Transferability of the two‐parameter fracture criterion for 2219 aluminium alloy cracked configurations

Two‐dimensional elastic–plastic finite‐element fracture simulations with the critical crack‐tip‐opening‐angle fracture criterion were used to evaluate the two‐parameter fracture criterion (TPFC). Three different crack configurations under tension and bending loads made of thin‐sheet 2219‐T87 aluminium alloy were analysed. A very wide range of widths (w = 76 to 2440 mm) and initial crack‐length‐to‐width ratios (c_i/w = 0.05 to 0.95) were considered. A relation from the original TPFC was shown to fit the simulated fracture behaviour fairly well for the three different specimen types for net‐section stresses less than the yield stress (σ_y) of the material. Comparisons were also made on measured and simulated fracture tests on middle‐crack‐tension specimens. A relation between the elastic stress‐intensity factor, K_Ie, and net‐section stress, S_n, at failure was found to be linear for S_n < σ_y. The results demonstrated the transferability of the TPFC for different crack configurations for S_n < σ_y, but further study is needed for S_n > σ_y.     

A hybrid approach to determine fracture resistance for mode I and mixed‐mode I and II fracture specimens

This paper proposes a hybrid approach to determine the fracture resistance for mode I and mixed‐mode I and II fracture specimens, combining both numerically computed and experimentally measured load (P) versus load‐line displacement (LLD or Δ) relationships for metallic fracture specimens. The hybrid approach predicates on the same principle as the conventional, multiple‐specimen experimental method in determining the energy release rate. The hybrid method computes the P–Δ curves from multiple finite element (FE) models, each with a different crack depth. The experimental procedure measures the P–Δ curve from a standard fracture specimen with a growing crack. The intersections between the experimental P–Δ curve and the numerical P–Δ curves from multiple FE models dictate the LLD levels to compute the strain energy (U) using the area under the numerical P–Δ curves. This method provides accurate estimates of the J resistance data for both SE(B) specimen under mode I loading and single‐edge notched specimens under mixed‐mode I and II loading.     

Effects of microstructural through‐thickness non‐uniformity and crack size on fatigue crack propagation and fracture of rolled Al‐7075 alloy

Some of the fatigue tests performed using the standard compact tension (CT) and a non‐standard specimen made of rolled 7075 aluminium alloy exhibit fatigue crack growth (FCG) lagging in a small region along the crack front. Through‐thickness microstructural evaluation shows that material grains in this region did not flatten as much as other regions. In the non‐standard specimen, surface cracks are either grown under fatigue loading or broken under monotonically increasing quasi‐static loads at different crack sizes. The aforementioned lagging also exists in a narrow region of 3‐D FCG for specimens with microstructural through‐thickness non‐uniformity. A more important feature for this type of specimen with surface crack is the deflection of fast fracture direction into the grain interfaces, namely from L‐T orientation to S‐L and S‐T directions. It is proved that this is due to significant levels of second principal stresses near the free surface for small cracks and lower fracture toughness of the material in S‐L and S‐T directions.     

A node release approach to estimate J‐R curve for single‐edge‐notched tension specimen under reversed loading

This paper proposes a node release approach to estimate the fracture resistance curve, often known as the J‐R curve, for monotonic and cyclic fracture tests. The node release approach simulates the crack extension by releasing the constraints imposed on the node at the crack tip and estimates the J‐R curve by coupling the domain integral value with the corresponding crack extension. This proposed node release approach estimates closely the J‐R curve for SE(B) and SE(T) specimens subjected to monotonic loading. For SE(T) specimen under cyclic loading, this study implements the node release analysis in two approaches: (1) an equivalent monotonic analysis corresponding to the envelope of the cyclic load‐CMOD response and (2) a direct cyclic simulation. Both approaches lead to close estimations of the experimentally measured J‐R curve. The numerical analysis also confirms the path independence of the domain integral values in the direct cyclic simulation.     

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.     

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.     

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.     

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.     

CTOA of a stable crack in a thin aluminum fracture specimen

A crack tip opening angle (CTOA) resistance curve was generated from the moiré interferometry data of thin single edge notched (SEN) and central notched (CN), 2024-T3 aluminum fracture specimens. This CTOA resistance curve, which has a steady state value of 6°, was then used to propagate the cracks in elastic–plastic finite element models of the CN specimen and a CN specimen with a simulated multiple site damage. The CTOA of curved crack growth in a biaxial fracture specimen scattered between 4° and 8° but the resultant crack tip opening displacement, which is the vector sum of the mode-I and the mode-II crack tip sliding displacement, remained a constant 0.18 mm. The CTOA of a rapidly propagating crack in 1.6 mm thick, 7075-T6 SEN specimens increased from 4.5° at a low-crack velocity to a constant 7° at the terminal crack velocity.     

Residual strength of unidirectional fibre-metal laminates based on JC toughness of C(T) and SE(B) specimens: comparison with M(T) test results

Fibre‐metal laminates (FMLs) are structural composites designed with the aim of producing very low fatigue crack‐propagation rate, damage‐tolerant and high‐strength materials, if compared to aeronautical Al alloys. Their application in aeronautical structures demands a deep knowledge of a wide set of mechanical properties and technological values, including both fracture toughness and residual strength. The residual strength of FMLs have been traditionally determined by using wide centre‐cracked tension panels M(T). The use of this geometry requires large quantities of material and heavy laboratory facilities. In this work, fracture toughness ( J_C) of some unidirectional FMLs laminates was measured using a recently proposed methodology for critical fracture toughness evaluation on compact tension C(T) and single‐edge bend SE(B) specimens. Additionally, residual strength values of wider M(T) specimens with different widths (W from 150 to 200 mm) and several crack to width ratios (2a/W) were experimentally obtained. Some experimental residual strength values of M(T) specimens (W from 150 to 400 mm and different 2a/W ratios) of Arall were also obtained from the bibliography. Based on J_C results from C(T) and SE(B) specimens, and either using or not using crack‐tip plasticity corrections, the residual strengths of the M(T) specimens were predicted and compared to the experimental ones. The results showed good agreement, especially when crack‐tip plasticity corrections were applied.     

A continuum damage mechanics method for fracture simulation of quasi‐brittle materials

This paper addresses a novel continuum damage‐based method for simulating failure process of quasi‐brittle materials starting from local damage initiation to final fracture. In the developed method, the preset characteristic length field is used to evaluate damage instead of element, which is used to reduce the spurious sensitivity. In addition, damage is only updated in the most dangerous location at a time for considering stress redistribution due to damage evolution, which is used to simulate competitive fracture process. As cases study, representative numerical simulations of two benchmark tests are given to verify the performance of the developed continuum damage‐based method together with a used damage model. The simulation results of the crack paths for two concrete specimens obtained from the developed method matched well with the corresponding experimental results. The results show that the developed continuum damage‐based method is effective and can be used to simulate damage and fracture process of brittle or quasi‐brittle materials. And the simulation results based on the developed method depend only the preset characteristic length field and not grid mesh.     

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.     

Experimental studies on mixed‐mode dynamic fracture behaviour of aluminium alloy plates with narrow U‐notch

Mixed‐mode dynamic fracture behaviour of cast aluminium alloy ZL205A thin plates with narrow U‐notch was studied by split Hopkinson tensile bar apparatus. Specimens with different loading angles were designed to realize different fracture modes. The same loading condition was maintained during the tests. Recovery specimens show that crack propagates along the notch direction. Force–elongation relations show that with the loading angle increasing, the fracture force increases while the final elongation decreases. Deformation and fracture process was observed by a high‐speed camera. Displacement distribution around the crack was calculated through digital image correlation technique. Based on the photos and displacement results, initiation time of the crack was derived. Besides, two stress components (normal stress and shear stress) applied on the fracture surface were investigated. Results show that crack initiation stresses at different loading angles satisfy the ellipse equation. Pure mode I and II fracture stresses are 425.3 and 236.7 MPa, respectively. Furthermore, specific fracture energy of different specimens was calculated. The energy data vary with loading angle and located on an approximate upward parabolic curve. From the curve, the minimum specific fracture energy of the thin plate specimen is 42.0 kJ/m² under loading angle of 76.3°.     

Three‐dimensional analyses of in‐plane and out‐of‐plane crack‐tip constraint characterization for fracture specimens

Three‐dimensional elastic–plastic finite element analyses have been conducted for 21 experimental specimens with different in‐plane and out‐of‐plane constraints in the literature. The distributions of five constraint parameters (namely T‐stress, Q, h, T_z and A_p) along crack fronts (specimen thickness) for the specimens were calculated. The capability and applicability of the parameters for characterizing in‐plane and out‐of‐plane crack‐tip constraints and establishing unified correlation with fracture toughness of a steel were investigated. The results show that the four constraint parameters (T‐stress, Q, h and T_z) based on crack‐tip stress fields are only sensitive to in‐plane or out‐of‐plane constraints. Therefore, the monotonic unified correlation curves with fracture toughness (toughness loci) cannot obtained by using them. The parameter A_p based on crack‐tip equivalent plastic strain is sensitive to both in‐plane and out‐of‐plane constraints, and may effectively characterize both of them. The monotonic unified correlation curves with fracture toughness can be obtained by using A_p. In structural integrity assessments, the correlation curves may be used in the failure assessment diagram (FAD) methodology for incorporating both in‐plane and out‐of‐plane constraint effects in structures for improving accuracy.     

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.     

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.     

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.     

Fatigue crack propagation under in‐phase and out‐of‐phase biaxial loading

Fatigue damage characteristics of aluminium alloy under complex biaxial loads such as in‐phase and out‐of‐phase loading conditions and different biaxiality ratios have been investigated. The effects of microscale phenomena on macroscale crack growth were studied to develop an in‐depth understanding of crack nucleation and growth. Material characterization was conducted to study the microstructure variability. Scanning electron microscopy was used to identify the second phase particles, and energy dispersive X‐ray spectroscopy was performed to analyse their phases and elements. Extensive quasi‐static and fatigue tests were conducted on Al7075‐T651 cruciform specimens over a wide range of load ratios and phases. Detailed fractography analysis was conducted to understand the crack growth behaviour observed during the fatigue tests. Significant differences in crack initiation and propagation behaviour were observed when a phase difference was applied. Primarily, crack retardation and splitting were observed because of the constantly varying mode mixity caused by phase difference. The crack growth behaviour and fatigue lives under out‐of‐phase loading were compared with those under in‐phase loading to understand the effect of mixed‐mode fracture.     

Estimation of high‐temperature fracture parameters for small punch specimen with a surface crack

An outline of a newly proposed methodology for evaluating creep crack growth (CCG) parameters using cracked small‐punch (SP) specimens is explained. Three‐dimensional finite element analyses were performed to calculate the stress intensity factor along the crack front for a surface crack formed at the centre of a SP specimen. Effects of crack ratio, (a/t); crack aspect ratio, (a/c); and thickness of the specimen, (t), on the fracture parameters were studied. It was observed that the minimum variation of K‐value along the crack front can be achieved when a/c was 0.50 except the location very near the intersection of the crack and free surface. This condition is similar to the case of constant K‐values along the crack front of the conventional compact tension specimen. Thus, it can be argued that the SP specimen with a surface crack is a suitable specimen geometry for CCG testing. The proposed CCG test method was found to be practically applicable for the crack geometry of 0.10 to 0.30 of a/t with constant aspect ratio of 0.50. An estimation of the K and C_t‐parameter under the small scale creep condition was derived. Future work for further development of the suggested CCG testing is discussed.     

Three‐dimensional brittle fracture: configurational‐force‐driven crack propagation

This paper presents a computational framework for quasi‐static brittle fracture in three‐dimensional solids. The paper sets out the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of configurational mechanics, consistent with Griffith's theory. Resolution of the propagating crack by the FEM is achieved by restricting cracks to element faces and adapting the mesh to align it with the predicted crack direction. A local mesh improvement procedure is developed to maximise mesh quality in order to improve both accuracy and solution robustness and to remove the influence of the initial mesh on the direction of propagating cracks. An arc‐length control technique is derived to enable the dissipative load path to be traced. A hierarchical hp‐refinement strategy is implemented in order to improve both the approximation of displacements and crack geometry. The performance of this modelling approach is demonstrated on two numerical examples that qualitatively illustrate its ability to predict complex crack paths. All problems are three‐dimensional, including a torsion problem that results in the accurate prediction of a doubly‐curved crack. Copyright © 2013 John Wiley & Sons, Ltd.