Failure Assessment Curve Research Articles

A Probabilistic Fatigue Assessment Diagram To Get A Guaranteed Lifetime With A Low Probability Of Failure

In order to guarantee a fatigue lifetime with a conventional and low probability of failure, a probabilistic fatigue assessment diagram is proposed as a tool. The safe domain is limited by the fatigue failure assessment curve, which depends on material properties through Basquin's exponent, endurance limit and low cycle fatigue domain. From the double-truncated distribution of the targeted maximum applied stress, it is possible to find the failure probability and its associated safety factor. An example of an aeronautical component made of TA6V titanium alloy welded by laser and exhibiting an undercut at the weld toe is given.

Use of the Failure Assessment Diagram to Evaluate the Safety of the Reactor Pressure Vessel

Analysis of multiple failure modes is the key element of the integrity evaluation of the nuclear reactor pressure vessel (RPV). While the simple single-criterion failure code provides the guidance for structural integrity, the guidance ignores the interaction between fast fracture and plastic collapse. In this paper, the differences between the reserve factor (RF) in the R6 two-criteria failure procedure and the safety coefficient (SC) in the single-criterion failure code were compared. Based on 3D finite element (FE) analyses, the option 3 failure assessment diagram (FAD) of the beltline of the RPV was established according to the R6 basic route and alternative approaches, respectively. Also, the nonconservation of the secondary stress correction parameter ρ was reviewed. In this paper, it was shown that the effect of crack sizes on the FAD is considered to be limited, and the influence of the thermal stress on the FAD is obvious in the transition region of the failure assessment curve (FAC). The FAD only considering the mechanical load encloses the FAD considering the thermal–mechanical load for the Lr smaller than 1, but it is contrary when the Lr is bigger than 1. It is not enough to just satisfy the requirement in the IWB-3612 of the ASME code because the risk of plastic-collapse failure is ignored. And in this study, the maximum nonconservation of the fracture toughness RF is more than 7% due to the approximate value of ρ. Accordingly, the accurate method in the R6 procedure should be used in the integrity assessment of the RPV under the faulted transient.

Elastic-plastic failure assessment of cold worked stainless steel pipes

The change in fracture strength due to cold working was investigated for cracked stainless steel pipes. The cold working was introduced into Type 316 stainless steel plates. Then, material properties were identified in order to make elastic–plastic fracture assessments for a pipe with a circumferential crack under bending load. The two-parameter method was employed for deriving fracture strength considering the change in the flow stress (yield and ultimate strengths), fracture toughness and stress–strain curve caused by the cold working. It was found that the fracture strength was not reduced even if 40% cold working was introduced, while the failure mode was altered from the plastic collapse mode to the elastic–plastic failure mode. Although cold working decreased the fracture toughness, the change in the stress–strain curve reduced the driving force for fracture (J-integral) and increased the fracture strength. It was shown that the failure assessment curve of cold worked material can be derived using the yield and ultimate strengths of the material that is free of cold working.

The Strain-Based Failure Assessment Diagram for Commercially Pure Titanium TA2

Strain-based failure assessment methods have been usually used in recent years to propose the fitness-for-service flaws. In this paper, the stress-based and strain-based failure assessment diagram (SB-FAD) approaches were reviewed firstly. Then, SB-FAD approach was used to the material commercially pure titanium TA2 with high strain-hardening coefficient. Several failure assessment curves obtained from strain-based method for four typical specimens, i.e., CCP (center-cracked plate), DECP (double edge cracked plate), SECP (single edge cracked plate) and CT (compact tension) were proposed. It was found that the geometries and crack sizes had obvious effects on the failure assessment curves. By comparing with the stress-based failure assessment curves, the traditional strain-based failure assessment curves could lead to more conservatism in the stage after yielding. However, the SB-FAD modified by Ainsworth can be used.

A Probabilistic Safety Assessment Method Based on Latin Hypercube Sampling Method

Based on the shortcomings of traditional probabilistic assessment methods, an improved probabilistic safety assessment method was proposed, which used Latin hypercube sampling, considered the change process about fatigue crack propagation, as well as the effect of random variables on the failure assessment curve. The paper also analyzed the specific example with this method. The results showed that this method was simpler and more effective, which had some value of applications in engineering.

A deformation limit based on failure assessment diagram for fatigue-cracked X-joints under in-plane bending

This study develops a deformation limit based on the failure assessment diagram (FAD) for fatigue-cracked circular hollow section (CHS) X-joints subjected to brace in-plane bending. The proposed approach calibrates against two reported experimental tests on CHS X-joints. The subsequent numerical study considers CHS X-joints with two different brace-to-chord intersection angles. The parametric study focuses on both the material toughness level and the geometric parameters. The proposed, dimensionless deformation limit covers a wide range of material fracture-toughness and geometric parameters. The option 1 and option 3 failure assessment curves provide consistent deformation limits compared to the toughness-based deformation limits proposed in a previous study. The lower bound deformation limit exhibits an approximately linear relationship with respect to the crack-depth ratio for X-joints with different brace-to-chord intersection angles. The extrapolated deformation level at a zero crack-depth ratio represents a conservative estimation on the deformation level for intact joints.

Application of the Failure Assessment Method for Cracked Pipeline

A new failure assessment curve of pipeline containing crack is provided in this paper. The new failure assessment curve is based on the J integral calculation method of the effective remote stress, and it is as simple as the R6 option 2. The result of the new failure assessment curve is as accurate as the result of the curve based on strict J integral. Moreover, the new failure assessment curve could be used for any stress-strain relationship material, including Ramborg-Osgood (R-O) material and non-R-O materials under monotonic increasing loading, such as long plastic yield plateau steel. The new failure assessment curve is applied to a case that came from the three pipes burst in a proof test of an oil pipeline. Comparison with the result in the proof test shows the result of the new failure curve presented in this paper is accurate.

Experiment, Finite Element Analysis and EPRI Solution for J-integral of Commercially Pure Titanium

Abstract In this paper, the J -integral of commercially pure titanium (CP Ti) for standard compact tensile (CT) specimen was obtained by four methods containing fracture experiment, two-dimensional (2-D) finite element analysis (FEA), three-dimensional (3-D) FEA, and the calculation formula in electric power research institute (EPRI). Although the J -integral obtained by EPRI solution is consistent with that by 2-D FEA, they are lower than the result of the experiment. Moreover, the J -integral obtained by 3-D FEA is more close to that of the experiment. In order to improve the prediction accuracy of J -integral by EPRI solution, the improved EPRI solution was developed based on 3-D FEA and verified by the experiment. In addition, two failure assessment curves (FACs) of CP Ti corresponding to traditional EPRI solution and the improved one were compared with the experimental results, which indicates that the improved EPRI solution not only improve the prediction accuracy of J -integral, but also increases the reliability of FAC.

Non-probabilistic defect assessment for structures with cracks based on interval model

Traditional defect assessment methods conservatively treat uncertainty of parameters as safety factors, while the probabilistic method is based on the clear understanding of detailed statistical information of parameters. In this paper, the non-probabilistic approach is introduced to the failure assessment diagram (FAD) to propose a non-probabilistic defect assessment method for structures with cracks. This novel defect assessment method contains three critical processes: establishment of the interval failure assessment curve (IFAC), determination of the assessment rectangle, and solution of the non-probabilistic reliability degree. Based on the interval theory, uncertain parameters such as crack sizes, material properties and loads are considered as interval variables. As a result, the failure assessment curve (FAC) will vary in a certain range, which is defined as IFAC. And the assessment point will vary within a rectangle zone which is defined as an assessment rectangle. Based on the interval model, the establishment of IFAC and the determination of the assessment rectangle are presented. Then according to the interval possibility degree method, the non-probabilistic reliability degree of IFAC can be determined. Meanwhile, in order to clearly introduce the non-probabilistic defect assessment method, a numerical example for the assessment of a pipe with crack is given. In addition, the assessment result of the proposed method is compared with that of the traditional probabilistic method, which confirms that this non-probabilistic defect assessment can reasonably resolve the practical problem with interval variables.

The Probabilistic Safety Assessment of the Rail Mounted Gantry Cranes

The technology of PSA(probabilistic safety assessment) based on fracture mechanics has been applied on the engineering field. However therere few application on the port machines still with some problems. A comprehensive discuss on PSA method was presented in this paper. Firstly, the experiment of the fracture mechanics parameters of Q345 steel used on the port machines structures was made to provide the parameters for PSA. Secondly, probabilistic analysis with the series of the Q345 steels FAC(Failure Assessment Curve) provides the PSA criterion. By using stress analysis, defect detection and material properties, the structures safety of a RMG(Rail Mounted Gantry) of one port in service were assessed, the result show that the key points of the crane are safe in one point service. The technology presented in this paper will be significant for the operation and management of the port equipment.

Failure assessment diagrams for circular hollow section X- and K-joints

This paper reports the failure assessment curves for semi-elliptical surface cracks located at hot-spot positions in the circular hollow section X- and K-joints. The failure assessment curves derive from the square root of the ratio between the linear–elastic and the elastic–plastic energy release rates, computed from the domain-integral approach. This study examines both the material and geometric dependence of the failure assessment curves. The area reduction factor, used in defining the strength of the cracked joints, imposes a significant effect on the computed failure assessment curve. The failure assessment curves indicate negligible variations with respect to the crack-front locations and the material yield strength. The crack depth ratio exerts a stronger effect on the computed failure assessment curve than does the crack aspect ratio. This study proposes a parametric expression for the failure assessment curves based on the geometric parameters for surface cracks in circular hollow section X- and K-joints.

Elastic-Plastic Fracture Assessment for the Cracks Emanating from a Circular Hole under a Biaxial Loading Condition

In this study, elastic-plastic stress and strain fields were analyzed on hole-edge cracks in an aluminum alloy plate under the biaxial load. And the effects of the load parallel to the crack face on failure parameters were discussed. By quantifying the effects of the crack size and the loading mode on the crack propagation driving force, J integral, and the plastic limit load, the corresponding failure assessment curves of the hole-edge cracked plate were established with the new R6 failure assessment diagram (FAD) method. The result shows that the transverse load has a larger effect on the failure assessment curve than crack length does, the safety zone of the failure assessment diagram gradually becomes smaller while transverse loading stress changes from tensile condition to compressed. Especially, when the transverse load acts as pressure, the Option 3 failure assessment diagram results to a smaller safety zone than the Option 1 failure assessment diagram does.

Predictions of elastic–plastic crack driving force and redistribution under combined primary and secondary stresses – Part 1: Analytical investigation

Many engineering components, particularly those containing weldments, may enter service with or develop small crack-like defects. In non-stress-relieved welds, or under thermal stresses, such defects will experience both primary and secondary stresses combined. This paper describes a new function, g, that has been introduced to detail the plasticity interaction under combined loading within structural integrity assessment methods. This function has been based on the Option 2 failure assessment curve in the R6 approach to structural integrity assessment and has been determined from finite element analyses of an externally cracked cylinder under combined primary and secondary loadings. The g function method has been used in the assessment of a series of other cracked geometries subject to loadings which include secondary stresses arising from both thermal gradients and weld residual stresses. The results presented show that the g approach can successfully be extended to the assessment of these other geometries and loading combinations and provides reasonably accurate and less conservative assessments than existing methods presented in R6. A second paper, “Part 2: Experimental Application”, compares the application of the g approach with data from experiments performed over a range of plasticity development.

Ductile tearing assessment of high-strength steel X-joints under in-plane bending

This study reports an experimental investigation of a fatigue-cracked, pre-notched circular hollow section X-joints fabricated from high strength steels (with the yield strength higher than 800MPa) subjected to brace in-plane bending. The circular hollow section X-joint entails a prefabricated V-notch near the weld toe at the crown position. The experimental procedure applies a fatigue pre-cracking cyclic load followed by a monotonic brace in-plane bending, which leads to brittle through-thickness crack propagation after some amount of ductile tearing. The ductile tearing assessment, integrating the fracture resistance curve obtained from the small-scale fracture specimens and the crack extension in the large-scale tubular joint, predicts closely the load level at which unstable crack extension takes place. The generic level 2A curve outlined in the BS7910 provides an un-conservative estimate on the failure load of the X-joint specimen. The parametric numerical investigation reveals that the strength definition for the cracked joints imposes a significant effect on the shape of the failure assessment curve.

Effects of Initial Crack Location on Failure Assessment Curves in Dissimilar Metal Weld Joints in Nuclear Power Plants

Based on detailed three-dimensional finite element analyses, accurate, option 3, failure assessment curves (FACs) based on the R6 are constructed for a dissimilar metal weld joint (DMWJ) connecting the safe end to the pipe-nozzle of a reactor pressure vessel. The effects of initial crack location in the DMWJ structure on FACs are investigated. The results show that the plastic collapse of the DMWJ structure and the limit moment ML is mainly dominated by the plastic yield of the 316L material with lowest yield stress, and the crack locations in the DMWJ structure have less effect on the ML. When the load ratio Lr is less than 0.8, the crack locations have almost no effect on the FACs; while after the Lr is larger than 0.8, the crack locations have significant effect on the FACs. With the crack location moving from the safe end through the DMWJ toward the thickness transition in the pipe-nozzle, the FACs shift upward, which leads to a enlargement of the safe region in the failure assessment diagrams (FADs). This is mainly caused by the different properties of the materials in the DMWJ structure. To accurately assess the integrity of the DMWJ structure, the R6 option 3 FACs based on three-dimensional finite element analyses should be constructed and used for the cracks with different positions.

Reliability Assessment on Pipeline with Axial Surface Crack

Stress constraints have a significant impact on the stress-strain fields of the crack front. In this paper, the weight function method is used to calculate the stress intensity factor K and constraint parameter T-stress at the crack front of pressure pipeline with a axial semi-elliptical surface crack. Based on the R6 procedure and considering the influence of stress constraint on fracture toughness, a modified failure assessment curve(FAC) and a computational formula are proposed to predict the fracture probability. In the end, a typical numerical example is presented to illustrate the proposed methodology and analyze the influences of crack geometry and axial stress on the failure probability of pipeline,where the crack size, material property parameter and load follow certain probability distribution.

Fracture Analysis Procedure for Cast Austenitic Stainless Steel Pipes with an Axial Surface Crack

Since the ductility of cast austenitic stainless steel pipes decreases due to thermal aging embrittlement after long term operation, not only plastic collapse failure but also unstable ductile crack propagation (elastic-plastic failure) should be taken into account for the structural integrity assessment of cracked pipes. In the fitness-for-service code of the Japan Society of Mechanical Engineers (JSME), Z-factor is used to incorporate the reduction in failure load due to elastic-plastic failure. However, the JSME code does not provide the Z-factor for axial cracks. In this study, Z-factor for axial cracks in aged cast austenitic stainless steel pipes was derived. Furthermore, an optimized failure assessment curve (FAC) for the two-parameter method, which can also derive elastic-plastic failure load, was obtained. Then, a comparison was made for the elastic-plastic failure load obtained from different analysis procedures. It was shown that the optimized FAC as well as the obtained Z-factor could derive reasonable elastic-plastic failure loads, although the failure loads were more conservative than those obtained by the two-parameter method using FAC obtained J-value solutions. The reference stress method was found to be applicable to evaluation of the FAC. It was concluded that elastic-plastic failure loads could be derived by the Z-factor and two-parameter methods in which FAC was obtained using J-value solutions, the optimized curve and the reference stress method.

Crack Size Tolerance of Under-Matched Joints of Hull Steel with Different Weld Toughness

In order to investigate the safety performance of welding structure of 10CrNi3MoV hull steel, with the application of FAD method provided by SINTAP, this paper made safety assessment for 2 joints with the same yield stress under-matching ratio but different weld toughness. Based on tensile test and CTOD test results, assessment was carried out. Several different sizes (2a) of weld central crack were given. Then the crack size tolerance for each joint can be found. Through relative analysis, a few conclusions were gained. As long as the assessment level is selected, FAD shape changed little. Weld toughness influenced weakly on a joint’s resistance to plastic instability, but significantly on its anti-brittle capacity. The higher weld toughness is, the more likely assessment point located within failure assessment curve, i.e. the safety performance is correspondingly better.

Reference stress method for evaluation of failure assessment curve of cracked pipes in nuclear power plants

In order to obtain a precise failure assessment curve (FAC) in the R6 defect assessment procedure, it is necessary to evaluate the J-value of cracked components. The reference stress method can be used for estimating J-values. However, the accuracy of estimation depends on the limit load used for evaluating the reference stress. In this study, the applicability of several limit load solutions was investigated through comparison with the results of elastic-plastic finite element analyses (FEA). A pipe containing a circumferential surface crack was analyzed under pure bending load. Six materials used in nuclear power plants were assumed. It was shown that the reference stress method is valid for FAC evaluation. The maximum non-conservativeness caused by using the reference stress method is less than 20% compared to the results obtained by FEA.

参照応力J積分簡易解析法の破壊評価曲線評価への適用性の検討

In the rules on fitness-for-service for nuclear power plants of the Japan society of mechanical engineers (JSME), the two-parameter approach is prescribed for failure assessment of defects. In JSME rule, the failure assessment curve (FAC) for the two-parameter approach has to be determined using J-integral value when existing FAC is not available. The reference stress method can estimate J-integral value using stress-strain relation of the material. However, the accuracy of estimation depends on the limit load used for an evaluation of the reference stress. In this study, applicability of several limit load solutions was investigated by comparing with results of elastic-plastic finite element analyses. Pipes containing axial or circumferential flaw were analyzed under internal pressure or bending load. Appropriate limit load solutions were suggested for evaluation of FAC, based on analyses of 2880 cases for different flaw and pipe geometries and materials used in nuclear power plants.