Effective Stress Intensity Factor Research Articles

Theoretical and experimental study of fatigue growth of interacting cracks

Life assessment of structures weakened by interacting cracks represents an important and very challenging problem. Subsequently, the main objective of this paper is to address this problem by developing a new computational technique. It is based on the classical strip-yield model and plasticity-induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle-by-cycle calculations of the effective stress intensity factors and crack increments. The modelling results are validated against an experimental study focusing on fatigue behaviour of two closely spaced collinear cracks in wide plates with different thicknesses. It is confirmed that non-linear effects associated with crack interaction have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components.

Stress intensity factor solutions for adhesive-bonded lap-shear specimens of magnesium and steel sheets with and without kinked cracks for fatigue life estimations

In this paper, stress intensity factor solutions for adhesive-bonded lap-shear specimens of magnesium alloy AZ31 and hot-dip-galvanized (HDG) mild steel sheets with and without kinked cracks are investigated for fatigue life estimations. First, the kinked fatigue crack failure mode of the adhesive-bonded lap-shear specimens is briefly reviewed. Then, the analytical global J integral and effective stress intensity factor solutions for main cracks in lap-shear specimens of three dissimilar sheets under plane strain conditions are developed based on the beam bending theory. The global effective stress intensity factor solutions for the main cracks in the lap-shear specimens from the corresponding finite element analyses are then presented and validated by the analytical solutions. Next, the local stress intensity factor solutions for kinked cracks with the experimentally observed kink angle as functions of the kink length from the corresponding finite element analyses are presented and the computational solutions are also compared with the analytical solutions at small kink lengths. The results indicate that the computational local stress intensity factor solutions for kinked cracks approach to the analytical solutions as the kink length decreases to a small value and the kinked crack is under dominant mode I loading conditions. The computational results also indicate that the local stress intensity factor solutions at a small kink length of microstructural significance may be used as the stress intensity factor solutions for zero or near zero kink length for fatigue life estimations when the computational results are not available. The computational local stress intensity factor solutions are then adopted to estimate the fatigue lives of the lap-shear specimens based on a kinked crack growth model and available material constants for the Paris law. The fatigue life estimations are lower than the experimental results. However, the general trend of fatigue life estimations agrees with that of the experimental results.

Near-threshold fatigue propagation of physically through-thickness short and long cracks in a low alloy steel

In this paper, the near-threshold fatigue behavior of physically through-thickness short cracks and of long cracks in a low alloy steel is investigated by experiments in ambient air. Physically through-thickness short fatigue cracks are created by gradually removing the plastic wake of long cracks in compact tension specimens. The crack closure is systematically measured using the compliance variation technique with numerical data acquisition and filtering for accurate detection of the stress intensity factor (SIF) at the crack opening. Based on the experimental results, the nominal threshold SIF range is shown to be dependent on the crack length and the characteristic of the crack wake which is strongly dependent on the loading history. The effective threshold SIF range and the relation between the crack propagation rate and the effective SIF range after the crack closure correction are shown to be independent on crack length and loading history. The shielding effect of the crack closure is shown to be related to the wake length and load history. The effective threshold SIF range and the relationship between the crack growth rate and the effective SIF range appear to be unique for this material in ambient air. These properties can be considered as specific fatigue properties of the couple material/ambient air environment.

3-D stress intensity factors due to autofrettage for an inner radial lunular or crescentic crack in a spherical pressure vessel

Three dimensional Mode I Stress Intensity Factor (SIF) distributions along the front of an inner radial lunular or crescentic crack emanating from the bore of an autofrettaged spherical pressure vessel are evaluated. The 3-D analysis is performed using the finite element (FE) method employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is applied to the vessel. The residual stress field is simulated in the FE analysis using an equivalent temperature field. SIFs for three vessel geometries (R0/Ri=1.1, 1.2, and 1.7), a wide range of crack depth to wall thickness ratios (a/t=0.01–0.8), various ellipticities (a/c=0.2–1.5), and three levels of autofrettage (ε=50%, 75%, and 100%) are evaluated. In total, about two hundred and seventy different crack configurations are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly indicate the possible favorable effect of autofrettage in considerably reducing the prevailing effective stress intensity factor i.e., delaying crack initiation, slowing crack growth rate, and thus, substantially prolonging the total fatigue life of the vessel. Furthermore, the results emphasize the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three dimensional analysis herein performed.

Near threshold fatigue crack growth in ultrafinegrained copper

The near threshold fatigue crack growth in ultrafine-grained (UFG) copper at room temperature was studied in comparison to conventional coarse-grained (CG) copper. The fatigue crack growth rates da/dN in UFG copper were enhanced at ΔK ≤ 7 MPa√m compared to the CG material. The crack closure shielding, as evaluated using the compliance variation technique, was shown to explain these differences. The effective stress intensity factor amplitude AKeff appears to be the same driving force in both materials. Tests performed in high vacuum on UFG copper demonstrate the existence of a huge effect of environment with growth rates higher of about two orders of magnitude in air compared to high vacuum. This environmental effect on the crack path and the related microstructure is discussed on the basis of fractography observations performed using scanning electron microscope and completed with field emission scanning electron microscope combined with the focused ion beam technique.

Generalized Irwin plastic zone correction for a Griffith crack near a coated-circular inclusion

Elastic-plastic stress analysis on a radial crack interacting with a coated-circular inclusion in a matrix has been carried out with the aid of a generalized Irwin plastic zone correction. The crack line is assumed to be at the angle of 90° − θ from a remote tensile loading. In the mathematical formulation, the distributed dislocation method is used to simulate the crack. By solving a set of singular integral equations, three quantities, the effective stress intensity factor, the plastic zone size and the crack tip opening displacement (CTOD), are evaluated with the generalized Irwin model proposed. Numerical examples are given to show the influence of the key parameters such as the crack orientation angle θ, the normalized crack distance, the normalized coating phase thickness and the shear modulus ratio ([Formula: see text], coating phase/matrix) on the fracture behavior. The results indicate that the influence of angle θ is the greatest, while the effect of shear modulus ratio [Formula: see text] is relatively small. A validation checking is performed by the finite element method (FEM) for one case. The result obtained from the FEM simulation matches well with that from the current method.

ELASTIC-PLASTIC FRACTURE BEHAVIOR ANALYSIS ON A GRIFFITH CRACK IN THE CYLINDRICAL THREE-PHASE COMPOSITES WITH GENERALIZED IRWIN MODEL

Elastic-plastic stress analysis on a matrix crack interacting with near-by circular inclusions (the fibers) in fiber-reinforced composites has been carried out. The crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. To more accurately study the fracture behavior of the crack, plastic zone correction is introduced first time for such a crack-inclusion interaction problem. To determine the plastic zone sizes (PZSs) at the crack tips, a generalized Irwin model is proposed for the current mixed-mode problem where the von Mises stress yielding criterion is employed. With the aid of distributed dislocation method, the physical problem is formulated into a set of singular integral equations and solved through a numerical schism. The effective stress intensity factor (SIF), the PZS, crack tip opening displacement (CTOD) are evaluated accordingly. In the numerical examples, the influence of the crack orientation angle, the fiber/matrix shear modulus ratio, and fiber volume fraction on the fracture behavior of the crack is discussed in detail. It is found that the crack orientation angle has great effect on the normalized values of PZS, CTOD, and effective SIF, while the effects of shear modulus ratio and fiber volume fraction depend highly on the conditions of the inclusion (the fiber) and matrix.

Predicting fatigue resistance of nano-twinned materials: Part II – Effective threshold stress intensity factor range

The determination of ΔKth,eff for fatigue crack growth has been a challenging task. A model is forwarded to assess this parameter in presence of nano-scale twins for Cu, Ni and Al. The model utilizes the concept of irreversibility of crack emitted dislocation glide. Incremental crack extension is formulated on the basis of force balance of continuum dislocations during cyclic flow. Peierls stresses for free and twin boundary restricted glide, computed in Part I, constitute an essential ingredient in devising crack growth threshold founded on relative positions of dislocations. Predicted ΔKth,eff for relatively short cracks is shown to be substantially enhanced with a refinement in twin lamellar thickness and twin spacing as indicated experimentally in recent literature. The theoretical values of ΔKth,eff in Ni, Cu and Al are in good agreement with experimental literature for longer cracks as well. Saturation effects are observed in ΔKth,eff levels with respect to gradual increase in twin nano-dimensions as well as crack length. Mechanistic origin of these observations is discussed.

A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness

ABSTRACTFatigue and fracture assessment of structures weakened by multiple site damage, such as two or more interacting cracks, represents a very challenging problem. A proper analysis of this problem often requires advanced modelling approaches. The objective of this paper is to develop a general theoretical approach and investigate the fatigue behaviour of two interacting cracks. The developed approach is based on the classical strip yield model and plasticity induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle‐by‐cycle calculations of the effective stress intensity factors and crack increments. The modelling results were validated against experimental data available in the literature. Further, the nonlinear effects of the crack interaction and plate thickness on the crack opening stresses and crack growth rates were studied with the new approach for the problem geometry. It was demonstrated that the both effects could have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components with multiple site damage.

A Zener–Stroh crack interacting with a coated inclusion with generalized Irwin plastic zone correction

The elastic–plastic fracture behavior of a Zener–Stroh crack interacting with a coated inclusion in composite materials has been investigated with crack tip plastic zone corrections. With the distributed dislocation method, the crack problem is formulated into a set of singular integral equations which are solved numerically. The plastic zone sizes at the both crack tips are determined by a generalized Irwin model where Von Mises stress yielding criterion is used. The stress intensity factor (SIF), the plastic zone size (PZS), the crack tip opening displacement (CTOD) and the effective stress intensity factor have been evaluated. In the numerical examples, the influence of the inclusion shear modulus, the coating-layer thickness and shear modulus, as well as the distance between the crack and inclusion, on the SIF, the PZS and the CTOD are discussed in detail. Numerical examples show that increasing the shear modulus or the thickness of the coating phase, the influence of the inclusion on the normalized SIF and the normalized PZS will be shielded.

Cold hole expansion effect on the fatigue crack growth in welds of a 6061-T6 aluminum alloy

Compact test specimens were extracted from a 6061-T6 aluminum alloy welded plate with a thickness of 9mm to analyze the cold hole expansion effect on fatigue crack growth tests conducted in mode I cyclic loading. At R=0.1, a sharp crack in base metal, weld metal and heat affected zone was propagated from 17 to 24mm. The fatigue crack growth at 24mm (α=a/W=0.3) was delayed by drilling a hole at the crack tip and applying a cold hole expansion of 4.1%. The residual stress fields due to cold hole expansion were determined with the finite element method. The fatigue crack growth testing was continued up to a crack length of 35mm (α∼0.43) at the same R, and crack opening displacements of the post-expansion crack were also determined with the finite element method. The results were expressed in terms of crack length versus number of cycles, as well as, fatigue crack growth rate as a function of applied and effective stress intensity factor range. The cold hole expansion contributed to delay the fatigue crack growth in base metal, and to a lesser extent in the weld metal and heat affected zone. A crack closure effect was determined by means of load versus crack opening displacement curves of the post-expansion crack, which was, completely or partially closed, in welded zones with compressive residual stress fields. The fracture surfaces of each welded zone were analyzed to elucidate the crack nucleation zone and its relation with the residual stress field. In all cases the crack was initiated at the surface of the specimen where the residual stresses were positive.

Quarter elliptical crack growth using three dimensional finite element method and crack closure technique

Shape evolution of a quarter-elliptical crack emanating from a hole is studied. Three dimensional elastic-plastic finite element analysis of the fatigue crack closure was considered and the stress intensity factor was calculated based on the duplicated elastic model at each crack tip node. The crack front node was advanced proportional to the imposed effective stress intensity factor. Remeshing was applied at each step of the crack growth and solution mapping algorithm was considered. Crack growth retardation at free surfaces was successfully observed. A MATLAB-ABAQUS interference code was developed for the first time to perform crack growth on the basis of crack closure. Simulation results indicated that crack shape is sensitive to the remeshing strategy. Predictions based on the proposed models were in good agreement with Carlson’s experiments results.

Multiscale fatigue crack growth modelling for welded stiffened panels

ABSTRACTThe influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, KI, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, Ktot, is derived by a part due to the applied load, Kappl, and by a part due to welding residual stresses, Kres. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.

A Zener–Stroh crack in fiber-reinforced composites with generalized Irwin plastic zone correction

Abstract Elastic–plastic stress analysis on a matrix Zener–Stroh crack interacting with nearby inclusions (the fibers) in fiber-reinforced composites has been carried out. The Zener-Stroh crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. Plastic zone correction is introduced the first time for such a crack-inclusion interaction problem so that the fracture behavior can be analyzed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed-mode loading problem where the Von Mises stress yielding criterion is employed. Different to a Griffith crack, a Zener–Stroh crack propagation always occurs from the sharp tip whose relative position to the near-by fiber has great effect on the fracture behavior of the crack. In our study, the effective stress intensity factor (SIF), plastic zone size (PZS) and crack tip opening displacement (CTOD) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fiber) shear modulus, inclusion volume fraction and the crack sharp tip position on the fracture behavior of the crack is discussed. It is found that the shear modulus ratio has great effect on the normalized values of PZS and CTOD, while the effect of fiber volume fraction depends highly on the conditions of the inclusion/matrix properties and the crack sharp tip position.

Finite Element Simulation of Stable Fatigue Crack Growth Using Critical CTOD Determined by Preliminary Finite Element Analysis

Finite element simulation of stable fatigue crack growth using critical crack tip opening displacement (CTOD) was done. In the preliminary finite element simulation without crack growth, the critical CTOD was determined by monitoring the ratio between the displacement increments at the nodes above the crack tip and behind the crack tip in the neighborhood of the crack tip. The critical CTOD was determined as the vertical displacement at the node on the crack surface just behind the crack tip at the maximum ratio. In the main finite element simulation with crack growth, the crack growth rate with respect to the effective stress intensity factor range considering crack closure yielded more consistent result. The exponents m in the Paris law were determined.

3D Numerical Study on how the Local Effective Stress Intensity Factor Range Can Explain the Fatigue Crack Front Shape

The plasticity-induced crack closure of through-thickness cracks, artificially obtained from short cracks grown in CT specimens of 304L austenitic stainless steel, is numerically simulated using finite elements. Crack advance is incremented step by step, by applying constant ΔK amplitude so as to limit the loading history influence to that of crack length and crack wake. The calculation of the effective stress intensity factor range, ΔKeff, along curved shaped crack fronts simulating real crack fronts, are compared to calculation previously performed for through-thickness straight cracks. The results for the curved crack fronts support that the front curvature is associated to constant ΔKeff amplitude, thus assumed to be the propagation driving force of the crack all along its front.

Rate‐ and strain‐dependent brittle deformation of rocks

We develop a unifying framework to quantify rate‐dependent deformation in the brittle field and establish links between the microscale time‐dependent crack growth processes and the macroscopically observed rate dependency. Triaxial deformation experiments have been performed under both constant strain rate and constant stress (creep) conditions on three types of sandstone. The measured relative evolution of P wave speeds as a function of inelastic axial strain is similar for both types of test, despite differences in strain rate of up to 3 orders of magnitude. This similarity indicates that there exists a direct, time‐independent link between the microstructural state (as reflected by the variations in P wave speed) and the inelastic axial strain. Comparison of applied stresses between constant strain rate and creep experiments as a function of inelastic strain indicates that creep deformation requires less mechanical work to bring the sample to failure. This energy deficit corresponds to a stress deficit, which can be related to a deficit in energy release rate of the microcracks. We establish empirically that the creep strain rate is given by , where ΔQ is the stress deficit (negative) and σ∗ is an activation stress. This empirical exponential relation between creep strain rate and stress deficit is analogous to rate‐and‐state friction law. We develop a micromechanical approach based on fracture mechanics to determine the evolution of an effective stress intensity factor at crack tips during creep deformation and estimate the activation volume of the stress corrosion reaction responsible for brittle creep.

Fatigue Short Crack Growth and Mechanism of GH4133B Superalloy Used in Turbine Disk of Aero-Engine

The short fatigue crack growth tests for circular notched compact tension specimens of GH4133B superalloy used in turbine disk of aero-engine are carried out at ambient temperature and atmospheric pressure. The stress intensity factor ranges and the fatigue crack growth rates at various stress ratios are measured, and the corresponding effective stress intensity factor ranges considering the crack closure effect are calculated. It is shown that the effective stress intensity factor range ΔKeff, can be applied to describe the deceleration and acceleration of crack growth rate during the short crack propagation. The fatigue fracture surface morphologies in the short crack growth region are investigated using a scanning electron microscopy. It is found that there is a cleavage step between two adjacent radial striations, a series of early fatigue striations exist on the cleavage step, and some secondary cracks perpendicular to the direction of main crack propagation emerge on the fracture surface, the superalloy exhibits a mixed fracture mode in the short crack growth region, which reveals the microscopic mechanism of short crack propagation that the fatigue crack growth rate is primarily higher, and then gradually decreases with the propagation of short crack.

Assessment of the Stability of a Surface Crack in Laminates

The critical configuration of a crack arrested at a bimaterial interface is estimated. The stability of the crack in the soft material, whose front is situated at the interface between soft and stiff materials and who grows continuously sideways, is analyzed. A laminate with an ABAB structure containing a surface crack is considered in this study. The effective value of the stress intensity factor for the central segment of the crack front lying at the material interface is calculated for various geometrical and material configurations. Comparing the effective value of the factor with the corresponding threshold values, the stability of the configuration studied can be assessed. It is found that a 3D solution for estimating the effective stress intensity factor is necessary to describe the crack behavior at the interface even for a relatively shallow crack. The results presented can be helpful for the inspection of lamellar structures.

Cooperative toughening mechanism of nanocrystalline materials by grain rotation and shear-coupled migration of grain boundaries

A theoretical model is proposed to illustrate the cooperative effect of nano-grain rotation and shear-coupled migration of grain boundaries on toughening of nanocrystalline materials. The toughening mechanism is embodied by an effective stress intensity factor near the tip of a mode I crack. The result shows a possibly effective toughening mechanism in nanocrystalline materials.