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.     

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.     

Plastic J-integral calculations using the load separation method for the double edge notch tension specimen

The load separation method was used to determine the plastic work factor (η_pl) for the double edge notch tension (DENT) geometry for power-law hardening materials. The resulting expression for η_pl compares favorably to the results of Rice, Paris, and Merkle. The results were also compared to η_pl calculated from the plastic J results in EPRI Handbook NP-1931 and substantial differences were noted. A dependence on gage length was identified in the load separation results which indicate a gage length to half-width ratio of at least 3 is required to ensure that all of the plastic displacement is fully sensed and that η_pl is independent of gage length. Additionally, a coupling term between crack size and material hardening exponent was identified in the geometric load separation function G.     

A method to evaluate ductile fracture toughness based on load separation principle

In combination with load separation principle, the P‐V curves of blunt‐notched specimens with different stationary cracks can be explicitly expressed as a unified formula. Further, a load separation‐based direct calibration (LSDC) method to predict instantaneous crack size and J‐resistance curve of growing cracked specimen has been developed. Two specimen configurations, compact tension and single edge‐notched bending, which are made of Cr2Ni2MoV and Q345B, respectively, are employed to verify the validity of LSDC method. The results show that the estimated J‐resistance curves are more reasonable in comparison with those obtained by unloading compliance and normalization method.     

Comparison of using the crack mouth displacement (CMOD) and load line displacement (LLD) methods in the determination of critical J integral in SENB specimens

Various methods for direct and indirect determination of LLD and CMOD were used to determine J from SENB specimens in three different steels. The influence of the displacement measurement on J is discussed, and shows that the values of J using LLD determined from clip gauge methods to the ASTM E1820 or ISO 12135 standards are consistent with values of J determined from CMOD (either directly or using clip gauge methods), as defined in ASTM E1820. From this work it is recommended that standard methods such as ISO 12135 should permit load‐CMOD and load‐LLD as alternative methods to determine J. Methods to determine LLD by corrections to the ram displacement were also shown to be effective in determining J, for applications where the use of clip gauges may be challenging, such as fracture toughness testing in sour environments, dynamic tests, or testing at very high temperature.     

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.     

Study of mode I crack dynamic propagation behaviour and rock dynamic fracture toughness by using SCT specimens

To study crack dynamic propagation behaviour and rock dynamic fracture toughness, a single cleavage triangle (SCT) specimen was proposed in this paper. By using these specimens and a drop‐weight test system, impact experiments were conducted, and the crack propagation velocity and the fracture time were measured by using crack propagation gauges. To examine the effectiveness of the SCT specimen and to predict the test results, finite difference numerical models were established by using AUTODYN code, and the simulation results showed that the crack propagation path agrees with the test results, and crack arrest phenomena could happen. Meanwhile, by using these numerical models, the crack dynamic propagation mechanism was investigated. Finite element code ABAQUS was applied in the calculation of crack dynamic stress intensity factors (SIFs) based on specimen dimension and the loading curves measured, and the curves of crack dynamic SIFs versus time were obtained. The fracture toughness (including initiation toughness and propagation toughness) was determined according to the fracture time and crack speeds measured by crack propagation gauges. The results show that the SCT specimen is applicable to the study of crack dynamic propagation behaviour and fracture toughness, and in the process of crack propagation, the propagation toughness decreases with crack propagation velocity, and the crack arrest phenomena could happen. The critical SIF of an arrest crack (or arrest toughness) was higher than the crack propagation toughness but was lower than the initiation toughness.     

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.     

Plastic J-integral calculations using the load separation method for the center cracked tension specimen

The load separation method was used to determine the plastic work factor (η_pl) for the center crack tension geometry for power law hardening materials with Ramberg-Osgood hardening exponents n ranging from 2 to 20 and crack sizes a/W ranging from 0.4 to 0.8. The resulting expression for η_pl compares favorably to the analytical work of Rice, Paris, and Merkle and to Sharobeam and Landes. The results were also compared to η_pl calculated from the plastic J results in EPRI Handbook NP-1931. Unlike the EPRI results, η_pl from the load separation method are not a function of crack size.     

J-Resistance curve testing of HY80 steel using SE(B) specimens and normalization method

The normalization method is adopted for standard and nonstandard specimens in this paper to develop J-R curves for HY80 steel directly from load versus load-line displacement records without use of automatic crack length measurement. The standard specimens usually contain high crack-tip constraints, while the nonstandard specimens involve low crack-tip constraints. To obtain J-R curves with different constraints, a series of single edge notched bend (SE(B)) specimens with different crack lengths for an HY80 steel are tested in accordance with ASTM standard E1820. The normalization method is then used for determining crack extension and J-R curves for these SE(B) specimens.To validate the normalization method, the J-R curves determined using the normalization method are compared with those obtained by the elastic unloading compliance method for the SE(B) specimens. The comparison shows that good agreements exist between the two methods, and the normalization method is a viable tool to be used to determine J-R curves of the HY80 steel for the standard as well as nonstandard SE(B) specimens. In the J-integral calculations, the resistance curve test method, the basic test method and the modified basic test method specified in ASTM E1820 are evaluated. The results indicate that the modified basic method can be equivalent to the resistance curve method.     

On combination of the equivalent material concept and J‐integral criterion for ductile failure prediction of U‐notches subjected to tension

The aim of the present research is to check the capability of the equivalent material concept (EMC) combined with the J‐integral failure criterion, called EMC‐J criterion, in predicting the load‐carrying capacity (LCC) of U‐notched ductile aluminium plates subjected to tension by considering the 2 moderate and large‐scale yielding regimes. For this purpose, first, a set of experimental results on LCC of 2 groups of thin U‐notched rectangular plates made of Al 7075‐T6 and Al 6061‐T6 are gathered from the recent literature. Then, because the Al 7075‐T6 and Al 6061‐T6 plates have ductile behaviour, EMC is employed to avoid performing elastic‐plastic failure analysis for LCC predictions. Up to now, different failure models in the context of the linear‐elastic notch fracture mechanics have been successfully utilized in combination with EMC for ductile failure prediction of notched members. However, this is the first time in this research that J‐integral, as a well‐known brittle failure criterion, is linked to EMC for predicting LCC of the U‐notched rectangular aluminium plates. Finally, it is shown that EMC‐J criterion can predict well the experimental results of tensile LCC.