Effect of thickness on fracture criterion in general yielding fracture mechanics

In this research work, the effect of thickness on fracture criterion is studied for extra deep drawn (EDD) steel sheets. Experimental results are generated on fracture toughness of EDD steel sheets using compact tension specimens and a ‘maximum load’ as a fracture criterion. Critical crack tip opening displacement (CTOD) is found with the help of three methods: plastic hinge model (PHM), crack flank opening angle (CFOA) and finite element model (FEM). The fracture toughness is found to increase with increase in thickness of specimens. The fracture behaviour exhibited characteristics of general yielding fracture mechanics.     

Crack tip opening displacement in micro-cracked concrete by an embedded optical fiber sensor

Crack tip opening displacement (CTOD) is an important parameter that is often employed in characterization of fracture in engineering materials. Due to inherent difficulties in direct determination of CTOD, the crack mouth opening displacement (CMOD) has been measured during fracture tests of concrete beams and then related to CTOD. Analytical schemes are used for the determination of CTOD from the measured crack mouth opening displacements, which leads to the determination of other fracture parameters of importance. The research presented here describes development of an experimental technique for direct determination of CTOD based on embedded fiber optic sensors. The transduction mechanism is based on the correlation between the applied strain and the light intensity variation of speckle patterns generated at the output end of the multimode optical fiber due to mode redistribution.The measured displacements, CTOD, and CMOD, are compared and the validity of analytical schemes in estimation of CTOD is evaluated.     

Further developments in <Emphasis Type="Italic">J</Emphasis> evaluation procedure for growing cracks based on LLD and CMOD data

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ _p ) and CMOD (V _p ) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.     

A new approach for ctod evaluation in slow crack growth situations

In ductile materials slow crack growth often follows crack initiation, and the R-curve analysis characterizes both the crack initiation and crack growth behaviour of a material. The existing standards determine the crack tip opening displacement (CTOD) from the total clip gauge output by separating it into elastic and plastic components. The present work outlines the need for further separation of the plastic part of CMOD into the displacements due to slow crack growth and true plastic yielding. While the CTOD values for the elastic and true plastic yielding parts may be inferred according to the present methods, a new and simplified approach is proposed to infer crack growth CTOD from the corresponding displacement. The crack growth displacements may be obtained by using unloading compliance variation with crack growth. The present work is conducted on two materials, namely a steel and a 7004 grade aluminium alloy. The crack growth displacement in aluminium is found to be three times that in steel for a given crack growth. Geometrical as well as analytical comparison between the CTOD values obtained by the standard method and the proposed method is made. The comparison reveals that the existing method overestimates the CTOD value as reported by others. However, as the crack growth continues, the difference in CTOD values is found to diminish.     

Process zone analysis for the single-edge notched specimen: Part II. Process zone growth and crack propagation

Process zone growth and crack propagation in the single-edge notched (SEN) specimen are studied using the relations among applied load, notional crack and process zone lengths, and crack opening displacement derived in the first part of this work [1]. Process zone growth is simulated by increasing the notional crack length while keeping the traction-free crack length constant. A model for crack propagation based on either critical crack tip opening displacement (CTOD) or critical process zone length, as criteria for traction-free crack extension is proposed. The influence of closing pressure distribution, initial traction-free crack length, and crack extension criterion on the behavior of load vs. CMOD curves is discussed. The present model can be used to model load-deformation behavior from initial loading through softening to failure of nonlinear materials, as is verified by comparing the theoretical and experimentally determined load vs. crack mouth opening (CMOD) curves for concrete beams.     

Composite crack profile model for CTOD determination III: An experimental application to elastic-plastic crack growth situations

A composite crack profile (CCP) model has been applied for the evaluation of CTOD in the elastic-plastic crack growth situations prevailing in a structural steel. The results have been compared with the ones obtained by conventional method (using plastic hinge model such as Wells etc.) The CTOD-Resistance Curves (δ_R-curves) have also been obtained as a function of specimen thickness, a/w ratio and the loading geometry by using the CCP model. The significance of crack initiation CTOD (δ_i) and the maximum load CTOD (δ_m) has been discussed in relation to various geometrical parameters (i.e. thickness, a/w ratio and loading geometry).     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

Plastic CTOD as fatigue crack growth characterising parameter in 2024‐T3 and 7050‐T6 aluminium alloys using DIC

The plastic range of crack tip opening displacement (CTOD) has been used for the experimental characterisation of fatigue crack growth for 2024‐T3 and 7050‐T6 aluminium alloys using digital image correlation (DIC). Analysis of a complete loading cycle allowed resolving the CTOD into elastic and plastic components. Fatigue tests were conducted on compact tension specimens with a thickness of 1 mm and a width of 20 mm at stress ratios of 0.1, 0.3 and 0.5. The range of plastic CTOD could be related linearly to da/dN independent of stress ratio for both alloys. To facilitate accurate measurements of CTOD, a method was developed for correctly locating the crack tip and a sensitivity analysis was performed to explore the effect of measurement position behind the crack tip on the CTOD. The plastic range of CTOD was demonstrated to be a suitable alternate parameter to the stress intensity factor range for characterising fatigue crack propagation. A particularly innovative aspect of the work is that the paper describes a DIC‐based technique that the authors believe gives a reliable way to determine the appropriate position to measure CTOD.     

CTOD‐R Curve Tests of API 5L X90 By SENT Specimen Using a Modified Normalization Method

A modified normalization method is presented for obtaining crack tip opening displacement (CTOD) resistance curves of single edge‐notched tension specimens. For the applied load mode, the normalization method should be based on force‐crack mouth opening displacement. A formula is proposed for C_LL(i), the core parameter used in the normalization calculation. The modified method is validated using the unloading compliance method. The study of specimen geometry shows that side‐groove depth and crack depth have significant impacts on the obtained CTOD resistance curves, and the shape of the crack front affects the determination accuracy of crack length.     

Plastic η factor solutions of homogeneous and bi-material SE(T) specimens for toughness and creep crack growth testing

Based on slip line field analysis and finite element analysis of elastic-perfectly plastic materials, plastic η factor solutions for single edge-cracked specimens in tension (SE(T)) with a wide range of crack lengths are proposed, both for homogeneous specimens and for bi-material specimens with interface cracks. Moreover, two different plastic η factor solutions are given: one based on experimental load–load line displacement records, ηVLLp , and the other based on experimental load–crack mouth opening displacement (CMOD) records, ηCMODp . Comparison with existing finite element results shows good agreement. For deep cracks (a/w > ∼0.45), the ηVLLp solutions are insensitive to the strain hardening, to the specimen length and to the specimen thickness. However, for shallower cracks (a/w < ∼0.45), the ηVLLp solutions are sensitive to the specimen thickness, to the strain hardening and to the specimen length, suggesting difficulties associated with a robust determination of J and C * integrals from experimental data. On the other hand, the ηCMODp solution is not sensitive to the crack length, to the specimen thickness, to strain hardening and to the specimen length, even for shallow cracked specimens. This suggests that the use of CMOD can provide robust J and C * estimation schemes even for shallow crack testing.     

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 σ_max. 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.     

Constraint-corrected fracture failure criterion based on CTOD/CTOA

In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson–Tvergaard–Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value.     

Effects of crack depth on elastic-plastic fracture toughness

Short crack test specimens (a/W 0.50) are frequently employed when conventional deep crack specimens are either inappropriate or impossible to obtain, for example, in testing of particular microstructures in weldments and in-service structures containing shallow surface flaws. Values of elastic-plastic fracture toughness, here characterized by the crack tip opening displacement (CTOD), are presented for square (cross-section) three-point bend specimens with a/W ratios of 0.15 and 0.50 throughout the lower-shelf and lower-transition regions. Three dimensional, finite-element analyses are employed to correlate the measured load and crack mouth opening displacement (CMOD) values to the corresponding CTOD values, thus eliminating a major source of experimental difficulty in previous studies of shallow crack specimens. In the lower-transition region, where extensive plasticity (but no ductile crack growth) precedes brittle fracture, critical CTOD values for short crack specimens are significantly larger (factor of 2–3) than the CTOD values for deep crack specimens at identical temperatures. Short crack specimens are shown to exhibit increased toughness at the initiation of ductile tearing and decreased brittle-to-ductile transition temperatures. Numerical analyses for the two a/W ratios reveal large differences in stress fields ahead of the crack tip at identical CTOD levels which verify the experimentally observed differences in critical CTOD values. Correlations of the predicted stresses with measured critical CTOD values demonstrate the limitations of single-parameter fracture mechanics (as currently developed) to characterize the response.     

Finite element analysis of crack mouth opening displacement compliance in crack length evaluation for clamped single edge tension specimens

In the unloading compliance method developed for clamped single edge tension (SE(T)) specimens, six crack mouth opening displacement (CMOD)‐based compliance equations (i.e. a/W = f(BCE′)) were proposed for the crack length evaluation without clearly clarifying the corresponding predictive accuracies. In addition, the effective elastic modulus (E_e) that reflects the actual state of stress should also be introduced in the crack length evaluation for SE(T) specimens, because the actual state of stress in the remaining ligament of the test specimen is neither plane stress (E) nor plane strain (E′). In this study, two‐dimensional (2D) plane strain and three‐dimensional (3D) finite element analyses (FEAs) are carried out to investigate predictive accuracies of the six compliance equations. In both 2D and 3D FEA, specimens with a wide range of crack lengths and geometric configurations are included. For a given specimen, the value of E_e that presents the equivalent stress state in the remaining ligament is calculated on the basis of 3D FEA data. A set of formulae for the clamped SE(T) specimen is proposed that allows to evaluate E_e from the corresponding CMOD compliance. This approach is verified using numerical data. The observations of the numerical verification suggest that the use of E_e instead of E or E′ in CMOD‐based compliance equations markedly improves the accuracy of the predicted crack length for clamped SE(T) specimens.     

温度对结构钢材裂纹尖端张开位移(CTOD)的影响分析

裂纹尖端张开位移(CTOD)与钢材的弹性模量、屈服强度、几何条件和荷载大小等因素有关.结构钢材的相关力学指标随着温度发生变化,因此温度变化也会改变CTOD的数值.从含穿透缺口无限大受拉平板的Dugdale-Barrenblett模型(D-B模型)出发,推导出了温度对裂纹尖端张开位移影响规律的基本公式,并把分析进一步扩展到含跨中裂纹的三点弯曲试样.并对带跨中裂纹的三点弯曲试样进行了有限元分析和低温试验,其结果和公式进行了对比.结果表明,CTOD值随着温度降低而减小,温度对CTOD的影响程度与裂纹尖端的塑性发展程度有关.     

A new method of crack-tip opening displacement determined based on maximum crack opening displacement

In this paper a new method is presented to determine the crack-tip opening displacement (CTOD) for the center cracked plate with uniaxial uniform tension load. The maximum crack opening displacement (MCOD) is adopted to estimate CTOD. Based on the series of calculation results by elastic–plastic finite element simulation, an explicit function expression for the CTOD versus MCOD is determined, which enables to consider the influence effects of crack geometries, plate sizes, applied loads, plane state and material properties. Hence, the presented method of CTOD determined by MCOD is suitable to any center crack finite plate of any material under uniaxial tension.     

SENSITIVITY ANALYSIS OF THE DOUBLE CLIP GAUGE METHOD

During fracture toughness testing, the stable crack growth measurement is necessary for the construction of the R-curves of J vs Δa or CTOD vs Δa. One possible measurement technique uses the Double Clip Gauge Method, which is based on the assumption that the specimen is deformed like two rigid arms that rotate around an apparent centre of rotation located in front of the crack tip. This apparent centre moves as the crack grows in a stable way, and its position can be estimated through the measurement of two crack opening displacements located at different heights. As a consequence the crack growth can be calculated. In this paper the behaviour of the equations that govern the Double Clip Gauge Method are described, and the zones of greatest sensitivity for the location of the clip gauges are determined. A sensitivity analysis of the most influential intervening variables is also made.     

Object Grating Method Application in Strain Determination on CTOD Tests

Abstract:  Standard fracture toughness tests require standard specimens with the presumption that mechanical properties are uniform in the crack growth direction. Standards for crack tip opening displacement (CTOD) fracture tests prescribe remote crack mouth opening displacement, which can lead to inadequate results in the case of heterogeneous materials properties. This paper describes the application of an object grating method (OGM) on the fracture behaviour of a heterogeneous specimen. Fracture behaviour is described by measuring deformation on the surface of a specimen, in terms of CTOD and, consequently, by strain determination. An OGM is advantageously used when measuring modified CTOD tests on two specimens with an initial crack in a macroscopic heterogeneous welded joint. Results significantly show that fracture behaviour depends on the material in the vicinity of the crack tip concerning the direction of crack propagation.     

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.     

A new approach to determination of CTOD and axis of rotation in small scale yielding situation

A theoretical model for predicting crack tip opening displacement (CTOD) in small scale yielding situation has been developed by combining the elastic solution of Muskhelishvili with Irwin's idea of notional crack. The model is used to calculate the CTOD from the displacement at the mouth of the crack, without the use of rotational factor, r. An attempt has also been made to relate the rotational factor, r with the yield strength of the material.

The above model has been used to compute CTOD values in a low alloy steel with yield strength ranging from 400–2100 MPa and the results have been compared with Wells' as well as Xiao's CTOD values. The significance of the factor m' in the K-CTOD relationship has been investigated in the light of the results observed in the present investigation.