Mode Crack Growth Research Articles

Fatigue Crack Propagation Under Complex Loading

The paper describes the recent progress of the understanding of fatigue crack propagation under complex loading. The behavior of fatigue crack propagation is dependent on the macroscopic mode of crack growth : tensile mode and shear mode growth. Tensile mode growth takes place on the plane perpendicular to the maximum tangential stress range, satisfying the local symmetry. Shear mode growth takes place on the plane of the maximum shear stress when a precrack is subjected to high cyclic shear stress. When the shear stress is low, a bent or branched crack is formed at the precrack tip, showing tensile crack growth. Under an intermediate stress, a crack first shows shear mode growth and turns to tensile mode after some extension. This transition is caused by the decrease in the mode II crack-tip stress intensity factor due to increasing crack surface contact. The criterion of the maximum crack growth rate may control the mode of fatigue crack growth. In notched components under complex loading, the life of crack initiation at the notch root is calculated from the critical plane model using the stress and strain at a critical distance from the notch root. The propagation of a fatigue crack from a notch is dependent on the geometry of notched component. The resistance-curve method is applicable for the prediction of fatigue thresholds of thin walled tubular specimens subjected to in-phase and out-of-phase combination of cyclic torsion and tension-compression.

Residual stress analysis and fatigue of multi-pass welded tubular structures

The purpose of this study is to investigate the residual stresses near the weld root and the weld toe for multi-pass welded tube-to-plates. Two different tubular joint configurations were studied; a three-pass single-U weld groove for maximum weld penetration and a two-pass fillet (no groove) welded tube-to-plates for minimum weld penetration. A 2D axi-symmetric finite element model was developed to calculate the temperature distribution, HAZ, penetration depth and the residual stress distribution for the sequentially coupled thermo-mechanical analysis. The calculated residual stresses was compared with experimental results and showed qualitatively good agreement. Torsion fatigue tests were performed in order to study crack propagation from the weld root, lower and upper weld toe in mode III. Some of the tube structures were loaded with a static internal pressure in order to separate the root crack and initiate the crack growth in mode III. Another batch was PWHT and fatigue tested, in order to study the influence of residual stresses.

Cyclic Plasticity of a Cracked Structure Subjected to Mixed Mode Loading

Cyclic plasticity in the crack tip region is at the origin of various history effects in fatigue. For instance, fatigue crack growth in mode I is delayed after the application of an overload because of the existence of compressive residual stresses in the overload’s plastic zone. Moreover, if the overload’s ratio is large enough, the crack may grow under mixed mode condition until it has gone round the overload’s plastic zone. Thus, crack tip plasticity modifies both the kinetics and the crack’s plane. Therefore modeling the growth of a fatigue crack under complex loading conditions requires considering the effects of crack tip plasticity. Finite element analyses are useful for analyzing crack tip plasticity under various loading conditions. However, the simulation of mixed mode fatigue crack growth by elastic-plastic finite element computations leads to huge computation costs, in particular if the crack doesn’t remain planer. Therefore, in this paper, the finite element method is employed only to build a global constitutive model for crack tip plasticity under mixed mode loading conditions. Then this model can be employed, independently of any FE computation, in a mixed mode fatigue crack growth criterion including memory effects inherited from crack tip plasticity. This model is developed within the framework of the thermodynamics of dissipative processes and includes internal variables that allow modeling the effect of internal stresses and to account for memory effects. The model was developed initially for pure mode I conditions. It was identified and validated for a 0.48%C carbon steel. It was shown that the model allows modeling fatigue crack growth under various variable amplitude loading conditions [1]. The present paper aims at showing that a similar approach can be applied for mixed mode loading conditions so as to model, finally, mixed mode fatigue crack growth.

Transient and steady state crack growth kinetics for stress corrosion cracking of a cold worked 316L stainless steel in oxygenated pure water at different temperatures

The stress corrosion cracking (SCC) growth kinetics for a cold worked 316L stainless steel was continuously monitored in high purity water at different temperatures and dissolved oxygen (DO) levels under a K (or K max) of 30 MPa m 0.5. The total SCC test time was more than 8000 h to make sure the steady state crack growth rate under each test condition could be reached. Crack growth rate (CGR) increases with increasing temperature in the range 110–288 °C. A typical intergranular-cracking mode is identified. Depending on the previous test condition, especially the temperature, three kinds of crack growth kinetics, i.e., increasing with testing time then becoming steady, being constant during the whole period, or decreasing with test time then becoming steady, are identified and discussed. Time-dependent and testing history-dependent crack growth modes were confirmed in two series of tests in 2 ppm DO and 7.5 ppm DO pure water. The apparent activation energies are calculated and compared with other data in different environments under different applied loading levels for understanding the cracking mechanism.

Influence of yield strength levels on crack growth mode in delayed fracture of structural steels

A mechanistic aspect of the susceptibility to the delayed fracture is studied with an emphasis on the critical behaviour of the subsurface growth of Quasi-Cleavage (QC) and Inter-Granular (IG) cracks. The materials employed are 0.35%C plain carbon steel and boron added bolt steel which were quenched and tempered to have various levels of yield strength ranging from 500 to 1400 MPa. Fractographic analysis shows us that QC + IG cracking process can be an essential mode in the delayed fracture of steels. A low susceptibility to delayed fracture can be explained by the crack growth behavior when the crucial blunting occurs at the crack tip.

Microstructure effects on high temperature fatigue crack initiation and short crack growth in turbine disc nickel-base superalloy Udimet 720Li

An assessment of the effects of microstructure on fatigue crack initiation and short crack growth in a turbine disc nickel-base superalloy at 650 °C in air is presented. U720Li and microstructural variants of U720Li, i.e. U720Li-LG (large grain variant) and U720Li-LP (large intragranular coherent γ′ precipitate variant) have been assessed by uninterrupted and replicated short crack tests in polished U-notch specimens using a 1-1-1-1 trapezoidal loading cycle at nominal stress levels ranging between 700 and 850 MPa (calculated in the uncracked ligament). Crack initiation was primarily due to porosity on or near the surface but also due to grain boundary oxidation. Initial transgranular crack growth across four to six grains in air was noted at short crack lengths before oxidation-assisted intergranular crack growth modes were established at larger crack lengths. At a nominal applied stress of 840 MPa, U720Li and U720Li-LP show similar fatigue lifetimes while U720Li-LG demonstrates a significantly improved fatigue lifetime, particularly when lifetimes are compared on a local strain range basis. A larger grain size gave the most significant performance benefits in terms of overall fatigue lifetime under these test conditions.

On small fatigue crack growth and crack closure under mixed-mode and through zero loading in the aluminium alloys 2024-T351 and 8090-T8771

In situ SEM measurements and observations of crack opening displacement (COD) have been made during unloading of small mode I and mixed-mode fatigue cracks in samples of the aluminium alloys 2024-T351 and 8090-T8771. Changes in COD with decreasing load were used to measure mode I and mode II crack closure levels. The cracks were self-initiated, surface-breaking, semi-elliptical or corner cracks that were produced by constant amplitude loading at R ratios of 0.05, 0.1 or −1. Mode I crack closure was present in both alloys for small mode I cracks grown at R ratios near zero. Both mode I and mode II crack closure were usually found in the mixed-mode cracks. The level of mode II closure was generally less than that for the mode I component and so a greater effective proportion of the nominal load range would be available to produce crack growth in mode II. A residual plastic shear offset was present at the tips of the mixed-mode cracks due to incomplete reversibility of plastic flow and a consequent ratcheting of the shear deformation during crack growth. The mode II damage process ahead of the crack tip would occur during cyclic shear superimposed upon an increasing residual offset. Similarly, the elastic shear strain behind the crack tip was offset and this would enhance the likelihood of developing mode I crack closure at crack surface irregularities. In some mixed-mode cracks in the 8090 alloy it was found that mode II crack closure could be absent during part or all of the compressive loading during testing at R=−1. This suggests that procedures for predicting fatigue life cannot always assume that compressive loads do not contribute to fatigue crack growth.

An elastic strip with periodic surface cracks under thermal shock

The problem of two periodic edge cracks in an elastic infinite strip located symmetrically along the free boundaries under thermal shock is investigated. It is assumed that the infinite strip is initially at constant temperature. Suddenly the surfaces containing the edge cracks are quenched by a ramp function temperature change. Very high tensile transient thermal stresses arise near the cooled surface resulting in severe damage. The degree of the severity for a subcritical crack growth mode is measured by determining the stresses intensity factors. The thermoelastic problem is treated as uncoupled quasi-static. The superposition technique is used to solve the problem. The thermal stresses obtained from the uncracked strip with opposite sign are utilized as the only external loads to formulate the perturbation problem. By expressing the displacement components in terms of finite and infinite Fourier transforms, a hypersingular integral equation is derived with the crack surface displacement as the unknown function. Numerical results for stress intensity factors are carried out and presented as a function of time, cooling rate, crack length, and periodic crack spacing.

環状切欠き材の繰返しねじり疲労におけるファクトリールーフの形成について

The formation behavior of factory-roof in circumferential notched specimen was examined. To achieve an observation of cracks in internal of material, two plastics were used for testing. One was acryl and the other was polycarbonate. Cyclic torsional tests were performed with and without application of static tension. With the polycarbonate, a factory-roof was not formed in fracture surface. However, using acryl, that was observed when cyclic torsion tests were conducted with static tension. Therefore, the discussion was focused at the results in acryl. When the factory-roof was formed, many small cracks were initiated and grew by shear mode, followed by coalescence and branching of them. After that, the crack growth mode was changed from shear mode to mode I. During mode I crack growth, the formation of the factory-roof was observed.

Contact Fatigue Analysis of an Elastic-Plastic Layered Medium With a Surface Crack in Sliding Contact With a Fractal Surface

Contact fatigue of a layered medium consisting of an elastic surface layer and three elastic-plastic underlying layers in sliding contact with a rigid and rough surface was analyzed with the finite element method. To include multiscale roughness effects and self-affine surface features, the topography of the rough surface was characterized by scale-invariant fractal geometry. A contact algorithm was used to identify the critical segment of the rough surface to be used in the contact fatigue simulations. The tensile and shear stress intensity factors and the direction and dominant mode of crack growth were determined from the crack-tip stresses. The effect of surface cracking on the evolution of plasticity in the second layer and the significance of topography (fractal) parameters on crack growth are interpreted in terms of the contact pressure, stress intensity factors, and maximum equivalent plastic strain. It is shown that a transition from tensile to shear dominant mode of fatigue crack growth occurs as the crack tip approaches the interface, resulting in further crack growth almost parallel to the layer interface. The obtained results illustrate the important role of surface roughness in contact fatigue of layered media.

Finite element-based model for crack propagation in polycrystalline materials

In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.

Finite element-based model for crack propagation in polycrystalline materials

In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.

Damage zone characterization of composite panels with a modified crack growth model

Damage zone characterization of composite panels with a modified crack growth model

Damage zone characterization of composite panels with a modified crack growth model

In the present study a modified crack growth model (MCGM) is introduced to analyse the crack propagation status in the damaged zone of fibre reinforced composites. The damaged zone is modelled on the basis of a virtual crack being subjected to a cohesive closure stress. The residual strengths of composite laminates are evaluated characterizing the matrix crack density at the damaged zone and defining a relationship between the plate stiffness before and after damage. Experimental tests were performed employing epoxy/glass fibre reinforced composite laminates to determine the residual strength of centre cracked specimens. The residual strength of composite panels using the new model correlates well with experimental results when compared with previous models.

Effect of sandblasting on the long-term performance of dental ceramics.

A study has been made of the effects of sandblasting on the strength of Y-TZP and alumina ceramic layers joined to polymeric substrates and loaded at the top surfaces by a spherical indenter, in simulation of occlusal contact in ceramic crowns on tooth dentin. The sandblast treatment is applied to the ceramic bottom surface before bonding to the substrate, as in common dental practice. Specimens with polished surfaces are used as a control. Tests are conducted with monotonically increasing (dynamic) and sinusoidal (cyclic) loading on the spherical indenter, up to the point of initiation of a radial fracture at the ceramic bottom surface immediately below the contact. For the polished specimens, data from the dynamic and cyclic tests overlap, consistent with a dominant slow crack growth mode of fatigue. Strengths of sandblasted specimens show significant reductions in both dynamic and cyclic tests, indicative of larger starting flaws. However, the shift is considerably greater in the cyclic data, suggesting some mechanically assisted growth of the sandblast flaws. These results have implications in the context of lifetimes of dental crowns.

Effect of Constraint on the Initiation of Ductile Fracture in Shear Loading

Research studies for mode I cracks have shown that fracture toughness or the critical value of J for fracture initiation, Jcrit is not merely a material property but depends also on the geometry and loading configurations. The geometry dependency of fracture toughness can be attributed to the effect of the crack tip constraint. In this paper, the constraint effect is studies for the initiation stage in mode II ductile crack growth. Two major mechanisms of ductile fracture: 'void growth and coalescence' and 'shear band localization and de-cohesion' are considered. A boundary layer model is simulated using the finite element method and the effect of far-filed T-stress on the relevant stress parameters near the crack tip is studied. It is shown that the initiation of the ductile crack growth in mode II is influenced significantly by T for the mechanism of void growth and coalescence and is insensitive to T for the mechanism of shear localisation and de-cohesion.

低炭素鋼のStage I型疲労き裂進展挙動(S14-6 き裂の進展挙動と破壊機構,S14 金属材料の疲労特性と破壊機構)

As for initial fatigue crack, quantitative evaluation was onsidered to e difficulty for reasons of both sides of metal-lurgical factor and mechanics factor influence behavior and crack growth mode change. In this study, paid its attention to initial fatigue crack growth to a depth direction, and examined Stage I fatigue crack behavior. To examine a mechanics condition governing stage I fatigue crack growth, fully reversed uniaxial push-pull high cycle fatigue tests were carried out on a low carbon steel. As a result behavior of Stage I fatigue crack became clear.

The effect of T‐stress on plane strain dynamic crack growth in elastic–plastic materials

ABSTRACTIn this paper, the effects of T‐stress on steady, dynamic crack growth in an elastic–plastic material are examined using a modified boundary layer formulation. The analyses are carried out under mode I, plane strain conditions by employing a special finite element procedure based on moving crack tip coordinates. The material is assumed to obey the J2 flow theory of plasticity with isotropic power law hardening. The results show that the crack opening profile as well as the opening stress at a finite distance from the tip are strongly affected by the magnitude and sign of the T‐stress at any given crack speed. Further, it is found that the fracture toughness predicted by the analyses enhances significantly with negative T‐stress for both ductile and cleavage mode of crack growth.

Brittle fracture in polycrystalline microstructures with the extended finite element method

AbstractA two‐dimensional numerical model of microstructural effects in brittle fracture is presented, with an aim towards the understanding of toughening mechanisms in polycrystalline materials such as ceramics. Quasi‐static crack propagation is modelled using the extended finite element method (X‐FEM) and microstructures are simulated within the framework of the Potts model for grain growth. In the X‐FEM, a discontinuous function and the two‐dimensional asymptotic crack‐tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Hence, crack propagation can be simulated without any user‐intervention or the need to remesh as the crack advances. The microstructural calculations are carried out on a regular lattice using a kinetic Monte Carlo algorithm for grain growth. We present a novel constrained Delaunay triangulation algorithm with grain boundary smoothing to create a finite element mesh of the microstructure. The fracture properties of the microstructure are characterized by assuming that the critical fracture energy of the grain boundary (Gcgb) is different from that of the grain interior (Gci). Numerical crack propagation simulations for varying toughness ratios Gcgb/Gci are presented, to study the transition from the intergranular to the transgranular mode of crack growth. This study has demonstrated the capability of modelling crack propagation through a material microstructure within a finite element framework, which opens‐up exciting possibilities for the fracture analysis of functionally graded material systems. Copyright © 2003 John Wiley & Sons, Ltd.

High Temperature Fatigue Crack Growth Behavior of Ti-6Al-4V

Experimental evaluation of high temperature, Fatigue Crack Growth Rate (FCGR) data for Ti-6Al-4V, a titanium alloy, is presented. The FCGR data were measured at room temperature, 175, 230, 290 and 345°C using the Direct Current Potential Difference (DCPD) technique. Compact Tension (CT) specimens were used in the program and crack growth rates (da/dN) vs. Mode I stress intensity factor ranges (AK) were plotted as a function of temperature. A temperature rise from 175 to 345°C did not cause a substantial increase in crack growth rates within the Stage II region where a linear relationship describes the behavior. Formation of secondary cracks, observed at higher temperatures, may have slowed the crack propagation as observed in the fractography.