Characterization of stable crack extension in aluminium sheet material using the crack tip opening angle determined optically and by the δ5 clip gauge technique

Tests standards aimed at deriving fracture toughness data and crack resistance curves under low constraint condition have recently been finished by ASTM and ISO. These standards cover various experimental methods for determining critical crack tip opening angles, CTOA, for characterising stable crack extension in sheet material. In this paper, some key items of these standard methods are validated, namely the experimental determination of the crack tip opening angle by optical observation and using the δ₅ clip gauge method. When applying such standard methods to material characterization it is of particular interest to know how CTOA-data derived by different methods compare with each other. This paper compares CTOA-data as derived by the optical method with those derived by using the δ₅ clip gauge method. In order to study possible specimen size and geometry effects the methods have been applied to a wide range of specimen geometries. The results demonstrate that CTOA-data derived by the optical method are well suited to provide a specimen size and geometry independent characterization of stable crack extension where the thus obtained CTOA-data are constant over a large amount of stable crack extension. In contrast to this result, CTOA-data obtained from the δ₅ clip gauge method revealed a complex pattern of size and geometry effects, and only in case of compact specimens with a selected size the two CTOA-methods provide nearly identical CTOA-data over a large amount of crack extension.     

The crack propagating behavior of composite coatings prepared by PEO on aluminized steel during in situ tensile processing

This paper investigates the in situ tensile cracks propagating behavior of composite coatings on the aluminized steel generated using the plasma electrolytic oxidation (PEO) technique. Cross-sectional micrographs and elemental compositions were investigated by scanning electron microscopy (SEM) equipped with energy dispersive spectroscopy (EDS). The composite coatings were shown to consist of Fe-Al, Al and Al₂O₃ layers. The cracks propagating behavior was observed in real-time in situ SEM tensile test. In tensile process, the cracks were temporarily stopped when cracks propagated from Fe-Al layer to Al layer. The critical crack opening displacement δ_c was introduced to quantitatively describe the resistance of the Al layer. There was a functional relation among the thickness ratio tAl/tAl₂O₃, the δ_c of composite coatings and tensile cracks’ spacing. The δ_c increased with the increasing of the thickness ratio (tAl/tAl₂O₃). The high δ_c value means high fracture resistance. Therefore, a control of the thickness ratio tAl/tAl₂O₃ was concerned as a key to improve the toughness and strength of the aluminized steel.     

Engineering assessment of ductile tearing in uniaxial and biaxial tension

To decide between clearly different approaches for engineering assessment of plane stress tearing, we performed uniaxial and biaxial tensile tests on middle-cracked specimens at various in-plane constraint states. Attention was focused on determination of the crack tip opening spacing δ_n, crack tip opening angle ψ_c, crack mouth opening angle α_s, energy dissipation rate R, and specific work of fracture A_s. Our experimental results demonstrate that the values of δ_n, ψ_c, α_s, R, and A_s for a high-strength low-hardening aluminium alloy all depend on the specimen geometry, its size, and the load biaxiality ratio. However, assessment of ductile tearing by interconnected characteristic quantities α_s and A_s is more preferable over the use of δ_n, ψ_c, and R values for a number of basically important reasons discussed in this paper.     

THE ENGINEERING FLAW ASSESSMENT METHOD (EFAM)

This communication gives an introduction to the Engineering Flaw Assessment Method (EFAM) presently being developed at GKSS. The EFAM consists of various documents describing experimental procedures for determining fracture properties under various conditions, as well as analytical procedures for estimating the crack tip opening displacement in terms of δ₅ , the rate of δ₅ , (dδ₅ /dt), and the J-integral as driving force parameters.     

CTOD-R curve construction from surface displacement measurements

The construction of a fracture resistance δ–R (or J–R) curve requires the appropriate measurement of crack-tip opening displacement (CTOD) as a function of crack extension. This can be made by different procedures following ASTM E1820, BS7448 or other standards and procedures (e.g., GTP-02, ESIS-P2, etc.) for the measurement of fracture toughness. However, all of these procedures require standard specimens, displacement gauges, and calibration curves to get intrinsic material properties. This paper deals with some analysis and aspects related to the measurement of fracture toughness by observing the surface of the specimen. Tests were performed using three-dimensional surface displacement measurements to determine the fracture parameters and the crack extension values. These tests can be conducted without using a crack mouth opening displacement-CMOD or load-line displacement gauge, because CMOD can be calculated by using the displacement of the surface points. The presented method offers a significant advantage for fracture toughness testing in cases where a clip gauge is not easy to use, for example, on structural components. Simple analysis of stereo-metrical surface displacements gives a load vs. crack opening displacement curve. Results show that the initiation of stable crack propagation can be easy estimated as the point of the curve’s deviation. It is possible to determine the deviation point if the crack opening displacement measurements are close to crack tip in the plastic zone area. The resistance curve, CTOD-R, is developed by the local measurement of crack opening displacement (COD) in rigid body area of specimen. COD values are used for the recalculation with the CMOD parameter as a remote crack opening displacement, according to the ASTM standard.     

A new constraint based fracture criterion for surface cracks

A new methodology for predicting the location of maximum crack extension along a surface crack front in ductile materials is presented. Three-dimensional elastic-plastic finite element analyses were used to determine the variations of a constraint parameter (α_h) based on the average opening stress in the crack tip plastic zone and the J-integral distributions along the crack front for many surface crack configurations. Monotonic tension and bending loads are considered. The crack front constraint parameter is combined with the J-integral to characterize fracture, the critical fracture location being the location for which the product Jα_h is a maximum. The criterion is verified with test results from surface cracked specimens.     

On the effect of plastic constraint on ductile tearing in a structural steel

The effect of plastic constraint on the initiation of ductile tears in a structural steel has been studied by measuring the crack opening displacement at initiation in 3-point bend specimens with deep and shallow notches. It is shown that δ_i for shallow notches where plastic flow reaches the surface is about twice that for deep notches. The crack opening displacement at maximum load is shown to be proportional to the specimen size. It is also shown that sidegrooves reduce this crack opening displacement.     

Characteristic crack-tip distances in fracture criteria: Is crack propagation discontinuous?

The present paper describes a possible mechanism for discontinuous crack advance in which surface separation occurs initially not at the crack-tip itself but within the crack-tip plastic zone of size r_p, at the mid-point of the crack-tip characteristic distance d (identified here with the finite growth step Δa), i.e., at the region of maximum opening tensile stress, spreading towards (and also away from) the crack-tip. The crack extension occurs when the crack-tip is reached and full opening over the distance d is completed.Finite element analyses show that this mechanism causes the formation of a rippled crack face surface in elastic-plastic materials in which irreversible plastic deformations take place during each growth step, in sharp contrast with the smooth surface created in ideal elastic materials in which all deformations are fully reversible. Some pictorial evidence of void formation ahead of the crack tip and of ripples during propagation, found in the literature, is presented.Although the present analysis is from a continuum standpoint it is acknowledged that micro structural features and mechanisms can condition the fracture events taking place in the process zone.The implication to the brittle-ductile transition of the dependence of the energy release rate, G^ΔΞ, on the ratio q (=Δa/r_p) is also discussed.     

Elastic–plastic J and COD estimation schemes for 90° elbow with throughwall circumferential crack at intrados under in-plane opening moment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic–plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic–plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, such schemes for elbow (or pipe bend), which is one of the important components for LBB analyses, is very meager. Recently, elastic–plastic J and COD estimation scheme has been developed for throughwall circumferentially cracked elbow subjected to closing bending moment. However, it is well known that the elbow deformation characteristics are distinctly different for closing and opening bending modes because the ovalisation patterns of elbow cross section are different under these two modes. Development of elastic–plastic J and COD estimation scheme for an elbow with throughwall circumferential crack at intrados subjected to opening bending moment forms the objective of the present paper. Experimental validation of proposed J-estimation scheme has been provided by comparing the crack initiation, unstable ductile tearing loads and crack extension at instability with the test data. The COD estimation scheme has been validated by comparing the COD of test data with the predictions of the proposed scheme.     

Crack opening displacements of Vickers indentation cracks

Vickers indentation cracks are an appropriate tool to determine the crack-tip toughness K_I0 and, possibly, the bridging relation of ceramics with an R-curve behaviour from the total crack opening displacements. Two contributions to the total crack opening displacement field are addressed. First, the residual stresses occurring in the uncracked body are considered and then, the contact stresses generated by preventing crack face penetration are computed. The COD solution resulting from the superposition of residual and contact displacements is given and an analytical expression is provided. Near-tip displacements are represented by the first terms of series expansions. As an example of application, an evaluation of the actual stress intensity factor is presented for a window glass 1 h after Vickers indentation.     

Analytical and numerical study of cohesive zones for a crack in an adhesive layer between identical isotropic materials

A crack in a thin adhesive elastic-perfectly plastic layer between two identical isotropic elastic half-spaces is considered. Uniformly distributed normal stress is applied to the substrates at infinity. First, stress distribution in the cohesive zones and the J-integral values are defined numerically by the finite element method (FEM). Further, a mathematical formulation of the problem is given and its analytical solution is proposed. It is assumed that, at the crack continuations, there exist cohesive zones. The interlayer thickness is neglected since it is much smaller than the crack length. The distribution of the normal stress, which was obtained by means of the FEM, is now approximated by a piecewise-constant function and assumed to be applied at the faces of the cohesive zones. The formulated problem is solved analytically and an equation for determination of the cohesive zone lengths is derived. Also, closed expressions for the crack tip opening displacement and for the J-integral are obtained in an analytical form. These parameters are found with respect to the values of the normal stress applied at infinity. Finally, a universal approximating function, which describes the stress distribution in the cohesive zones, is constructed. This function depends on the ratio between the interlayer thickness and the crack length and on the ratio between the normal stress applied at infinity and the yield limit of the interlayer’s material. Once again, the problem is solved analytically, but this time for the stress distribution prescribed by the universal approximating function. The cohesive zone lengths, the values of the crack tip opening displacement and of the J-integral are calculated. A comparative analysis of the obtained results is carried out. A good agreement of the J-integral values calculated by means of the developed analytical models and by the associated finite element analysis is demonstrated.     

Improved J and COD estimation by GE/EPRI method in elastic to fully plastic transition zone

It is well known that conventional GE/EPRI method over-estimates the J-integral and crack opening displacement (COD)¹ in the elastic to fully plastic transition zone. The present paper investigates this issue and attempts to rectify this error. An improved GE/EPRI method is proposed with the modifications of α (Ramberg-Osgood coefficient) term in the equation of plastic J and COD. The proposed method has been experimentally and numerically validated.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

Simulation of hydrogen assisted stress corrosion cracking using the cohesive model

This paper investigates the effect of hydrogen diffusion on stable crack propagation by using numerical finite element simulations based on the cohesive model. The model with its two common parameters, cohesive strength, T₀, and critical separation, δ₀, and its two additional parameters for stress corrosion cracking, the effective diffusivity, D_eff, and a material parameter, α, which represents the reduction of the cohesive strength, is described. This model is then employed to predict the stable crack propagation in C(T) specimens made from a high strength structural steel which were tested under hydrogen charging conditions in rising displacement tests using various deformation rates. It is shown that, in general, the prediction of stable crack propagation is promising, but may be further improved by the use of a more sophisticated diffusion equation. Finally, the influence of variations of the effective diffusivity and the cohesive strength reduction on the thus simulated crack growth resistance curves is studied.     

Fracture behaviour of chemical vapour deposited and hot isostatically pressed zinc sulphide ceramics

Fracture behaviour of zinc sulphide ceramics prepared by chemical vapour deposition (CVD) followed by hot isostatic pressing (CVD + HIP) was investigated in terms of flexural strength (σ_f), plane-strain fracture toughness (K_Ic), even conditional fracture toughness (K_IQ), R-curve behaviour (variation of total fracture energy release rate, J_c with crack extension, δ/δ_c) and fracture mode. The corresponding Knoop Hardness number (KHN) and its correlations to flexural strength (σ_f) are also evaluated and reported. The present study showed that the zinc sulphide (ZnS) ceramics processed by CVD exhibited higher fracture resistance compared to ZnS processed by CVD + HIP condition. This observation is principally attributed to higher grain size associated with post-CVD HIPing process. In both conditions, the ZnS materials exhibited conditional fracture toughness (K_IQ) that decreased moderately with increased crack length due to the change in fracture mode form grossly tensile to predominant shear. A constantly rising R-curve behaviour was indicated in both the materials with significant increase in total fracture energy release rate (J_c with the normalised displacement (δ/δ_c), a parameter representing crack extension.     

Experimental analysis of the practical LBZ effects on the brittle fracture performance of cryogenic steel HAZs with respect to crack arrest toughness near fusion line

Focusing on crack arrest behavior, this study investigates the practical influence of local brittle zones (LBZs) on the brittle fracture resistance of heat-affected zones (HAZs) in advanced 9% Ni cryogenic steel welds, and discusses whether the LBZs of this steel in practice have potentially deleterious effects as previously thought, or not. By analyzing the variations in brittle crack arrest toughness (K_a) and brittle crack initiation toughness (K_c) within actual HAZ, it is found that LBZs of this steel may not be harmful in consideration of crack arrest toughness near fusion line.     

Fracture and damage mechanics modelling of thin-walled structures - An overview

This paper reviews the most important current approaches for residual strength prediction of thin-walled structures. Crack driving force parameters such the linear elastic stress intensity factor and its plastic zone corrected extension for contained yielding conditions, the crack tip opening displacement δ₅, the crack tip opening angle CTOA, the cohesive zone model parameters, separation energy, critical tensile stress and critical separation and the parameters of the damage models of Gurson-Tvergaard-Needleman type are introduced and discussed with respect to their benefits and limitations for the simulation of plane and stiffened panels. In addition, specific aspects of modern non-integral and integral structures which pose a challenge are addressed. These comprise multi-site damage, crack deviation and branching, welding residual stresses, strength mismatch in material compounds and problems in bonded structures, such as delamination. A number of examples are provided to illustrate the potential of the various approaches.     

Fracture toughness of unidirectional fiber-metal laminates: crack orientation effect

Fiber-metal laminates (FMLs) are structural composites developed for aeronautical applications. The application of FMLs to structures demands a deep knowledge of a wide set of properties, including fracture toughness. The objective of this work was to evaluate the effect of crack orientation on the fracture toughness (critical J-integral and CTOD δ₅) of unidirectional FMLs. Small C(T) and SE(B) specimens with notches parallel and perpendicular to the fibers direction were tested. A study of the relation and equivalence between J_C and δ_5C, which heavily depend on the yield strength and on the stress state, was performed motivated by apparently contradictory experimental results. These results can be explained by the direction-dependent yielding properties of unidirectional FMLs. The best overall equivalence between J_C and δ_5C was obtained considering plane stress state and using the effective yield strength, both for unidirectional FMLs notched parallel and perpendicular to the fibers direction.     

Effect of sudden load decrease on the fatigue crack growth in cold drawn prestressing steel

This paper analyzes the overload retardation effect (ORE) on the fatigue crack growth (FCG) of cold drawn prestressing steel when different loading sequences are used. The ORE is more intense for elevated load decrease or for low initial stress intensity factor (SIF) range ΔK₀. A transient stage can be observed in the Paris curve (da/dN–ΔK) when the K_maxΔK value suddenly decreases, associated with the ORE and with the evolution of the plastic zone and compressive residual stresses near the crack tip. In tests with K_max decrease, a small zone appears related to FCG initiation, with a fatigue fractography resembling the tearing topography surface (TTS) mode, and associated with a decrease of crack tip opening displacement (CTOD).     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.