Crack Tip Opening Angle Values Research Articles

Constraint-dependent CTOA determination for stable ductile crack growth

The crack tip opening angle (CTOA) has been used as a reliable fracture toughness to characterize stable crack growth for thin-wall structures in low-constraint conditions. Recently, it is found that CTOA can also be utilized as a robust fracture parameter to describe the arrest fracture toughness for gas transmission pipelines in ductile steels. For better understanding the concept of CTOA, this paper presents a brief review on the CTOA definitions and its test methods. And then, four CTOA models are developed for determining the CTOA toughness using conventional single edge notched bend (SENB) specimens, including the load–displacement linear fit model, the logarithmic load–displacement linear fit model, the stable tearing energy model, and the J-differentiation model. Fracture test data from SENB specimens in A285 carbon steel are employed to evaluate the proposed CTOA models. The results show that these CTOA models can determine either identical or comparable critical CTOA values for stable ductile crack growth using the SENB specimens. A constraint-corrected CTOA resistance curve and a constraint-corrected critical CTOA equation are also obtained for A285 carbon steel.

Dynamic measurement of CTOA of unstable ductile fracture of high pressure gas pipelines

Demand for natural gas is increasing worldwide and pressure and diameter of gas pipelines are increasing. In such high-pressure gas pipelines, prevention of unstable ductile fracture is an important issue. Crack tip opening angle (CTOA) is widely used for fracture criterion of unstable ductile fracture, and measured by Drop Weight Tear Test (DWTT). But, measuring CTOA during dynamic crack propagation in pipe burst is very limited. Therefore, in this study, we measured CTOA in a pipe burst test. The crack propagation was photographed by high-speed camera. The CTOA values by the DWTT and the burst tests were found somewhat different. A care should be taken when using CTOA value obtained by DWTT for analyzing dynamic crack propagation behavior in pipelines.

Evaluation of cracking behavior and critical CTOA values of pipeline steel from DWTT specimens

A regression based algorithm, load-line displacement method has been developed from the Martinelli–Venzi ductile fracture model to measure the crack-tip-opening-angle (CTOA) of high strength and toughness pipeline steels. Key-curve method is employed on the instrument force–displacement curve to estimate the dynamic cracking behavior of a standard pressed-notch DWTT specimen, also conveniently to identify the stable fracture propagation. From the above laboratory procedure, the critical CTOA is found to be constant over the steady-state stage, independence of the thickness in the range 19–31mm as studied.

A new data analysis technique to examine crack tip opening angle values tested in API X65 pipe steel

ABSTRACTThis paper presents a new data analysis technique to rapidly identify the region of stable crack growth in crack tip opening angle (CTOA) testing of a modified double cantilever beam. The technique basically used the load–displacement data from CTOA testing on API X65 steel, which demonstrated a region of constant slope after the peak load. In total, 22 data points (out of 90) fell in this region, for which the variation of CTOA versus crack length remained almost constant. The CTOA measurement was conducted from crack edges and from a fine reference grid, using photographs from two cameras in front and rear sides of the CTOA specimen. As the visual analysis of the individual photographs is tedious and rather lengthy, the presented technique can be easily used for rapid and precise identification of the mean CTOA from those data in the constant slope region of the load–displacement plot.

Crack Tunnelling and Crack Tip Opening Angle in Drop-Weight Tear Test Specimens

Interrupted drop-weight tear tests (DWTT) of typical low-strength and high-strength pipe steels were performed at quasi-static and impact loading rates, to quantitatively characterize crack tunnelling and crack-tip opening angle (CTOA). Crack front tunnelling was observed in all interrupted DWTT specimens, but the extent of tunnelling varied with the steel grade and the loading rate. CTOA values measured optically at the surface were higher than those measured at a cross-section close to mid-thickness. This is attributed to the effect of crack tunnelling, i.e. the effect of constraint, on CTOA. CTOAs derived from load vs. load-line displacement, using the simplified single-specimen method, are in good agreement with values measured at the mid-thickness.

Measurement and analysis of crack tip opening angle in pipeline steels

The quasi-static tearing tests were conducted to analyze the crack propagation process and fracture mechanism in X70 and X80 pipeline steels. The crack tip opening angle (CTOA) was measured by a single specimen method using modified double-cantilever beam (MDCB) specimen. Some influence factors of CTOA toughness were discussed including specimen thickness, precrack types, loading rate and crack tunneling. Experimental results showed that critical CTOA values increase with increasing specimen thickness, which indicated an opposite trend in comparison with the earlier aerospace aluminum alloy studies. The crack tunneling transformed from “triangular shape” to “parabolic shape”, as specimen thickness increased.

Crack Tip Opening Angle Measurement Methods and Crack Tunnelling in 2024‐T351 Aluminium Alloy

Abstract: The crack tip opening angle (CTOA) fracture criterion is one of the most promising fracture criterion used to characterise the stable tearing process in metallic materials. Traditional methods used for the experimental characterisation of the CTOA involve accurate identification of the crack tip at each tearing event. Recently alternative methods have been proposed that reduce the necessity of accurately defining the current crack and rely more on the shape of the crack flanks to define the CTOA. In addition, these methods define an ‘apparent crack tip’, which may be different from the actual surface crack tip and may provide insight into the amount of crack‐front tunnelling that is occurring. In the current research, compact tension specimens fabricated from 6.35 mm thick 2024‐T351 aluminium alloy plate were evaluated to investigate different CTOA measurement methods and their potential for estimating crack‐front tunnelling. In addition to characterizing the CTOA, fatigue marker bands were employed to map the evolution of crack‐front tunnelling. The experimental critical CTOA values obtained from the alternative methods were noticeably lower than that obtained from the traditional approach and showed noticeably more scatter. When compared to the experimentally obtained marker bands, the alternative methods indicated limited potential for predicting crack‐front tunnelling.

Ductile fracture assessment of Indonesian wearing course mixtures using critical J integral and crack tip opening angle

At normal service temperatures, a wearing course asphalt mixture may exhibit ductile fracture. The objectives of the present study are to evaluate and discuss the ductile fracture properties of Indonesian wearing course mixtures (IWCM) using the critical J integral (J c) and crack tip opening angle (CTOA). The notched semi circular bending (SCB) beam test was employed to determine these values. For the notched SCB beam test, six types of IWCM specimens were prepared. The test results showed that the J c and CTOA values varied within the ranges of 0.13–0.76 kJ m− 2 and 0.0–8.07°, respectively. J c and CTOA are useful to comprehensively evaluate the ductile fracture properties of IWCM. The present paper also addresses the effect of stone and manufactured sand particles on the J c and CTOA of IWCM.

Effects of measurement techniques on the experimental characterization of crack tip opening angle-Δa resistance curves

One of the most promising approaches to characterizing the stable tearing process for lower constraint configurations in metallic materials has been indicated to be the crack tip opening angle (CTOA) criterion. In this paper we examine the effect of measurement distance selection and the impact of measurement procedures/analysis on the experimental CTOA-Δa resistance curve behavior of a Ti-6Al-4V and an Al5083 alloy. A new, systematic procedure for carrying out the experimental, surface CTOA measurement process has been used, which has uncovered artifacts of measurement distance selection that have not been presented prior to this study. By studying the CTOA-Δa behavior using a rigidly defined and consistent method, it is apparent that the measurement distance behind the crack tip at which angles are measured has a direct impact on the shape of the early transitional behavior of the CTOA-Δa behavior as well as the critical, experimental CTOA values produced.

A specimen for studying the resistance to ductile crack propagation in pipes

The paper describes a novel DCB-like specimen designed for studying the resistance of running axial cracks in pipelines. It is long enough for steady-state conditions to govern a large proportion of the crack growth, a condition monitored by direct observation of the crack tip opening angle (CTOA) using video cameras. To avoid possible inaccuracies due to pre-straining the material, realistic specimens must be cut from the pipe and tested without flattening. The geometry of the specimen design allows this, and also includes a measure of gauge-length thinning. Extra thickness due to loading side-plates accentuates two desirable features of gauge thinning, by providing directional stability in the advancing crack tip, and by increasing the level of constraint. Tests on specimens from API X80 grade pipe demonstrated a common pattern of CTOA development for 4, 8 and 10 mm gauge thickness material. All showed a reduction of CTOA with growth towards a constant, steady-state value, with the steady state being associated with slant fracture. The region of reducing CTOA started with flat fracture, and gradually developed increasingly definite slant fracture. The most accurate tests produced a steady-state mean value of CTOA of 11.2° and a standard deviation of 1°.

Two-dimensional and three-dimensional finite element analysis of critical crack-tip-opening angle in 2024-T351 aluminum alloy at four thicknesses

Although the crack-tip-opening angle (CTOA) has been shown to be well suited for modeling stable crack growth and instability for thin-sheet aluminum alloys, its behavior for increasing thickness has not been thoroughly evaluated. This paper presents the results of two-dimensional and three-dimensional finite element based fracture analyses that were performed to characterize the critical CTOA for C(T) specimens made of 2024-T351 aluminum alloy with thicknesses of 2.3, 6.35, 12.7, and 25.4 mm. Computed CTOA, based on a center-node release methodology, was generally higher than experimentally determined surface CTOA measurements for the same thicknesses. For the C(T) specimens analyzed in this work, with the crack length and uncracked ligament generally greater than four times the specimen thickness, the generated global constraint factor data fell within those reported for M(T), DE(T), and SE(B) specimen configurations that also satisfy the above mentioned dimensional guideline. Strengthening the observation that, although critical CTOA is dependent on absolute material thickness, the CTOA characterization process is independent of specimen/loading types and specimen dimensions for cases satisfying this dimensional guideline. The CTOA values generated using 3D finite element analyses were used within a 2D finite element analysis framework to estimate plane strain core (PSC) height values for all evaluated thicknesses. The resulting PSC heights increased with increasing specimen thickness and appear to be on the order of specimen thickness.

Experimental investigation of CTOA in linepipe steels

The crack-tip-opening angle (CTOA) criterion has been introduced to the natural gas transmission industry for pipeline applications but has not yet achieved widespread use. There have been ongoing efforts funded by TransCanada PipeLines Limited to establish a fundamentally based test procedure to extract a true measure of the dynamic, ductile, and steady-state fracture toughness of linepipe steels, i.e., the critical CTOA. This paper summarizes experimental results being used in establishing a test procedure that will produce a measure of the steady-state ductile fracture toughness for linepipe steels. Several drop-weight-tear-test type specimens were tested and the CTOA was measured using high-speed video equipment. Comparisons of the measured CTOA values are made for different crack speeds and between standard critical CTOA calculations. The anticipated goal of this research is a test method that is suitable for use at the pipe mills.

Microtopography for ductile fracture process characterization Part 2: application for CTOA analysis

The crack tip opening angle (CTOA) is seeing increased use to characterize fracture in so-called “low constraint” geometries, such as thin sheet aerospace structures and thin-walled pipes. With this increase in application comes a need to more fully understand and measure actual CTOA behavior. CTOA is a measure of the material response during ductile fracture, a “crack tip response function”. In some range of crack extension following growth initiation, a constant value of CTOA is often assumed. However, many questions concerning the use of CTOA as a material response-characterizing parameter remain. For example, when is CTOA truly constant? What three-dimensional effects may be involved (even in thin sheet material)? What are the effects of crack tunneling on general CTOA behavior? How do laboratory specimen measurements of CTOA compare to actual structural behavior? Measurements of CTOA on the outer surface of test specimens reveal little about three-dimensional effects in the specimen interior, and the actual measurements themselves are frequently difficult. The Idaho National Engineering and Environmental Laboratory (INEEL) use their microtopography system to collect data from the actual fracture surfaces following a test. Analyses of these data provide full three-dimensional CTOA distributions, at any amount of crack extension. The analysis is accomplished using only a single specimen and is performed entirely after the completion of a test. The resultant CTOA distributions allow development of full and effective understanding of CTOA behaviors. This paper presents underlying principles, various sources of measurement error and their corrections, and experimental and analytical verification of CTOA analysis with the microtopography method.

Three-dimensional modeling of ductile crack growth in thin sheet metals: computational aspects and validation

This work describes the development of two types of three-dimensional (3D) finite element models to predict stable, Mode I crack growth in thin, ductile aluminum alloys. The two presented models extend the standard 2D form of the Crack Tip Opening Angle (CTOA) methodology, which determines crack extension based on obtaining a critical angle at the crack tip. The more general 3D model evaluates the CTOA at each node along the crack front which enables the development of tunneled profiles. The alternative, constant front approach, enforces uniform growth along the crack front, thereby growing the crack in a self-similar manner. For the constant front approach, evaluation of the CTOA occurs at a specified distance behind the crack front which decouples CTOA evaluation from mesh refinement. Both CTOA-based models include adaptive load control strategies to minimize the effects of discrete load increments on the growth response. Example analyses demonstrate that the more general 3D approach requires cube-shaped elements on the crack plane to eliminate a bias in growth directions. To evaluate the effectiveness of the constant front approach, this work also describes a validation study using load-crack extension data from 2.3 mm thick Al 2024-T3 specimens tested at NASA-Langley. The test matrix includes C(T) and M(T) specimens, with varying widths (50–600 mm), a/ W ratios, and levels of mechanical restraint to suppress out-of-plane bending. Comparisons of load-crack extension curves from experiments and analyses of a 150 mm C(T) specimen, with out-of-plane bending prevented, provide a calibrated (critical) CTOA value of 5.1°. Analyses using the calibrated CTOA value and the constant front approach provide predictions of peak load for constrained and unconstrained specimens in good agreement with the experimental values.

Line-spring finite element for fully plastic crack growth—II. Surface-cracked plates and pipes

Crack-tip opening angle (CTOA) is generally considered as the most operable fracture descriptor for fully plastic, quasi-steady, extensive crack extension. In Part I, based on the CTOA crack growth criterion, a line-spring finite element model was presented to resolve through-thickness crack growth in plane strain single-edge-cracked specimens and surface-cracked plate/shell structures under fully plastic loading. With constraint-dependent CTOA and some supplemental kinematic relations given, the line-spring model ultimately monitors crack extension from the history of generalized displacements. The model was implemented in the implicit ABAQUS finite element code (1993b) in a user-defined element form. Following the plane strain parametric studies in Part I, we further apply the line-spring model to the problems of surface-cracked plates and pipes in Part II here. Effects of material hardening, configuration and location of the surface crack on the histories of penetration-displacement/pressure are examined in a remotely-stretched plate and a pressurized cylindrical vessel. As the most plausible exercise of a stable crack propagation leading to leak-before-break failure, a circumferentially cracked pipe subject to pure bending is selected. Evolution of CTOA along the crack-front and surface crack enlargement pattern are examined for each case. Experimentally-observed CTOA values for the remotely-stretched plate are interpreted in light of the model prediction.

APPLICATION OF ENERGY DISSIPATION RATE ARGUMENTS TO STABLE CRACK GROWTH

Abstract— Energy dissipation rate, D, and crack tip opening angle (CTOA) have been related for large amounts of ductile crack growth in a fully plastic two‐dimensional model of real elastic plastic material. Several J‐type rising R‐curves have been constructed and related, some based on the cumulative energy dissipated and some as a characterising term that relates closely to the far‐field J contour value. These two meanings co‐exist but the relationship is geometry dependent. For deep notch bend (DNB) cases the non‐dimensional group Lα/r* (where L is normalised load, α is CTOA and r* defines the position of the instantaneous centre of rotation) governs the value of dJ. Certain DNB cases where R‐curves vary with size are resolved by this group rather than by CTOA itself whereas for centre‐cracked tension there is a higher value of CTOA than for DNB.