. The high SIF at the surface location, and the concomitant reduction in crack-tip constraint, meant that it was not possible to demonstrate the material response with conventional tests, such as those using shallow-notched bend specimens. Instead it was necessary to develop modified specimens in which semielliptical defects were introduced into a geometry which replicated the notch acuity at the root of a screw thread. These feature tests were used to demonstrate the principle, prior to testing with more conventional specimens to fit more accurately the parameters required to represent the material response in a defect tolerance assessment. Margins in defect tolerance assessments are usually measured against the initiation of tearing, even though the final failure for the material may occur at a higher load following stable crack extension. This work measured and assessed the benefit of reduced crack-tip constraint on both the point of initiation and on the development of the tearing resistance curve. This demonstrated that the effect of constraint was valid with tearing for this material and that there was additional margin available beyond the onset of tearing. The feature test geometry also provided evidence of the tearing behaviour at the surface and deepest points of a surrogate component under representative loading. This paper provides an overview of the range of tests performed and the post-test interpretation performed in order to provide the R6 α and k constraint parameters.

scholarly journals Estimation of C∗-Integral for Central Cracked Plate Under Biaxial Loading

2020 ◽  
Vol 12 (07) ◽  
pp. 2050079
Author(s):  
Yanwei Dai ◽  
Fei Qin ◽  
Yinghua Liu ◽  
Weizhe Feng ◽  
Guian Qian
Keyword(s):  
Loading Condition ◽  
Biaxial Loading ◽  
Classical Method ◽  
Creep Crack ◽  
Cracked Plate ◽  
Reference Stress ◽  
Creep Time ◽  
Relationship Of ◽  
The Relationship ◽  
Better Than

The reference stress method (RSM) is a classical method to estimate [Formula: see text]-integral of creep crack. An extended reference stress method (ERSM) is given for the central cracked plate (CCP) under biaxial loading in this paper. The applicability and verification for the proposed ERSM is given. The study finds that the solutions with the proposed ERSM agree better than those of RSM under biaxial loading condition. A theoretical form to predict the relationship of [Formula: see text]-integral between biaxial loading and uniaxial loading is discussed. Relation between [Formula: see text]-integral and creep time under biaxial loading is validated and discussed.

Evaluation of Crack Tip Constraint Effects on the Assessment of Pipes Subjected to Combined Loading Conditions

2008 ◽  
Author(s):  
Sebastian Cravero ◽  
Richard E. Bravo ◽  
Hugo A. Ernst
Keyword(s):  
Q Methodology ◽  
Biaxial Loading ◽  
Crack Tip ◽  
Combined Loading ◽  
Combined Loads ◽  
Loading Effects ◽  
Resistance Curves ◽  
Material Fracture ◽  
Constraint Effects ◽  
Crack Tip Constraint

Under certain conditions, pipelines may be submitted to biaxial loading situations. In these cases, questions arise about how biaxial loading influence the driving force (i.e.: CTOD, J-integral) of possible presented cracks and how affects the material fracture toughness. For further understanding of biaxial loading effects on fracture mechanics behavior of cracked pipelines, this work presents a numerical analysis of crack-tip constraint of circumferentially surface cracked pipes and SENT specimens using full 3D nonlinear computations. The objective is to examine combined loading effects on the correlation of fracture behavior for the analyzed cracked configurations. The constraint study using the J-Q methodology and the h parameter gives information about the fracture specimen that best represents the crack-tip conditions on circumferentially flawed pipes under combined loads. Additionally, simulations of ductile tearing in a surface cracked plate under biaxial loading using the computational cell methodology demonstrate the negligible effect of biaxial loadings on resistance curves.

Shallow Flaws Under Biaxial Loading Conditions—Part I: The Effect of Specimen Size on Fracture Toughness Values Obtained From Large-Scale Cruciform Specimens1

2000 ◽  
Vol 123 (1) ◽  
pp. 10-24 ◽  
Author(s):  
Wallace J. McAfee ◽  
B. Richard Bass ◽  
Paul T. Williams
Keyword(s):  
Fracture Toughness ◽  
Transition Temperature ◽  
Temperature Region ◽  
Large Scale ◽  
Biaxial Loading ◽  
Crack Tip ◽  
Specimen Size ◽  
Biaxial Stress ◽  
Lower Transition ◽  
Crack Tip Constraint

A technology to determine shallow-flaw fracture toughness of reactor pressure vessel (RPV) steels is being developed. This technology is for application to the safety assessment of RPVs containing postulated shallow-surface flaws. It has been shown that relaxation of crack-tip constraint causes shallow-flaw fracture toughness of RPV material to have a higher mean value than that for deep flaws in the lower transition temperature region. Cruciform beam specimens developed at Oak Ridge National Laboratory (ORNL) introduce far-field, out-of-plane biaxial stress components in the test section that approximates the nonlinear stresses resulting from pressurized-thermal-shock (PTS) loading of an RPV. The biaxial stress component has been shown to increase stress triaxiality (constraint) at the crack tip, and thereby reduce the shallow-flaw fracture toughness enhancement. The cruciform specimen permits controlled application of biaxial loading ratios, resulting in controlled variation of crack-tip constraint. An extensive matrix of intermediate-scale cruciform specimens with a uniform depth surface flaw was previously tested and demonstrated a continued decrease in shallow-flaw fracture toughness with increasing biaxial loading. This paper describes the test results for a series of large-scale cruciform specimens with a uniform depth surface flaw. These specimens were all of the same size with the same depth flaw and were tested at the same temperature and biaxial load ratio (1:1). The configuration is the same as the previous set of intermediate-scale tests, but has been scaled upward in size by 150 percent. These tests demonstrated the effect of biaxial loading and specimen size on shallow-flaw fracture toughness in the lower transition temperature region for RPV materials. For specimens tested under full biaxial (1:1) loading at test temperatures in the range of 23°F (−5°C) to 34°F (1°C), toughness was reduced by approximately 15 percent for a 150-percent increase in specimen size. This decrease was slightly greater than the predicted reduction for this increase in specimen size. The size corrections for 1/2T C(T) specimens did not predict the experimentally determined mean toughness values for larger size shallow-flaw specimens tested under biaxial (1:1) loading in the lower transition temperature region.

JEDI: A Code for the Calculation of J for Cracks Inserted in Initial Strain Fields and the Role of J and Q in the Prediction of Crack Extension and Fracture

2008 ◽  
Author(s):  
David W. Beardsmore
Keyword(s):  
Fracture Toughness ◽  
Strain Field ◽  
Crack Extension ◽  
Crack Tip ◽  
Initial Strain ◽  
Small Scale ◽  
Assessment Procedure ◽  
Crack Tip Fields ◽  
Crack Tip Constraint ◽  
Inelastic Strains

When crack tip constraint is high, the crack tip contour integral J characterises the asymptotic stress, strain and displacement fields of a stationary crack in an elastic-plastic material. In other cases, the crack tip fields can be related to J and a second parameter Q which governs the crack tip constraint. These observations are the basis of J-Q fracture mechanics assessments. In the most usual procedure J is compared to an effective, constraint-corrected fracture toughness Jc which is derived from Q and the fracture toughness of the material. The difference Jc – J is a measure of the margin of safety. The assessment procedure assumes there are no initial inelastic strains in the component or the fracture toughness specimen prior to introducing the crack and subsequent loading. However, plant components may contain inelastic strains prior to cracking arising from welding and other manufacturing or fit-up processes. This initial strain field can be established by a finite element analysis that simulates the welding and/or manufacture sequence. Weld residual stresses develop due to the accumulation of incompatible, inelastic strains, including thermal, plastic and transformation strains in the material. If a crack is inserted into an initial strain field, a procedure is required to calculate J by analysis of the resulting crack tip fields. Moreover, for the fracture assessment method to remain valid, it must be demonstrated that the values of J and Q continue to govern the onset of crack extension or fracture so that a meaningful comparison of J with Jc can be made. This paper describes a domain integral for calculating J when inelastic strains exist prior to cracking, and its implementation in the JEDI computer code. The code is used to determine J for a crack inserted into a three-point bend specimen containing an initial inelastic strain field representative of one that might develop during welding. The extent to which the crack tip stress field is characterised by J and Q is examined by comparing it to the field for high constraint, small-scale yielding conditions.

Constraint Quantification of Single Edge Notched Bend Specimens Under Large-Scale Yielding

2003 ◽  
Author(s):  
Yuh J. Chao ◽  
Xian-Kui Zhu ◽  
Yil Kim ◽  
M. J. Pechersky ◽  
M. J. Morgan ◽  
...  
Keyword(s):  
Large Scale ◽  
Crack Tip ◽  
Bending Moment ◽  
Additional Term ◽  
Small Scale ◽  
Bending Stress ◽  
Single Edge ◽  
Crack Tip Fields ◽  
Scale Yielding ◽  
Crack Tip Constraint

Because crack-tip fields of single edge notched bend (SENB) specimens are significantly affected by the global bending moment under the conditions of large-scale yielding (LSY), the classical crack tip asymptotic solutions fail to describe the crack-tip fields within the crack tip region prone to ductile fracture. As a result, existing theories do not quantify correctly the crack-tip constraint in such specimens under LSY conditions. To solve this problem, the J-A2 three-term solution is modified in this paper by introducing an additional term derived from the global bending moment in the SENB specimens. The J-integral represents the intensity of applied loading, A2 describes the crack-tip constraint level, and the additional term characterizes the effect of the global bending moment on the crack-tip fields of the SENB specimens. The global bending stress is derived from the strength theory of materials, and proportional to the applied bending moment and the inverse of the ligament size. Results show that the global bending stress near the crack tip of SENB specimens is very small compared to the J-A2 three-term solution under small-scale yielding (SSY), but becomes significant under the conditions of LSY or fully plastic deformation. The modified J-A2 solutions match well with the finite element results for the SENB specimens at all deformation levels ranging from SSY to LSY, and therefore can effectively model the effect of the global bending stress on the crack-tip fields. Consequently, the crack-tip constraint of such bending specimens can now be quantified correctly.

Correlation of Fracture Behavior in Circumferentially Cracked Pipes Under Combined Load Conditions Using SENT Specimens: Effects on J-R Resistance Curves

2008 ◽  
Author(s):  
Sebastian Cravero ◽  
Richard E. Bravo ◽  
Hugo A. Ernst
Keyword(s):  
Q Methodology ◽  
Fracture Behavior ◽  
Biaxial Loading ◽  
Crack Tip ◽  
Combined Loading ◽  
Combined Loads ◽  
Loading Effects ◽  
Resistance Curves ◽  
Crack Tip Constraint ◽  
Fracture Specimens

Single edge cracked under tension (SENT) specimens appear as an alternative to conventional fracture specimens to characterize fracture toughness of circumferentially cracked pipes. The similarities of stress and strains fields between SENT specimens and cracked pipes are now well known. However, these similarities are not so well established for the case of circumferentially cracked pipes under combined loading conditions (i.e. internal pressure plus bending). This work presents a numerical analysis of crack-tip constraint of circumferentially surface cracked pipes and SENT specimens using full 3D nonlinear computations. The objective is to examine combined loading effects on the correlation of fracture behavior for the analyzed crack configurations. The constraint study using the J-Q methodology and the h parameter gives information about the fracture specimen that best represents the crack-tip conditions on circumferentially flawed pipes under combined loads. Additionally, simulations of ductile tearing in a surface cracked plate under biaxial loading using the computational cell methodology demonstrate the negligible effect of biaxial loadings on resistance curves.

Constraint Based Assessment of Postulated Nozzle Corner Cracks

2002 ◽  
Author(s):  
Dieter Siegele ◽  
Igor Varfolomeyev ◽  
Gerhard Nagel
Keyword(s):  
Fracture Toughness ◽  
Brittle Failure ◽  
Thermal Stresses ◽  
Crack Tip ◽  
Pressure Vessels ◽  
Significant Loss ◽  
Large Shift ◽  
Corner Crack ◽  
Crack Tip Constraint ◽  
Corner Cracks

Brittle failure for reactor pressure vessels (RPV) under loss of coolant accidents (LOCA) considering strip and plume cooling show the nozzle corner as leading region in load level (e.g. Siegele et al., 1999). For such transients postulated nozzle corner cracks are also leading in crack driving force compared to the fracture toughness of the material. On the other hand, the crack tip constraint and consequently the failure probability is reduced by yielding caused by high thermal stresses and in addition by the crack size being small relative to the bulk of the flange material. Under these conditions, the flaw assessment in the nozzle corner using fracture toughness data obtained on standard specimens with high constraint level is over-conservative. In this situation it is suitable to introduce the loss of crack tip constraint into the brittle failure analysis of the nozzle corner. This investigation focuses on the assessment of surface cracks in the nozzle corner of an RPV. Using the finite element method temperature and stress calculations are carried out for a postulated LOCA event. For crack postulates in the nozzle corner of various size and geometry in the nozzle corner, crack driving parameters (such as the J-integral and the stress intensity factor) are determined as functions of the crack tip temperature. To account for the crack tip constraint, the T-stress is then evaluated and used along with the master curve approach as suggested by Wallin (2001). Significant loss of constraint is found for the nozzle corner resulting in a large shift of the fracture toughness curve to lower temperatures, thus excluding initiation of the crack postulates.

scholarly journals A Simplified SSY Estimate Method to Determine EPFM Constraint Parameter for Sensor Design

Sensors ◽  
2019 ◽  
Vol 19 (3) ◽  
pp. 717
Author(s):  
Ping Ding ◽  
Xin Wang
Keyword(s):  
Loading Condition ◽  
Biaxial Loading ◽  
External Loading ◽  
Small Scale ◽  
Cracked Plate ◽  
T Stress ◽  
Estimate Method ◽  
Parameter Values ◽  
Parameter Approach ◽  
Two Parameter

To implement a sensor structure analysis and design (as well as other engineering applications), a two-parameter approach using elastic–plastic fracture mechanics (EPFM) could be applied to analyze a structure more accurately than a one-parameter approach, especially for structures with low crack constraint. The application of the J-A two-parameter approach on sensors and other structures depends on the obtainment of a constraint parameter A. To conveniently and effectively obtain the A parameter values, the authors have developed a T-stress-based estimate method under a small-scale yielding (SSY) condition. Under a uniaxial external loading condition, a simplified format of the T-stress-based estimate has been proposed by the authors to obtain the parameter A much more conveniently and effectively. Generally, sensors and other practical engineering structures endure biaxial external loading instead of the uniaxial one. In the current work, the simplified formation of the estimate method is extended to a biaxial loading condition. By comparing the estimated A parameter values with their numerical solutions from a finite element analysis (FEA) results, the extension of the simplified formation of T-stress-based estimate method to biaxial loading was discussed and validated. The comparison procedure was completed using a wide variety of materials and geometrical properties on three types of specimens: single edge cracked plate (SECP), center cracked plate (CCP), and double edge cracked plate (DECP).

The Effects of Nonproportional Loading on the Elastic-Plastic Crack-Tip Fields

2016 ◽  
Vol 853 ◽  
pp. 83-87 ◽  
Author(s):  
Zhao Yu Jin ◽  
Xin Wang ◽  
Dun Ji Yu ◽  
Xu Chen
Keyword(s):  
Stress Field ◽  
Outer Boundary ◽  
Crack Tip ◽  
Loading Path ◽  
Small Scale ◽  
Proportional Loading ◽  
Nonproportional Loading ◽  
Elastic Plastic ◽  
Loading Paths ◽  
Crack Tip Constraint

In this paper, the loading path effects on the plane strain elastic-plastic crack-tip stress field are investigated computationally. Three different loading sequences include one proportional loading and two non-proportional loading paths are applied to the modified boundary layer (MBL) model under small-scale yielding conditions. For the same external displacement field applied at the outer boundary of the MBL model, the mode I K field and T-stress field combined as the different loading paths are applied to investigate the influence of the nonproportional loading. The results show that for either the compressive or tensional T-stress, the loading path which applied K field followed by T field generates the lower crack-tip constraint. There is only slightly difference between the proportional loading path and that with the T-stress field following by K field. The results show that it is very important to include the load sequence effects in fracture analysis when dealing with nonproportional loading conditions.

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