Surface flaws behavior under tension,bending and biaxial cyclic loading

Fatigue surface crack growth and in-plane and out-of-plane constraint effects are studied through experiments and computations for the aluminum alloy D16T. A tension/bending central notched plate and cruciform specimens under different biaxial loadings with external semi-elliptical surface cracks are studied. The variation of the fatigue crack growth rate and surface crack paths is studied under cyclic tension, bending and biaxial tension–compression loading. For the experimental surface crack paths in the tested specimens, the T-stress, out-of-plane T_z factor, local triaxiality parameter h and the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of the I_n-integral are calculated as a function of the aspect ratio by finite element analysis to characterize the constraint effects along the semi-elliptical crack front. The plastic stress intensity factor approach is applied to the fatigue crack growth on the free surface, as well as at the deepest point of the semi-elliptical surface crack front, of the tested tension/bending plate and cruciform specimens. From the results, characteristics of the fatigue surface crack growth rate as a function of the loading conditions are established.     

An alternative formulation of the Ritchie-Knott-Rice local fracture criterion

In the paper an alternative formulation of the RKR local fracture criterion is proposed. It is based on the features of the stress distribution in front of a blunted crack in an elastic-plastic material. The stress distribution is computed using the finite strain option in the finite element method. It is postulated that the opening stress in front of the crack should be greater than the critical one, σ_c, over the distance l ? l_c, where l_c is considered as a material parameter. The hypothesis is applied to estimate the influence of the in-plane constraint on fracture toughness. New formulas to compute the critical value of the J-integral are derived both for the small scale yielding and large plastic deformations in front of the crack. The results obtained are compared with the Sumpter and Forbes experimental results and with the O’Dowd analytical formula concerning the J_c = J_c(J_IC,Q) relation.     

Essential work of fracture compared to fracture mechanics—towards a thickness independent plane stress toughness

The essential work of fracture (EWF) and the J-integral methods were applied in a study of the effect of the thickness on the cracking resistance of thin plates. The paper discusses two themes: (1) the relationships between the two methods or concepts is elucidated, and (2) a new, thickness independent plane stress toughness parameter is proposed. For that purpose, cracked aluminium 6082O thin plates of 1-6 mm thickness were tested in tension until final separation. The EWF, w_e, and the J-integral at cracking initiation, J_i, increase identically with thickness except at larger thickness for which the increase of J_i levels off. J_i reaches a maximum for 5-6 mm thickness whereas w_e keeps increasing linearly with thickness. This difference is related to the more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation. A linear regression on the fracture toughness/thickness curve allows partitioning the two contributions of the work of fracture: the plastic work per unit area for crack tip necking and a plane stress work per unit area for material separation. The pertinence of this new measure of the pure plane stress cracking resistance is critically discussed based on a micromechanical model for ductile fracture. The micromechanical void growth model incorporates void shape effects, which is essential in the low stress triaxiality regime.     

Fully plastic J-integral solutions for surface cracked plates under biaxial loading

In this paper, surface cracked plates under biaxial tension are studied. Three-dimensional elastic-plastic finite element analyses have been carried out to calculate the J-integral for surface cracked plate for a wide range of geometry, biaxiality and material properties. Fully plastic J-integral solutions along the front of the surface cracks are presented for Ramberg-Osgood power law hardening material of n = 3, 5, 10 and 15. Geometries considered are a/c = 0.2, 1.0 and a/t = 0.2, 0.4, 0.6 and 0.8 and the biaxial ratios of 0, 0.5 and 1. Based on these results, the J-integral along the crack front for general elastic-plastic loading conditions can be estimated using the EPRI scheme. These solutions are suitable for fracture analyses for surface cracked plates under biaxial loading.     

Prediction of mode I crack growth resistance based on a comparative investigation of J-integral and energy dissipation rate concept

An energy dissipation rate concept is employed in conjunction with the J-integral to calculate crack growth resistance of elastic-plastic fracture. Different from Rice’s J-integral, the free energy density is employed in place of the stress working density to define an energy-momentum tensor, which yields that the slightly changed J-integral is path dependent regardless of incremental plasticity and deformational plasticity. The J-integral over the remote contour is split into the plastic influence term and the J _FPZ-integral over the fracture process zone which is an appropriate estimate of the separation work of fracture. Finite element simulations are carried out to predict the plane strain mode I crack growth behavior by an embedded fracture process zone. It can be concluded that J-integral characterization is in essence a stress intensity-based fracture resistance similar to the K criterion of linear elastic fracture, and energy dissipation rate fracture resistance can be taken as an extension of the Griffith criterion to the elastic-plastic fracture.     

A review of the J and I integrals and their implications for crack growth resistance and toughness in ductile fracture

The application of the J and the I-integrals to ductile fracture are discussed. It is shown that, because of the finite size of the fracture process zone (FPZ), the initiation value of the J-integral is specimen dependent even if the plastic constraint conditions are constant. The paradox that the I-integral for steady state elasto-plastic crack growth is apparently zero is examined. It is shown that, if the FPZ at the crack tip is modelled, the I-integral is equal to the work performed in its fracture. Thus it is essential to model the fracture process zone in ductile fracture. The I-integral is then used to demonstrate that the breakdown in applicability of the J-integral to crack growth in ductile fracture is as much due to the inclusion in the J-integral of progressively more work performed in the plastic zone as it is to non-proportional deformation during unloading behind the crack tip. Thus J _R -curves combine the essential work of fracture performed in the FPZ with the plastic work performed outside of the FPZ. These two work terms scale differently and produce size and geometry dependence. It is suggested that the future direction of modelling in ductile fracture should be to include the FPZ. Strides have already been made in this direction.     

A numerical and experimental investigation on the use of J-integral

Finite element analysis was used to determine numerically Rice's J-integral values in centrally notched plates of 4340 steel. These numerical values were compared with corresponding J-integral values using Dugdale model and antiplane strain model with a power law hardening of n = 0.3. J-integral was also computed for a crack extending into its own plastic yield region under constant loading. For increasing level of loading, σ, the rate of increase in J-integral decreases and J-integral remains almost constant at $\text{σ}\text{σ}{}_{\mathrm{YS}}\text{= 1}$ under such crack extension.A limited number of fracture tests were conducted with centrally notched 4340 steel specimens heat treated to yield strength levels of 150,180, 210 and 240 ksi. Fracture data showed that the critical J-integral, calculated and measured, is insensitive to crack tip sharpness for the lower strength 4340 material and thus the J_c fracture criteria appears suited in correlating fracture data.     

Elastic-plastic analysis of surface flaws using a simplified line-spring model

The line-spring model has proven to be an effective tool for evaluating fracture parameters in surface-cracked plates and shells. However, application of the model requires detailed numerical computations, necessitating the availability of a specialized computer code. For approximate engineering calculations a version of the model which is more convenient to implement computationally, would be useful.In this paper a simplified line-spring model is presented along with detailed illustration of its application. The simplification is accomplished by replacing the crack front with a crack of constant depth and treating the ligament “spring” as elastic perfectly plastic. Despite its simplicity the model gives reasonably accurate predictions of fracture parameters, such as the J-integral or crack opening displacement (COD) at the root of surface cracks. This will be demonstrated by comparing analytical results for J and COD with previously published experimental data for surface-cracked steel plates.     

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.     

Procedure for accurate calculation of the J-integral from digital volume correlation displacement data

The application of digital image and volume correlation techniques to obtain displacement fields from images has become ubiquitous in experimental fracture mechanics. In this paper, a procedure to extract the J-integral (J) from three-dimensional displacement fields obtained using digital volume correlation is presented. The procedure has been specially adapted to allow for experimental noise and errors, such as poorly defined crack front displacements, smearing of the displacement field across the crack faces, and knowledge of the imprecise crack front location. The implementation is verified using analytical crack-tip fields perturbed with synthetic image correlation errors to characterise the response of J. The method is then applied to experimental results using a Magnesium alloy WE43 loaded elastically in mixed mode. The steps outlined are intended as a guideline for the application of the volume integral from displacement fields to allow for accurate calculation of J along a crack front embedded within the volume.     

Two-parameter characterization of elastic-plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J-Q two-parameter characterization of elastic-plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic-plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c = 0.2, 1.0 and relative depths a/t = 0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J-Q two-parameter approach was then used in characterizing the elastic-plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. It is found that the J-Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis. These results are suitable for elastic-plastic fracture mechanics analysis of surface cracked plates.     

A study of stable crack growth using experimental methods,finite elements and fractography

Systematic analysis of the in-plane constraint influence on J-resistance curves is presented. J_R curves were also recorded and analyzed beyond the limits of crack extension inside which the stress field can be assumed to be dominated by J-integral. Three steels and four types of specimen: SEN(B), SEN(T), CCT and DENT have been tested. Along with the J_R curves the fracture mechanisms have been analyzed with the help of scanning microscopy. The numerical, finite element analysis has been adopted to compute the Q-stresses, as a measure of the in-plane constraint prior to the onset of crack growth. The analysis of the stress field in front of the crack has been performed to check whether the state of stress prior to the crack growth can predetermine the way the crack will grow. It turns out that characteristic features in the J_R curves runs can be predicted qualitatively from the Q(a/W) and Q(J) curves. However, there is a good correlation between Q-stress and voids diameters on fractured surfaces. Several patterns in J_R curves runs have been observed for tested specimens; e.g. no influence of specimen thickness on J_R curves runs was observed for side-grooved specimens. Strong influence of specimen thickness on J_R curve shape was observed for non-side-grooved specimens. J_R curve run higher for thinner specimens unless they are dominated by plane stress. For bent specimens J_R curves run higher for shorter cracks but they run lower for specimens in tension.     

CONSTRAINT EFFECTS ON DUCTILE CRACK GROWTH IN CLADDED COMPONENTS SUBJECTED TO UNIAXIAL LOADING

Abstract A two-parameter approach based on the J-integral and the parameter h, the ratio of the hydrostatic stress to the effective stress, was examined for ductile crack growth in cladded specimens. A series of cracked specimen configurations were tested and analysed by FEM to study the crack-tip constraint in different geometries. The test program consisted of homogeneous SEN specimens of a base material (A533-B steel), homogeneous SEN specimens of a cladding material (stainless steel weldment) and cladded specimens containing surface cracks through the cladding. Some issues concerning the cladding/base interface were also discussed from the basis of metallographical and fractographical examinations. While the crack growth initiation of the investigated materials appeared to be insensitive to the crack-tip constraints, the propagation of ductile crack growth was significantly influenced by crack-tip constraints. The crack-tip constraints in different specimen configurations could successfully be characterized by the parameter h. Prediction of crack growth along the crack fronts in two cladded specimens using the developed resistance laws accounting for constraint effects gave promising results.     

DAMAGE MECHANICS APPROACH TO REMOVE THE CONSTRAINT DEPENDENCE OF ELASTIC–PLASTIC FRACTURE TOUGHNESS

It is now generally agreed that the applicability of a one-parameter J-based ductile fracture approach is limited to so-called high constraint crack geometries, and that the elastic-plastic fracture toughness J_1c, is not a material constant but strongly specimen geometry constraint-dependent. In this paper, the constraint effect on elastic-plastic fracture toughness is investigated by use of a continuum damage mechanics approach. Based on a new local damage theory for ductile fracture(proposed by the author) which has a clear physical meaning and can describe both deformation and constraint effects on ductile fracture, a relationship is described between the conventional elastic-plastic fracture toughness, J_1c, and crack tip constraint, characterized by crack tip stress triaxiality T. Then, a new parameter J_dc (and associated criterion, J_d=J_dc) for ductile fracture is proposed. Experiments show that toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper, and that the new parameter J_dc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach for fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size-independent fracture toughness J_dc. The potential advantage is clear and the results are very encouraging.     

Quasi-static and dynamic fracture behavior of composite sandwich beams with a viscoelastic interface crack

Fracture analysis of sandwich beams with a viscoelastic interface crack under quasi-static and dynamic loading has been studied. Firstly, a three-parameter standard solid material model was employed to describe the viscoelasticity of the adhesive layer. And a novel interfacial fracture analysis model called three material media model was established, in which an interface crack was inserted in the viscoelastic layer. Secondly, a finite element procedure based on Rice J-integral and Kishimoto J-integral theories was used to analyze quasi-static and dynamic interface fracture behavior of the sandwich beam, respectively. Finally, the influence of viscoelastic adhesive layer on the quasi-static J-integral was discussed. In addition, comparison of quasi-static Rice J-integral with Kishimoto J-integral under various loading rates was carried out. The numerical results show that the oscillating characteristic of dynamic J-integral is more evident with shorter loading rise time.     

Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack,by the ‘equivalent domain integral’ method

In this paper, an equivalent domain integral (EDI) method and the attendant numerical algorithms are presented for the computation of a near-crack-tip field parameter, the vector J_?-integral, and its variation along the front of an arbitrary three-dimensional crack in a structural component. Account is taken of possible non-elastic strains present in the structure; in this case the near-tip J_?-values may be significantly different from the far-field values J_f, especially under non-proportional loading.     

Estimation and comparative study of JIC using different methods for 20MnMoNi55 steel

Fracture toughness is one of the key input variables to compute critical load of the structural components. The resistance against ductile fracture can be quantified either by the initiation value or by the entire resistance curve. Different standard methods like J_SZW, JSME and ASTM: E1820 etc. are mainly used to estimate the critical crack initiation value from the resistance curve developed by the J-integral test. However, the results vary from method to method and are even inconsistent for the same method. Pehrson and Landes suggested a simple method for estimation of the critical fracture toughness by identifying the critical point corresponding to the maximum load on load–displacement curve. In the present study, different standard methods along with the one suggested by Pehrson and Landes are used to find out the critical fracture toughness using 1T–CT and ½T–CT specimens of the material 20MnMoNi55 steel for varying temperatures and crack size. The results are analyzed to compare the merits of the different methods of estimation of fracture toughness.     

Upper and lower bounds for evaluation of nonlinear fracture parameters

Bound theorems for estimating small strain nonlinear fracture parameters are proposed. It is found that the lower bound for the J-integral can be obtained by a compatible displacement finite element method. On the other hand, the upper bound of the I1-integral, which is the dual counterpart of the J-integral, can be obtained by an equilibrium finite element method. To verify the theorems and avoid the difficulty of designing equilibrium finite element models, the popular Pian–Sumihara hybrid stress model is modified by incorporating a penalty-equilibrium constraint. Moreover, an incremental formulation of the I1-integral for nonlinear finite element computation is developed. Numerical examples on different crack and loading configurations are presented. All the results indicate the validity of the theorems.     

Relations between structural intensity and J-integral

The present study introduces the concept of structural intensity, which can be interpreted as power flux, into fracture mechanics. It is derived theoretically that the normal component of the structural intensity along crack edge equals J-integral. SI is the power flux or vector representation of the J-integral at the crack tip. Using the finite element method, the structural intensity can be easily calculated. The numerically calculated structural intensity is adopted to visualize the J-integral of a crack tip. Directional power flow path and magnitude at the crack tip is demonstrated schematically with the structural intensity, which facilitates convenient evaluation of the crack propagation status.