A new method for determining the fracture toughness of main pipeline steels

One of the fundamental aims of fracture mechanics is to define fracture toughness K_IC of a material. Hence, the ASTM E399 standard was developed. However according to the standard, large‐sized specimens are required to determine the fracture toughness of low alloy carbon steels. ASTM E1921 standard was developed on the fracture toughness of ferritic steels. In this study, a new method was proposed to determine the fracture toughness of ferritic steels. The purpose of the present paper is to compare the results of the method with the experimental results. Two steels that are used in gas and oil main pipelines were investigated in this study.     

Study on ASTM E399 and ASTM E1921 standards

Costs of ASTM E399 and ASTM E1921 tests, which were developed to determine the fracture toughness (K_Ic) and the ductile–brittle transition temperature of ferritic steels, respectively, are considered high and the procedures are also very complicated. In this study, a method, which is more cost‐effective and easier to carry out, is proposed.     

A K0‐based calibration procedure for the Weibull stress cleavage model

This paper presents a simplified calibration procedure for the microscopic Weibull stress model to estimate the cumulative probability of cleavage fracture for ferritic steels. The proposed method requires two discrete values of the macroscopic Weibull scale parameter (K₀) in contrast to the two sets of statistically significant fracture toughness data mandated in previous calibration schemes. The proposed approach predicates on the fundamental assumption that the macroscopic toughness, for specimens dominated by cleavage mechanisms, follow the three‐parameter Weibull model outlined in the testing standards. The calibration procedure thus generates two sets of fictitious toughness data corresponding to two sets of specimens with marked differences in crack‐front constraints. The calibrated Weibull parameters agree closely with the calibration results based on the conventional approach for the Euro steels. The proposed calibration also leads to an improved method to determine a limiting load level, beyond which extensive plastic deformation propagates in the specimen.     

A new method to estimate the plane strain fracture toughness of materials

Although the testing method for fracture toughness K_IC has been implemented for decades, the strict specimen size requirements make it difficult to get the accurate K_IC for the high‐toughness materials. In this study, different specimen sizes of high‐strength steels were adopted in fracture toughness testing. Through the observations on the fracture surfaces of the K_IC specimen, it is shown that the fracture energy can be divided into 2 distinct parts: (1) the energy for flat fracture and (2) the energy for shear fracture. According to the energy criterion, the K_IC values can be acquired by small‐size specimens through derivation. The results reveal that the estimated toughness value is consistent with the experimental data. The new method would be widely applied to predict the fracture toughness of metallic materials with small‐size specimens.     

Correlation of fracture toughness with microstructural features for ultrafine‐grained 6082 Al alloy

In the present work, cryorolling (CR) and room temperature rolling (RTR) followed by annealing (AN) at 200°C were carried out to investigate the effects of grain size, precipitates (Mg‐Si‐phases), and AlFeMnSi‐phases on the fracture toughness of 6082 Al alloy. Using the values of the conditional fracture toughness, (K_Q), in the critical fracture toughness (K_IC) validation criteria, it was found that the sample size is inappropriate, which implies that the conditional fracture toughness obtained cannot be considered as the critical fracture toughness. Therefore, to establish the relative improvement in fracture toughness, the equivalent energy fracture toughness (K_ee) and J‐integral were calculated and used. The results show that the values of K_ee (89.91 MPa √m) and J (89.86 kJ/m²) obtained for the sample processed via CR followed by AN (CR + AN) are the highest when compared with the other samples processed through CR, RTR, and RTR followed by AN, RTR + AN. Microstructural features such as high fraction of low Taylor factor, high fraction of kernel average misorientation, Si‐rich particles, small size AlFeMnSi‐phases, and mixed mode of failure (transgranular shear and micro‐void coalescence) also support the high fracture toughness in the CR + AN sample. It was also observed that the effect of residual stresses on the fracture toughness of CR and RTR samples is minimal. Therefore, the correlation between microstructure and residual stresses is not considered in the present work due to very small values of the residual stresses for CR and RTR samples and the absence of residual stress from the heat‐treated samples.     

Application of the small punch test to determine the fracture toughness of metallic materials

A new methodology to determine the elasto‐plastic fracture toughness, J_Ic, by means of notched small punch tests (SPT) samples is reported. Standard SPT samples were used after being longitudinally notched machined from the centre of one side of the sample to the centre of the opposite side, producing a notch depth‐to‐thickness ratio a/t= 0.4. The onset of crack initiation was experimentally determined directly from the experimental load‐displacement plot of the test and also with the aid of scanning electron microscope observations performed on different samples, with tests being interrupted at different percentages of the maximum registered load. The test was also modelled using finite element analysis and the J‐integral was evaluated as a contour integral in ABAQUS. The obtained results were compared with the critical J values of the steel determined using standard tests (J–R curves) and the differences found were duly justified.     

A local approach to cleavage fracture in ferritic steels following warm pre-stressing

Quantification of the enhancement in cleavage fracture toughness of ferritic steels following warm pre‐stressing has received great interest in light of its significance in the integrity assessment of such structures as pressure vessels. A Beremin type probability distribution model, i.e., a local stress‐based approach to cleavage fracture, has been developed and used for estimating cleavage fracture following prior loading (or warm pre‐stressing, WPS) in two ferritic steels with different geometry configurations. Firstly, the Weibull parameters required to match the experimental scatter in lower shelf toughness of the candidate steels are identified. These parameters are then used in two‐ and three‐dimensional finite element simulations of prior loading on the upper shelf followed by unloading and cooling to lower shelf temperatures (WPS) to determine the probability of failure. Using both isotropic hardening and kinematic hardening material models, the effect of hardening response on the predictions obtained from the suggested approach has been examined. The predictions are consistent with experimental scatter in toughness following WPS and provide a means of determining the importance of the crack tip residual stresses. We demonstrate that for our steels the crack tip residual stress is the pivotal feature in improving the fracture toughness following WPS. Predictions are compared with the available experimental data. The paper finally discusses the results in the context of the non‐uniqueness of the Weibull parameters and investigates the sensitivity of predictions to the Weibull exponent, m, and the relevance of m to the stress triaxiality factor as suggested in the literature.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

A COMPARISON OF THE STRAIN INTENSITY AND CYCLIC J APPROACHES TO CRACK GROWTH

Two parameters describing the growth of fatigue cracks are compared. They are the cyclic J integral ΔJ and the strain intensity expressed as an equivalent stress intensity ΔK_eq-. By referring to cyclic stress-strain data obtained from hysteresis loops in high strength ferritic steels at room temperature and austenitic and ferritic steels at elevated temperature it is shown that: (i) for short cracks the parameters are simply related and (ii) both parameters adequately link fatigue crack growth rates observed in the separate high strain fatigue (HSF) and linear elastic fracture mechanics (LEFM) regimes. Correction factors for thumbnail cracks and the conditions under which the relations need further modification are discussed.     

Study on cleavage fracture criteria of the quasi-brittle and micro-inhomogeneous materials

On the bases of recent achievements on the micro-mechanism of cleavage this paper analyses the inherent deficiencies of the stress intensity factor K _I which is used to evaluate the fracture toughness of quasi-brittle and micro-inhomogeneous materials. The K _I parameter can uniquely determine the field intensity ahead of a crack tip in the condition of elastic and small scale yielding (SSY). However, the K _I cannot uniquely determine the critical condition triggering the cleavage fracture in a quasi-brittle and inhomogeneous steel where the cleavage fracture process is not a direct extension of the precrack but is initiated at a variable distance from the precrack tip. The variable distances of cleavage initiations invoke varied critical values of K _I. On the bases of authors' experiments, this paper analyses the physical meaning of the local fracture stress _f, its stability and the feasibility to be used as an engineering parameter for assessing the fracture toughness.     

DYNAMIC CRACK PROPAGATION AND CRACK ARREST INVESTIGATED WITH A NEW SPECIMEN GEOMETRY: PART II: EXPERIMENTAL STUDY ON A LOW-ALLOY FERRITIC STEEL

The novel experiment developed in our Institute to investigate crack initiation, rapid crack propagation and crack arrest with one specimen, the ring test, was applied to a ferritic HSLA pipeline steel. The maximum crack speed achieved in these experiments was between 230 m/s and 1165 m/s. The fracture toughness at crack arrest, K_Ia, was determined by a static analysis of this specific test. In all cases, it was found that K_Ia was much lower than K_Ic. The values of K_Ia decrease when the maximum crack speed increases, the results being largely scattered. The fracture toughness at crack arrest is therefore not an intrinsic parameter of the material for a given temperature. Cleavage fracture obtained under these conditions is characterized by the existence of numerous cleavage microcracks, mechanical twins and unbroken ligaments. The decrease in fracture toughness when crack speed increases is related, using the Beremin or the RKR model, to the high strain rates at the tip of a rapid propagating crack. A model which takes into account the effect of unbroken ligaments left in the wake of a propagating crack is developed to account for the large values of K_Ia which were occasionally measured.     

Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens

Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding K_Ic and K_IIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of K_IIIc/K_Ic obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio K_IIIc/K_Ic . Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.     

On the Applicability of the Schwalbe's Model to the Fracture Toughness Calculation in 7075 Aluminum Alloys

Four 7075-T651 aluminum alloys have been tested in tension in order to assess the applicability of the Schwalbe's model to the fracture toughness calculation. Standard K _IC tests were performed on compact tension samples at room temperature, and the results compared with those from the Schwalbe's model which takes into account several mechanical properties derived from a conventional tensile test applied on round unnotched tensile samples, and the average dimple size of the corresponding fracture surfaces. The values of K _IC calculated through the Schwalbe's model, correlate qualitatively well with those from the standard technique.Fracture toughness deterioration is accompanied by a loss of the true fracture strain, strain hardening capacity and average dimple size. On the other hand, the higher the Zn/Mg ratio, the volume fraction of precipitates and the yield strength, the lower the fracture toughness. All these effects are originated in the presence of matrix precipitates. Therefore, the reduction in K _IC can be explained in terms of the matrix response to the applied stress field as a function of the differences in volume fraction of the strengthening precipitates.The round tension samples corresponding to the four materials, failed in a predominantly ductile transgranular fashion, which facilitates the application of the Schwalbe's model based in the characteristic dimples, developed in this mode of fracture, as a microstructural element size.     

Evaluating the linear normalization technique for deriving J-resistance curves

In this paper, results from the linear normalization (LN) technique of Reese and Schwalbe for deriving J‐crack resistance (J–R) curves have been compared, related to J–Δa (J‐integral–ductile crack growth) data points, to those obtained from traditional elastic compliance technique. Research results regarding a nuclear grade steel exhibiting a wide range of elastic–plastic fracture resistance agree quite well for both techniques until a certain level of toughness of the material. Below this critical level, LN produces inconsistent results for the sub‐sized compact tension specimens (0.4T C[T]). The evidence suggests that the loss of applicability of the LN technique can be determined on the basis of the η plastic factor (η_pl) for the best linear correlation achieved for ΔP_N–Δa (normalised load gradient–ductile crack growth) data.     

Specific aspects on crack advance during J-test method for structural materials at cryogenic temperatures

Cryogenic elastic plastic, J‐integral investigations on metallic materials often show negative crack extension values with respect to resistance curve J‐R. According to the present ASTM standard, the use of unloading compliance technique relies on the estimation procedure of the crack lengths during the unloading sequences of the test. The current standard, however, does not give any specific procedure for treating such negative data. To date, the applied procedure uses the shifting of the negative crack extension values either to the onset of the blunting line or to the offset of the resistance curve. The present paper represents a solution of the negative crack length problem on the basis of a mechanical evaluation procedure of the unloading slopes. The achieved progress using this evaluation technique is demonstrated on different materials such as cryogenic high toughness stainless steels, low carbon ferritic steel and aluminum alloys from the series of 7000 and 5000. In addition, this work deals with the crack tunnelling phenomenon, observed for high toughness materials, and shows the reduction of this crack extension appearance by using electro discharge machining (EDM) side groove technique. The differences between EDM processed side grooves and standard V‐notch machining have been investigated within these test series.     

Large scale testing and statistical analysis of dynamic fracture toughness of ductile cast iron

The present paper deals with the experimental determination and statistical analysis of dynamic fracture toughness values of ductile cast iron. K_Id data from 140 mm thick single edge bend specimens of two dynamic fracture toughness test series on ductile cast iron from heavy-walled castings were analysed.At first, the statistical analysis of data at −40 °C was done based on ASME Code Case N-670 using a two-parameter Weibull distribution function. Weibull analyses of three samples covering different pearlite contents (?4%, ?9%, ?20%) were performed and characteristics of the distribution functions as well as two-sided confidence intervals were calculated. The calculated characteristics show that K_Id of ductile cast iron decreases with increasing pearlite content.In a second step, the applicability of the Master curve procedure according to ASTM E 1921 to ductile cast iron materials was investigated and it was formally used for statistical analysis of ductile cast iron dynamic fracture toughness data. Although the Master curve method was originally introduced for static fracture toughness data of ferritic steels, the successful individual analyses performed here support the engineering way taken to apply the method to ductile cast iron materials too. The results of both methods, the Master curve procedure and the ASME Code Case N-670, show acceptable congruity. At the same time, it is concluded from the present study that further investigations and experiments are required to improve precision and for verification before the results could be applied within component safety analyses.     

Fracture toughness measurement by cylindrical specimen with ring-shaped crack

A method for measuring the plane strain fracture toughness of metals by means of cylindrical specimen in tension with axi-symmetrical ring-shaped crack is discussed. Owing to the fact that the crack tip of such a specimen is closer to ideal plane strain state, the K_1c value measured is effective and reliable. This investigation has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen dimensions.In both safety evaluation and life estimation of engineering components by linear elastic fracture mechanics, it is necessary to measure the fracture resisting parameter—fracture toughness under plane strain. According to the ASTM-E399-74 standard[1], when measuring the fracture toughness K_1c values of medium and low strength steels with a standard compact tension specimen or three-point bending specimen, it is necessary to use specimens of large dimensions, great tonnage fatigue testing machine and universal testing mechine. Naturally, this presents great difficulties to the investigation and application of fracture mechanics and it is precisely for the purpose of overcoming these difficulties that we have studied the method of measuring the plane strain fracture toughness by a cylindrical specimen in tension with axi-symmetrical ring-shaped crack. This method has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen size. Owing to the fact that the field around the crack tip of such a specimen is closer to ideal plane strain state, the results obtained are values smaller than those by using compact tension and three-point bending specimens and are more reliable fracture resisting constants for materials in linear elastic fracture mechanics analysis. Moreover, this method is more practical and economical because no expensive large fatigue testing machine is needed and the specimen size is small.