Critical Crack Tip Opening Angle Research Articles

Experimental measurement of critical crack tip opening angle in API X65 steel using drop weight tear test specimen

Experimental measurement of critical crack tip opening angle in API X65 steel using drop weight tear test specimen

Constraint-dependent CTOA determination for stable ductile crack growth

The crack tip opening angle (CTOA) has been used as a reliable fracture toughness to characterize stable crack growth for thin-wall structures in low-constraint conditions. Recently, it is found that CTOA can also be utilized as a robust fracture parameter to describe the arrest fracture toughness for gas transmission pipelines in ductile steels. For better understanding the concept of CTOA, this paper presents a brief review on the CTOA definitions and its test methods. And then, four CTOA models are developed for determining the CTOA toughness using conventional single edge notched bend (SENB) specimens, including the load–displacement linear fit model, the logarithmic load–displacement linear fit model, the stable tearing energy model, and the J-differentiation model. Fracture test data from SENB specimens in A285 carbon steel are employed to evaluate the proposed CTOA models. The results show that these CTOA models can determine either identical or comparable critical CTOA values for stable ductile crack growth using the SENB specimens. A constraint-corrected CTOA resistance curve and a constraint-corrected critical CTOA equation are also obtained for A285 carbon steel.

Effect of accurate prediction of real-time crack tip position on dynamic crack behaviors in gas pipeline

One of the difficulties in the simulation of ductile crack propagation in the gas pipeline is the implementation of complex loading. It is difficult for traditional loading methods to accurately predict the real-time crack tip position and then update the boundary conditions accordingly, which makes the simulation results inaccurate. To solve this problem, an iterative loading method considering the prediction of crack tip position (CTPI method) is proposed in this paper. Firstly, the effectiveness of the proposed loading method is checked by comparing the results of the simulation and full-scale burst test. Secondly, the generally used uniform loading method (NGD Method), simplified iterative loading method (S-CTPI Method) and the proposed CTPI method are systematically compared for their ability to describe dynamic crack behaviors in the gas pipeline. Finally, the crack tip opening angle (CTOA) evolution histories of the full-scale pipeline under different internal pressure levels are studied. The results in this paper show that the damage model coupled with the proposed CTPI method which is based on the accurate prediction of real-time crack tip position can simulate the ductile fracture behaviors for gas pipeline well. Further analysis shows that the critical CTOA of the pipeline is independent of the internal pressure and crack velocity, which provides strong proof for the applicability of the CTOA-based arrest criterion.

Unified correlation of constraints with crack arrest toughness for high-grade pipeline steel

There is much controversy surrounding using laboratory specimens to predict the fracture behavior of high-grade pipeline steel due to their different constraints. Since there is a lack of unified parameters to quantitatively characterize the constraint effects, a model for the transformation of crack arrest toughness between different specimens and pipes has not been formed. In order to solve this problem, the evolution law of the plastic zone of the crack tip with the crack tip opening degree under different in-plane and out-of-plane constraints is explored using the finite element simulation technology. On this basis, a constraint parameter η which is based on the area APEEQ surrounded by the isoline of equivalent plastic strain εp at the crack tip is proposed. The feasibility of this parameter to characterize both in-plane and out-of-plane constraints is discussed, and a quantitative correlation model between it and the crack arrest toughness, critical crack tip opening angle (CTOAC), is established. The results show that the proposed parameter can be used to characterize the overall constraints caused by different specimens with different loading forms and geometries. The normalized arrest toughness, CTOAC/CTOAref, has a linear relationship with η1/2, and the correlation line is only related to the material. The quantitative correlation model has universal applicability for different specimens and is expected to predict the transformation of crack arrest toughness between laboratory specimens and pipelines.

A novel unified characterization parameter of in‐plane and out‐of‐plane constraints based on critical CTOA

AbstractThere is much controversy in using laboratory specimens to predict the fracture behavior of large industrial constructions because of their different constraints. Although several parameters have been proposed to characterize the constraint effect, there are still some limitations. To address this issue, a novel unified characterization parameter of constraint based on the critical crack tip opening angle (CTOAC) is defined. Firstly, the calibrated finite element technologies for simulation of static and dynamic crack are used to determine the equivalent plastic strain (εp) distribution around the crack tip and the evolution history of CTOA for specimens with different in‐plane and out‐of‐plane constraints, respectively. Secondly, the feasibility of the equivalent plastic strain at the crack tip when CTOA reaches its critical value to unified measure both in‐plane and out‐of‐plane constraints is investigated. The results indicate that the area APEEQ surrounded by the isoline of equivalent plastic strain εp can describe both in‐plane and out‐of‐plane constraints and the interaction between them. Finally, a novel constraint characterization parameter η is defined. It is found that there is a linear relationship, which depends only on the material and regardless of the selection of the εp isoline, between the normalized fracture toughness CTOAC/CTOAref and η1/2. The work in this paper is expected to realize the matching of constraints between different laboratory specimens or industrial constructions.

Evaluation of ductile tearing resistance of an interstitial free steel sheet using SENT specimens

Ductile tearing resistance of a 1 mm thick interstitial free steel sheet has been characterized using single edge notched tensile (SENT) specimens with or without fatigue precracks at quasistatic strain rates. In this study, the critical Crack Tip Opening Angle (CTOA), and also crack initiation parameters, namely the initiation energy per unit ligament area (wi), critical value for the J-integral (Jc), and critical crack tip opening displacement (δc) have been examined and compared with the corresponding parameters from the Essential Work of Fracture (EWF) method. Dependence of these parameters on specimen geometry has also been examined. The EWF paradigm has been extended to the initial mixed-constraint regime of crack extension. 3D cohesive zone modelling for flat fracture becomes reasonably successful in simulating crack growth in the SENT specimens.

Crack resistance behavior of particulate reinforced composites at various test speeds and temperatures

AbstractIn this study, the fracture behavior and characteristics of particulate‐reinforced composite materials were evaluated by performing wedge splitting tests. The crack resistance of the materials was evaluated using the crack tip opening displacement and crack tip opening angle. The composites were tested under various temperatures and test speeds. The digital image correlation method was used to analyze the strain field at the crack tip. The fracture surface under test conditions was observed using a scanning electron microscope. The test results showed that the fracture energy increased with decreasing temperature, and the crack resistance increased with increasing test speed. The crack tip opening angle is divided into an unstable region and stable region. The critical crack tip opening angle can be defined as the fracture mechanics parameter measured in a stable region. The surface strain fields obtained by digital image correlation method are distributed in the range from 1.5 % to 4.5 % at the initiation of the crack. A crack grows with dewetting phenomenon at the temperature range from 60 °C to −40 °C, and the crack propagates with fracture of ammonium perchlorate oxidizer particles at the glass transition temperature of −70 °C.

A novel method to determine critical CTOA directly by load-displacement curve

The critical Crack Tip Opening Angle (CTOAC) has been proved to be a promising parameter to characterize the crack arrest toughness of natural gas pipeline. However, the accuracy and consistency of its experimental measuring results are seriously affected by the uncertainties in locating the crack tips and the points on both crack surfaces at a certain distance behind the crack tips. Load-displacement curve is a comprehensive reflection of geometry, mechanical property and fracture behaviour of a loaded specimen. It would be highly advantageous to deduce CTOAC from load-displacement curve directly. This is exactly what this paper has done. Firstly, in order to combine the load, displacement and deformation of single edge notched bend (SENB) specimen together organically, the Martinelli-Venzi ductile fracture model is used to analyze its dynamic fracture process together with energy equilibrium theory and a correlation between CTOA and the slope of the energy-load curve is established. Secondly, based on the fact that load decreases almost linearly with the increment of displacement during steady-state crack growth, attempts have been made to regress the load-displacement curve linearly and express the slope of the energy-load curve by the linear regression equation. Thirdly, the correlation between the load-displacement curve and instantaneous CTOA is found by the bridge of energy load gradient. Finally, CTOAC can be determined by averaging the stable state CTOA values. The experiments and corresponding finite element simulations of SENB specimens with X80 pipeline steel are conducted. CTOAC results obtained by both methods are in good agreements with the theoretical ones, indicating that the method proposed in this paper is satisfactory. The CTOAC derived from the published Drop Weight Tear Test (DWTT) load-displacement curves is also consistent with the experimental results, which further proves its wide applicability in different steel grades and loading rates. The method presented in this paper can significantly improve the analysis efficiency and has great potentialities for industry application.

Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

AbstractFor many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.

Relationship between incremental J integral and crack tip opening angle in elastic plastic materials

Crack tip opening angle (CTOA) was found to be nearly a constant during stable crack propagation, and thus it is suitable for modeling stable crack growth and instability. The purpose of this paper is to shed some further lights on the physical nature of CTOA. Starting from the power available for separating crack surfaces, a crack driving force parameter was defined. Two different incremental J integrals (one is based on stress work density, and the other is based on free energy density) were proved to be consistent with this crack driving force when the integral contour shrinks to the crack tip. Taking the fracture process zone (FPZ) into consideration, a relationship between critical CTOA and crack driving force was established under steady state condition. In particular, critical CTOA was associated with the incremental J integral directly when crack grows steadily. A rudimentary verification was also provided. By dividing the fracture process into two steps (Crack grows firstly while the load keeps invariant, and then a load increment is enforced under fixed crack length), a general relation between incremental J integral and critical CTOA was then obtained. In this relation, critical CTOA was related to both the incremental J integral and the slope of incremental J resistance curves. According to this relation, three main conclusions are obtained: 1) critical CTOA was consistent with crack driving force during steady crack growth; 2) crack tunneling is one reason of the initial non-constant CTOA phase; 3) critical CTOA was insensitive to thickness when the thickness is small or large enough. In the last part, the single-edge notched bend (SENB) specimen with fully yielded ligament was discussed. Critical CTOA was only dependent upon the slope of incremental J curves in this case. This special case has proved both terms of the general relation are necessary.

Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 2 TL-Orientation

In the present paper, the two-parameter-fracture-criterion (TPFC) validity and transferability are analysed using two-dimensional (2D) elastic-plastic finite-element fracture simulations with the critical crack-tip-opening-angle (CTOA) fracture criterion and plane-strain-core concept. Fracture simulations were performed on three crack configurations: (1) middle-crack-tension, M(T), (2) single-edge-crack-tension, SE(T), and (3) single-edge crack-bend, SE(B), specimens to predict failure loads and moments. They were made of 2014-T6 (TL) aluminum alloy. Fracture test data from Orange (NASA) were only available on M(T) specimens (one-half width, w = 38–152 mm), which were all tested at cryogenic (−200 °C) temperature. The critical crack-tip-opening-angle (CTOA) and a plane-strain-core height, hc, were selected to match the failure loads on the M(T) specimens. Fracture test data on the M(T) specimens were also used to determine the two fracture parameters (KF and m). All crack configurations were analysed over a very wide range of widths (w = 19–610 mm) and initial crack-length-to-width (ci/w) ratios ranged from 0.05–0.95. The TPFC was shown to fit the M(T) test data (±5%) and the simulated fracture data fairly well (within 6.5%) for all crack configurations for net-section stresses (Sn) less than the material proportional limit (σplσ). For M(T) specimens, a simple approximation was shown to work well for Sn > σpl. Further study is needed for Sn > σpl, for the SE(T) and SE(B) specimens.

Validation of the two-parameter fracture criterion for various crack configurations made of 2014-T6 aluminum alloy using finite-element fracture simulations – Part 1 LT-Orientation

A two-parameter fracture criterion (TPFC), derived by Newman, related the linear-elastic stress intensity factor, KIe, and net-section stress, Sn, at failure with two material fracture parameters, KF and m. The objective of this work was to validate the TPFC using two-dimensional elastic–plastic finite-element analyses (FEA). The critical crack-tip-opening-angle (CTOA) fracture criterion and a plane-strain core were used to match the failure loads on middle-crack-tension, M(T), specimens made of thin-sheet 2014-T6 (LT) aluminum alloy. The same analyses were then used on other M(T), single-edge-crack-tension, SE(T), and bend, SE(B), specimens to predict failure loads and moments. Test data was not available on SE-type specimens. A wide range in specimen widths (w = 19–610 mm) were considered. The finite-element code, ZIP2D, was used to calculate critical stress-intensity factors at failure corresponding to all crack configurations for crack-length-to-width (ci/w) ratios of 0.05–0.95. The FEA results agreed very well with the TPFC predictions for net-section stresses less than the material proportional limit. Further studies are needed for net-section stresses greater than the proportional limit on both tension and bend specimens.

An analytical method to predict residual strength based on critical CTOA

An analytical method to predict residual strength based on critical crack tip opening angle (CTOA) is proposed in this paper. According to a previous study, the plastic wake profile and then the stationary crack opening profile can be considered as a kind of crack growth resistance. The core idea of the proposed method is transferring critical CTOA to stationary crack opening profile based crack growth resistance curve. M(T) and C(T) specimens are taken to validate this method. All of these predicted results have an accuracy of 4%. In addition, the proposed method has successfully predicted the residual strength of rivet stiffened panels (the accuracy is 5%) by assuming that stiffeners are only geometry constraints of simple specimens that don’t affect the crack growth resistance. It is worth stressing that no finite element analysis is used in this paper.

A simple model to explain transferability of crack tip opening angle

A stable crack growth model based on critical crack tip opening angle (CTOA) is proposed. This model considers the growing crack opening profile as corresponding stationary crack opening profile minus plastic wake profile. A relationship between CTOA and stationary crack tip opening displacement is established. Relations between CTOA and K-R curves, J integral are then obtained from this relationship and the crack growth model is thus verified. Based on this model, the transferability of CTOA is discussed by dimensional analysis. The critical CTOA is independent of initial crack size, structural size, and structural configuration for a given material and stress state if the plastic zone stress distribution is invariable. A method to predict residual strength based on a critical CTOA is proposed and rudimentary verification is performed using previously published fracture test results.

New numerical tools to calibrate the Two Curves Method using the CTOA criterion

Based on the Crack-Tip Opening Angle (CTOA) fracture criterion and the finite element method coupled with the node release technique, a New Two-Curve method (TCM) was proposed for the prediction of gas pipelines' crack arrestability. Arrest pressure, crack propagation velocity and length were predicted successfully.A modern high-toughness pipeline made in API 5L X65 pipeline steel with 19 mm wall thickness and a 355 mm external diameter was investigated. The critical CTOA (CTOAC) property was measured with a Modified Compact Tension (MCT) specimen at room temperature. A new method for evaluating the CTOAC by combining experimental load–deflection data and finite element analysis was implemented. The results of the CTOAC were compared with the available CTOAC data.The results for the New Two-Curve method were discussed and compared with those obtained by well-established methods such as Battelle-TCM, HLP and HLP-Sumitomo.

Determining critical CTOA from energy-load curves with DWTT specimen

Running ductile fracture is one of the most catastrophic accidents of pipelines for natural gas transportation. Crack arrest toughness is important for preventing crack extension to a long distance along pipeline. Critical crack tip opening angle (CTOAC) is a promising parameter for characterizing crack arrest toughness. In this study, a new method is proposed to calculate the CTOAC from the energy-load curves in an instrumented drop weight tearing test (DWTT). Numerical analyses with the Gurson damage model have been conducted to verify the proposed method. It shows that results calculated from the energy-load curves are slightly lower than the results measured from specimen surface. Results calculated from the proposed method also agree well with experimental results reported in the literature.

An experimental study of the fracture behavior of particulate reinforced composites using digital image correlation

AbstractThis study aims to investigate the fracture behavior of particulate reinforced composites to determine resistance properties. It is important to evaluate the crack propagation characteristics of the materials under various temperatures and strain rates. The tests using a wedge splitting specimen are conducted under temperatures ranging from 60 °C to −60 °C and strain rates of 5 and 50 mm/min. KI is calculated using an equation suggested by ASTM (American society for testing and materials) E399. The splitting loads and crack resistance for crack extension at various temperatures are estimated. Also, the crack tip opening angle is calculated from the crack tip opening displacement and crack extension measured via the optical method. The crack tip opening angle consists of an unstable and stable region by which the critical crack tip opening angle can be determined. In addition, digital image correlation is used to calculate the strain fields around the crack tip as well as the whole specimen.

Validation of the Two-Parameter Fracture Criterion using 3D finite-element analyses with the critical CTOA fracture criterion

A Two-Parameter Fracture Criterion (TPFC) was derived from Inglis’ elastic-stress-concentration equation for an elliptical hole under remote uniform stress and Neuber’s equation relating the plastic stress and strain concentration factors to the elastic stress-concentration factor at the maximum stress location. Elastic–plastic 3D finite-element analyses (FEA) employing the critical crack-tip-opening-angle (CTOA) fracture criterion was used to simulate fracture on thin-sheet middle-crack-tension, M(T), and compact, C(T), specimens made of 7249-T76511 aluminum alloy over a wide range in crack-length-to-width ratios to validate the TPFC. A critical CTOA (7.6°) and the fracture parameters (KF and m) were determined from M(T) test specimens, and these values were then used to predict the failure on C(T) specimens. The FEA predicted failure loads on C(T) specimens were within a few percent; whereas, the TPFC generally over predicted the failure loads (5–15%). The TPFC over prediction on the C(T) specimens is likely related to net-section stress (Sn) being greater than the yield stress of the material for all test data, while the M(T) specimens all had Sn less than the yield stress.

Evaluation of fracture toughness of thin sheet of interstitial free high strength steel through critical crack tip opening angle (CTOA $$_\mathrm{c}$$ c ) measurement

Conventional testing of fracture toughness measurement for thin metallic sheets is not possible owing to the large plastic zone ahead of the crack tip. Hence, the critical-crack tip opening angle \((\hbox {CTOA}_\mathrm{c})\) has been considered to be the key parameter to evaluate resistance of a thin sheet against stable crack propagation. In the present work, attempt has been made to measure the \(\hbox {CTOA}_\mathrm{c}\) of interstitial free high strength steel (IFHS) with 1 mm thickness using compact tension C(T) specimen. A high speed camera has been used for monitoring and imaging the progress of the crack length and crack tip angle during loading. The CTOA\(_\mathrm{c}\) measured from these photographs found to be \(12^{\circ }\,\pm \,1.5^{\circ }\). In these experiments, the crack tip velocity was also varied from 1.9 to 960 mm/min and no changes in the \(\hbox {CTOA}_\mathrm{c}\) value were observed. The high ductility of IFHS steel along with prevailing plane stress condition might be the reason of appreciably large \(\hbox {CTOA}_\mathrm{c}\) value.

Validation of the Two-Parameter Fracture Criterion using finite-element analyses with the critical CTOA fracture criterion

Elastic–plastic finite-element analyses employing the critical crack-tip-opening-angle (CTOA) fracture criterion were used to simulate fracture on thin-sheet middle-crack-tension, M(T), specimens made of several aluminum alloys over an extremely large range of widths (18–5700-mm) for a wide range in crack-length-to-width ratios. A linear relation between elastic stress-intensity factor (KIe) and net-section stress (Sn) at failure was observed for Sn less than yield stress of the material. Test data on two aluminum alloys (2024-T3 and 2219-T87) over a wide range of M(T) specimen widths (76–600-mm and 76–1200-mm, respectively) supported the linear relationship that validated the Two-Parameter Fracture Criterion.