Dynamic ductile fracture of aluminum SEN specimens an experimental-numerical analysis

Hybrid experimental-numerical and experimental analyses were used to explore possible dynamic ductile fracture parameters associated with rapid crack propagation in 7075-T6 and 2024-T3 aluminum alloy, single edge notched (SEN) specimens of 1.6 mm thickness. Dynamic Moiré interferometry was used to record the displacement field, which was used either to drive a dynamic elasto-plastic finite element (FE) model of the fracturing SEN specimen or by itself, to determine the crack-tip J-integral, the $T_\varepsilon ^* $ -integral and the crack tip opening angle (CTOA). The near-field J vanished but the near-field $T_\varepsilon ^* $ reached a constant value with crack propagation. The CTOA associated with a low crack velocity also remained constant during crack propagation but fluctuated at higher crack velocity. The results of this preliminary study suggest that either the $T_\varepsilon ^* $ or the CTOA criteria proposed for stable crack growth could be a suitable parameter for characterizing rapid crack propagation in these thin aluminum specimens.     

Crack tip opening angle measurement through a girth weld in an X100 steel pipeline section*

Crack tip opening angle (CTOA) is becoming one of the most accepted methods for characterizing fully plastic fracture. It provides a measure of the resistance to fracture for a material in cases where there is a large degree of stable‐tearing crack extension during the fracture process. Our current pipeline research uses the CTOA test as an alternative, or addition, to the CTOD (crack tip opening displacement) and the fracture energy characterization provided by the J‐integral approach. A test technique was developed for measurement of CTOA that uses a modified double cantilever beam (MDCB) specimen. A digital camera and image analysis software were used to record the progression of the crack tip and to estimate the CTOA. In this article, CTOA data on crack growth orientations perpendicular to pipeline girth welds are presented. The CTOA for X100 high strength bainitic gas pipeline steel is reported. Two different specimen gauge sections, 3 mm and 8 mm, were used and the effect of the specimen thickness on the CTOA is discussed. The results show a change in the CTOA as the crack grows into the heat affected zone (HAZ). A slight improvement in the fracture resistance is measured, and through the weld, a slight decrease in fracture resistance is observed.     

Constraint-corrected fracture failure criterion based on CTOD/CTOA

In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson–Tvergaard–Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value.     

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.     

AN ENGINEERING FRACTURE PARAMETER FOR NON-J-CONTROLLED CRACK GROWTH

Abstract— An engineering fracture parameter (CTOA) is studied under non- J -controlled growth. Based on the asymptotic solution of the crack tip field and the concept of the ₁ integral, an analytical relation linking the crack tip opening angle (CTOA) and the ₁ integral is established. A numerical investigation of the process of crack growth is carried out by the finite element method. The whole field solution, fracture parameters and indeterminate parameters are determined by FE analysis. An experimental investigation on a ductile structural steel has also been conducted and the crack resistance curve (CTOA)_R is obtained. The numerical and experimental results validate the theoretical analysis and show that they are consistent. It can be concluded that CTOA is always constant during steady crack propagation.     

Microtopography for ductile fracture process characterization: Part 1: Theory and methodology

The mechanics of ductile fracture is receiving increased focus as the importance of integrity of structures constructed from ductile materials is increasing. The non-linear, irreversible mechanical response of ductile materials makes generalized models of ductile cracking very difficult to develop. Therefore, research and testing of ductile fracture have taken a path leading to deformation-based parameters such as crack tip opening displacement (CTOD) and crack tip opening angle (CTOA). Constrained by conventional test techniques and instrumentation, physical values (e.g. crack mouth opening displacement and CTOA angles) are measured on the test specimen exterior and a single through-thickness “average” interior value is inferred. Because of three-dimensional issues such as crack curvature, constraint variation, and material inhomogeneity, inference of average parameter values may introduce errors. The microtopography methodology described here measures and maps three-dimensional fracture surfaces. The analyses of these data provide direct extraction of the parameters of interest at any location within the specimen interior, and at any desired increment of crack opening or extension. A single test specimen can provide all necessary information for the analysis of a particular material and geometry combination.     

Comparison of the measured and predicted crack propagation behaviour of Zr–2.5Nb pressure tube material

The crack propagation behaviour of Zr–2.5Nb pressure tube material was studied through comparison of the measured and predicted behaviour. Three-dimensional finite element simulations of compact tension and burst specimens were performed using the crack tip opening angle (CTOA) as a fracture criterion to allow for crack propagation. To obtain reasonable agreement with the measured force, crack extension, displacement, and crack tunnelling behaviour from compact tension simulations, a non-constant CTOA profile was required. This CTOA profile was then used as the crack propagation criterion in simulations of burst specimens where it was again found that there was reasonable agreement obtained with experiment.     

Crack tip opening angle optical measurement methods in five pipeline steels

Crack tip opening angle (CTOA) is becoming one of the more widely accepted properties for characterizing fully plastic fracture. In fact, it has been recognized as a measure of the resistance of a material to fracture in cases where there is a large degree of stable-tearing crack extension during the fracture process.Our current pipeline research uses the CTOA concept as an alternative or an addition to the fracture energy characterizations provided by the Charpy V-notch (CVN) and drop weight tear test (DWTT). A test technique for direct measurement of CTOA was developed by use of a modified double cantilever beam (MDCB) specimen. A digital camera and image analysis software were used to record the progression of the crack tip and to estimate CTOA. In this report, different optical measurement methods are compared, three using the crack edges adjacent to the crack tip (defined in the ISO draft standard and ASTM standard) and one using the specimen surface grid lines. Differences in CTOA resulting from the various measurement methods are evaluated. The CTOAs for five different grades of gas pipeline steel are reported, and the effect of microstructure on CTOA is discussed.     

Slow-crack propagations through bimaterial interfaces studied by scanning electron microscopy

The scanning electron microscope (SEM) is used for the study of slow crack propagation through a bimaterial interface. This work is concerned with the variation of crack velocity, the variation of crack tip opening angle (CTOA) and the stress intensity factor (K) at the crack tip, and the investigation of crack arrest phenomena at the bimaterial interface. It was observed that the crack accelerates to a maximum velocity as the crack tip approaches the interface and then decreases rapidly to a minimum value at the interface. The interface acts as a decelerator to crack propagation. The position and the value of the maximum velocity depends on the mechanical properties of two phases and specimen configuration. The crack propagates at a constant CTOA until it arrests at the interface. During the crack-arrest time the CTOA increases rapidly to a limiting value. Then the crack passes across the interface and propagates in the next phase with almost the same CTOA as the initial crack in phase I. The stress intensity factor,K, increases to a maximum value near the bimaterial interface.     

The effect of specimen thickness on the experimental characterization of critical crack-tip-opening angle in 2024-T351 aluminum alloy

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. To investigate this behavior, fracture tests were performed on specimens made of 2024-T351 aluminum alloy with thicknesses of 2.3, 6.35, 12.7, and 25.4 mm. The surface CTOA exhibited an initially high value followed by a transition to a “constant” value after a short amount of crack extension, with this transition decreasing significantly with increasing specimen thickness. The critical CTOA was shown to decrease with increasing specimen thickness and appears to possibly be approaching a lower limiting value.     

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

This 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.     

Ductile tearing in thin aluminum panels: experiments and analyses using large-displacement, 3-D surface cohesive elements

This paper describes a large-displacement formulation for a 3-D, interface-cohesive finite element model and its application to predict ductile tearing in thin aluminum panels. A nonlinear traction-separation relationship defines the constitutive response of the initially zero thickness interface elements. Applications of the model simulate crack extension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Tests of the M(T) specimens without guide plates exhibit significant out-of-plane (buckling) displacements during crack growth which necessitates the large-displacement, cohesive formulation. The measured load vs. outside surface crack extension behavior of high constraint (T-stress>0) C(T) specimen drives the calibration process of the cohesive fracture model. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a/W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and measured outside surface crack extensions. The models capture accurately the strong 3-D effects leading to out-of-plane buckling and various degrees of crack front tunneling in the C(T) and M(T) specimens. Previous analyses of these specimens using a crack tip opening angle (CTOA) criterion for growth show good agreement with measured peak loads. However, without the ability of the interface-cohesive model to predict tunneling behavior, the CTOA approach overestimates crack extensions early in the loading when tunneling behavior dominates the response.     

CTOD‐R Curve Tests of API 5L X90 By SENT Specimen Using a Modified Normalization Method

A modified normalization method is presented for obtaining crack tip opening displacement (CTOD) resistance curves of single edge‐notched tension specimens. For the applied load mode, the normalization method should be based on force‐crack mouth opening displacement. A formula is proposed for C_LL(i), the core parameter used in the normalization calculation. The modified method is validated using the unloading compliance method. The study of specimen geometry shows that side‐groove depth and crack depth have significant impacts on the obtained CTOD resistance curves, and the shape of the crack front affects the determination accuracy of crack length.     

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.     

Modelling of ductile fracture initiation in strength mismatched welded joint

In this paper, the effect of strength mismatch and width of the welded joints on the stress–strain distribution in the crack tip region has been discussed. The single-edge notched bend (SENB) specimens (precrack length a₀/W = 0.32) were experimentally and numerically analysed. The model of local approach to fracture, proposed by Gurson, Tvergaard and Needleman, was used. High-strength low-alloyed (HSLA) steel was used as a base metal in quenched and tempered condition. The flux-cored arc-welding process in shielding gas was used. Two different fillers were selected to make over- and undermatched weld metal. The experimental analysis of fracture behaviour of the over- and undermatched welded joints was followed by numerical computations of void volume fraction in front of the crack tip. The critical void volume fraction, f_c, used in prediction of the crack growth initiation on the SENB specimen had been previously determined on a round smooth specimen. Three widths of weld metal were considered: 6, 12 and 18 mm. A comparison of the crack tip opening displacement (CTOD) values corresponding to crack initiation in the SENB specimens is given, as determined both experimentally and using the GTN model.     

Notch root contraction as a fracture measurement

The value of displacement measurements in fracture toughness testing is discussed; in particular the measurement of notch root contraction. The mechanisms of plastic deformation at the notch tip are described, leading to a discussion of theoretical relationship between notch root contraction and crack opening displacement. Experimental work is described in which notched bend specimens of a low alloy steel were loaded to fracture. Each specimen was simultaneously instrumented with notch contraction, COD, and “clip-in” gauges. The equality between notch root contraction and COD was confirmed and observations are made on the relative value of the different measurements. Further observations on the distribution of contraction around the notch tip were made.     

扩展裂纹端变形的有限元计算结果和分析

本文使用与试样几何、加载类型一致的模型,用节点漂移和节点松驰相结合的方法模拟裂纹扩展,进行了扩展裂纹端变形的弹塑性有限元计算。结果表明,在裂纹稳定扩展过程中,裂尖后方微小距离γ_m处,裂纹上、下表面间的张开位移δ_m和裂尖张开角(CTOA)_m均为常值,与实验结果相符。这说明控制裂纹扩展的因素是δ和CTOA,它们应是描述裂纹稳定扩展过程的参量。     

Process zone analysis for the single-edge notched specimen: Part II. Process zone growth and crack propagation

Process zone growth and crack propagation in the single-edge notched (SEN) specimen are studied using the relations among applied load, notional crack and process zone lengths, and crack opening displacement derived in the first part of this work [1]. Process zone growth is simulated by increasing the notional crack length while keeping the traction-free crack length constant. A model for crack propagation based on either critical crack tip opening displacement (CTOD) or critical process zone length, as criteria for traction-free crack extension is proposed. The influence of closing pressure distribution, initial traction-free crack length, and crack extension criterion on the behavior of load vs. CMOD curves is discussed. The present model can be used to model load-deformation behavior from initial loading through softening to failure of nonlinear materials, as is verified by comparing the theoretical and experimentally determined load vs. crack mouth opening (CMOD) curves for concrete beams.     

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.     

Determination of the fracture properties of metallic materials using pre‐cracked small punch tests

In this paper, the use of pre‐cracked small punch test (p‐SPT) miniature specimens to obtain the fracture parameters of a material is presented. The geometry of the specimens used was square of 10 × 10 mm with a thickness of 0.5 mm. An initial crack‐like notch was created in the SPT specimens by means of a laser micro‐cutting technique. In order to obtain the fracture parameters from p‐SPT specimens three different approaches have been considered here. The first approach is based on the crack tip opening displacement concept, the second is based on the measure of the fracture energy using the area under the load–displacement curve for different crack sizes, and the third approach is based on the direct numerical simulation of the p‐SPT specimen and the numerical calculation of the J‐integral. In order to study the crack initiation in these p‐SPT specimens, several interrupted tests and the subsequent scanning electron microscope analysis have been carried out. The results indicate that p‐SPT specimens can be used as an alternative method for determining the fracture properties of a material in those cases where there is not enough material to undertake conventional fracture tests. For these p‐SPT specimens, the multi‐specimen method for the determination of the fracture energy is the most promising approach. The results indicate that this small specimen size allows the value of the material toughness, under low constraint conditions to be obtained.