Crack Tip Opening Displacement Values Research Articles

Finite element simulation of gaseous detonation-driven fracture in thin aluminum tube using cohesive element

Detonation-driven fracture problems in tube under dynamic load have received plenty of attention because of various ranges of applications, such as oil and gas pipeline systems, new rocket engine such as pulse detonation engine, and pressurized aircraft fuselages. This paper reports the crack growth modeling in a thin aluminum tube under gaseous detonation load. Because of three-dimensional fracture dynamics with gas dynamics coupled phenomena, analytical modeling is complicated. Thus, a finite element method was applied. The finite element modeling and simulation of the tube under detonation moving load were performed using commercial code Abaqus. This simulation leads to obtain structural response of the tube to detonation load. The simulations were compared with experimental and analytical results from the literature for elasto-dynamic response of cylindrical shells with finite length under internal detonation loading. Cohesive element with traction–separation law was used for crack growth modeling along with crack tip opening displacement value obtained from experimental–numerical analysis from previous research. The final section of the paper is dedicated to investigating differences and comparisons between the numerical crack propagation simulations and experimental results reported in the literature. It has been demonstrated that using cohesive elements with some modifications can improve the numerical accuracy. The obtained results are more similar to the experimental results than numerical results available in literature.

ELASTIC-PLASTIC FRACTURE BEHAVIOR ANALYSIS ON A GRIFFITH CRACK IN THE CYLINDRICAL THREE-PHASE COMPOSITES WITH GENERALIZED IRWIN MODEL

Elastic-plastic stress analysis on a matrix crack interacting with near-by circular inclusions (the fibers) in fiber-reinforced composites has been carried out. The crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. To more accurately study the fracture behavior of the crack, plastic zone correction is introduced first time for such a crack-inclusion interaction problem. To determine the plastic zone sizes (PZSs) at the crack tips, a generalized Irwin model is proposed for the current mixed-mode problem where the von Mises stress yielding criterion is employed. With the aid of distributed dislocation method, the physical problem is formulated into a set of singular integral equations and solved through a numerical schism. The effective stress intensity factor (SIF), the PZS, crack tip opening displacement (CTOD) are evaluated accordingly. In the numerical examples, the influence of the crack orientation angle, the fiber/matrix shear modulus ratio, and fiber volume fraction on the fracture behavior of the crack is discussed in detail. It is found that the crack orientation angle has great effect on the normalized values of PZS, CTOD, and effective SIF, while the effects of shear modulus ratio and fiber volume fraction depend highly on the conditions of the inclusion (the fiber) and matrix.

Elastic–plastic stress investigation for an arc-shaped interface crack in composite material

Abstract The plastic zone size and crack tip opening displacement have been investigated for a curved interface crack between a circular inclusion and an infinite matrix. The mixed-mode Dugdale model is used to study the plastic deformation where the stresses in the plastic zones satisfy the Von Mises yield criterion. The plastic zone size at the crack tip is calculated by satisfying the condition that the complex stress intensity factors induced by external load and those induced by closure stress cancel off. With the distributed dislocation method, the physical problem is formulated into a set of singular integral equations which are numerically solved by using Jacobi polynomials. The influence of the material properties and other geometric parameters on the stress intensity factors (SIF), plastic zone size (PZS) and crack tip opening displacement (CTOD) is discussed in detail. The numerical examples show that both the crack debonding angle and the inclusion/matrix shear modulus ratio have significant influence on the normalized values of SIF, PZS and CTOD. The normalized PZS reaches its maximum value when the crack debonding angle is 90°. The effect of shear modulus ratio is very significant when the inclusion is “softer” than the matrix. When the inclusion is much “stiffer” than the matrix, the inclusion plays a dominant role. Changing the shear modulus ratio does not have great influence on the plastic deformation ahead the crack tips.

A Zener–Stroh crack in fiber-reinforced composites with generalized Irwin plastic zone correction

Abstract Elastic–plastic stress analysis on a matrix Zener–Stroh crack interacting with nearby inclusions (the fibers) in fiber-reinforced composites has been carried out. The Zener-Stroh crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. Plastic zone correction is introduced the first time for such a crack-inclusion interaction problem so that the fracture behavior can be analyzed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed-mode loading problem where the Von Mises stress yielding criterion is employed. Different to a Griffith crack, a Zener–Stroh crack propagation always occurs from the sharp tip whose relative position to the near-by fiber has great effect on the fracture behavior of the crack. In our study, the effective stress intensity factor (SIF), plastic zone size (PZS) and crack tip opening displacement (CTOD) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fiber) shear modulus, inclusion volume fraction and the crack sharp tip position on the fracture behavior of the crack is discussed. It is found that the shear modulus ratio has great effect on the normalized values of PZS and CTOD, while the effect of fiber volume fraction depends highly on the conditions of the inclusion/matrix properties and the crack sharp tip position.

An experimental study on fatigue performance of cryogenic metallic materials for IMO type B tank

Three materials SUS304, 9% Ni steel and Al 5083-O alloy, which are considered possible candidate for International Maritime Organization (IMO) type B Cargo Containment System, were studied. Monotonic tensile, fatigue, fatigue crack growth rate and Crack Tip Opening Displacement tests were carried out at room, intermediate low (-100 oC) and cryogenic (-163 oC) temperatures. The initial yield and tensile strengths of all materials tended to increase with decreasing temperature, whereas the change in elastic modulus was not as remarkable. The largest and smallest improvement ratio of the initial yield strengths due to a temperature reduction were observed in the SUS304 and Al 5083-O alloy, respectively. The fatigue strengths of the three materials increased with decreasing temperature. The largest increase in fatigue strength was observed in the Al 5083-O alloy, whereas the 9% Ni steel sample showed the smallest increase. In the fatigue crack growth rate test, SUS304 and Al 5083-O alloy showed a decrease in the crack propagation rate, due to decrease in temperature, but no visible improvement in da/dN was observed in the case of 9% Ni steel. In the Crack Tip Opening Displacement (CTOD) test, CTOD values were converted to critical crack length for the comparison with different thickness specimens. The critical crack length tended to decrease in the case of SUS304 and increase for the Al 5083-O alloy with decreasing temperature. In case of 9% Ni steel, change of critical crack length was not observed due to temperature decrease. In addition, the changing material properties according to the temperature of the LNG tank were analyzed according to the international code for the construction and equipment of ships carrying liquefied gases in bulk (IGC code) and the rules of classifications.

Microstructural morphology effects on fracture resistance and crack tip strain distribution in Ti–6Al–4V alloy for orthopedic implants

The effects of microstructural morphology on the fracture behavior of Ti–6Al–4V ELI (extra-low impurity) alloy in two different heat treatment conditions were examined. Alloy was solution treated above (β ST) and below (α+β ST) β transus temperature followed by furnace cooling (FC) in order to obtain the fully lamellar and equiaxed microstructures. Tensile and fracture toughness tests were conducted. The crack tip opening displacement (CTOD) and strain distribution near the crack tip were measured on the compact tension (CT) specimen surface by digital stereometric method. The crack propagation resistance (CTOD-R) curves were developed by applying the modified normalization method and critical CTOD values were determined. To identify the microstructural length scale controlling the fracture resistance of this alloy, the crack propagation path and fracture surface morphology were evaluated. It was found that the reduction in the characteristic microstructural dimension of an order of magnitude and significant change in the α phase aspect ratio contribute to drastic increase in the tensile properties and decrease in the crack initiation and propagation resistance. The fully lamellar microstructure displays slightly better biocompatibility because of the lower elastic modulus and superior fracture resistance. The enhanced crack propagation resistance of this microstructure is associated with the larger propensity for crack tip tortuousity, due to the coarser microstructural dimensions (lamellar colony size vs. primary α grain size). The difference in the crack propagation modes affects the shape and size of the actual crack tip strain distribution. These results were discussed correlating the complex multiple fracture mechanisms with the stress state in two microstructures.

Simulation of stable tearing crack growth events using the cohesive zone model approach

A cohesive zone model (CZM) approach is applied to simulate Mode I and mixed-mode I/II stable tearing crack growth events in Arcan specimens made of 2024-T3 aluminum alloy. The material is treated as elastic–plastic following the J2 flow theory of plasticity, and the triangular cohesive law is employed to describe the traction-separation relation in the cohesive zone ahead of the crack front. Simulations are carried out using the 3D finite element method. CZM parameter values are chosen based on considerations of values suggested in the literature and by matching simulation predictions with experimental data of the load–crack extension curve for a Mode I stable tearing crack growth event. With the same set of CZM parameter values, simulations are performed for mixed-mode I/II stable tearing crack growth events. A good agreement is reached between simulation predictions of the load–crack extension curve and experimental results. To connect with a simulation approach based on the crack tip opening displacement (CTOD) at a fixed distance behind the current crack front, the variation of CTOD with crack extension is examined under both Mode I and Mode I/II conditions. It is found that CZM simulation predictions of the CTOD variation with crack extension agree well with experimental measurements. The results of this study suggest that CZM based simulations can predict the critical CTOD value which, in CTOD based simulations, is used as an input and is conventionally obtained from experimental measurements. The findings of the current study demonstrate the applicability of the CZM approach in mixed-mode stable tearing simulations and establish a connection between the CTOD and CZM based simulation approaches.

CTOD Evaluation for HAZ Toughness of Offshore Structure Steels with Heavy Thickness Based on API RP 2Z

The CTOD (Crack Tip Opening Displacement) evaluation and control for HAZ (Heat Affected Zone) toughness of welded joints are the most effective measures to the security of steel structures. This paper address the problem of the newly developed offshore structure steel API 2W 50Z with heavy thickness of 100mm. In accordance with the American Petroleum Institute standard Recommended Practice 2Z (API PR 2Z), the CTOD tests of two critical positions of HAZ in three kinds of heat inputs were carried out in low temperature (-10°C). All of these CTOD testing and assessments are finished under the witness of American Bureau of Shipping (ABS). The result shows that all of the CTOD values are greater than the required value (0.38mm) in API RP 2Z. This indicates that the newly developed offshore structure steel (API 2W 50Z) meet the requirement of the toughness. Further, the CTOD testing and assessments in several international standards about weld joints of steel plates are also compared and discussed in this paper.

Experimental Research on Fracture Toughness of High Grade Line Pipe

Crack tip opening displacement (CTOD) tests were carried out on different positions of X70, X80 and X100 pipe by three-point bend testing method. The results show that the crack propagation resistance and the tear modulus of base metal, heat affected zone (HAZ), and weld of X70 and X80 pipe are larger than that of X100 pipe. At the same time,The initial CTOD values and the CTOD values withmaximum load of X70 and X80 pipe are larger than that of X100 pipe.The test results suggest that the fracture toughness, crack initiation and propagation resistance of theX70 and X80 pipe are greater than that of X100 pipe, and the mechanismis analyzed finally.

Experimental Study on CTOD Fracture Toughness of Welded Joints of Low Temperature Steel

According to BS7448 fracture toughness test standard, crack tip opening displacement (CTOD) for ASTM A333 Gr.6 low temperature steel which is used in offshore platform were carried out in low temperature (0°C, -29°C). Three point bending tests were conducted on the specimens, the dimension of which is B×2B (B is the thickness) and notch direction is NP. The final value of CTOD was calculated by P-V curves of both the welds and HAZ (heat affected zone). And the experimental results were analyzed and discussed in the paper. The low temperature steel welded joints show good low temperature toughness, the selected welding procedure is applied to construction of pipelines.The CTOD value of HAZ is larger than weld metal and weld is the weakest position in the whole structure. The experiment results provide an important basis for the choice of welding method and welding process parameters, ECA assessment and construction of offshore platform.

Estimation of crack-tip-opening displacement and crack extension of glass fiber reinforced polymer mortars using digital image correlation method

Knowledge of crack-tip-opening displacement (CTOD) has a great importance for fracture criteria that are applied to numerous structural applications. The purpose of this paper is to investigate fracture behavior of chopped glass fiber reinforced polymer mortars evaluating the CTOD values and the crack extension by means of non-contact measurement method. Furthermore, the critical stress intensity factor ( K Ic) and the critical crack-tip opening displacement (CTOD c) are estimated. In order to do this, fracture test using a single-edge-cracked three-point bend specimens is performed. The experimental procedure is carried out using digital image correlation (DIC) method, which is a powerful optical-numerical method developed to determine displacement fields. These results are compared with K Ic and CTOD c achieved through Two Parameter Model (TPM) method. Overall, there is agreement between the two methods. By results, the fracture resistance to crack propagation of polymer mortars increases with the addition of glass fiber.

Experimental Study on Fracture Toughness of Q460C the High-Strength Construction Steel at Low Temperature

Three point bending tests were carried out on 14mm-thick Q460C the high-strength structural steel at low temperature, and scanning electronic microscope of the fracture appearance was analyzed. The results showed that the obvious feature of brittle mechanism was shown on the three point bending specimen fracture whose testing took place at -40°C. And the crack tip opening displacement value of Q460C steel, which was less than that of Q235 steel, Q345 steel and Q390 steel at low temperature, tended to decrease with respect to the temperature reduction. Moreover, a Boltzmann function fitting analysis was applied to the experimental data, and the ductile-brittle transition temperature and the changing regularity were obtained.

The fatigue crack growth rate and crack opening displacement in 18G2A-steel under tension

In the paper, the results of crack tip opening displacement (CTOD) and crack opening displacement (COD) in place of crack initiation as well as the fatigue crack growth rate in higher strength steel are presented. The investigation were carried out on flat specimens with central notch under constant amplitude tensile fatigue loading at stress ratio R=0.2 and different value of the stress σmax. The test results showed that with growth of crack length l grew values of the CTOD and COD. In the work, it was proposed calculation of the CTOD value on basis various dependence of plastic zone radius on crack tip.

Statistical analysis of fatigue crack growth behavior for grade B cast steel

Tests for fatigue crack growth rate (FCGR) and crack-tip opening displacement (CTOD) were performed to clarify the fatigue crack growth behavior of a railway grade B cast steel. The threshold values of this steel with specific survival probabilities are evaluated, in which the mean value is 8.3516 MPa m 1/2, very similar to the experimental value, about 8.7279 MPa m 1/2. Under the conditions of plane strain and small-scale yielding, the values of fracture toughness for this steel with specific survival probabilities are converted from the corresponding critical CTOD values, in which the mean value is about 138.4256 MPa m 1/2. In consideration of the inherent variability of crack growth rates, six statistical models are proposed to represent the probabilistic FCGR curves of this steel in entire crack propagation region from the viewpoints of statistical evaluation on the number of cycles at a given crack size and the crack growth rate at a given stress intensity factor range, stochastic characteristic of crack growth as well as statistical analysis of coefficient and exponent in FCGR power law equation. Based on the model adequacy checking, result shows that all models are basically in good agreement with test data. Although the probabilistic damage-tolerant design based on some models may involve a certain amount of risk in stable crack propagation region, they just accord with the fact that the dispersion degree of test data in this region is relatively smaller.

Difference between ASTM E1290 and BS 7448 CTOD Estimation Procedures

Since the British Standards Institution (BSI) standardized BS 5762 in 1979, a popular way of calculating the Crack Tip Opening Displacement (CTOD) has been the use of the plastic hinge model with an assumed rotational centre. The American Society for Testing and Materials (ASTM) previously accepted the plastic hinge model and standardized E1290 in 1989. However, ASTM revised E1290 in 2002, and has proposed a fracture parameter conversion from the J-integral to CTOD. These two different CTOD calculations probably lead to confusion for Fitness-for-Service (FFS). The Fracture Toughness Study Committee of the Japan Welding Engineering Society (JWES) organized a working group, and the effects of CTOD testing methodology on CTOD values were investigated. In this paper, the results of CTOD round-robin tests in the working group are summarized, and the difference between the critical CTOD values obtained by ASTM E1290–02 and those by BS 7448, which involves the plastic hinge model, is described.

Research on low temperature CTOD toughness for welded joints of the module stool of an FPSO

The module stool is a key structure to link the module and the deck in floating production, storage and off-loading (FPSO). The welded joints of the module stool should be guaranteed to possess enough toughness against cracking and rupture. Based on the international standard BS 7448 and DNV-OS-C401, a low temperature (−18°C) crack tip opening displacement (CTOD) test has been conducted on the weld centre and the fusion line of the module stool of a 300 kt FPSO, to be used in the Bohai PL19-3 offshore oil field. The results show that the CTOD values of the specimens of the module stools whose crack tips are located in the weld centre and the fusion lines, respectively (welded with preliminary welding procedure specification), meet the requirements of DNV-OS-C401 (not less than 0.150 mm). Therefore, the preliminary welding procedure specification test can be used to weld the module stool for which no further heat treatment is needed. Accordingly, the quality of the module stools is assured, the fabrication efficiency is improved and the production cost is reduced.

Comparison of CTOD standards: BS 7448-Part 1 and revised ASTM E1290

Crack tip opening displacement (CTOD) has been calculated using the plastic hinge model with an assumed rotational center since the British Standards Institution (BS) standardized BS5762 in 1979. The American Society for Testing and Materials (ASTM) accepted the plastic hinge model and standardized E1290 in 1989. However, ASTM revised E1290 in 2002, and has proposed a conversion from J to CTOD. CTOD-based fracture toughness evaluation has been widely used for the defect assessment of many welded structural components, and two different CTOD calculations could lead to confusion for Fitness-for-Service. In this study, the effects of CTOD testing methodologies on CTOD values were investigated according to round robin tests conducted by the Japan Welding Engineering Society (WES), and the concept of CTOD as a fracture parameter is discussed.

Elastic-Plastic Finite-Element Analyses of Compression Precracking and Its Influence on Subsequent Fatigue-Crack Growth

Abstract Compression precracking has been used in a renewed effort to generate fatigue-crack growth rates in the threshold and near-threshold regimes, as an alternative to the traditional load-reduction procedure. But concerns have been expressed on the influence of tensile residual stresses resulting from compressive yielding at the crack-starter notch. This paper uses elastic-plastic, finite-element analyses to study the influence of the tensile residual stresses induced by compression precracking on simulated crack growth under constant-amplitude loading. High-fidelity finite-element models (60 000 to 160 000 DOF) using two-dimensional plane-stress analyses were used to model plastic yielding during compressive loading and simulated fatigue-crack growth through the tensile residual-stress field. The finite-element code was ZIP2D and the course mesh had an element size of 2 μm. A refined mesh had an element size four times smaller (0.5 μm) than the course mesh. Fatigue-crack growth and crack-closure effects were simulated over a wide range in stress ratios (R=0 to 0.8) and load levels, after compression precracking. The crack-tip-opening displacement (CTOD) concept was used to judge the extent of the influence on the tensile residual stresses and the stabilization of the crack-opening loads. It was found that the tensile residual stress field decayed as the crack grew under cyclic loading. Once the crack had reached one compressive plastic-zone size, the tensile residual-stress field had dissipated. However, the stabilization of the crack-opening loads and merging of the CTOD values with and without compression precracking was found to be about 1.5 to 2 times the compressive plastic-zone size at R=0 loading. The effects dissipated at smaller distances from the notch tip for the higher stress ratios. The present results have validated the crack-extension criterion that had been proposed for use in the compressive precracking threshold test method, beyond which, cracks are growing under constant-amplitude (steady-state) behavior.

Three-Dimensional Crack Growth in Ductile Materials: Effect of Stress Constraint on Crack Tunneling

Crack tunneling is a crack growth feature often seen in stable tearing crack growth tests on specimens made of ductile materials and containing through-thickness cracks with initially straight crack fronts. As a specimen is loaded monotonically, the midsection of the crack front will advance first, which will be followed by crack growth along the rest of the crack front, leading to the formation of a thumbnail shaped crack-front profile. From the viewpoint of fracture mechanics, crack tunneling will occur if the operating fracture criterion is met first in the midsection of the crack front, which may be due to a higher fracture driving force and∕or a lower fracture toughness in the midsection. A proper understanding of this fracture behavior is important to the development of a three-dimensional fracture criterion for general stable tearing crack growth in ductile materials. In this paper, the phenomenon of crack tunneling during stable tearing crack growth in a single-edge crack specimen is investigated by considering the effect of stress constraint on the fracture toughness. Crack growth in the specimen under nominally Mode I loading conditions is considered. In this case, crack tunneling occurs while the initially flat crack surface (which is normal to the specimen’s lateral surfaces) evolves into a final slanted fracture surface. A mixed-mode crack tip opening displacement (CTOD) fracture criterion and a custom three-dimensional (3D) fracture simulation code, CRACK3D, are used to analyze the crack tunneling event (but not crack slanting) in the specimen. Results of this investigation suggest that the critical CTOD value (which is the fracture toughness) has a clear dependence on the crack-front stress constraint Am (the constraint measure in this work is the stress triaxiality, which is the ratio of the mean normal stress to the von Mises effective stress). For simplicity, this dependence can be approximated by a straight line within the range of stress constraint values found, with the toughness decreasing as the constraint increases. It is found that crack tunneling in this case is mainly the result of a higher stress constraint (hence a lower fracture toughness) in the midsection of the crack front. Details of the crack growth simulation and other findings of this study will also be presented.

Determination of Fracture Toughness of Underfill/Chip Interface With Digital Image Speckle Correlation Technique

The layered packages are prone to multimode damages and failures when they are subjected to complicated and coupling environmental loading. As a result, fracture toughness is usually used as a fracture criterion to evaluate the reliability of polymer/inorganic interface. In this study, an in-situ/real-time micro-digital image speckle correlation (mu-DiSC) system was established and employed to determine the fracture toughness of underfill/chip interface involved in flip chip assembly. The tests were carried out over a wide range of temperatures and at various loading angles. In order to verify the finding of the mu-DiSC technique, an interface fracture mechanics based finite element model is implemented into ANSYS to calculate the values of crack-tip opening displacement of underfill/chip joint under different loading configurations. The results obtained from the simulation are found to be in good agreement with those measured by the mu-DiSC system, indicating that the system can be used as an accurate and effective experimental tool for the electronic packages. The fractographs, with respect to different temperatures and loading angles, are further discussed