Elastic-plastic Fracture Mechanics Analysis Research Articles

Determination of the plastic J integral of ductile material using the XFEM with only Heaviside function and variable-node elements

In this paper, the extended finite element method (XFEM) with only Heaviside function is proposed for the elastic–plastic fracture mechanics (EPFM) modeling. The proposed method removes tip enrichment functions depending on the polar coordinates at the crack front, and a step function only determined by the level set function is utilized to track the crack front. To alleviate the volumetric locking phenomena caused by the plastic incompressibility, the B-bar method is incorporated into the three dimensional (3D) XFEM program. Therefore, the fully integration scheme can be chosen to ensure the accuracy when addressing large plastic deformation in EPFM analysis. Additionally, the material tangent stiffness matrix of Ramberg-Osgood constitutive is given, and the local refinement technique using variable-node elements is adopted to reduce the number of elements and nodes for efficient analysis. A Newton-Raphson iterative algorithm is developed to solve the nonlinear algebraic equations caused by material nonlinearity. Several numerical examples including the determination of crack opening displacement, and the fully plastic J integral in the ductile materials are presented to test the performance of the proposed method. Comparisons with the results from the existing methodologies show that the new enrichment scheme can save computational cost and obtain sufficient accuracy even in the case of 3D curved crack.

Applicability investigation on failure assessment diagram of ASME code section XI - Appendix H for ferritic nuclear piping

The failure assessment diagram (FAD) is a widely used tool for evaluating the fracture acceptance of structural components. In addition to linear elastic fracture mechanics, elastic-plastic fracture mechanics, and limit load analysis, the ASME Code incorporated FAD as an alternative safety evaluation method for flaws in nuclear pipes starting from 2004 edition. This paper conducts a series of finite element elastic-plastic fracture mechanics analyses to establish the specific J–based FAD curves considering various loading and geometry conditions for ferritic pipes containing various circumferential flaws. By comparing with the suggested FAD of ASME Code Section XI - Appendix H, it is found that the radius-to-thickness ratio of pipes and the flaw depth influence the applicability of FAD, but with minor effects of crack length. In addition, the effects of material properties between base metal and weld materials on FAD are also discussed. The result of this work could be a reference when applying the FAD to evaluate the flawed piping for nuclear power plants.

Fracture mechanics analysis of multipurpose canister for spent nuclear fuels under horizontal/oblique drop accidents

In this paper, elastic-plastic fracture mechanics analysis is performed to determine the critical crack sizes of the multipurpose canister (MPC) manufactured using austenitic stainless steel under dynamic loading conditions that simulate drop accidents. Firstly, dynamic finite element (FE) analysis is performed using Abaqus v.2018 with the KORAD (Korea Radioactive Waste Agency)-21 model under two drop accident conditions. Through the FE analysis, critical locations and through-thickness stress distributions in the MPC are identified, where the maximum plastic strain occurs during impact loadings. Then, the evaluation using the failure assessment diagram (FAD) is performed by postulating an external surface crack at the critical location to determine the critical crack depth. It is found that, for the drop cases considered in this paper, the principal failure mechanism for the circumferential surface crack is found to be the plastic collapse due to dominant high bending axial stress in the thickness. For axial cracks, the plastic collapse is also the dominant failure mechanism due to high membrane hoop stress, followed by the ductile tearing analysis. When incorporating the strain rate effect on yield strength and fracture toughness, the critical crack depth increases from 10 to 20%.

Elastic–Plastic Fracture Mechanics Guidance and Analysis Validation

Damage tolerance is an important consideration in space structures applications. However, many space and launch vehicle components experience large cyclic stresses and cannot be evaluated using linear elastic fracture mechanics (LEFM). In these instances, elastic–plastic fracture mechanics (EPFM) can be used in the damage tolerance verification process. This paper provides practical guidance on the use of LEFM and EPFM as they relate to space structures. The limitations of LEFM-based approaches to damage tolerance verification are explored, demonstrating that inappropriate application of LEFM can be unconservative. Criteria are provided to help the engineer determine if EPFM analysis is required for a given scenario. Finally, a practical method of EPFM-based damage tolerance analysis is introduced and validated against test data from several test campaigns with excellent correlation to experimental data.

Proposal of analysis method of global-local finite element method for finite strain elastic-plastic fracture mechanics analysis

The purpose of this study is to make it possible to perform a large number of paratric analyzes on the position and shape of cracks under finite elasto-plastic deformation. In this report, we propose a one-way coupled analysis method using displacement interpolation between a global finite element method analysis model created without assuming cracks and a local finite element method analysis model assuming cracks. The proposed method is based on the superconvergent patch recovery, and uses the least-squares method to apply the nodal displacements of the global finite element model to the nodes of the local finite element model as displacement boundary conditions. In addition, we will create an merged finite element method analysis model assuming a crack directly in the global finite element method analysis model and identify the application conditions that can be applied to the problem without loss of accuracy through relative comparison by J-integral calculation at the crack tip which is nonlinear fracture mechanics parameter.

Constraint-corrected fracture mechanics analysis of nozzle crotch corners in pressurized water reactors

This paper presents fracture mechanics analysis results for various cracks located at pressurized water reactor pressure vessel nozzle crotch corners taking into consideration constraint effect. Technical documents such as the ASME B&PV Code, Sec.XI were reviewed and then a fracture mechanics analysis procedure was proposed for structural integrity assessment of various nozzle crotch corner cracks under normal operation conditions considering the constraint effect. Linear elastic fracture mechanics analysis was performed by conducting finite element analysis with the proposed analysis procedure. Based on the evaluation results, elastic-plastic fracture mechanics analysis taking into account the constraint effect was performed only for the axial surface crack of the reactor pressure vessel outlet nozzle with cladding. The fracture mechanics analysis result shows that only the axial surface crack in the reactor pressure vessel outlet nozzle has the stress intensity factor exceeding the low bound of upper-shelf fracture toughness irrespectively of considering the constraint effect. It is confirmed that the J-integral for the axial crack of the outlet nozzle does not exceed the ductile crack initiation toughness. Hence, it can be ensured that the structural integrity of all the cracks is maintained during the normal operation.

Probabilistic Elastic-plastic Fracture Mechanics Analysis of Propagation of Cracks in Pipes under Internal Pressure

This study presents a three dimensional finite element method analysis of semi-elliptical surface cracks in pipes under internal pressure load. In the elastic–plastic case, estimates of the J-integral are presented for various ratios including crack depth to pipe thickness (a/t) and strain hardening index in the (R-O) Ramberg-Osgood (n). Finally, failure probability is accessed by a statistical analysis for uncertainties in loads and material properties, and structural reliability and crack size. The Monte Carlo method is used to predict the distribution function of the mechanical response. According to the obtained results, we note that the stress variation and the crack size are important factors influencing on the distribution function of (J/Je).

Fatigue crack growth prediction for small-scale yielding (SSY) and non-SSY conditions

A model to predict fatigue crack growth (FCG) for small-scale yielding (SSY) and non-SSY conditions where J-integral applies is established. The ΔJ-characterized elastic-plastic fracture mechanics (EPFM) analysis is performed based on a rearranged FCG process to achieve the crack-tip geometry and stress state. The root stress of blunted crack and the FCG rate are calculated from the cycle-wise local and global energy balance. To consider effects of geometry, load level and strain hardening, a correction factor is further developed in the governing equation of global energy balance. The model is validated using the test data of several types of metals.

Reconciling fracture toughness parameter contradictions in thin ductile metal sheets

AbstractThe well‐known trade‐off between strength and fracture toughness in bulk specimens is often used to explain the low fracture toughness of very thin ductile face‐centred cubic metal specimens, but this interpretation contradicts the relative length scales of thickness‐dependent strength and thickness‐dependent fracture toughness. This study uses the concept of similitude to demonstrate that linear elastic fracture mechanics analysis of 25.4 μm thick annealed aluminium is invalid, although the resulting fracture toughness measurements fit well with the existing literature and idea of a strength/fracture toughness trade‐off. Similarly, an elastic plastic fracture mechanics analysis is sensitive to out‐of‐plane deformation that cannot be practically eliminated or corrected for with a model. However, a plastic collapse analysis using a critical net section stress criterion is demonstrably valid by the concept of similitude, is insensitive to out of plane deformation, and agrees with the evidence of extensive plasticity in the fracture surfaces.

A simple intrinsic measure for rapid crack propagation in bimodal polyethylene pipe grades validated by elastic–plastic fracture mechanics analysis of data from instrumented Charpy impact test

Conventional test procedures, such as the S4 test to analyze the resistance against rapid crack propagation (RCP) of plastic pipe materials are characterized by usage of a lot of material, are far from saving of time and they are‐in need of special experimental set‐ups. Therefore, in the last decade, small‐scale accelerated reliable tests (SMART) are developed ‐ worldwide to overcome the disadvantage of such conventional tests. In this article, fracture mechanics based analysis of instrumented Charpy impact test data for a set of bimodal high‐density polyethylene pipe grades are compared with data of the conventional Charpy impact test. From this comparison the Charpy impact strength at −30°C comes forth as a robust reproducible measure of the resistance to RCP and it is therefore proposed as a SMART method to rank materials with respect to RCP resistance. POLYM. ENG. SCI., 57:13–21, 2017. © 2016 Society of Plastics Engineers

維持規格における弾塑性破壊力学評価のためのZ係数式

維持規格における弾塑性破壊力学評価のためのZ係数式

The probabilistic structural integrity assessment of reactor pressure vessels under pressurized thermal shock loading

The pressurized thermal shock (PTS) event poses a potentially significant challenge to the structural integrity of the reactor pressure vessel (RPV) during the long time operation (LTO). In the USA, the “screening criteria” for maximum allowable embrittlement of RPV material, which forms part of the USA regulations, is based on the probabilistic fracture mechanics (PFM). The FAVOR software developed by Oak Ridge National Laboratory (ORNL) is used to establish the regulation. As the technical basis of FAVOR is not the most widely-used and codified methodologies, such as the ASME and RCC-M codes, in most countries (with exception of the USA), proving RPV integrity under the PTS load is still based on the deterministic fracture mechanics (DFM). As the maximum nil-ductility-transition temperature (RTNDT) of the beltline material for the 54 French RPVs after 40 years operation is higher than the critical values in the IAEA-TECDOC-1627 and European NEA/CSNI/R(99)3 reports (while still obviously lower than the “screening criteria” of the USA), it may conclude that the RPV will not be able to run in the LTO based on the DFM. In the FAVOR, the newest developments of fracture mechanics are applied, such as the warm pre-stress (WPS) effect, more accurate estimation of the flaw information and less conservation of the toughness (such as the three-parameter Weibull distribution of the fracture toughness). In this paper, the FAVOR software is first applied to show both the methodology and the results of the PFM, and then the limits in the current FAVOR software (Version 6.1, which represents the baseline for re-assessing the regulation of 10 CFR 50.61), lack of the impact of the constraint effect, ductile–tearing initiation failure analysis, elastic–plastic fracture mechanics analysis, safety assessment of the crack front interface points and interaction among multiple cracks, are also discussed.

Estimation of Constraint Factor on the Relationship Between J Integral and CTOD for Offshore Structural Steel Weldments

Offshore structures are exposed to severe operating conditions because energy resource development has recently extended toward deeper seabed and lower temperature regions. Hence, fracture toughness evaluation for very thick and high strength steels is one of the most important parameters required for the structural integrity assessment of offshore structures. Fracture toughness is known as a property which describes the ability of a material containing a crack to resist unstable brittle fracture. Crack tip opening displacement (CTOD) and J integral are the most commonly employed parameters as fracture criteria in elastic plastic fracture mechanics (EPFM). There have been extensive research efforts to clarify the relationship between CTOD and J integral in elastic plastic regime. Plastic constraint factor (PCF) in the relationship between CTOD and J integral can serve as a parameter to characterize constraint effects in fracture involving plastic deformation. In this regard, the characteristics of the PCF are of significant importance in EPFM analysis. In this study, we evaluated fracture toughness of American Petroleum Institute (API) 2 W Gr. 50 steel in terms of CTOD in various temperatures using single edge notched bend (SENB) specimens. Test specimens are fabricated by submerged arc welding (SAW) and flux cored arc welding (FCAW). In addition, CTOD values are compared to absorbed impact energy with respect to the weld metal (WM) and heat affected zone (HAZ). Then, we investigated PCFs with respect to several regions of the weldment at various temperatures. Experimental values of PCFs were calculated and then compared against the predicted values according to the American Society for Testing and Materials (ASTM) standard. CTOD values of WM by SAW is found to be about three times higher than that of FCAW at −10 °C, and CTOD values calculated by the ASTM standard are approximately 30% lower than the CTOD according to British Standard (BS). In addition, the maximum of 40% discrepancy is observed in PCFs obtained between the experiment and the predicted values according to the ASTM standard. This may lead to too conservative fracture toughness estimation for the welded joints of API 2 W Gr. 50 steel when using PCF by ASTM. Based on the accurate estimated PCF values obtained from this study, it is believed that rational fracture design of offshore structures is possible.

Elastic-Plastic Fracture Mechanics Analyses of Surface Cracks in Drill String Subjected to Combined Loading

The drill pipe near the surface stands the largest tension and torsion load for the full hole during drilling operation. And fatigue crack growth is always the major cause of failure of drill string. As an example, 5ʺ drill pipe that was near the well head of an ultra-deep straight well and made of 30CrMo, whose constitutional relation was fitted by experiment, was analyzed here. Simplifying the initial crack of the drill pipe as circumferential semi-elliptical surface crack, we simulated the elastic-plastic fracture feature of the drill string with surface crack, partly through-wall crack and fully through-wall crack under combined loading of axial force and torsion. Crack front geometry evolvement is simulated for the different stages of crack propagation. This work would provide a basis for the full-range analysis of fatigue crack growth.

Determination of the elastic-plastic fracture mechanics Z-factor for alloy 182 weld metal flaws

One of the ways that the ASME Section XI code incorporates elastic-plastic fracture mechanics (EPFM) in the Section XI Appendix C flaw evaluation procedures for circumferential cracks is through a parameter called Z-factor. This parameter allows the simpler limit-load (or Net-Section-Collapse) solutions to be used with a multiplier from EPFM analyses. This paper shows how 3-D finite element (FE) analyses were employed to investigate the sensitivity of the crack-driving force as a function of crack location (i.e., crack in the center of weld, or closer to the stainless or low alloy steel sides) in an Alloy 182 dissimilar metal weld (DMW), and how an appropriate (or equivalent) stress-strain curve was determined for use in the J-estimation schemes. The J-estimation schemes are then used to cover a wider range of variables, i.e., pipe diameters, cracks lengths, and also incorporate crack growth by ductile tearing. The Z-factor equations as a function of pipe diameter were calculated using the LBB.ENG2 J-estimation scheme along with the most conservative equivalent stress-strain curve from the FE analyses. The proposed Z-factor approach was then validated against an Alloy 182 DMW full-scale pipe test that had a circumferential through-wall crack in the fusion line. The predicted EPFM maximum load showed excellent agreement with the experimental result. Furthermore, it was shown that the proposed Z-factor equation is not sensitive to the location of the crack.

Computations of energy release rate under monotonic and cyclic loading conditions

Abstract In case of an elastic–plastic fracture mechanics analysis, the determination of the energy release rate distribution is a crucial point. In the present paper, three numerical techniques: the virtual crack closure technique (VCCT), J-integral and energy derivative technique (EDT), are used to compute the energy release rate in a middle-crack tension specimen with the combined isotropic/kinematic hardening model. The results obtained by these methods are compared with each other under monotonic and cyclic loading conditions. Finally, it comes out that the difference of the VCCT method to the J-integral is rather insensitive to load increasing, especially when the traction >40% of yield stress, however, the deviation of the VCCT and J-integral results are within 10%, suggesting that one may use the VCCT for plastic cracked specimen analysis. The computations show that the EDT provides the same values for the monotonic as the J-integral if the plastic deformations are not large, but for high plastic loading the EDT overestimates the fracture energy. For cyclic loading case, VCCT method offers closer results as the elastic analytical results, also suggesting that the whole plastic dissipated energy in the loading process should be integrated. While EDT method gives the smaller results than the J-integral because of the energy dissipated in the unloading phase is considered in the loading process.

Two-parameter characterization of elastic–plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J–Q two-parameter characterization of elastic–plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic–plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c=0.2, 1.0 and relative depths a/t=0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J–Q two-parameter approach was then used in characterizing the elastic–plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. It is found that the J–Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis. These results are suitable for elastic–plastic fracture mechanics analysis of surface cracked plates.

Approximate J Estimates for Circumferential Cracks in between Elbows and Attached Pipes

The present work proposes a method for elastic-plastic fracture mechanics analysis of the circumferential through-wall crack in between elbows and attached straight pipes, subject to in-plane bending. Based on small strain finite element limit analyses, closed-form limit load solutions are given first. Then applicability of the reference stress based method to approximately estimate J is proposed. One interesting finding is that a popular approach to assume that the crack locates in the straight pipe could lead to significantly different assessment results.

Elastic–plastic fracture mechanics analyses of circumferential through-wall cracks between elbows and pipes

The present work proposes a method for elastic–plastic fracture mechanics analysis of the circumferential through-wall crack in weldment joining elbows and attached straight pipes, subject to in-plane bending. Heterogeneous nature of weldment is not explicitly considered and thus, the proposed method assumes cracks in homogeneous materials. Based on small strain finite element limit analyses using elastic–perfectly plastic materials, closed-form limit loads for circumferential through-wall cracks between elbows and straight pipes under bending are given. Then applicability of the reference stress-based method to approximately estimate J and crack opening displacement (COD) is evaluated. It was found that the limit moments for circumferential cracks between elbows and attached straight pipes can be much lower than those for cracks in straight pipes, particularly for a crack length of less than 30% of the circumference; this result is of great interest in practical cases. This result implies that, if one assumes that the crack locates in the straight pipe, limit moments could be overestimated significantly, and accordingly, reference stress-based J and COD could be significantly overestimated. For the leak-before-break analysis, accurate J and COD estimation equations based on the reference stress approach are proposed.

Elastic‐plastic fracture mechanics assessment for steam generator tubes with through‐wall cracks

ABSTRACTSThe present work provides an elastic‐plastic fracture mechanics (EPFM) assessment scheme for a steam generator tube with a through‐wall crack under internal pressure. Noting that the geometry and material are rather uniform for steam generator tubes, and furthermore the only loading to be considered is internal pressure, an engineering EPFM analysis method is proposed to assess through‐wall cracks in steam generator tubes. Important outcomes of the present work are closed‐form approximations for J and crack opening displacement (COD). Sufficient confidence in the proposed J and COD estimates is gained from good agreements with the finite element results over a wide range of the crack length and pressure magnitude. Another important element of the EPFM assessment is to determine relevant J‐resistance curve for steam generator tubes. To improve the accuracy of predicting tube failure, the present paper also proposes a new method to determine fracture toughness using an actual tubular specimen instead of using a standard specimen, from which J‐resistance curves of steam generator tubes are obtained. Using the proposed J and toughness estimates, maximum pressures of steam generator tubes with through‐wall crack are estimated based on EPFM analysis, which is compared with experimental results and predicted ones based on limit load approach.