Closure Level Research Articles

Analytical expressions for crack opening displacements of edge cracked specimens under a segment of uniform crack face pressure

In this paper, Muskhelishvili's complex variable method was used to derive the primary equations of crack opening displacements (CODs) for edge cracked specimens when only the boundary conditions of the crack surface are satisfied. By means of fitting the COD weight function solutions based on the obtained primary COD equations, approximate equations of COD were obtained for edge cracked specimens under a segment uniform pressure acting on the crack surfaces. The equations are more accurate outside the near crack tip region. Because the crack closure level is sensitive to the variation of CODs in the near crack tip region, approximate COD-expressions with high accuracy in the near crack tip region were also developed for the edge cracked specimens under the corresponding loading condition based on the COD-expression for a central crack in an infinite width plate subjected to segment uniform pressure acting on crack surface. The equations with better accuracy outside and in the near crack tip region can be combined to rapidly calculate the COD on the whole crack surface, thus greatly facilitating fatigue crack growth analysis for edge cracked specimens.

EXPERIMENTAL AND ANALYTICAL ESTIMATES OF FATIGUE CRACK CLOSURE IN AN ALUMINIUM‐COPPER ALLOY PART II: A FINITE ELEMENT ANALYSIS

Abstract— A numerical investigation of the fatigue crack closure phenomenon has been performed by an elastic‐plastic finite element analysis. Computer software was developed to consider many aspects affecting plasticity‐induced crack closure. Linear and power‐law hardening models are considered in the finite element analysis. The paper presents results from the study carried out on compact tension (CT) coupons at various crack lengths corresponding to different loading conditions. Finally the results of the analysis are compared with the experimental estimates of fatigue crack closure levels obtained from laser interferometry, scanning‐electron and transmission‐electron fractography presented in Part I of this paper on identical specimens.

Numerical prediction of laminar, transitional and turbulent flows in shrouded rotor-stator systems

The paper deals with numerical prediction of laminar, transitional and turbulent regimes in confined flow between rotating and stationary discs. For the laminar and transitional flows, a spectral tau-Chebyshev method associated with a multistep time scheme is used. This approach allows accurate prediction of the two laminar regimes mentioned by Daily and Nece (1960) in their experimental studies. For the geometry under consideration (1/11 aspect ratio), the transition to unsteady motion occurs abruptly without any oscillatory behavior. Thus, the instabilities develop in a region localized near the external shroud, primarily along the stator side, according with experimental findings. For calculating turbulent flow regimes, one point second-order transport modeling has been implemented in a finite volume code. The superiority of advanced Reynolds stress transport models over the classical k−ε model is decisive for predicting such a complex flow. This is particularly important in order to get a precise delineation of the adjacent turbulent and relaminarized regions within the cavity. This level of closure was crucial to produce numerical results in good agreement with experimental data.

Development of NDE technology to evaluate fatigue damage of steam generator tube: Goto, T., Enami, K., Fukui, S. and Uesugi, N. 13th International Conference on NDE in the Nuclear and Pressure Vessel Industries, Kyoto, Japan (22–25 May 1995) 427–434

In situ SEM observations and measurements were made of near-tip COD and crack growth at small, thumb-nail cracks subjected to a single overload during fatigue at constant load amplitude in 2024-T351 aluminium alloy. A delayed retardation in crack growth was observed at R = 0.05, but not at R = −1. During retarded growth at R = 0.05, near-tip COD decreased below that measured before overload and the level of crack closure increased. These events were not evident at R = −1. An elastic/plastic finite element modelling of the growth of similar small cracks predicted enhanced residual compressive stresses ahead of the crack tip for R = 0, but not for R = −1. The experimental and modelling work are consistent in linking differences in the crack growth profiles at the two R ratios with differences in COD, crack closure and residual compressive stress ahead of the crack tip following overload.

In situ SEM observations of the contrasting effects of an overload on small fatigue crack growth at two different load ratios in 2024-T351 aluminium alloy

In situ SEM observations and measurements were made of near-tip COD and crack growth at small, thumb-nail cracks subjected to a single overload during fatigue at constant load amplitude in 2024-T351 aluminium alloy. A delayed retardation in crack growth was observed at R = 0.05, but not at R = −1. During retarded growth at R = 0.05, near-tip COD decreased below that measured before overload and the level of crack closure increased. These events were not evident at R = −1. An elastic/plastic finite element modelling of the growth of similar small cracks predicted enhanced residual compressive stresses ahead of the crack tip for R = 0, but not for R = −1. The experimental and modelling work are consistent in linking differences in the crack growth profiles at the two R ratios with differences in COD, crack closure and residual compressive stress ahead of the crack tip following overload.

A Methodology for Predicting Variability in Microstructurally Short Fatigue Crack Growth Rates

A finite element model, which implements single crystal constitutive relationships, was used to simulate fatigue cracks growing at the microstructural level. Plastic deformation (slip) was allowed along two specified microscopic crystallographic planes. As the orientations of the slip systems were changed several crucial fatigue crack growth parameters, measured over all possible orientations, were found to vary: (1) crack tip forward slip band size, rp, 0.03 ≤ rp/(Kmax/λo)2 ≤ 0.31 where λo is the critical resolved shear stress on a slip system, (2) crack opening displacement, δ, 1.2 ≤ δ/(Kmax2/Emσo) ≤ 7.8 where Em and σo are the elastic modulus and yield stress of a polycrystalline material with many randomly oriented double slip crystals, and(3) crack closure level, Sopen/Smax, 0.02 ≤ Sopen/Smax ≤ 0.35. Corresponding to these differences in crack growth parameters, crack growth laws were used to estimate the expected changes in crack growth rates when microstructurally short cracks grow through grains with different crystallographic orientations. The resulting predictions form approximate upper and lower bounds on crack growth rates for microstructurally short cracks. For several different materials, the crack growth rate variability predictions were in the range 7 ≤ (da/dN)(max)/(da/dN)(min) ≤ 37, which is consistent with experimentally measured variations.

A risk assessment of chlorinated aliphatics in bioremediated soils

AbstractNatural microbes living in contaminated subsurface media can be enhanced to degrade large concentrations of contaminating compounds at a faster rate than the microbes could degrade under natural conditions. A feasibility study demonstrating this principle was performed on‐site in southern Louisiana to evaluate the effectiveness of two microbial degradation remediation methods used to decrease the human carcinogenic risks associated with exposure to ethylene dichloride and vinyl chloride concentrations in contaminated clay and sludge soils at the site. The results of the study are compared to an acceptable Louisiana Department of Environmental Quality closure level to evaluate in‐situ microbial enhancement in chlorinated aliphatic‐contaminated sludge and clay soils as a remediation/cleanup alternative in similar industrial situations.

Adult attachment style and information processing: individual differences in curiosity and cognitive closure.

Five studies examined the association between adult attachment style and information processing. Studies 1-2 focused on information search (curiosity-related beliefs and behaviors). Studies 3-5 focused on the integration of new information within cognitive structures; namely, the level of cognitive closure and its expressions in social judgements. Secure and anxious-ambivalent persons described themselves as more curious and held more positive attitudes toward curiosity than did avoidant persons. Time competition between information search and social interaction increased information search among avoidant persons, but decreased it among anxious-ambivalent persons. Finally, secure persons reported less preference for cognitive closure and were more likely to rely on new information in making social judgements than avoidant and anxious-ambivalent persons. The theoretical implications of the link between attachment and information processing are discussed.

A Two-Fluid Turbulence Model for Gas-Solid Two-Phase Flows.

On the basis of a two-equation turbulence model of single-phase flows, two-fluid turbulence models, namely, the k–e–kp–ep model and the k–e–kp model are developed to describe turbulent gas-solid two-phase flows. Governing equations for the turbulent kinetic energy and the kinetic energy dissipation rate of the particulate phase are derived from their momentum equations, and unknown terms at two-equation closure level are modeled. The developed models show that the turbulence intensity of the particulate phase is often larger than that of the gaseous phase in the gas-solid flow in a 90° bend, which is quite in accordance with the experimental results. The conventional k–e–Ap model using a k–e turbulence model for the carrier fluid and Tchen-Hinze’s formula for the eddy viscosity of the particulate phase, however, shows that the particulate turbulence intensity is always smaller than that of the gaseous phase. Therefore, the two-phase turbulence models developed here are superior to the conventional turbulence model. The turbulence models are also applied to predict the effect of particles on gaseous phase turbulence in the gas-solid flow in a vertical pipe. The predicted results are favorably compared with the available experimental data.

Near-Threshold Fatigue Crack Growth Behavior of SUS304 Steel at High Temperatures Using Interferometric Strain/Displacement Gage. 1st Report. Crack Closure Behavior.

Fatigue crack growth tests using center-cracked specimens [M (T) specimens] of SUS304 steel were conducted to examine the behavior of fatigue crack growth in the near-threshold regime at 450, 550, 650, and 700°C. Using the interferometric strain/displacement gage (I.S.D.G.), the crack closure behavior, which was thought to be significant due to oxide film accumulated on crack surfaces, was examined. It was shown that the crack closure level was measured with good accuracy even at high temperatures by I.S.D.G. modified using a platinum plate and a filter. It was found from the behavior observed at 650°C that crack closure did not occur at R=0.5, and that changes in the behavior of crack growth rate, da/dN, corresponded to those in the behavior of crack opening ratio, U, at each test temperature.

Effect of microstructure and load ratio on fatigue crack growth behavior of advanced Al-Cu-Li-Mg-Ag Alloys

Fatigue crack growth (FCG) behavior of recently developed three Al-Cu-Li-Mg-Ag alloys, Weldalite 049, X 2095 and MD 345, was examined in air at load ratios of 0.1 and 0.75. It was found that all three alloys showed better resistance to fatigue crack growth than conventional high strength Al alloys. The morphologies of crack growth paths were generally linear, but some showed deflection and branching. And the alloys revealed rough and transgranular fracture surfaces. Among the factors contributing to the excellent resistance of Al-Cu-Li alloys to fatigue crack growth are enhanced slip reversibility and high surface roughness causing a high crack closure level, thus reducing ΔKeff for crack extension. The fatigue threshold decreased and fatigue crack growth rates increased significantly with increasing the load ratio. This is caused by the decrease in crack closure level at high load ratio. But the fracture mode did not show a significant change with increasing the load ratio.

Fatigue crack propagation and closure behavior of modified 1070 steel: Finite element study

A new finite element modeling methodology for simulating plasticity-induced crack closure is developed for the general purpose, commercially available, finite element code called ABAQUS. This new method utilizes substructuring techniques to maximize computational efficiency. This is achieved without sacrificing model accuracy in depicting the structural behavior of the specimen. Model refinement studies were conducted to establish guidelines for model parameters such as mesh density and element aspect ratio for the elements in the crack plane region. These techniques and guidelines were used to model a compact tension specimen and simulate a series of four tests conducted during the experimental portion of this study. Comparison of stationary crack and propagating finite element models revealed that plasticity-induced crack closure produces a significant amount of crack tip shielding. Such behavior effectively reduces the strain range and mean strain experienced at the crack tip. Direct comparisons between finite element model and experimental results were performed in terms of crack closure level, crack mouth opening displacement and surface strain gage data. These comparisons revealed excellent agreement. As a result of the study, use of an experimentally verified finite element technique in conjunction with fatigue crack growth experiments is suggested as a potential means of developing future crack growth rate models in terms of the traditional fatigue parameters of strain range and mean strain.

INFLUENCE OF A NEGATIVE R RATIO ON THE CREEP‐FATIGUE BEHAVIOUR OF THE N18 NICKEL BASE SUPERALLOY

Abstract— Crack growth rate measurements, performed on smooth specimens during creep‐fatigue testing of the N18 nickel base superalloy at 650°C, reveal a strong detrimental effect of the compressive part of the loading cycle. This effect is attributed to the residual stresses in the wake of the crack, which promote early crack opening. A finite element analysis is conducted in order to predict the evolution of the opening stress level as a function of the stress ratio. Good agreement is found between numerical and experimental results. The influence of the constitutive equation of the material on the crack closure level is tested and the effects of kinematic hardening and viscosity are more specifically examined. An engineering simplified method is proposed to determine the opening stress intensity factor as a function of crack length, stress ratio and maximum stress. This method, developed for cracks in smooth specimens, is then applied to small cracks growing from a notch root. Good agreement is found between the results given by the engineering simplified method and the result of the finite element analysis.

Near-Threshold Fatigue Crack Growth Behavior of SUS304 Steel at High Temperatures Using Interferometric Strain/Displacement Gage. 2nd Report. Fatigue Crack Growth Behavior.

Fatigue crack growth tests were conducted at 450, 550, 650 and 700°C. Crack closure level was measured using the interferometric strain/displacement gage (I.S.D.G.), described in the previous paper, Crack growth rates for stress ratio R=-0.1 plotted against stress intensity factor range, ΔK, deviated from those for R=0.5. Using the effective stress intensity factor range, ΔKeff, which was calculated using crack opening ratio determined from the I.S.D.G. measurement, the R-dependence of the crack growth behaviors for R=-0.1 and R=0.5 were reconciled at each test temperature. A threshold value, ΔKeff, th, of fatigue crack growth was determined at each temperature. It was found that the threshold value reached a maximum at a temperature between 450 and 550°C.

Effects of crack aspect ratio on the behavior of small surface cracks in fatigue: Part II. Experiments on a titanium (Ti-8Al) alloy

The continuous variations in crack shape or aspect ratio, a/c (a is the crack depth and c is the halfsurface length), of small surface cracks, induced by grain boundaries, have been investigated during the fatigue crack growth of small cracks in a titanium (Ti-8Al) alloy. The significance of the aspect ratio variations in explaining the “anomalous” small-crack behavior was evaluated. The aspect ratio data were determined from the measurements of crack compliance, made using a laser interferometric system, and the measurements of surface crack length (2c), made using a photomicroscopic system. The variations in aspect ratio were found to be large at small crack sizes of the order of a few grain diameters. The experimental a/c data were compared with the patterns of crack aspect ratio variation, obtained from the oretical simulations. The simulated data were generated by assuming alternate crack propagation at the surface and at the depth, the details of which are presented in Part I of the study accompanying this article. A good agreement was found between the simulated and the experimentally observed variations. After incorporating the a/c variations in ΔK calculations, the scatter in the growth data of small cracks was significantly reduced and was found to be of the same order as in large cracks. Additionally, it is shown in this study that the conventional methods of analysis of small-crack data, performed with an assumption of a/c=1, can result in significant errors in ΔK calculation and an increased level of scatter in small-crack growth data. Small cracks also were found to exhibit low closure levels relative to large cracks. The results of the study strongly indicate that characteristics of small cracks, often referred to as anomalous, are due to the assumption of a/c=1 in situations of large variations in aspect ratio, the use of conventional methods of data analysis, and the lower levels of crack closure found naturally in small cracks.

Time dependent degradation of fiber/matrix interfaces under fatigue of SCS-6/TIMETAL 21S : Blatt, D., Jara, J.R. and Larsen, J.M. Script Metall. Mater. (1995) 33 (6), 939–944

In the present study, an analytical model of fatigue crack growth based on the plastic-blunting mechanism is developed. Both the plastic and reversed plastic flow during the process of cycling are considered. In each loading cycle, the size of the plastic and reversed plastic zone, the crack-tip opening displacement, and the stress intensity factor at crack-closure are determined. With an assumption of a crack-extension law, the crack-growth behavior under arbitrary load history is traced by making a step-by-step analysis. For the crack growing under constant-amplitude loading, the analysis of the steady-state crack-growth behavior is carried out with a simplified formulation. Regarding the crack-growth behavior near the fatigue threshold, although all of the near-threshold mechanisms are not incorporated into the model, the promoted crack-closure due to corrosion debris and surface roughness is introduced in terms of a material parameter CTOD∗. Under constant-amplitude loading, the results from the step-by-step analysis demonstrate that the closure level of the stress intensity considerably increases during the growth process due to accumulation of the residual strains. This may in part provide an explanation for the arrest a crack at a distance far from the root of a sharp notch, which is frequently observed in experiments. After a sufficiently large number of cycles, the crack-growth behavior from the step-by-step analysis reaches the steady state, and the results agree with the ones from the steady-state analysis. The crack growth law of second power is derived as a consequence of the assumed linear relation between Δa and ΔCTOD. The crack growth curves from the analysis agree with the ones obtained from experiments for Al 2024-T3 and Al 7075-T6. the ratio of Δa to ΔCTOD chosen for the calculation is in agreement with the direct, experimental measurement of Δa and ΔCTOD. With the presence of CTOD∗, the results show that the crack-growth behavior at low load changes drastically, and for each value of CTOD∗ a threshold exists below which no crack growth occurs at all. It is shown that under the action of variable-amplitude loading, the crack-growth, behavior from the model exhibits a transient behavior upon altering the loading condition. The study shows that the residual plastic deformation in the wake of an advancing crack has a large influence on the crack-growth behavior. The results also lend a theoretical support to the existence of the controversial plasticity-induced crack-closure under plane-strain conditions.

FEM study of fatigue crack closure under double slip

An elastic—plastic finite element analysis of Mode I crack growth and plasticity induced crack closure is presented. The simulation, which models crack tip plasticity using two slip planes, predicts slip patterns experimentally observed in real crystals or grains. The model shows that plasticity induced crack closure will occur when the crack tip plastic zone is smaller than the grain size. Closure levels are found to vary as the crystallographic orientation of the model with respect to the crack line is changed. For some orientations the closure levels are found to be negligible, while in others the levels approach 0.35 of the maximum applied load. Closure levels also vary as the angle between the slip planes is varied. The values span a similar range. The amount of crack closure for any particular crystallographic orientation and/or slip plane configuration is found to be a balance between several variables. Primarily, the closure levels are dictated by the magnitude of the static crack opening displacement and amount of residual plasticity along the crack line.

A procedure to minimize error in fatigue crack growth testing: Oore, M. Fatigue Fract. Engng. Mater. Struct. (1995) 18 (7–8), 905–915

Fatigue crack propagation behaviour after shot peening was investigated in compact tension specimens of AISI 304 stainless steel. The test specimens were exposed to shot stream at Almen intensity of 12C on the specified regions of both side surfaces. These regions were located behind, around and ahead of the fatigue crack tip as well as adjacent to the starter notch. Subsequently, re-initiation life, propagation rate, closure level and the resulting crack growth retardation were studied. Both crack closure and the attendant growth retardation were shown from the experimental observations to be dependent on the location of peened regions. Closure effect was stronger in the case of peening process behind the crack tip, and an order of up to 560,000 cycles was assigned for an extension of the specimen life.

Natural convection in partitioned two-dimensional enclosures at higher Rayleigh numbers

The flow pattern and the temperature field in empty and partitioned, two-dimensional (2D) rectangular enclosures were studied numerically at Rayleigh numbers 10 10–10 12, using an algebraic model for turbulent heat transport θ u i . The geometries considered, with partial, downward-extending and full adiabatic and conductive vertical partitions, imitate neighbouring rooms in real buildings with a doorway in between. Two closure levels were applied in parallel: three- and four-equation models, κ-ε- θ 2 and κ-ε- θ 2 -ε θ, both incorporating the low- Re-number modifications, which allow integration up to the wall and prediction of turbulence transition. The computations confirmed earlier experimental findings that in this range of Ra numbers the flow becomes turbulent, but the turbulence remains confined to only some regions of the enclosure. Noticeable improvements in capturing details of turbulence field, particularly at transitional Rayleigh numbers, are achieved with the algebraic model for turbulent heat transport θ u i , with both the three- and four-equation models, as compared with eddy diffusivity hypotheses. The paper presents some results for the mean flow and turbulence field, as well as for Nusselt number, in several cases of undivided and partitioned enclosures at transitional and higher Ra numbers and for several combinations of boundary conditions, including heating from sides and from below.

Recent advances in fatigue crack growth modeling

Recent advances in our understanding of fatigue crack growth processes and respective crack growth modeling techniques are reviewed. Much of the observed experimental behavior (such as the effects of notches, maximum applied stress, crack length, in-plane biaxiality, out-of-plane constraint, and transient loadings) can be explained based on crack closure concepts. Both Dugdale based models and finite element techniques have been utilized. However, so far neither approach has accounted for crystallographic slip effects, grain orientation effects, or microstructural barriers. A model for crack closure with two microscopic crystallographic slip directions is used to model microscopic cracks. The model predicts variations in closure levels as the orientations of the two slip directions, with respect to the crack growth direction, are changed. In addition, a solution is proposed for the asperity micro-contact problem through a unique roughness induced closure model using a statistical description of asperity heights, asperity densities, and material flow properties.