A node release approach to estimate J‐R curve for single‐edge‐notched tension specimen under reversed loading

This paper proposes a node release approach to estimate the fracture resistance curve, often known as the J‐R curve, for monotonic and cyclic fracture tests. The node release approach simulates the crack extension by releasing the constraints imposed on the node at the crack tip and estimates the J‐R curve by coupling the domain integral value with the corresponding crack extension. This proposed node release approach estimates closely the J‐R curve for SE(B) and SE(T) specimens subjected to monotonic loading. For SE(T) specimen under cyclic loading, this study implements the node release analysis in two approaches: (1) an equivalent monotonic analysis corresponding to the envelope of the cyclic load‐CMOD response and (2) a direct cyclic simulation. Both approaches lead to close estimations of the experimentally measured J‐R curve. The numerical analysis also confirms the path independence of the domain integral values in the direct cyclic simulation.     

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

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

Numerical investigation on J-integral testing of heterogeneous fracture toughness testing specimens: Part I – weld metal cracks

Based on extensive two‐dimensional (2D) finite element (FE) analyses, the present work provides the plastic η factor solutions for fracture toughness J‐integral testing of heterogeneous specimens with weldments. Solutions cover practically interesting ranges of strength mismatch and relative weld width, and are given for three typical geometries for toughness testing: a middle cracked tension (M(T)) specimen, single edge cracked bend (SE(B)) specimen and (C(T)) specimen. For mismatched M(T) specimens, both plane strain and plane stress conditions are considered, whereas for SE(B) and C(T) specimens, only the plane strain condition is considered. For all cases, only deep cracks are considered, and an idealized butt weld configuration is considered, where the weld metal strip has a rectangular cross section. Based on the present solutions for the strength mismatch effect on plastic η factors, a window is provided, within which the homogeneous J estimation procedure can be used for weldment toughness testing. The effect of the weld groove configuration on the plastic η factor is briefly discussed, concluding the need for further systematic analysis to provide guidance to practical toughness testing.     

In‐plane and out‐of‐plane constraint parameters along a three‐dimensional crack‐front stress field under creep loading

Full‐field three‐dimensional (3D) numerical analyses was performed to determine in‐plane and out‐of‐plane constraint effect on crack‐front stress fields under creep conditions of finite thickness boundary layer models and different specimen geometries. Several parameters are used to characterize constraint effects including the non‐singular T‐stresses, the local triaxiality parameter, the T_z ‐factor of the stress‐state in a 3D cracked body and the second‐order‐term amplitude factor. The constraint parameters are determined for centre‐cracked plate, three‐point bend specimen and compact tension specimen. Discrepancies in constraint parameter distribution on the line of crack extension and along crack front depending on the thickness of the specimens have been observed under different loading conditions of creeping power law hardening material for various configurations of specimens.     

Estimation procedure of J-resistance curves for SE(T) fracture specimens using unloading compliance

This work provides an estimation procedure to determine J-resistance curves for pin-loaded and clamped SE(T) fracture specimens using the unloading compliance technique and the η-method. A summary of the methodology upon which J and crack extension are derived sets the necessary framework to determine crack resistance data from the measured load vs. displacement curves. The extensive plane-strain analyses enable numerical estimates of the nondimensional compliance, μ, and parameters η and γ for a wide range of specimen geometries and material properties characteristic of structural and pipeline steels. Laboratory testing of an API 5L X60 steel at room temperature using pin-loaded SE(T) specimens with side-grooves provide the load-displacement data needed to validate the estimation procedure for measuring the crack growth resistance curve for the material. The results presented here produce a representative set of solutions which lend further support to develop standard test procedures for constraint-designed SE(T) specimens applicable in measurements of crack growth resistance for pipelines.     

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.     

Plastic limit load and its application to the fracture toughness testing for heterogeneous single edge notch tension specimens

The current investigation pursues the confirmation of the applicability of the limit load solutions in determination of the η factors necessary for fracture toughness testing protocols. The procedure begins with the correct calculation of limit load values in welded single edge notch tension (SE(T)) fracture specimens containing centreline cracks. Hence, the η factor is inferred through the principle of potential energy. Additionally, such results are compared with those obtained from finite element analyses, including strain hardening effects available in the literature. SE(T) specimens subject to pin‐loading display that the η factors are insensitive to the configurational effects and hardening properties. On the other hand, in clamped SE(T) specimens, such effects become meaningful, making its usage in fracture toughness experiments questionable. This work provides an alternative methodology to compute fully plastic proportionality coefficients (η) based on limit load solutions for heterogeneous cracked SE(T) specimens. These analyses also consider the limitations and potentialities of such an approach in experimental measurements of ductile crack growth.     

Three‐dimensional analyses of unified characterization parameter of in‐plane and out‐of‐plane creep constraint

Based on extensive three‐dimensional finite element analyses, the unified characterization parameter A_c of in‐plane and out‐of‐plane creep constraint based on crack‐tip equivalent creep strain for three specimen geometries (C(T), SEN(T) and M(T)) were quantified for 316H steel at 550 °C and steady‐state creep. The distributions of the parameter A_c along crack fronts (specimen thickness) were calculated, and its capability and applicability for characterizing a wide range of in‐plane and out‐of‐plane creep constraints in different specimen geometries have been comparatively analysed with the constraint parameters based on crack‐tip stress fields (namely R*, h and T_Z). The results show that the parameter A_c in the centre region of all specimens appears uniform distribution and lower value (higher constraint), and in the region near free surface it shows protuberant distribution and higher value (lower constraint). The parameter A_c can simultaneously and effectively characterize a wide range of in‐plane and out‐of‐plane creep constraints, while the parameters R*, h and T_Z based on crack‐tip stress fields cannot achieve this. The different capabilities of these parameters for characterizing in‐plane and out‐of‐plane creep constraints originate from their underlying theories. The parameter A_c may be useful for accurately characterizing the overall constraint level composed of in‐plane and out‐of‐plane constraints in actual high‐temperature components, and it may be used in creep life assessments for improving accuracy.     

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.     

Effect of material gradation on K-dominance of fracture specimens

This work describes the effect of material gradation (parallel to the crack plane) on stress intensity factors and K-dominance, i.e. the dominance of the singular region, of fracture specimens; SE(T), SE(B) and C(T). The extent of K-dominance is investigated by comparing the actual stress field with the Williams’ asymptotic stress field. Linear-elastic finite element analyses are performed using graded elements which incorporate graded material properties at the element level. Material gradation and crack geometry are systematically varied to perform the parametric study. Results reveal that the effect of material gradation on K_I is most pronounced when a short crack is located on the stiffer side of the fracture specimen. For a given specimen and crack geometry, the extent of K-dominance yields a curve with a peak point at a certain material gradation. Results of the present study provide valuable insight into the K-dominance of FGMs.     

Back-face strain compliance relation for compact specimens for wide range in crack lengths

A back-face strain (BFS) compliance relation has been developed for the standard compact C(T) specimen for a very wide range in crack-length-to-width (a/W) ratios. Both finite-element and boundary-element methods were used to develop the BFS relation for a/W ratios from 0.2 to 0.95. In addition, experimentally determined compliance values on four metallic materials compared well with the new relation over nearly the complete a/W range. The new relation can be used to monitor crack-length-against-cycles using computerized crack-monitoring systems that are currently used with the crack-mouth-opening-displacement (CMOD) gage method, and the relation has been cast in a standard form compatible with existing compliance crack length monitoring systems.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens. Part II: 3-D effects on constraint

This study describes an extensive set of 3-D analyses conducted on conventional fracture specimens, including pin-loaded and clamped SE(T) specimens, and axially cracked pipes with varying crack configurations. The primary objective is to examine 3-D effects on the correlation of fracture behavior for the analyzed crack configurations using the J-Q methodology. An average measure of constraint over the crack front, as given by an average hydrostatic parameter, denoted Q_avg, is employed to replace the plane-strain measure of constraint, Q. Alternatively, a local measure of constraint evaluated at the mid-thickness region of the specimen, denoted Q_Z0, is also utilized. The analysis matrix considers 3-D numerical solutions for models of SE(T) fracture specimens with varying geometries (i.e., different crack depth to specimen width ratio, a/W, as well as different loading point distance, H) and test conditions (pin-loaded ends vs. clamped ends). The 3-D numerical models for the cracked pipes cover different crack depth to pipe wall thickness ratio, a/t, and a fixed crack depth to crack length ratio, a/c. The extensive 3-D numerical analyses presented here provide a representative set of solutions which provide further support for using constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

Corrected stress intensity factor solution for a British standard single edge notched tension (SENT) specimen

This paper revisits a complicated analytical solution of the stress intensity factor K adopted in a newly published British standard BS 8571:2014 for clamped single edge notched tension (SENT) specimens. Comparison with existing numerical results of K shows that the analytical K solution in BS 8571 is correct only for the crack length to specimen width ratio a/W ≤ 0.6, but incorrect for a/W > 0.6. A reinvestigation is thus performed using the crack compliance method, and a corrected K solution is obtained for the BS 8571 clamped SENT specimens over the full range of a/W. On this basis, a simple closed‐form solution of K is obtained using the best curve fitting with an accuracy within 1% for crack sizes up to a/W = 0.98. Results show that the proposed closed‐form solution of K agrees well with the numerical results of K for the clamped SENT specimens.     

Limited weld residual stress measurements in fatigue crack propagation: Part II. FEM-based fatigue crack propagation with complete residual stress fields

Using a limited set of residual stress measurements acquired by neutron diffraction and an equilibrium‐based, weighted least square algorithm to reconstruct the complete residual stress tensor field from the measured residual stress data, the effect of weld residual stress on fatigue crack propagation is investigated for 2024‐T351 aluminium alloy plate joined by friction stir welding. Through incorporation of the least squares, complete equilibrated residual stress field into a finite element model of the Friction Stir Weld (FSW) region, progressive crack growth along a direction perpendicular to the welding line is simulated as part of the analysis. Both the residual stress redistribution and the stress intensity factor due to the residual stress field, K_res, are calculated during the crack extension process. Results show that (a) incorporation of the complete, self‐equilibrated residual stress field into a finite element (FE) model of the specimen provides a robust, hybrid approach for assessing the importance of residual stress on fatigue crack propagation, (b) the calculated stress‐intensity factor due to the residual stress field, K_res, has the same trend as measured experimentally by the ‘cut‐compliance method’ and (c) the da/dN results are readily explained with reference to the effect of the residual stress field on the applied stress intensity factor.     

Numerical modeling of ductile crack growth in 3-D using computational cell elements

This study describes a 3-D computational framework to model stable extension of a macroscopic crack under mode I conditions in ductile metals. The Gurson-Tvergaard dilatant plasticity model for voided materials describes the degradation of material stress capacity. Fixed-size, computational cell elements defined over a thin layer at the crack plane provide an explicit length scale for the continuum damage process. Outside this layer, the material remains undamaged by void growth, consistent with metallurgical observations. An element vanish procedure removes highly voided cells from further consideration in the analysis, thereby creating new tractionfree surfaces which extend the macroscopic crack. The key micro-mechanics parameters are D, the thickness of the computational cell layer, and f ₀ , the initial cell porosity. Calibration of these parameters proceeds through analyses of ductile tearing to match R-curves obtained from testing of deep-notch, through-crack bend specimens. The resulting computational model, coupled with refined 3-D meshes, enables the detailed study of non-uniform growth along the crack front and predictions of specimen size, geometry and loading mode effects on tearing resistance, here described by J-a curves. Computational and experimental studies are described for shallow and deep-notch SE(B) specimens having side grooves and for a conventional C(T) specimen without side grooves. The computational models prove capable of predicting the measured R-curves, post-test measured crack profiles, and measured load-displacement records.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Fatigue of shot peened 7075-T7351 SENB specimen – A 3-D analysis

As‐received or shot peened 7075‐T7351 single‐edged notch bend (SENB) specimens, 8.1‐mm thick, were fatigued at a constant maximum load and at stress ratios of R= 0.1 and 0.8 to predetermined numbers of fatigue cycles or to failure. The SENB specimens were then fractured by overload and the tunnelling crack profiles were recorded. The crack‐growth rate, da/dN, after crack initiation at the notch was determined by crack‐profile measurement and fractography at various fatigue cycles. The shot peened surface topography and roughness was also evaluated by three‐dimensional (3‐D) laser scanning microscopy. Residual stresses in the as‐received specimens and those generated by shot peening at Almen scales of 0.004A, 0.008A, 0.012A and 0.016A, were measured by an X‐ray diffraction stress analyser with an X‐ray target, CrK, every 0.1 mm to a depth of 1 mm. The 3‐D stress intensity factor of the curved crack front was determined by the superposition of the 3‐D finite element solutions of the stress intensity factor of the loaded SENB specimen without the residual stress and the stress intensity factor of the unloaded SENB specimen with a prescribed residual stress distribution. da/dN versus the resultant stress intensity factor amplitude, ΔK_I, plots showed that while the residual stress locally retarded the crack‐growth rate it had no effect on the overall crack‐propagation rate.     

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T_max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.     

Effects of side‐groove depth on creep crack‐tip constraint and creep crack growth rate in C(T) specimens

The effects of side‐groove depth on creep crack‐tip constraint and creep crack growth (CCG) rate in C(T) specimens have been quantitatively studied. The results indicate that with increasing side‐groove depth, the constraint level and CCG rate increase and constraint distribution along crack front (specimen thickness) becomes more uniform. The constraint and CCG rate of thinner specimen are more sensitive to side‐groove depth. Two new creep constraint parameters (namely R^* and A_c) both can quantify constraint levels of the specimens with and without side‐grooves, and the quantitative correlations of CCG rate with constraint have been established. The mechanism of the side‐groove depth effect on the CCG rate has also been analyzed.