Clamped Single-edge Tension Research Articles

Constraint effect on fracture toughness resistance curves of an X60 pipe steel

The fracture toughness resistance curve (e.g. J-R curve and crack tip opening displacement (CTOD) or δ-R curve) is important in facilitating strain-based design and integrity assessment of oil and gas pipelines, where influence of ground movements and presence of planar weld flaws must be accounted for. In this paper, duplicate single edge bend (SE(B)) and clamped single edge tension (SE(T)) specimens with two different initial crack sizes were prepared from an X60 pipe steel. The longitudinally-oriented specimens were notched in the through-thickness direction and experimentally tested at room temperature. In general, the results showed the expected trends of higher resistance curves for both shallow-cracked versus deeply-cracked specimen types and tension versus bending loading modes. Eleven constraint parameters (i.e. QHRR, QSSY, QLM, QBM, A2, A2BM, h, Tz, Cp, Ap, Vp) were calculated based on three-dimensional (3-D) finite element analyses (FEA) for various tested SE(B) and SE(T) specimens.The results and analysis indicated that the shallow-cracked SE(B) specimens exhibited a constraint condition similar to the intrinsically low-constraint deeply-cracked SE(T) specimens. Among all of the constraint parameters, the Ap parameter based on the normalized equivalent plastic strain contour was found to have the most promising trend in terms of correlating the material’s toughness to constraint level for currently tested specimens. Further on-going investigations are underway to extend the evaluation to resistance curves for specimens made from X100, X80 and X70 pipe steels to allow for the characterization of strain hardening effect, as well as the evaluation of their associated weld metals and heat affected zones (HAZs).

Effective Modulus for Crack Size Measurement With SE(T) Specimens using Unloading Compliance

Abstract Low-constraint toughness tests have been increasingly used in pipeline flaw assessment. A number of protocols have been published using a test employing a clamped single-edge tension (SE(T)) specimen with the distance between the clamps H equal to ten times the specimen width W, and specimen width W equal to thickness B. For this geometry, the constraint over the bulk of the specimen varies between plane stress and plane strain. This affects the elastic compliance, commonly used to estimate crack size. It was the intent of the present work to assess the effects of constraint on the compliance and to identify the best combination of compliance equation and modulus to estimate crack size from CMOD compliance where CMOD is the crack mouth opening displacement. To do this, values of compliance from finite element analyses were provided by the authors of this paper from three separate laboratories. 2D plane strain, 3D plane-sided, and 3D side-grooved specimens were analyzed. The data were used to assess available compliance equations and to propose a new one for the specific geometry of interest in this work.

Effective Thickness of Side-Grooved Clamped SE(T) Specimens for J-R Curve Testing

Abstract Three-dimensional (3D) finite element analyses (FEA) of clamped single-edge tension (SE(T)) specimens were performed to investigate the effective thickness used in the calculations of the stress intensity factor (K) and plastic eta factor-based J-integral (J). The SE(T) specimens with six relative crack lengths (a/W ratios from 0.2 to 0.7), one relative thickness (B/W = 1), and eleven depths of side groove (i.e., BN/B = 1, 0.94, 0.92, 0.9, 0.88, 0.86, 0.85, 0.84, 0.82, 0.8, and 0.75) were considered in the analyses. Based on the FEA results, new effective thickness expressions and values for K and J estimations for side-grooved SE(T) specimens were proposed and validated.

Effects of crack front curvature on J–R curve testing using clamped SE(T) specimens of homogeneous materials

Three-dimensional (3D) finite element analyses (FEA) of clamped single-edge tension (SE(T)) specimens are performed to investigate the impact of the crack front curvature on the elastic compliance, compliance rotation correction factor and average J-integral evaluated over the crack front. Specimens with six average crack lengths (i.e. aave/W = 0.2–0.7) and three thickness-to-width ratios (i.e. B/W = 0.5, 1 and 2) are analyzed. The curved crack front is assumed to be bowed symmetrically and characterized by a power-law expression with a wide range of curvatures. Several crack front straightness requirements for SE(B) and C(T) specimens specified in BS7448, ISO and ASTM E1820 standards are reviewed. Based on results of the numerical investigation, new crack front straightness criteria for the SE(T) specimen are proposed in the context of the nine-point measurement by using as a criterion that the errors in the estimated compliance and average J values should be no more than five percent. The proposed criteria depend on both aave/W and B/W, and are more advantageous than those specified in the BS, ISO and ASTM standards in terms of controlling the differences in J and compliance between the specimens with curved and straight crack fronts.

A Study on CMOD-Based Compliance Calibration Functions for Clamped Single-Edge Tension Specimens

Abstract The compliance calibration function for the clamped single-edge tension (SE(T)) specimen has not been reported in the literature. Based upon the inverse fitting of the three existing CMOD-based compliance equations, three CMOD-based compliance calibration equations are proposed for specimens with a crack length-to-width ratio 0.05 ≤ a/W ≤ 0.75. The fitting errors of the equations here employed are no greater than 1 %.

Investigation of plastic eta factors for clamped SE(T) specimens based on three-dimensional finite element analyses

Three-dimensional finite element analyses of clamped single-edge tension (SE(T)) specimens are performed to evaluate the plastic eta factors (i.e. ηpl) for computing the J-integral. The analysis covers both plane-sided and side-grooved specimens with a wide range of specimen configurations (a/W from 0.2 to 0.7 and B/W equal to 1 and 2) and strain hardening exponents (n=5, 8.5, 10, 15 and 20). Based on the analysis results, a set of expressions for ηpl are proposed.

J-CTOD relationship for clamped SE(T) specimens based on three-dimensional finite element analyses

Three-dimensional (3D) finite element analyses (FEA) of clamped single-edge tension (SE(T)) specimens are performed to evaluate the plastic constraint factors (m) that are used to relate the crack tip opening displacement (CTOD) and the J-integral (J). The analysis covered both plane-sided and side-grooved specimens with a range of specimen configurations (a/W=0.2 to 0.7 and B/W=1 and 2) and strain hardening exponents (n=5, 8.5, 10, 15 and 20). Based on the analysis results, a new empirical m-factor equation is proposed as a function of a/W, B/W, the yield-to-tensile strength ratio and the loading level.

Three-dimensional finite element analysis of crack-tip fields of clamped single-edge tension specimens – Part I: Crack-tip stress fields

A systematic study has been carried out based on three-dimensional finite element analyses to investigate the impact of the in-plane and out-of-plane dimensions on the crack-tip stress fields of clamped SE(T) specimens. Both plane-sided and side-grooved specimens with a wide range of thickness-to-width ratios (B/W=1/2, 1, 2 and 4), crack lengths (a/W=0.3, 0.4, 0.5, 0.6 and 0.7) and strain hardening exponents (n=5, 10 and 20) are included in this study. The through-thickness distributions of J and CTOD as well as the distribution of the opening stress (σθθ) ahead of the crack tip at different crack front locations are presented. The distributions of J and CTOD over the crack front and those of σθθ ahead of the crack tip are impacted by a/W, B/W, n and the type of specimens (i.e. plane-sided or side-grooved). In addition, the empirical equation for calculating CTOD from J for SE(T) specimens developed by Shen and Tyson based on two-dimensional plane-strain finite element analyses is found inadequate to be applied to three-dimensional SE(T) specimens except for the plane-sided specimens with n=10 and side-grooved specimens with n=5.

Three-dimensional finite element analysis of crack-tip fields of clamped single-edge tension specimens – Part II: Crack-tip constraints

This study investigates the in-plane and out-of-plane constraint parameters (namely Q, A2, h and Tz) for clamped single-edge tension (SE(T)) specimens based on a comprehensive set of three-dimensional finite element analyses reported in a companion paper (Part I). The impact of the crack length (a/W), thickness-to-width ratio (B/W) and strain hardening exponent (n) on the constraint parameters, and the interaction between the constraint parameters are examined. For specimens with a given B/W, Q, h and A2 at the mid plane in general increase as a/W increases, but Tz at the mid plane is independent of a/W. The impact of B/W on the distributions of Q, A2 and h over the crack front is dependent on a/W, but Tz decreases as B/W decreases regardless of a/W. The Q, A2 and h values are impacted by n, but Tz is essentially independent of n. For SE(T) specimens, Tz is more appropriate to capture the out-of-plane constraint. The investigation of the interaction between the constraint parameters indicates that Q is essentially equivalent to h and correlated to both the in-plane and out-of-plane constraints, whereas A2 is more suited to characterize the in-plane constraint.