Crack Mouth Opening Displacement Compliance Research Articles

On the fracture toughness testing for single-edge notched bend specimen of orthotropic materials

Majority of the fracture toughness tests on orthotropic materials reported in the literature are based on the testing methods developed for isotropic materials since there is no available testing standards specifically dealing with orthotropic materials. In this study, a systematic two-dimensional finite element analyses (2D FEA) of orthotropic single-edge notched bend (SENB) specimens are performed to evaluate the stress intensity factor (SIF) and crack mouth opening displacement (CMOD), which are two key parameters used in the fracture toughness tests. The analysis matrix covers a wide range of material orthotropy. Highly accurate regression solutions for SIF, CMOD compliance and its inverse function were developed as functions of orthotropy parameters. Applications of the proposed equations on experimental data are presented and further discussed. The research outcome is expected beneficial to the standardization of the fracture toughness testing on orthotropic composite materials such as wood, bone and unidirectional fiber-reinforced polymer composites.

An η‐compliance method to estimate the J‐Δa curve for pipes with a circumferential surface crack

AbstractThis paper presents an η‐compliance method to measure the J‐Δa curve for pipes with a circumferential surface crack, using the experimentally recorded load versus the crack mouth opening displacement (CMOD) relationship. This study modifies the η method commonly practiced for standard through‐thickness fracture specimens to measure the energy release rate, J, from P‐CMOD curve for pipes with a circumferential surface crack. The non‐dimensional parameter η for the surface‐cracked pipes derives from elastic–plastic finite element analyses. The relationship between the crack size and the CMOD‐based compliance, coupled with crack profiles interpolated linearly between the fatigue crack profile and the crack profile after ductile tearing, allows determining the crack depth corresponding to the measured CMOD compliance. The measured location‐specific J‐Δa curves indicate consistency with the fracture resistance curve measured from through‐thickness fracture specimens at small crack extension levels. The difference between the fracture resistances becomes significantly larger as the crack extends beyond 0.5 mm.

A Numerical Study on CMOD Compliance for Single-Edge Notched Bending Specimens

Several well-known equations for estimating the crack length in the single-edge notched bending (SE(B)) specimens from the normalized crack mouth opening displacement (CMOD) compliance are evaluated based on two-dimensional (2D) and three-dimensional (3D) finite element analyses (FEAs). Two-dimensional FEAs are first carried out to verify the reported accuracy and applicable ranges for each equation based on the plane strain models with six different crack lengths. Three-dimensional FEAs are then carried out to estimate the errors of prediction of equations that evaluate the crack length from the plane stress- and plane strain-based CMOD compliances. Both plane-sided and side-grooved models are included in 3D FEAs and have seven different thickness-to-width ratios. The error of prediction of a given equation is largely impacted by the thickness-to-width ratio, the crack length, the presence of side grooves, and the use of the plane stress- or plane strain-normalized CMOD compliance. Based on the errors of prediction, the relevance of the actual state of stress in the ligament of the SE(B) specimens to the plane strain condition or the plane stress condition is inferred. Knowledge of the relevance of the plane stress condition or the plane strain condition can be used to select the corresponding CMOD compliance in crack length-CMOD equations, and, therefore, the corresponding predictive accuracy can be improved.

Finite element analysis of crack mouth opening displacement compliance in crack length evaluation for clamped single edge tension specimens

ABSTRACTIn 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 (Ee) 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 Ee 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 Ee from the corresponding CMOD compliance. This approach is verified using numerical data. The observations of the numerical verification suggest that the use of Ee instead of E or E′ in CMOD‐based compliance equations markedly improves the accuracy of the predicted crack length for clamped SE(T) specimens.

Dimensionless Compliance With Effective Modulus in Crack Length Evaluation for B × B Single Edge Bend Specimens

In ASTM standard E1820, the crack size, a, may be evaluated during J-integral or crack-tip opening displacement (CTOD) resistance testing using the measured crack-mouth opening displacement (CMOD) elastic unloading compliance C (UC). The equation given to relate a to dimensionless compliance BCE (the product of thickness B, the compliance C and the modulus of elasticity E) in E1820 incorporates Young's modulus E rather than the plane-strain modulus E/(1 − υ2) where υ is Poisson's ratio. However, the three-dimensional (3-D) single edge bend (SE(B)) specimens used in fracture toughness tests are in neither plane-stress nor plane-strain condition, especially for B×B SE(B) specimens which are popular in characterizing fracture toughness of pipes with surface notches. In the present study, 3-D finite element analysis (FEA) was used to evaluate the CMOD compliance of plain- and side-grooved B×B SE(B) specimens with shallow and deep cracks. Crack sizes evaluated using plane-stress and plane-strain assumptions with the CMOD compliance calculated from FEA for the 3-D specimen were compared with the actual crack size of the specimens used in FEA. It was found that the errors using plane-strain or plane-stress assumptions can be as high as 5–10%, respectively, especially for shallow-cracked specimens. In the present study, an effective modulus with value between plane-stress and plane-strain is proposed and evaluated by FEA for the 3-D B×B SE(B) specimens for use in estimating the dimensionless compliance for crack size evaluation of B×B SE(B) specimens. It is shown that the errors in crack size evaluation can be reduced to 1% and 2% for plain-sided and side-grooved specimens, respectively, using this effective modulus. The effect of material removal to accommodate integral knife edges on the CMOD compliance was studied and taken into account in the crack length evaluations in the present study. Elastic unloading tests were conducted to measure the compliance of SE(B) specimens with two widths W and notch depths a/W from 0.1 to 0.5. Notch depths of the specimens evaluated by using the measured compliance and assumptions of plane stress, plane strain, and effective moduli were compared with the notch depths of the specimens used in the tests. It was found that best agreement of notch depth was achieved using the effective modulus.

A Numerical Study on Effective Modulus of Elasticity in Crack Length Evaluation for Single-Edge Bending Specimens

Abstract The actual state of stress in the remaining ligament of a single-edge bending (SE(B)) specimen, which is neither plane stress nor plane strain, is critical in accurately predicting the crack length in the specimen involved in the unloading compliance method. Three-dimensional finite element analyses were carried out in this study to evaluate the effective modulus of elasticity that reflects the actual state of stress corresponding to the crack mouth opening displacement (CMOD) compliance of the SE(B) specimen. Both plane-sided and side-grooved specimens with a wide range of geometric configurations and crack lengths were included in the study. A practical approach is further proposed to quickly evaluate the effective modulus from the CMOD compliance determined based on the test data. The proposed approach was verified using experimental data and numerical analysis results. The results of the verification suggest that replacing the elastic modulus corresponding to the plane stress or plane strain condition with the effective modulus in commonly used a/W–CMOD compliance equations can markedly improve the accuracy of the predicted crack length.

A Study on the Fitting Accuracy of CMOD Compliance Equations

Abstract The maximum error of the inverse fitting of Tada et al.’s equation of the a/W–crack mouth opening displacement (CMOD) compliance equation proposed by Joyce and adopted in ASTM E1820-11 for single edge bend [SE(B)] specimens with shallow cracks (0.05 ≤ a/W < 0.45) is observed to be 2.03 % for 0.05 < a/W < 0.1. A new a/W–CMOD compliance equation with the same fifth-order polynomial fitting applicable for SE(B) specimens with 0.05 ≤ a/W ≤ 0.7 is therefore proposed. The maximum fitting error of the proposed equation is approximately 0.19 %.

Crack Size Evaluation Using Unloading Compliance in Single-Specimen Single-Edge-Notched Tension Fracture Toughness Testing

Abstract Crack-mouth-opening displacement (CMOD) unloading compliances of single-edge-notched tension (SE(T)) specimens, both pin-loaded and clamped, have been evaluated by finite element analysis (FEA), including evaluation of the effect of rotation during testing on compliance. For pin-loaded specimens, FEA results are compared with compliance correction equations based on a rigid-body rotation model recommended by Joyce and Link. The results agree reasonably well when the load line is far from the midsection of the ligament. However, the discrepancy increases when the load line approaches the midsection of the ligament where the bending load becomes small or negligible compared with the tension component and the rigid-rotation model breaks down. For clamped SE(T) specimens, factors affecting specimen rotation, such as the ratio H/W of span between load points H to width of the specimen W, normalized crack size, a/W, and material strain hardening coefficient, N, were investigated. This work was performed for specific application to surface circumferential cracks in pipes, for which the best constraint matching has been found to occur for clamped specimens with H/W = 10. For this geometry, an equation is proposed to correct compliance for rotation and to estimate crack size from rotation-corrected CMOD compliance. Crack sizes evaluated using this equation are compared with measurements on broken specimens. Excellent agreement has been achieved for initial and final crack sizes of both plain-sided and side-grooved SE(T) specimens.

Fatigue crack growth of high-strength concrete in wedge-splitting test

In this study, a wedge-splitting testing was carried out for the investigation of fatigue crack growth behavior of high strength concrete. Selected test variables were concrete compressive strength (28, 60, and 118 MPa) and stress ratio (6, 13%). In order to apply the target stress ratio, the maximum and the minimum fatigue loadings were 75–85 and 5–10% of ultimate static load, respectively. Fatigue testing was preceded by crack mouth opening displacement (CMOD) compliance calibration, and then the fatigue crack growth was computed by crack length vs. the CMOD compliance relations acquired by the CMOD compliance calibration technique. In the fatigue test, the frequency of loading cycle was 1 Hz, and the initial notch length a 0 was 30% of specimen height. To verify the applicability of the CMOD compliance calibration technique to wedge-splitting testing, the crack lengths measured by this method were compared with those predicted by linear elastic fracture mechanics (LEFM) and dye penetration testing. On the basis of the experimental results, an LEFM-based empirical model for fatigue crack growth rate ( da/dn − Δ K I relationship) that takes strength into account was suggested. The fatigue crack growth rate increased with the strength of concrete. It appeared that the da/dN − Δ K I relationship depended on stress ratio, and the effect was evaluated by the proposed equation. In addition, the comparisons between the CMOD compliance calibration technique and the other methods supported the validity of this technique in the wedge splitting test.

Elevated temperature fracture resistance of a sic whisker reinforced/polycrystalline [formula omitted] matrix composite

The fracture resistance of a SiC whisker/Al 2O 3 matrix composite for the test temperature range of 20° to 1400°C was determined using chevron-notched and straightnotched, three-point bend specimens. Crack mouth opening displacement (CMOD) was continuously monitored throughout the fracture tests, using a laser interferometric strain gage (LISG). The crack growth resistance curves ( R- curves ) were determined from previously established relations between the CMOD compliance, effective crack length, and the load point displacement (LPD).