A study of stable crack growth using experimental methods,finite elements and fractography

Systematic analysis of the in-plane constraint influence on J-resistance curves is presented. J_R curves were also recorded and analyzed beyond the limits of crack extension inside which the stress field can be assumed to be dominated by J-integral. Three steels and four types of specimen: SEN(B), SEN(T), CCT and DENT have been tested. Along with the J_R curves the fracture mechanisms have been analyzed with the help of scanning microscopy. The numerical, finite element analysis has been adopted to compute the Q-stresses, as a measure of the in-plane constraint prior to the onset of crack growth. The analysis of the stress field in front of the crack has been performed to check whether the state of stress prior to the crack growth can predetermine the way the crack will grow. It turns out that characteristic features in the J_R curves runs can be predicted qualitatively from the Q(a/W) and Q(J) curves. However, there is a good correlation between Q-stress and voids diameters on fractured surfaces. Several patterns in J_R curves runs have been observed for tested specimens; e.g. no influence of specimen thickness on J_R curves runs was observed for side-grooved specimens. Strong influence of specimen thickness on J_R curve shape was observed for non-side-grooved specimens. J_R curve run higher for thinner specimens unless they are dominated by plane stress. For bent specimens J_R curves run higher for shorter cracks but they run lower for specimens in tension.     

A finite element analysis of stable crack growth in an aluminium alloy

Extensive stable cracking has been observed in large test pieces of 25 mm thick weldable AlMgZn alloy which is used in the construction of a portable bridge. Standard fracture specimens produced valid K_IC values, with short cracks exhibiting unstable fracture. Finite element analysis of the large specimens determined a valid J_R-curve that can increase the effective K_C by several times the K_IC value. The R-curve has an unusual ‘concave’ shape that is associated with the change from initially flat fracture to fully slant fracture. The early stages of the R-curve are affected by in-plane constraint that can be indexed by the T-stress. The R-curve can be used to explain the stability of long cracks in full-scale tests on a bridge prototype, compared with the instability of short cracks in small, standard test pieces.     

An alternative formulation of the Ritchie-Knott-Rice local fracture criterion

In the paper an alternative formulation of the RKR local fracture criterion is proposed. It is based on the features of the stress distribution in front of a blunted crack in an elastic-plastic material. The stress distribution is computed using the finite strain option in the finite element method. It is postulated that the opening stress in front of the crack should be greater than the critical one, σ_c, over the distance l ? l_c, where l_c is considered as a material parameter. The hypothesis is applied to estimate the influence of the in-plane constraint on fracture toughness. New formulas to compute the critical value of the J-integral are derived both for the small scale yielding and large plastic deformations in front of the crack. The results obtained are compared with the Sumpter and Forbes experimental results and with the O’Dowd analytical formula concerning the J_c = J_c(J_IC,Q) relation.     

Fracture toughness of grade D ship steel

Results from fracture mechanics tests on 15 mm thick grade D ship steel and weld are organised into a toughness distribution indexed to the Charpy 27 joule temperature, T_27J. The tests are carried out at 300 MPa√m/s to simulate the strain rate appropriate to a long (≈1 m) through thickness crack in the deck of a ship under storm conditions. Most of the data are in the brittle to ductile transition region and end in cleavage fracture. A best fit to the data is found using the exponential curve fit (ECF) method. Lack of censoring of invalid results means that the trend line is not a true ‘plane strain’ fit. It is argued that inclusion of ‘plane stress’ data makes the resultant toughness distribution more relevant to ship fracture predictions. Equations are presented which allow the toughness to be plotted at any chosen probability level as a function of temperature relative to T_27J. A safe lower bound to the data is given by the 0.1% probability trend assuming that T_27J for grade D plate and weld is no higher than −20 °C. The data are also used to propose that it is impossible to generate an elastic ductile tearing instability in ship steel with Charpy upper shelf values of 100 J or more.     

Application of ultrasonic stress measurements to nondestructive evaluation of the J integral in elastic-plastic deformation

A technique was proposed in [1] for nondestructively evaluating the J integral in cracked specimens through use of ultrasonic measurements of stress, and tested on several specimen configurations with the deformation confined to linear elastic fracture mechanics [1,2]. In this paper the application of this procedure to the evaluation of J in the presence of elastic-plastic deformation is described. Experimental results are presented for the case of an edge-cracked panel in tension, which compare favorably with numerical predictions.     

Interaction of residual stress with mechanical loading in an austenitic stainless steel

Single edge notched bend, SEN(B), fracture specimens fabricated from AISI Type 316H austenitic stainless steel and containing a residual stress field were used to quantify the interaction of a residual stress field on subsequent fracture behaviour when the specimens were subjected to an applied load. Autogenous welding (where no additional filler material is used) was used to impart the residual stress field following a procedure which had been extensively characterised numerically and experimentally. Crack growth resistant curves were obtained for the specimens, and for similar specimens containing no residual stress field. It was observed that the residual stress field had negligible impact on the fracture behaviour of the specimens, in contrast to recently reported work which demonstrated a large influence of a residual stress field when the test specimens were fabricated from a ferritic steel. A numerical programme was conducted to consider the results in the context of a structural integrity assessment. The test results were assessed using both the procedures described in R6, a well-known structural integrity assessment procedure, and by explicit calculation of a modified J -integral via two-dimensional cracked body finite element analysis. It was shown that the assessments were pessimistic, all predicting an influence of the residual stress field on fracture when none was observed experimentally.     

Effect of crack depth on the shift of the ductile-brittle transition curve of steels

Nuclear reactor pressure vessel (RPV) steels degrade due to neutron irradiation during normal operation. As a result, the ductile-brittle transition curve of the steel shifts to higher temperature which decreases operation margins in both the temperature and pressure. The loss of these margins however can be offset somewhat by appealing to arguments based on constraint of potential/postulated shallow cracks. In this paper, it is demonstrated that the fracture toughness values for shallow flaws are higher than those determined from standard deep cracked test specimens based on constraint consideration. The J-A₂ three-term solution is used to characterize the crack-tip stress field where J represents the level of loading and A₂ quantifies the level of constraint. Based on the RKR cleavage model, procedures to quantify the temperature shift between specimens with different constraint levels are developed. The experimental data by Sherry et al. [Sherry AH, Lidbury DPG, Beardsmore DW. Validation of constraint based structural integrity assessment methods. Final report, Report No. AEAT/RJCB/RD01329400/R003, AEA Technology, UK, 2001] for the A533B RPV steel are used to demonstrate the procedure and it is shown that the ductile-brittle transition curve shifts to lower temperature from high constraint to low constraint specimens.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

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.     

On the application of the damage work density as a new initiation criterion for ductile fracture

In this paper the ‘damage work’ proposed by Chaouadi et al. is used to formulate an energy crack initiation criterion to describe ductile crack initiation. The traditional assessment of structural integrity by the J-integral, a property of elastic-plastic fracture mechanics is compared. Two free-cutting and one structural steel are investigated. The measured values for the critical damage work density at initiation W_di are compared with values for copper and RPV steel. As the fracture mechanical approach is limited to sharp cracks in the material (high-constraint stress state) the present damage mechanics approach is regarded as important as a more general concept closer to reality. While old void growth models of damage mechanics cannot formulate a simple criterion for crack initiation the applied damage work reaches a constant value at initiation W_di which is independent of the stress state during the deformation process. We recommend W_di as a material property of toughness for testing and engineering purposes.     

Prediction of fatigue life with interspersed mode-I and mixed-mode (I and II) overloads by an exponential model: Extensions and improvements

The current work is an extension of the authors’ earlier work and presents a life prediction methodology under interspersed mode-I and mixed-mode (I and II) overloads. The important controlling parameter in the model is ‘specific growth rate’ (m). It depends on two crack driving forces i.e. stress intensity factor range and maximum stress intensity factor as well as material parameters i.e. fracture toughness, Young’s modulus, and yield stress. The dependence of ‘m’ on these parameters is correlated through a dimensionless parameter ‘l’. It is observed that the present model predicts the end life of post-overload period well in case of 7020 T7 and 2024 T3 Al-alloys.     

The stress-level effect on fatigue-crack growth under constant-amplitude loading

The fatigue-crack-closure concept has been successfully used with stress-intensity factors to predict the growth of cracks under a wide variety of load histories and in complex crack configurations. Both test and crack-closure analyses have shown that the stress-intensity-factor-range-against-rate curves are affected by the stress ratio (R), the applied stress or load level (S_max or P_max), and the crack-front constraint (plane-stress or plane-strain behavior). However, most life-prediction codes use only linear-elastic fracture mechanics (LEFM) concepts, which neglect stress-level effects, to make life predictions. Thus, under some loading conditions, such as negative R ratios or high-applied stress levels, non-conservative life predictions are made using only LEFM procedures.Fatigue-crack-growth tests have been conducted on middle-crack tension M(T) specimens made of 2024-T3 thin-sheet (B = 2.3 mm) aluminum alloy over a wide range in applied stress levels (0.1–0.5 times the flow stress of the material) and for two stress ratios (R = 0.05 and −1). The FASTRAN life-prediction code, using either the crack-closure model or LEFM procedures, and the AFGROW code, which uses only LEFM procedures, were used to make crack-growth predictions from an initial crack size to failure in the M(T) specimens. The results from AFGROW and FASTRAN, using LEFM procedures, agreed very well with each other. The crack-closure model predicted all results with ±20%, whereas, the codes using LEFM procedures (neglecting stress-level effects) resulted in non-conservative life predictions as large as a factor-of-3 from the test results.     

Constraint loss correction for assessment of CTOD fracture toughness under welding residual stress. Part I: Methodology using the equivalent CTOD ratio

This part I of a two-part paper presents a method of assessing the effects of welding residual stress and constraint loss on the cleavage fracture of a wide plate subjected to membrane stress based on the Weibull stress criterion. It has been found that the Weibull stress criterion is efficient for evaluating the fracture instability of wide plates with and without a welding residual stress field. The concept of an equivalent crack-tip opening displacement (CTOD) ratio β_r under a welding residual stress field is introduced for assessment of constraint loss effects on CTOD fracture toughness of wide plates. The equivalent CTOD ratio β_r is defined as the ratio of the CTOD in the standard fracture toughness specimen to the CTOD in a wide plate with a welding residual stress at the same level of the Weibull stress. Fracture assessment procedures using β_r for wide plates are shown within the framework of the failure assessment diagram. It has been found that the excessive conservatism observed in the conventional procedure can be reduced reasonably by applying the proposed method. The companion part II of the paper presents applications of the CTOD toughness correction method using β_r to the fracture test data of welded joints and verifies the proposed method in the ductile-brittle transition temperature region.     

J-integral-based approach to fatigue assessment of laser stake-welded T-joints

The aim of this paper is to investigate the influence of the plate thickness on the fatigue strength of laser stake-welded T-joints under the tension loading condition. Fatigue tests were conducted on specimens with plate thicknesses below 5 mm subjected to tension loading with the load ratio R = 0. The statistical analysis of the weld geometry showed a normal distribution of the each parameter that was measured. In addition, the parameters had similar proportions in comparison to the specimens with plate thicknesses above 5 mm. FE analysis was performed with the aim of determining the stress state in the joint along with the J-integral. If the square root of the J-integral, √ΔJ, is used as the fatigue strength assessment parameter, the fatigue strength obtained at five million cycles is similar as in the case of other steel welded joint types. The investigation concluded that the stress state changes with the reduction of the plate thicknesses and the contribution of fracture mode II becomes significant. However, using √ΔJ as a fatigue strength assessment parameter ensures that the complex state of the mixed fracture mode loading is accurately accounted for. This fact further enables the fatigue strength of laser stake-welded T-joints of any plate thicknesses to be described by means of a narrower scatterband than the one obtained by the nominal stress approach.     

Elastic-plastic J and COD estimation schemes for throughwall circumferentially cracked elbow under in-plane closing moment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic-plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic-plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, no such schemes are available for throughwall circumferentially cracked elbow (or pipe bend), an important component for LBB analysis. In this paper, simple J and COD estimation schemes are proposed for throughwall circumferentially cracked elbow subjected to closing bending moment. The ovalisation of elbow cross-section has a significant bearing on its fracture behavior. Therefore, unlike conventional deformation theory plasticity analysis, incremental flow theory is adopted considering both material and geometric non-linearities in the development of the proposed estimation schemes. Although it violates Ilyushin’s theorem, it has been shown that the resulting estimation schemes is still reasonably accurate for engineering purposes. Finally, experimental/numerical validation has been provided by comparing the J-integral and COD between numerical/test data and predictions of the proposed estimation schemes.     

Compatibility of linear elastic (k1c) and general yielding (COD) fracture mechanics

An investigation of the applicability of the general yielding fracture mechanics concept of crack opening displacement is made in relation to the well established concepts of linear elastic fracture mechanics. The nature of the relationship between crack opening displacement and stress intensity factor is explored using the concepts of linear elasticity and model analyses proposed by Dugdale. Tests on C/Mn steel, a low alloy steel and a manual metal arc weld deposit define the nature of this relationship in the stress region for which the theoretical compatibility is no longer to be expected. Based on this relationship a single fracture test procedure may be used to determine COD or K_1c (depending on the stress conditions at failure). The results of the tests analysed in terms of J, the contour integral, determine the significance of J as a fracture characterising parameter. Defect tolerance parameters for the assessment of the significance of flaws in welded structures are also introduced.     

Prediction of ductile fracture initiation using micromechanical analysis

In the paper ductile fracture initiation analysis of low-alloyed ferritic steel has been made by application of two micromechanical models: the Rice–Tracey void growth model and the Gurson–Tvergaard–Needleman (GTN) model. The aim of the study was to analyse transferability of micromechanical parameters determined on specimens without initial crack to pre-cracked specimens. A significant part of the research has been carried out through participation in the round robin project organised by the European Structural Integrity Society (ESIS). Tensile tests have been performed on cylindrical smooth specimens and CT specimens. Critical values of micromechanical parameters determined on smooth specimen for both applied models, have been used for prediction of the crack growth initiation in CT specimen. Modelling of the first phase of ductile fracture––void nucleation––has been carried out using quantitative metallographic analysis of non-metallic inclusion content in tested steel. For determination of critical values of model parameters corresponding to ductile fracture initiation a simple procedure has been applied based on a combination of experimental and numerical results. Evaluated J-integral values corresponding to onset of crack growth, J_i, are in good agreement with experimental result and both models have proved to be suitable for determination of the ductile fracture initiation in tested steel. The effect of FE size at a crack tip on J_i-value has been particularly analysed: it has been established that the calculation with FE size corresponding to the mean free path λ between inclusions in steel gives results that are in accordance with the experimental ones.     

Constraint loss correction for assessment of CTOD fracture toughness under welding residual stress - Part II: Application of toughness correction methodology

This part II paper presents the verified results of the toughness correction methodology for welded joints of wide plates. The equivalent CTOD ratio, β_r, is applied to the fracture data of the welded joints from lower to upper ductile-brittle transition temperature region. In the part I paper, β_r is defined as the ratio of CTOD in the standard fracture toughness specimen to CTOD in the wide plate with welding residual stress at the same level of the Weibull stress. In this part II paper, the equivalent CTOD ratio, β_r, under the welding residual stress field has been verified for assessment of constraint loss effects on CTOD fracture toughness of wide plate. Fracture assessments have been conducted by applying the methodology for “After Weld Notch” and “Before Weld Notch” type welded joints. It has been found that an excessive conservatism observed in the conventional procedure is reasonably reduced by applying the proposed methodology.     

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised in-plane constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide effective thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised -plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.