Methods of Physical Simulation of Electrochemical Processes at the Tip of a Crack

We analyze stresses and the degree of plastic deformation at the contours of cracks of two types, namely, a sharp crack and a crack with slip lines. We show that at the tip of a crack of the second type, at the contour of the bottom–walls of the crack galvanic couple, there appear two symmetric microgalvanic couples at the slip lines. Microinhomogeneities of a metal (grain boundaries, nonmetallic inclusions, etc.) are submicrogalvanic couples whose activity increases due to inhomogeneity of microplastic deformations of their vicinities. We distinguished the mechanisms of corrosion-cyclic fracture and corrosion-static cracking. Under cyclic loading, breaking of grains occurs and grain boundaries and nonmetallic inclusions fail, which levels the influence of currents of submicrogalvanic couples on the growth rate of a crack. Under static loading, micro- and submicrogalvanic couples are permanently operating, the cold work of the surfaces of the metal of the walls of the crack is lower than that under cyclic loading, while the difference of potentials and the current of the bottom–walls of the crack galvanic couple are greater than those under cyclic loading. This explains both the phenomenon of branching and the higher growth rate of a crack of corrosion-static cracking with time. In addition to the electrode potential and pH of the medium, we propose to consider the following parameters as defining factors of the growth of a crack: currents of a galvanic couple, micro-, and submicrogalvanic couples and the time of repassivation of freshly formed metal surfaces appearing in the process of the growth of a crack. According to analysis of the literature data, these parameters cannot be experimentally determined. For this reason, we propose to use methods of simulation to investigate distributions of the potentials and currents of corrosion at the tip of a crack. We propose certain structures of physical and mechanoelectrochemical models of a crack and methods for measurement of distributions of the current density and the electrode potential at their surfaces.     

Viscoelastic Creep Crack Growth: A Review of Fracture Mechanical Analyses

The study of time dependent crack growth in polymers using a fracture mechanics approach has been reviewed. The time dependence of crack growth in polymers is seen to be the result of the viscoelastic deformation in the process zone, which causes the supply of energy to drive the crack to occur over time rather than instantaneously, as it does in metals. Additional time dependence in the crack growth process can be due to process zone behavior, where both the flow stress and the critical crack tip opening displacement may be dependent on the crack growth rate. Instability leading to slip-stick crack growth has been seen to be the consequence of a decrease in the critical energy release rate with increasing crack growth rate due to adiabatic heating causing are duction in the process zone flow stress, a decrease in the crack tip opening displacement due to a ductile to brittle transition at higher crack growth rates, or an increase in the rate of fracture work due to more rapid viscoelastic deformation. Finally, various techniques to experimentally characterize the crack growth rate as a function of stress intensity have been critiqued. This revised version was published online in July 2006 with corrections to the Cover Date.     

A plastic flow-induced fracture theory for fatigue crack growth

A plastic flow-induced fracture theory for fatigue crack growth is presented. A new formulae for the fatigue stress intensity threshold and the fatigue crack growth rate law are derived by applying the principle of energy conservation in considering the fatigue crack growth process in the presence of local plastic flow ahead of the crack-tip. The present theory predicts not only the fatigue crack growth rate being just proportional to the rate of creation of dislocation at the crack-tip, but also the fatigue stress intensity threshold, which can be determined according to the applied fatigue stress amplitude and the characteristic size of microstructural fracture process ahead of the crack-tip, and can account for the fatigue crack growth characteristics at both low and high levels of applied fatigue stress intensity amplitude. All the results are universal and agree with the existing empirical results and experimental observations.     

3D adaptive finite element modeling of non-planar curved crack growth using the weighted superconvergent patch recovery method

In this paper, an adaptive finite element analysis is presented for 3D modeling of non-planar curved crack growth. The fracture mechanical evaluation is performed based on a general technique for non-planar curved cracks. The Schollmann’s crack kinking criterion is used for the process of crack propagation in 3D problems. The Zienkiewicz-Zhu error estimator is employed in conjunction with a weighted SPR technique at each patch to improve the accuracy of error estimation. Applying the proposed technique to 3D non-planar curved crack growth problems shows significant improvements particularly at the boundaries and near crack tip regions. Several numerical examples are presented to illustrate the robustness of the proposed technique.     

A non-equilibrium thermodynamic model for the crack propagation rate

A non-equilibrium thermodynamics-based evolution model describes the nonsteady, crack propagation rate for both brittle fracture and for viscoplastic behavior at the crack tip. This model for dynamic crack propagation under dynamic or quasi-static loading is developed from an energy functions viewpoint and extends a non-equilibrium thermodynamics construction based on a instantaneous maximum dissipation criterion and a thermodynamic relaxation modulus that permits multi-scale modeling. The evolution equations describing the non-equilibrium fracture process are generated from a generalized energy function whose zero gradient manifold gives the assumed quasi-static crack propagation equations. The class of models produced includes the classical Freund model and a modification that is consistent with the experimental maximum crack velocity. In unstable propagation, the non-equilibrium process is repelled from the quasi-static manifold. If the initial state is stable, then the crack growth process approaches the quasi-static manifold and eventually the crack is arrested. An application of the construction gives the craze growth in PMMA. A simple viscoplastic model for metals predicts the change in temperature at the crack tip as the crack grows.     

Elevated Temperature Fatigue Crack Growth rate model for NI-BASE Superalloys

Several time-dependent mechanisms are operational in the crack growth process of Ni-base superalloys at elevated temperature. Creep deformation during periods of sustained loading, oxygen diffusion at the crack tip, and oxidation reactions at and in front of the crack tip all contribute to the kinetics of crack growth. A crack growth rate model has been derived that attempts to capture the physics of these various rate processes. The proposed model assumes small-scale creep at the crack tip and incorporates the Hutchinson-Rice-Rosengren stress field equations to satisfy this condition. The model also includes stress-assisted diffusion of an environmental species at the crack tip. A process reaction rate is related to the time-rate of crack growth providing a model that accounts for these time-dependent processes. An evaluation of the form of the model is provided by comparison of the model with experimental crack growth data.     

Mixed mode I/II fracture of 2024-T3 friction stir welds

For the first time, a series of mixed mode I/II fracture experiments have been performed on both base material and three families of friction stir welds (FSWs) in 6.4 mm thick, 2024-T351 aluminum plate; the FSW joints are designated hot, medium and cold due to the level of nominal weld energy input per unit weld length (specific weld energy) during the joining process.Results from the fracture tests indicate that the measured critical crack opening displacement (COD) at a fixed distance behind the crack tip properly correlates both load-crack extension response and microstructural fracture surface features for both the base metal and all FSWs, providing measure of a quantitative fracture toughness. The COD values also indicate that transition from mode I to mode II dominant crack growth occurs at lower loading angles for FSW joints having higher specific weld energy input, with a truly mixed mode I/II COD measured during crack growth in the medium FSW joint. Using results from recent detailed FSW metallographic studies, specific features in the fracture process are correlated to the FSW microstructure. Finally, the observed ductile crack growth path in all three welds tends to exit the under-matched FSW weld region as the far-field applied shear loading is increased, with the medium FSW being the only case where the flaw remained within the FSW region for all combinations of shear and tensile loading.     

Fatigue life and crack path predictions in generic 2D structural components

This paper proposes a reliable and cost-effective two-phase methodology to predict crack propagation life in generic two-dimensional (2D) structural components. First, the usually curved fatigue crack path and its stress-intensity factors are calculated at small crack increments in a specialized finite-element software, using automatic remeshing algorithms, special crack tip elements and appropriate crack increment criteria. Then, the computed stress-intensity factors are transferred to a powerful general-purpose fatigue-design program, which has been designed to predict both initiation and propagation fatigue lives by means of classical design methods. Particularly, its crack propagation module accepts any K_I expression and any crack growth rate model, considering sequence effects such as overload-induced crack retardation to deal with 1D and 2D crack propagation under variable amplitude loading. Non-trivial application examples compare the numerical simulation results with those measured in physical experiments.     

Application of the crack layer theory to modeling of slow crack growth in polyethylene

A crack and a domain of highly fibrillated and stretched material ahead of the crack (process zone), commonly observed in polyethylene, are considered as a system called the crack layer. Slow crack layer growth is assumed to be a result of interactions between the crack, process zone and the rest of the body, as well as of degradation of the process zone material. The energy balance for process zone formation and crack layer advance is presented. The equations governing crack layer propagation are formulated and numerically solved. The proposed mechanism of fracture process models the discontinuous crack growth often observed in polyethylene, and predicts the relationship between the crack growth rate and the stress intensity factor consistent with the experimental one. The dependence of the lifetime on load is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Corrosive fatigue of structures with dimple holes under spectrum loading

ABSTRACT Experimental investigation and life prediction are made for structures with straight holes and dimple holes in both laboratory ambient conditions and 3.5% NaCl solution under spectrum loading. With the aid of acoustic emission, label loading and fractography technique, the crack‐growth data are obtained in both environments. Stress‐intensity factors for the corner crack emanated from the dimple hole are evaluated by three‐dimensional (3D) finite element (FE) method. Life prediction of the tested structures is made by using the modified FASTRAN‐II code on the basis of corresponding fatigue crack‐growth rate curves. It is shown that once the initial defect size a₀ is determined by one set of test data, it can be used together with the 3D crack‐growth method in order to provide accurate life prediction in alternative structure and loading condition. By comparison, life prediction by the traditional local strain method is also made which is shown to be less reliable than the 3D crack‐growth method.     

Scale levels for fatigue fracture mechanisms of in-service crack growth in longerons of helicopter rotor blades

Cases of in-service fatigue crack growth in aluminium longerons of helicopter Mi-8 rotor blades were reviewed. Fatigue fracture surface patterns for micro- and meso-scale levels of crack growth mechanisms for in-service fatigued longerons are discussed. Meso-beach-marks were used to estimate the fatigue crack growth period in one of the damaged longerons with the least crack size. Results of these estimations showed the effectiveness of the special device in in-service operation, which was used in longerons for in-service fatigue crack detection.     

Scale levels for fatigue fracture mechanisms of in-service crack growth in longerons of helicopter rotor blades

Cases of in-service fatigue crack growth in aluminium longerons of helicopter Mi-8 rotor blades were reviewed. Fatigue fracture surface patterns for micro- and meso-scale levels of crack growth mechanisms for in-service fatigued longerons are discussed. Meso-beach-marks were used to estimate the fatigue crack growth period in one of the damaged longerons with the least crack size. Results of these estimations showed the effectiveness of the special device in in-service operation, which was used in longerons for in-service fatigue crack detection.     

Fatigue crack growth under C.O.D. cycling

The possibility of using the parameter crack opening displacement as the basis for describing fatigue crack growth behavior in mild steel has been examined. Results are reported on crack growth rates under constant C.O.D. cycling for both plain and welded mild steel of two thicknesses. They show that a power law relationship exists between the crack tip opening displacement and the crack growth rate which fits both the $\text{1}\text{4}$ and $\text{1}\text{2}$ in thick material. Some preliminary results on welded specimens also fit the same power law. Extension of this relationship to the high cycle growth region also gave a reasonable correlation with experimental results.     

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.     

The effect of constraint on creep fracture assessments

This paper describes a preliminary examination of the effect of in-plane constraint on creep crack growth under widespread creep conditions using the Q stress. Plane strain is assumed. Damage models for fracture of the process zone based on both ductility exhaustion and stress rupture are shown to predict a variation of the crack growth rate with Q. Lower levels of constraint lead to lower crack growth rates for a given C*. The results are used to outline a high temperature failure assessment diagram approach to constraint-dependent creep crack growth. This revised version was published online in July 2006 with corrections to the Cover Date.     

Statistical modeling of fatigue-crack growth in a nickel-base superalloy

Two fracture mechanics-based statistical models for the fatigue crack propagation of engine materials are developed. The models are applied to fatigue crack growth rate data for IN 100, a nickel-based superalloy used in F100 engine disks, at various elevated temperatures, loading frequencies and stress ratios. The lognormal and the randomized parameter models allow the incorporation of the statistical variability associated with crack growth data into the life prediction process. The statistical distributions of (i) the crack growth rate, (ii) the propagation life to reach a given crack size (iii) the crack size at any given service life have been derived. A correlation analysis is performed to compare the results of the statistical models with test data. The correlation is demonstrated to be very good.     

Correlations among growth law of small cracks,low-cycle fatigue law and applicability of miner's rule

The initiation and propagation process of a small crack in low-cycle fatigue of a medium carbon steel is observed in detail by the plastic replica method. It is found that the Manson-Coffin relation is virtually the same as the crack growth law of a small crack; more than 90% (almost 100%) of the fatigue life of plain specimens is occupied by the crack propagation process. From this viewpoint, the ambiguity in the definition of the initiation of “an engineering-size crack” can be removed.The effects of prior fatigue history on the growth rate of a small crack are investigated systematically using special specimens containing an artificial small hole with diameters of 40, 100 and 200 μ m.Prior fatigue history which may be accumulated at the region where a crack will later propagate hardly influences the crack growth rate, i.e. prior fatigue history itself should not be regarded as fatigue damage. This is an essential condition for Miner's rule to apply.     

有限板共线多孔MSD疲劳裂纹扩展有限元模拟

介绍了二维断裂分析有限元软件FRANC2D/L在疲劳裂纹扩展模拟方面的基本步骤．利用该软件对有限板中心孔边对称裂纹的疲劳裂纹扩展进行模拟计算,对比模拟结果和试验数据,发现两者吻合良好,证明了利用该方法模拟疲劳裂纹扩展的可靠性．将FRANC2D/L应用到有限板共线多孔MSD疲劳裂纹扩展的有限元模拟上,得到了各孔边裂纹的长度和疲劳扩展寿命之间的关系曲线．模拟计算结果表明,在相同条件下,有限板中心孔边对称裂纹的裂纹扩展寿命要远远高于MSD结构中中心孔边裂纹的疲劳扩展寿命;由于MSD结构中影响各孔边裂纹的因素有所差异,各条裂纹的疲劳扩展寿命也会有所不同．另外,还给出了不含主裂纹的MSD和含主裂纹的MSD两种情况下的疲劳裂纹扩展历程,通过比较得知,含主裂纹的MSD结构更容易发生裂纹的合并和贯穿致使结构发生破坏．     

On the interactions between strain accumulation, microstructure, and fatigue crack behavior

Fatigue crack growth is a complex process that involves interactions between many elements ranging across several length scales. This work provides an in-depth, experimental study of fatigue crack growth and the relationships between four of these elements: strain field, microstructure, crack path, and crack growth rate. Multiple data sets were acquired for fatigue crack growth in a nickel-based superalloy, Hastelloy X. Electron backscatter diffraction was used to acquire microstructural information, scanning electron microscopy was used to identify locations of slip bands and crack path, and optical microscopy was used to measure crack growth rates and to acquire images for multiscale digital image correlation (DIC). Plastic strain accumulation associated with fatigue crack growth was measured at the grain level using DIC. An ex situ technique provided sub-grain level resolution to measure strain variations within individual grains while an in situ technique over the same regions showed the evolution of strain with crack propagation. All of these data sets were spatially aligned to allow direct, full-field comparisons among the variables. This in-depth analysis of fatigue crack behavior elucidates several relationships among the four elements mentioned above. Near the crack tip, lobes of elevated strain propagated with the crack tip plastic zone. Behind the crack tip, in the plastic wake, significant inhomogeneities were observed and related to grain geometry and orientation. Grain structure was shown to affect the crack path and the crack growth rate locally, although the global crack growth rate was relatively constant as predicted by the Paris law for loading with a constant stress intensity factor. Some dependency of crack growth rate on local strain and crack path was also found. The experimental comparisons of grain structure, strain field, and crack growth behavior shown in this work provide insight into the fatigue crack growth process at the sub-grain and multi-grain scale.