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.     

Surface crack and cracks networks in biaxial fatigue

Semi-elliptical fatigue crack growth in 304 L stainless steel, under biaxial loading, was investigated. Compared to those of through-cracks under uniaxial loading, the growth rate of surface cracks is increased by a non-singular compressive stress and reduced by a tensile stress, when R = 0. Plasticity-induced crack closure under biaxial loading was investigated through 3D finite element simulations with node release. Roughness and phase-transformation-induced closure effects were also discussed. The interactions in two-directional crack networks under biaxial tension were investigated numerically. It appears that the presence of orthogonal cracks should not be ignored. The beneficial influence of interaction-induced mode-mixities was highlighted.     

Solutions of the second elastic-plastic fracture mechanics parameter in test specimens

Extensive finite element analyses have been conducted to obtain solutions of the A-term, which is the second parameter in three-term elastic-plastic asymptotic expansion, for test specimens. Three mode I crack plane-strain test specimens, i.e. single edge cracked plate (SECP), center cracked plate (CCP) and double edge cracked plate (DECP) were studied. The crack geometries analyzed included shallow to deep cracks. Solutions of A-term were obtained for material following the Ramberg-Osgood power law with hardening exponent of n = 3, 4, 5, 7 and 10. Remote tension loading was applied which covers from small-scale to large-scale yielding. Based on the finite element results, empirical equations to predict the A-terms under small-scale yielding (SSY) to large-scale yielding conditions were developed. In addition, by using the relationships between A and other commonly used second fracture parameters such as Q factor and A₂-term, the present solutions can be used to calculate parameters A₂ and Q as well. The results presented in the paper are suitable to calculate the second elastic-plastic fracture parameters for test specimens for a wide range of crack geometries, material strain hardening behaviors and loading conditions.     

Effect of biaxial loads on elastic-plastic <Emphasis Type="Italic">J</Emphasis> and crack tip constraint for cracked plates: finite element study

Based on detailed two-dimensional (2-D) and three-dimensional (3-D) finite element (FE) analyses, this paper attempts to quantify in-plane and out-of-plane constraint effects on elastic-plastic J and crack tip stresses for a plate with a through-thickness crack and semi-elliptical surface crack under positive biaxial loading. For the plate with a through-thickness crack, plate thickness and relative crack length are systematically varied, whereas for the plate with a semi-elliptical surface crack, the relative crack depth and aspect ratio of the semi-elliptical crack are systematically varied. It is found that the reference stress based approach for uniaxial loading can be applied to estimate J under biaxial loading, provided that the limit load specific to biaxial loading is used, implying that quantification of the biaxiality effect on the limit load is important. Investigation on the effect of biaxiality on the limit load suggests that for relatively thin plates with small cracks, in particular with semi-elliptical surface cracks, the effect of biaxiality on the limit load can be neglected for positive biaxial loading, and thus elastic-plastic J for a biaxially loaded plate could be estimated, assuming that such plate is subject to uniaxial load. Regarding the effect of biaxiality on crack tip stress triaxiality, it is found that such effect is more pronounced for a thicker plate. For plates with semi-elliptical surface cracks, the crack aspect ratio is found to be more important than the relative crack depth, and the effect of biaxiality on crack tip stress triaxiality is found to be more pronounced near the surface points along the crack front.     

The T-stress solutions for through-wall circumferential cracks in cylinders subjected to general loading conditions

The elastic T-stress is a parameter used to define the level of constraint at a crack tip. It is important to provide T-stress solutions for practical geometries to apply the constraint-based fracture mechanics methodology. In the present work, T-stress solutions are provided for circumferential through-wall cracks in thin-walled cylinders. First, cylinders with a circumferential through-wall crack were analyzed using the finite element method. Three cylinder geometries were considered; defined by the mean radius of the cylinder (R) to wall thickness (t) ratios: R/t = 5, 10, and 20. The T-stress was obtained at eight crack lengths (θ/π = 0.0625, 0.1250, 0.1875, 0.2500, 0.3125, 0.3750, 0.4375, and 0.5000, θ is the crack half angle). Both crack face loading and remote loading conditions were considered including constant, linear, parabolic and cubic crack face pressures and remote tension and bending. The results for constant and linear crack face pressure were used to derive weight functions for T-stress for the corresponding cracked geometries. The weight functions were validated against several linear and non-linear stress distributions. The derived weight functions are suitable for T-stress calculations for circumferential cracks in cylinders under complex stress fields.     

Three-dimensional stress state around quarter-elliptical corner cracks in elastic plates subjected to uniform tension loading

Detailed full-field three-dimensional (3D) finite element analyses have been conducted to study the out-of-plane stress constraint factor T_z around a quarter-elliptical corner crack embedded in an isotropic elastic plate subjected to uniform tension loading. The distributions of T_z are studied in the forward section (0° ? θ ? 90°) of the corner cracks with aspect ratios a/c of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. In the normal plane of the crack front line, T_z drops radially from Poisson’s ratio at the crack tip to zero beyond certain radial distances. Strong 3D zones (T_z > 0) exist within a radial distance r/a of about 4.6-0.7 for a/c = 0.2-1.0 along the crack front, despite the stress-free boundary conditions far away. At the same radial distance along the crack front in the 3D zones, T_z increases from zero on one free surface to a peak value in the interior, and then decreases to zero on another free surface. The distributions of T_z near the corner points are also discussed. Empirical formulae describing the 3D distributions of T_z are obtained by fitting the numerical results, which prevail with a sufficient accuracy in the valid range of 0.2 ? a/c ? 1.0 and 0° ? θ ? 90° except very near the free surfaces where T_z is extremely low. Combined with the K-T solution, the transition of approximate plane-stress state near the surfaces to plane-strain state in the interior can be characterized more accurately.     

Crack observation methods, their application and simulation of curved fatigue crack growth

The observation of cracks with curved crack path has to be done optically. It is shown that a modified commercial flat bed scanner and a combination of a high-resolution scanner camera system with 10,000 × 10,000 pixels with a telecentric lens are appropriate for high-resolution (up to 8 μm/pixel) optical recording of multiple crack ends on sample areas up to 210 mm × 290 mm. The high-resolution photographs are suitable for determination of crack lengths. It is also possible to observe crack paths or geometrical crack tip parameters and strain fields by image correlation. The method is used to determine static crack resistance and cyclic crack growth curves on center crack tension and biaxial cruciform samples.Furthermore, the paper presents an improved finite element technique for the simulation of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under biaxial plane stress loading applying a predictor-corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method including the consideration of the plastic limit loads. For this, the program PCCS-2D was extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the failure assessment diagram procedure in combination with a numerical crack path simulation. Finally, the simulation is verified experimentally.     

Approximate J estimates for tension-loaded plates with semi-elliptical surface cracks

This paper provides a simplified engineering J estimation method for semi-elliptical surface cracked plates in tension, based on the reference stress approach. Note that the essential element of the reference stress approach is the plastic limit load in the definition of the reference stress. However, for surface cracks, the definition of the limit load is ambiguous (“local” or “global” limit load), and thus the most relevant limit load (and thus reference stress) for the J estimation should be determined. In the present work, such limit load solution is found by comparing reference stress based J results with those from extensive 3-D finite element (FE) analyses. Based on the present FE results, the global limit load solution proposed by Goodall for surface cracked plates in combined bending and tension was modified, in the case of tension loading only, to account for a weak dependence on w/c and was defined as the reference normalizing load. Validation of the proposed equation against FE J results based on actual experimental tensile data of a 304 stainless steel shows excellent agreements not only for the J values at the deepest point but also for those at an arbitrary point along the crack front, including at the surface point. Thus the present results provide a good engineering tool for elastic-plastic fracture analyses of surface cracked plates in tension.     

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.     

J-T characterized stress fields of surface-cracked metallic liners bonded to a structural backing - I. Uniaxial tension

Surface crack-tip stress fields in a tensile loaded metallic liner bonded to a structural backing are developed using a two-parameter J-T characterization and elastic-plastic modified boundary layer (MBL) finite element solutions. The Ramberg-Osgood power law hardening material model with deformation plasticity theory is implemented for the metallic liner. In addition to an elastic plate backed surface crack liner model, elastic-plastic homogeneous surface crack models of various thicknesses were tested. The constraint effects that arise from the elastic backing on the thin metallic liner and the extent to which J-T two parameter solutions characterize the crack-tip fields are explored in detail. The increased elastic constraint imposed by the backing on the liner results in an enhanced range of validity of J-T characterization. The higher accuracy of MBL solutions in predicting the surface crack-tip fields in the bonded model is partially attributed to an increase in crack-tip triaxiality and a consequent increase in the effective liner thickness from a fracture standpoint. After isolating the effects of thickness, the constraint imposed by the continued elastic linearity of the backing significantly enhanced stress field characterization. In fact, J and T along with MBL solutions predicted stresses with remarkable accuracy for loads beyond full yielding. The effects of backing stiffness variation were also investigated and results indicate that the backing to liner modulus ratio does not significantly influence the crack tip constraint. Indeed, the most significant effect of the backing is its ability to impose an elastic constraint on the liner. Results from this study will facilitate the implementation of geometric limits in testing standards for surface cracked tension specimens bonded to a structural backing.     

An experimental investigation of the effect of biaxial loading on the master curve transition temperature in RPV steels

During the 1990s considerable work was conducted to characterize the effect of biaxial loading on the ductile to brittle transition temperature. The work centered on a series of tests using large cruciform bend specimens from an experimental A533B test plate denoted as HSST Plate 14 (Heavy Section Steel Technology Plate 14). Recently a series of similar biaxial cruciform tests has been conducted on the steel used for an extensive European Round Robin that investigated the ductile-to-brittle transition master curve and associated T₀ reference temperature. The results of these tests have been used to promote the concept of a “Biaxial Effect” which corresponds to a shift in the shallow crack transition master curve of +20 °C or more when biaxial stresses are present, in comparison with the master curve for uniaxially loaded shallow crack specimens. A comprehensive analysis of the all of the available HSST Plate 14 data and data from two other structural steels was performed to investigate the extent of a biaxial effect on the reference temperature, T₀. The analysis included many additional biaxial cruciform test results on three different materials. The results of all three materials discussed in this paper fail to clearly demonstrate that biaxial loading, imposed through the use of a cruciform specimen geometry, has an effect on the fracture toughness, characterized using a master curve approach and reference temperature T₀. The analysis utilized in this paper assumes that the toughness distribution and temperature dependence of shallow cracked specimens can be modeled by using the master curve approach. This assumption has not been rigorously validated and would benefit from further study. Additional detailed stress analysis of the constraint evolution in the cruciform specimens may better define the precise conditions under which a biaxial effect on the fracture toughness could be realized.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens. Part II: 3-D effects on constraint

This study describes an extensive set of 3-D analyses conducted on conventional fracture specimens, including pin-loaded and clamped SE(T) specimens, and axially cracked pipes with varying crack configurations. The primary objective is to examine 3-D effects on the correlation of fracture behavior for the analyzed crack configurations using the J-Q methodology. An average measure of constraint over the crack front, as given by an average hydrostatic parameter, denoted Q_avg, is employed to replace the plane-strain measure of constraint, Q. Alternatively, a local measure of constraint evaluated at the mid-thickness region of the specimen, denoted Q_Z0, is also utilized. The analysis matrix considers 3-D numerical solutions for models of SE(T) fracture specimens with varying geometries (i.e., different crack depth to specimen width ratio, a/W, as well as different loading point distance, H) and test conditions (pin-loaded ends vs. clamped ends). The 3-D numerical models for the cracked pipes cover different crack depth to pipe wall thickness ratio, a/t, and a fixed crack depth to crack length ratio, a/c. The extensive 3-D numerical analyses presented here provide a representative set of solutions which provide further support for using constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

An elastic-plastic finite element analysis of crack tip fields under biaxial loading conditions

A square plate containing a central crack and subjected to biaxial stresses has been studied by a finite element analysis. An elastic analysis shows that the crack opening displacement and stress of separation ahead of the crack tip are not affected by the mode of biaxial loading and therefore the stress intensity factor adequately describes the crack tip states in an elastic continuum.

An elastic-plastic analysis involving more than localized yielding at the crack tip provides different solutions of crack tip stress fields and crack face displacements for the different modes of biaxial loading.

The equi-biaxial loading mode causes the greatest separation stress but the smallest plastic shear ear and crack displacement. The shear loading system induces the maximum size of shear ear and crack displacement but the smallest value of crack tip separation stress.

     

Numerical simulation study of fatigue crack growth behavior of cracked aluminum panels repaired with a FRP composite patch using combined BEM/FEM

A combined boundary element method and finite element method (BEM/FEM) is employed to investigate the fatigue crack growth behavior of cracked aluminum panels repaired with an adhesively bonded fiber-reinforced polymer (FRP) composite patch. Numerical simulation of crack growth process of a cracked aluminum panel repaired with a FRP composite patch under uniaxial cyclic loading has been carried out. The curve of crack length on unpatched side of the cracked panel versus the number of cyclic loading is determined by the numerical simulation, and it agrees well with experimental data. Furthermore, the crack front profiles of the cracked panel during fatigue crack growth and the distributions of stress intensity factors along crack fronts are also numerically simulated.     

Fracture mechanics global approach concepts applied to creep slow crack growth in a medium density polyethylene (MDPE)

Creep fracture by slow crack growth is studied in a medium density polyethylene at 60 °C and 80 °C. Whereas elastic-plastic fracture mechanics load parameters fail to provide a unique temperature-independent correlation, that of the fracture mechanics for creeping solids C^∗ is proved to be relevant since this parameter correlates very well with the time to failure. Correlation established on both full notched creep tensile and double edge notched tensile tests was validated on cracked gas-pipe samples tested under hydrostatic pressure, extending the use of time to failure versus C^∗ diagram to predict lifetime of engineering components.     

Effects of component size, geometry, microstructure and aging on the embrittling behavior of creep crack growth correlated by the Q parameter

The driving force for creep crack growth is dominated by local elastic-plastic stress in the creep damage zone around a crack tip, temperature and microstructure. In previous work, C^∗, C_t, load line displacement rate dδ/dt and Q^∗ parameters have been proposed as formulations of creep crack growth rate (CCGR). Furthermore, using parameters mentioned above, the construction of the algorithm of predictive law for creep crack growth life is necessary for life assessment procedures. The aim of this paper is to identify the effects of component size, geometry, microstructure, aging and weldment on the embrittling behavior of creep crack growth and incorporate these effects in a predictive law, using the Q^∗ parameter. It was found that for specimen size (width and thickness) and of material softening due to aging the values of the activation energy were the same whereas for grain size change and structural brittleness, which affected crack tip multi-axial stress state the values for the activation energy for CCGR differ.     

Crack arrest testing of high strength structural steels for naval applications

The crack arrest fracture toughness of two high strength steel alloys used in naval construction, HSLA-100, Composition 3 and HY-100, was characterized in this investigation. A greatly scaled-down version of the wide-plate crack arrest test was developed to characterize the crack arrest performance of these tough steel alloys in the upper region of the ductile-brittle transition. The specimen is a single edge-notched, 152 mm wide by 19 mm thick by 910 mm long plate subjected to a strong thermal gradient and a tensile loading. The thermal gradient is required to arrest the crack at temperatures high in the transition region, close to the expected service temperature for crack arrest applications in surface ships. Strain gages were placed along the crack path to obtain crack position and crack velocity data, and this data, along with the applied loading is combined in a “generation mode” analysis using finite element analysis to obtain a dynamic analysis of the crack arrest event. Detailed finite element analyses were conducted to understand the effect of various modeling assumptions on the results and to validate the methodology compared with more conventional crack arrest tests.Brittle cracks initiation, significant cleavage crack propagation and subsequent crack arrest was achieved in all 15 of the tests conducted in this investigation. A crack arrest master curve approach was used to characterize and compare the crack arrest fracture toughness. The HSLA-100, Comp. 3 steel alloy had superior performance to the HY-100 steel alloy. The crack arrest reference temperature was T_KIA = −136 °C for the HSLA-100 plate and T_KIA = −64 °C for the HY-100 plate.