Crack Advances Research Articles

Electrochemical noise analysis of cathodically polarised AISI 4140 steel. III. Influence of hydrogen absorption for stressed electrodes

In this third part of the study of the electrochemical noise generated by hydrogen evolution on cathodically-polarised AISI 4140 steel specimens in 0.5 M sulphuric acid, a tensile stress was applied to the specimens. The two components of the measured potential fluctuations Δ V, namely ohmic-drop fluctuations Δ R e I and faradaic potential fluctuations Δ E, were analysed. After bubble size homogenisation, the effect of an applied stress was an increase in the level of the power spectral densities (PSD) Ψ V and Ψ E of the Δ V and Δ E fluctuations, indicating a change in metal-hydrogen-interactions related to damages in the metal induced by the combined actions of stress and hydrogen embrittlement. In the meanwhile, the PSD Ψ R e I of the ohmic-drop fluctuations did not exhibit any change, revealing that the departure rate and size of hydrogen bubbles were not modified by the internal damages in the specimen. The time evolution of Ψ E up to fracture could be explained by the enhancement of hydrogen penetration into the metal induced by the increase in the density of microdefects or crack advances inside the metal.

Dynamic stability of a propagating crack

In this work we investigate the stability of a straight two-dimensional dynamically propagating crack to small perturbation of its path. Willis and Movchan (J. Mech. Phys. Solids 43 (1995) 319; J. Mech. Phys. Solids 45 (1997) 591) constructed formulae for the perturbations of the stress intensity factors induced by a small three-dimensional dynamic perturbation of a nominally plane crack. Their solution is exploited here to derive equations for the in-plane and out-of-plane perturbations of the crack path making use of the Griffith fracture criterion and the principle of “local symmetry” (i.e the crack propagates so that local K II=0). We consider a crack propagating in a body loaded by a pair of point body forces and subjected to a remote uniaxial stress, aligned with the direction of the unperturbed crack. We assume that the loading follows the crack as the crack advances and is such that the unperturbed crack is subjected to Mode I loading. We perform an analysis of the stability of the dynamic crack in a similar way as in earlier work (Obrezanova et al., J. Mech. Phys. Solids 50 (2002) 57) on the quasistatically advancing crack. We present numerical results illustrating the influence of the crack velocity on the crack stability. Numerical computations of the possible crack paths have been performed which show that at velocities of crack propagation exceeding about one-third of the speed of Rayleigh waves the crack may admit one or more oscillatory modes of instability.

706 ボイド・介在物を含む材料の破壊経路予測数値シミュレーション

In this paper, fracture-path prediction simulations were carried out for cracks in elastic materials containing inclusions and voids, using the moving finite element method based on Delaunay automatic mesh generation was used. The fracture path in each step was determined by the maximum hoop stress criterion and the local symmetry criterion (K_<II>=0 criterion). Both criteria predicted almost the same fracture paths. It was found that when the inclusions are harder than the matrix material, the crack advances avoiding the inclusions.

Stability of an advancing crack to small perturbation of its path

In this work we investigate the stability of a nominally straight two-dimensional quasistatically growing crack to a small perturbation of its path. Formulae for perturbations of stress intensity factors induced by slight deviation of the crack trajectory were developed by Movchan et al. (Int. J. Solids Struct. 35, 3419) Their solution is exploited to derive an equation for the perturbation of the crack path on the assumption that the crack advances in pure “opening” mode (i.e. local K II=0). Various types of loading conditions are considered, including a cracked body loaded by a pair of point body forces and a crack whose faces are subjected to given tractions acting in the direction normal to the crack boundary. The body is also subjected to a remotely maintained uniaxial stress, aligned with the direction of the unperturbed crack. The loading is assumed to advance as the crack advances, to maintain the critical value of Mode I stress intensity factor. Numerical computations of possible crack paths have been performed, extending results on crack stability obtained by Cotterell and Rice (Int. J. Fract. 16, 155). The results show that in the case of loading by point body forces the stability of the crack path depends on the positions of the points of application of the applied forces and the magnitude of the applied stress acting parallel to the crack. There exists a critical value of this stress such that the crack path is stable for values less than critical and unstable otherwise. It is shown that the crack is always unstable in the case of point force tractions applied normal to the crack faces.

Atomistic Studies of Intrinsic Crack-Tip Plasticity

One of the most interesting unsolved problems in fracture mechanics is the precise understanding of the energy-dissipation mechanisms that occur as a crack advances. In most cases, this energy-release rate is many times the surface energy created. One of the main reasons for this difference is the fact that plastic deformation can occur in the crack-tip region as dislocations nucleate and are emitted from the crack tip. Experimental studies provide little insight into the precise mechanisms for this process because they cannot reach the atomistic scale. For example, a crack that may seem experimentally sharp, and therefore indicative of brittle fracture, may not be sharp at the atomic level. Continuum mechanics has a similar limitation, since the assumptions of elasticity theory usually break down in the crack-tip region. Atomistic simulation studies provide researchers an opportunity to obtain precise atomic configurations in the crack-tip region under various loading conditions and to observe the basic energy-dissipation mechanisms.

Shape evolution of surface cracks in fatigued round bars with a semicircular circumferential notch

The shape of the fronts of surface cracks in semicircularly notched round bars under fatigue loading is predicted by a numerical procedure developed recently by the authors. This procedure utilizes a linear elastic three-dimensional finite element analysis to estimate the stress intensity factor along the crack front, and then employs an experimental Paris-type fatigue crack growth relation to calculate local crack advances at a few points along the crack front. Re-creating a finite element model for the new crack front and repeating the calculation of the crack growth increment simulates further crack propagation. This method can avoid making the usually necessary assumption of crack shape during the fatigue life calculation for surface cracks in notched round bars. Both remote cyclic tension and bending loads are considered. Characteristics of the crack shape change are also investigated by examining deviations of the crack profiles from the widely assumed elliptical-arc shape, and aspect ratio changes with crack growth.

Dynamic overshoot in -iron by atomistic simulations

We present large-scale molecular dynamic simulations of microcrack growth in -iron based on an N-body potential model which gives a good description of defect energetics, anisotropic elasticity and phonon frequency spectra. We demonstrate dynamic overshoot of a pre-existing microcrack under impact loading. We show that the basic behaviour of the simulations is in agreement with the predictions of continuum models. Dynamic phenomena, such as scattering of stress waves at crack faces, acoustic emission (due to bond breakage) and reflections of the stress waves from sample borders, are studied here in detail. The results on microcrack growth, unimpeded by the wave reflections from external sample borders, indicate that under fast loading or at high crack velocities, i.e. under high strain rates, transient twin formation is possible from the crack tip with later detwinning at free crack faces as the crack advances: a twinning equivalent to virtual Knott dislocations.

On the behavior of crack surface ligaments

Small ligaments connecting the fracture surfaces just behind a moving crack front are assumed to exist under certain conditions. The ligaments are rapidly torn as the crack advances. Inelastic straining of such ligaments influences the energy balance in the fracture process. The rapid tearing of a single ligament is studied both numerically and experimentally. An elastic visco-plastic material model is adopted for finite-element calculations. The results show that relatively large amounts of energy are dissipated during the tearing process. Further, the energy needed to tear a ligament increases rapidly with increasing tearing rate. The computed behavior is partly verified in a few preliminary experiments. The implications for slow stable crack tip speeds during dynamic fracture are discussed.

Monitoring Crack Advance Using Acoustic Emission and Combined Acoustic Emission and Potential Drop in Zr-2.5% Nb

Abstract Experithental results are reported on the application of acoustic emission (AE) and combined acoustic emission and potential drop (PD) in crack advance measurement. Acoustic emission by itself is not a quantitastive technique for measuring crack advance. Compared with the application of only PD, using both simultaneously turns out to be quite beneficial. Used to measure delayed hydride cracking velocity in Zr-2.5% Nb, combined AE and PD, together with other techniques such as fractography, produces more reliable results with higher accuracy for isothermal conditions and particularly during temperature transients. Information about the correlation between AE and PD signals has been also obtained, which improves our understanding of the processes being studied.

Contact of crack surfaces during fatigue: Part 2. Simulations

sp0 Normalizations permit application to a wide range of materials. The results, for selected levels of asperity density, are consolidated upon comparing the crack opening displacement (COD) with the roughness (s0) over four orders of magnitude. Specifically, a nonlinear relationship between COD/s0 and crack opening stress was established that can be readily used to determine crack opening stress over a broad range of conditions. The model has been utilized to predict crack opening stress levels for several materials, including 0.8 pct C steels, 9Cr-1Mo steels, Ti-4Al, Ti-46Al (g-aluminide), and Al 2124 alloys. Experimental measurements of crack roughness and asperity density were conducted on titanium aluminide specimens using confocal microscopy, and crack closure predictions were made with the model. The predictions demonstrated very good agreement with the experimentally measured closure levels. I. INTRODUCTION THE modification of the stress intensity factor based on crack closure has been universally applied to explain the experimental observations of fatigue crack growth behavior under various mechanical loading conditions and in various metallic alloys. For an overview of the topic, the reader is referred to the textbook by Suresh [1] and the overview by Sehitoglu et al. [2] However, to develop a better understanding of the intrinsic mechanisms of crack growth in various materials due to mechanical and microstructural factors, it is particularly important to determine the individual influences of crack closure due to plasticity, roughness, and oxide effects. Then, the effect of each of these mechanisms can be isolated to develop more advanced models for crack advance. Since a quantitative description of crack roughness effects has not been previously derived, the present work has undertaken this task. In many materials, when the crack advance is influenced by crystallographic slip or when the crack encounters microstructural barriers, the crack paths are nonflat and the crack can deviate from the normal mode I growth plane. The nonflatness of crack surfaces has been known to enhance the resistance of a material to fatigue crack growth. This resistance can develop in cases when the crack surfaces are viewed as nominally flat at the macrolevel, but there could be many periodic deviations from a smooth crack surface in the forms of asperities at the microlevel. These asperities could interlock at very low loads, or slide and crush in the presence of sufficient loading, resulting in an alteration of the crack surface profile as the crack advances. Combining the interaction of many asperities results in stresses in the crack wake which, in turn, have to

Numerical analysis of fatigue growth of external surface cracks in pressurised cylinders

Fatigue crack growth is modelled by a novel numerical technique for various external surface cracks with initially either semi-elliptical or irregular crack fronts. The technique employs a three-dimensional finite element analysis to estimate the stress intensity factors at a set of points of the crack front, then calculates local crack advances by integrating a type of Paris fatigue crack growth law at this set of points, and finally establishes a new crack front and its corresponding finite element model. The multiple degrees-of-freedom model enables the crack shape to be predicted directly during crack growth without having to make the common semi-elliptical assumption, and therefore provides more accurate predictions. Fatigue analysis results are presented and discussed, including fatigue shape developments and deviations from the semi-elliptical shape, together with aspect ratio changes, stress intensity factor variations during crack growth and fatigue life predictions. Some of these results are also compared with those obtained by two simplified predictive methods based on one and two degrees-of-freedom models together with a stress linearisation.

Cohesive crack with rate-dependent opening and viscoelasticity: I. mathematical model and scaling

The time dependence of fracture has two sources: (1) the viscoelasticity of material behavior in the bulk of the structure, and (2) the rate process of the breakage of bonds in the fracture process zone which causes the softening law for the crack opening to be rate-dependent. The objective of this study is to clarify the differences between these two influences and their role in the size effect on the nominal strength of stucture. Previously developed theories of time-dependent cohesive crack growth in a viscoelastic material with or without aging are extended to a general compliance formulation of the cohesive crack model applicable to structures such as concrete structures, in which the fracture process zone (cohesive zone) is large, i.e., cannot be neglected in comparison to the structure dimensions. To deal with a large process zone interacting with the structure boundaries, a boundary integral formulation of the cohesive crack model in terms of the compliance functions for loads applied anywhere on the crack surfaces is introduced. Since an unopened cohesive crack (crack of zero width) transmits stresses and is equivalent to no crack at all, it is assumed that at the outset there exists such a crack, extending along the entire future crack path (which must be known). Thus it is unnecessary to deal mathematically with a moving crack tip, which keeps the formulation simple because the compliance functions for the surface points of such an imagined preexisting unopened crack do not change as the actual front of the opened part of the cohesive crack advances. First the compliance formulation of the cohesive crack model is generalized for aging viscoelastic material behavior, using the elastic-viscoelastic analogy (correspondence principle). The formulation is then enriched by a rate-dependent softening law based on the activation energy theory for the rate process of bond ruptures on the atomic level, which was recently proposed and validated for concrete but is also applicable to polymers, rocks and ceramics, and can be applied to ice if the nonlinear creep of ice is approximated by linear viscoelasticity. Some implications for the characteristic length, scaling and size effect are also discussed. The problems of numerical algorithm, size effect, roles of the different sources of time dependence and rate effect, and experimental verification are left for a subsequent companion paper.

The micromechanics of fiber pull-out

Results of experimental and modeling studies on the micromechanics of fiber pull-out are reported. For the experiment an optical glass fiber coated with a layer of acrylate or gold-palladium alloy is embedded in an epoxy matrix and then pulled out at various speeds. The fiber has a diameter of 125 or 200 μm. While the fiber is pulled out, the coating is left embedded in the epoxy matrix, producing frictional sliding between the contact surfaces of the glass fiber and the coating. As the thin and long fiber is pulled out, the trace of pull-force versus displacement shows several distinct stages corresponding to different pull-out processes. In the debonding process of the glass-acrylate interface, stable crack growth was observed prior to unstable sliding. The stable crack growth behavior is believed mainly to be caused by the fact that the interface fracture toughness is strongly mode dependent and the mode mixity of the debonding crack varies towards tougher mode as the crack advances. After the interface is completely debonded, the trace of pull-force versus displacement shows stick-slip oscillations about a constant mean full force. Through the use of photoelasticity it is found that the unstable stick-slip sliding of the glass-acrylate interface is caused by the propagation of a highly concentrated active sliding zone, a dislocation, along the interface. When a thin gold-palladium coating is introduced at the interface to produce debonding and sliding along the glass-gold-palladium interface, the initial stable crack growth is not observed and the interface dislocation emission is suppressed. The interface fracture toughness and the frictional sliding resistance are found to depend on the thickness of the coating; the interface fracture toughness is higher for thicker gold-palladium coatings, while the frictional sliding resistance is higher for thinner gold-palladium coatings. The sliding at the glass-gold-palladium interface also shows a stick-slip behavior under certain conditions. However, unlike the stick-slip process accompanying dislocation emission observed in the sliding process of glass-acrylate interface, the stick-slip is generated, while the entire contact interface slides simultaneously, by rate-dependent softening and hardening of the frictional interface. It is demonstrated that significant features of this type of stick-slip process can be predicted using a phenomenological friction law with an internal state variable.

Temperature effect on impact fracture toughness and fracture mechanism of phenolphthalein poly(ether ketone)

AbstractPhenolphthalein poly(ether ketone) (PEK‐C) was tested using an instrumented impact tester to determine the temperature effect on the fracture toughness Kc and critical strain energy release rate Gc. Two different mechanisms, namely the relaxation processes and thermal blunting of the crack tip were used to explain the temperature effect on the fracture toughness. Examination of the fracture surfaces revealed the presence of crack growth bands. It is suggested that these bands are the consequence of variations in crack growth along crazes that are formed in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances.

Micromechanical modeling of reinforcement fracture in particle-reinforced metal-matrix composites

Finite element analyses of the effect of particle fracture on the tensile response of particle-reinforced metal-matrix composites are carried out. The analyses are based on two-dimensional plane strain and axisymmetric unit cell models. The reinforcement is characterized as an isotropic elastic solid and the ductile matrix as an isotropically hardening viscoplastic solid. The reinforcement and matrix properties are taken to be those of an Al-3.5 wt pct Cu alloy reinforced with SiC particles. An initial crack, perpendicular to the tensile axis, is assumed to be present in the particles. Both stationary and quasi-statically growing cracks are analyzed. Resistance to crack growth in its initial plane and along the particle-matrix interface is modeled using a cohesive surface constitutive relation that allows for decohesion. Variations of crack size, shape, spatial distribution, and volume fraction of the particles and of the material and cohesive properties are explored. Conditions governing the onset of cracking within the particle, the evolution of field quantities as the crack advances within the particle to the particle-matrix interface, and the dependence of overall tensile stress-strain response during continued crack advance are analyzed.

Mechanics of transonic debonding of a bimaterial interface: The anti-plane shear case

The recent experiment reported by Liu, Lambros and Rosakis (1993) (Highly transient elastodynamic crack growth in a bimaterial interface : higher order asymptotic analysis and optical experiments. J. Mech. Phys. Solids41, 1887–1954) raised the issue of transonic debonding. As a preliminary study, the present paper focuses on transonic debonding under anti-plane shear. The interfacial crack advances at a velocity higher than the shear wave speed of the compliant component but lower than that of the stiff component of the bimaterial. The governing equation for a steady state growing crack is elliptical in the stiff material and hyperbolic in the compliant material. We obtain a closed-form analytical solution that describes the transmission of the mechanics fields from the elliptical region to the hyperbolic region. The interface data travel along the inclined characteristic lines in the compliant material to the crack wake. The stress singularity at the crack tip depends on the crack propagation speed and varies from being constant-like when passing the lower shear wave speed to being square root singular when approaching the higher shear wave speed. The stress intensity coefficient measuring the strength of this singularity is determined for the case of a semi-infinite debonding crack subject to a steady state crack-face traction. The total energy release rate for transonic debonding vanishes and the energy flows from the stiff material to the compliant one along the characteristic lines, without deposition at the crack tip. We also conclude that the debonding speed cannot exceed the higher shear wave speed provided the energy flow through the interface is bounded.

&lt;i&gt;R&lt;/i&gt;-Curve Behavior of Silicon Nitride Ceramics under a Cyclic Loading Condition at Elevated Temperature

Static fatigue, cyclic fatigue and constant stress rate tests were carried out at 1200°C in nitrogen atmosphere for toughened silicon nitride exhibiting a significant rising R-curve. The R-curves both in static and cyclic loading conditions were determined with measuring crack advance and fracture strength, in order to evaluate cyclic loading effects. The KR value under a static loading condition increases as a crack advances and it reaches 12.5MPa⋅m1/2 at the crack advance greater than 1.5mm. On the contrary, the KR value under cyclic loads increases with advancing a crack and it reaches 9.5MPa⋅m1/2 when the crack advances greater than 1.2mm. This different R-curve behavior suggests that bridging grains responsible for the toughening are damaged with the cyclic loads, resulting in a decrease in the maximum KR value. Applying a Dugdale model to the bridging stress analysis, the bridging stresses under static and cyclic loading conditions were determined 100MPa and 65MPa, respectively.

Modelling the evolution of columnar joints

Cooling cracks, developing from the margins of solidifying lava flows or intrusive dykes or sills, often propagate inward and divide the rock into prismatic columns. It has been shown that: (1) the initial crack pattern that forms at the surface of the body is not as regular as the pseudo-hexagonal pattern which evolves later; (2) columnar structures develop by repeated, step-wise crack advances, forming cm to dm transverse bands on the column faces; (3) even within well-developed colonnades, the polygonal outlines continue to shift slightly from one crack advance to the next.We propose that each new crack should propagate parallel to the highest thermal gradient ahead of the current crack tip. When adjacent columns are of unequal size, the local asymmetry of the isotherms drives the new crack toward the biggest and hottest column. We present a geometrical model and algorithm that follows this rule and mimics the successive crack advances as the cooling front migrates into the lava sheet, or dyke. The model polygonal pattern obtained consists of convex, irregular polygons with a variable number of sides, but in which pentagons and hexagons predominate. The algorithm successfully reproduces the rapid evolution from an initial, immature crack pattern to a pseudo-hexagonal, mature one in which the average number of sides approaches six. It predicts also the predominance of Y-type crack junctions, the rapid evolution toward columns of approximately equal sizes, and the persistent changes in length and diverging orientation of growth steps observed along the sides of columns. The model polygonal patterns exhibit geometrical properties which are very similar to those observed in well-developed columnar jointed flows such as the Giant's Causeway.

Simulation of RPG load

Newman showed crack opening/closing model during fatigue crack propagation under uniform stress field which was based on the Dugdale model, but modified to leave plastically deformed materials along the crack surface as the crack advances. In his model, however, he neglected the change of stress distribution ahead of a crack during loading process in the calculation of crack opening load. Moreover he also neglected the elastic deformation for a materials along the crack surface. Therefore he introduced plastic constrainted factor of 3.5 which was larger than the appropriate value of 1.21 obtained from comparison between COD's by elasto plastic FEM and those by Dugdale model for center notched specimens for the purpose of fitting experimental crack opening load.In this paper, Newman's model is modified to solve his neglected problems mentioned above and is expanded to arbitrary stress distribution field for the purpose of obtaining re-tensile plastic zone's generated load (RPG load). Moreover we consider plastic shrinkage at newly generated fracture surface during unloading process which corresponds to a part of deformation due to emancipation of acting force with a magnification of yield stress at an immediate growth of a crack in the region of fictitious crack in Dugdale model.Some calculation results are shown for understanding the effect of the plastic shrinkage at newly generated surfaces and the change of loading. Simulated results suggest that the effect of stress ratio and the effect of delayed reterdation due to decreasing maximum load become small as the plastic shrinkage becomes large.

Phenomena of Delayed Reterdation and Crack Stopping Condition for a Long Fatigue Crack

Fatigue crack propagation tests with various stress ratios and stepwise decreasing maximum load while keeping minimum load are carried out for center notched tension specimens. In these tests, RPG load (Re-tensile Plastic zone's Generated load), crack length and number of cycles are measured by using our newly developed measuring system in the 1st report.We also calculate RPG load by using our developed simulation model of crack opening/closing phenomena based upon Dugdale model in the 5th report with various shrinkage coefficients α of plastic deformation due to emancipate internal force in newly generated crack surface at an immediate crack growth. Then we obtain α value for the steel used with comparing between simulated RPG load and measured one for the testing condition of R=0.05. By using the obtained α value, RPG loads for other stress ratios (R=0.3 and 0.5) are calculated by using the simulation model. As a result, simulated RPG loads are in very good agreement with measured RPG loads for R=0.3 and R=0.5.Then a crack growth curve for each testing condition is calculated by using ΔKRP from simulated RPG load and also shows in very good agreement with measured crack growth curve for each stress ratio.RPG load increases just after decreasing maximum load and reaches maximum and then decreases gradually as a crack advances in the cases of decreasing load with small magnification. Then delayed deterdation effects appear and delayed life increases with larger decrement of maximum load. It is also comfirmed that simulated RPG load using above α value is in good agreement with measured RPG load for these cases. It becomes also clear that crack growth curve in case of decreasing maximum load can be assessed quantitatively by using ΔKRP based upon the simulated RPG load.Moreover it is confirmed that larger decrement of maximum load in stepwise loading leads to stopping a crack even when final maximum load with large decrement of maximum load is larger than RPG load. This is because RPG load increases rapidly just after decreasing maximum load and approaches to final maximum load in case of large decrement of maximum load both in experiments and simulations. Simulated crack growth curve by ΔKRP using calculated RPG load in this case is also in good agreement with experimental one.Therefore it can be expressed that the condition of stopping a crack is ΔKRP_??_0 for a long crack. In other word, it becomes clear that ΔKth or (ΔKeff)th is not a material constant.