Showing papers on "Paris' law published in 1996"

Fatigue Damage, Crack Growth and Life Prediction

Abstract: Some general concepts concerning fatigue. Cyclic stress-strain response. Phenomenological approach to fatigue life prediction under uniaxial loading. Fatigue failure under multiaxial states of stress. Multiaxial experimental facilities. Constitutive laws for transient and stable behaviour of inelastic solids. Fatigue crack growth. Fatigue of notched members. Growth and behaviour of small cracks. Probabilistic fatigue crack growth. References. Index.

Transition from pitting to fatigue crack growth—modeling of corrosion fatigue crack nucleation in a 2024-T3 aluminum alloy

Abstract: The nucleation of fatigue cracks from corrosion pits was investigated by conducting fatigue experiments on open-hole specimens of a 2024-T3 aluminum (bare) alloy in 0.5 M NaCl solution at room temperature and different load frequencies from 0.1 to 20 Hz. The maximum cyclic stresses applied at the hole ranged from 144 to 288 MPa and the load ratio, R , was 0.1. A specimen subjected to pre-corrosion in the NaCl solution prior to corrosion fatigue was also investigated. Pitting was found to be associated with constituent particles in the hole and pit growth often involved coalescence of individual particle-nucleated pits. Fatigue cracks typically nucleated from one or two of the larger pits, and the size of the pit at which the fatigue crack nucleates is a function of stress level and load frequency. The observations indicate that the nucleation of corrosion fatigue cracks essentially results from a competition between the processes of pitting and crack growth. Pitting predominates in the early stage of the corrosion fatigue process, and is replaced by corrosion fatigue crack growth. Based on these results, two criteria are proposed to describe the transition from pit growth to fatigue crack growth: (1) the stress intensity factor of the equivalent surface crack has to reach the threshold stress intensity factor, Δ K th , for fatigue crack growth, assuming that a corrosion pit may be modeled by an equivalent semi-elliptical surface crack, and (2) the time-based corrosion fatigue crack growth rate also exceeds the pit growth rate.

A study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading

Abstract: A comprehensive elastic-plastic constitutive model is employed in a finite element analysis of fatigue crack closure. An improved node release scheme is used to simulate crack growth during cyclic loading, which eliminates the associated numerical difficulties. New definitions of crack opening and closing stresses are presented in this paper. Special attention is paid to a discussion of some basic concepts of fatigue crack growth and crack closure behaviour. Residual tensile deformation and residual compressive stress are found to be two major factors in determining the crack opening stress. A comparison of crack tip node release at the maximum or minimum load of each cycle is made and the disadvantage of releasing crack tip node at the minimum load are pointed out.

The effects on fracture toughness of ductile-phase composition and morphology in Nb-Cr-Ti and Nb-Si in situ composites

Abstract: Niobium-chromium alloys, both single and two phase, were alloyed with titanium in order to enhance fracture toughness and fatigue crack growth resistance. The selection of titanium as an alloying element and the relationship of electronic bonding to toughness are examined. The results indicated that toughness increased with a decreasing number of D +s electrons. Titanium was found to increase the toughness of solid-solution Nb-Cr alloys from ≈8 to 87 MPa√m, while for the twophase “insitu composites,” toughness was increased from ≈5 to 20 MPa√m, although this is less than expected. Fracture toughness of the composites correlated nonlinearly with the volume fraction of the phases. The evidence suggests that the toughness of the composites is decreased due to fracture of the intermetallic particles and constraint on matrix deformation imposed by the intermetallic. Fracture characteristics of the Nb-Cr-Ti materials are compared to those of Nb-Cr and Nb-Si materials.

Bayesian Neural Network Analysis of Fatigue Crack Growth Rate in Nickel Base Superalloys

Abstract: The fatigue crack growth rate of nickel base superalloys has been modelled using a neural network model within a Bayesian framework. A committee' model was also introduced to increase the accuracy of the predictions. The rate was modelled as a function of some 51 variables, including stress intensity range ΔK, log ΔK, chemical composition, temperature, grain size, heat treatment, frequency, load waveform, atmosphere, R-ratio, the distinction between short crack growth and long crack growth, sample thickness and yield strength. The Bayesian method puts error bars on the predicted value of the rate and allows the significance of each individual factor to be estimated. In addition, it was possible to estimate the isolated effect of particular variables such as the grain size, which cannot in practice be varied independently. This demonstrates the ability of the method to investigate new phenomena in cases where the information cannot be accessed experimentally.

Fatigue Crack Growth Behavior of PWA 1484 Single Crystal Superalloy at Elevated Temperatures

Abstract: A study was done to determine the fatigue crack growth behavior of a PWA 1484 single-crystal nickel-base superalloy in a temperature range of 427 C to 871 C. Two distinctive failure modes were observed, which were a function of both temperature and frequency. At lower temperatures and higher frequencies crack growth occurred on the {l_brace}111{r_brace} octahedral slip planes at an oblique angle to the loading direction. Higher temperatures and decrease in frequencies favored a Mode I type failure process. The failure mode transitions were explained by invoking arguments based on environmental damage mechanisms. The fatigue crack growth rate data were analyzed using three different crack driving force parameters. The parameters investigated consisted of the Mode I stress intensity parameter corrected for the inclined crack trajectory, and two different octahedral Mode II parameters, which are based on the calculation of resolved shear stresses on the {l_brace}111{r_brace} slip systems. The Mode I {Delta}K parameter did a fair job in correlating the data but did not collapse it into a single narrow band. The two octahedral crack driving force parameters, {Delta}K{sub RSS} and a newly proposed {Delta}K{sub OCT}, collapsed all the data into a single narrow band. In addition to correlating the fatiguemore » crack growth rates, the two octahedral parameters also predicted the {l_brace}111{r_brace} planes on which the crack growth took place.« less

Effect of BaSO4 on the fatigue crack propagation rate of PMMA bone cement

Abstract: To determine the effect of BaSO4 on the fatigue crack growth rate, da/dN = (ΔK)n, of poly(methyl methacrylate) (PMMA) bone cement, radiopaque bone cement, radiolucent bone cement, and commercial PMMA (Plexiglas®) were tested using a methodology based on ASTM E647. The crack growth rate of radiopaque bone cement was one order of magnitude less than that of radiolucent. Fractographic analysis showed that the regions of rapid catastrophic fracture were smooth for all materials tested. The radiopaque fatigue surface was rough and characterized by ragged-edged stacked plateaus, a morphology consistent with the model of crack propagation through the interbead matrix. Voids were visible in the interbead matrix on the order of the size of BaSO4 particles. The fatigue surface of radiolucent bone cement was relatively smooth, a morphology consistent with crack propagation through both the PMMA beads and interbead matrix. Fatigue striations were visible, and their spacing correlated well with crack propagation rates. The striations indicated an increased crack growth rate through the PMMA beads. © 1996 John Wiley & Sons, Inc.

Recent advances in fatigue crack growth modeling

Abstract: 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.

Some aspects of fatigue crack growth retardation behaviour following tensile overloads in a structural steel

Abstract: The effects of specimen thickness, stress intensity levels and R ratio following single tensile overloads, multiple overloads and overload/underload events have been investigated in a BS4360 Grade 50D steel. The amount of fatigue crack growth retardation increased with both decreasing applied baseline AK and increasing overload block size. Smaller increases in retardation were obtained for overload/underload block events compared with block overloads. The data suggests that crack flank plasticity resulting in crack closure adequately accounts for much of the observed behaviour. Near crack tip plasticity was thought to play a more important role in generating crack closure than that remote from the crack tip.

A test method for mode ii fatigue crack growth relating to a model for rolling contact fatigue

Abstract: From fractographic observations of specimens that have failed due to rolling contact fatigue, it has been concluded that the first stage of damage is the formation of mode II fatigue cracks parallel to the contact surface due to the cyclic shear stress component of the contact stress. Although these initial subsurface cracks, in both metals and ceramics, are produced in a direction parallel to the cyclic shear stress, cracks eventually grow in a direction close to the plane of the maximum tensile stress if we apply a simple mode II loading to them. The difference between crack growth in simple mode II loading and crack growth due to rolling contact fatigue is, we suppose, whether or not there is a superimposed compressive stress. Based on this hypothesis, we developed an apparatus to obtain the intrinsic characteristics of mode II fatigue crack growth, and developed a simplified model of subsurface crack growth due to rolling contact fatigue. Some results in terms of da/dN versus ΔK IE relations have been obtained using this apparatus on specimens of steel and aluminum alloys. Fractographs of the mode II fatigue fracture surfaces of the various materials are also provided.

Fracture and fatigue-crack growth behavior in ductile-phase toughened molybdenum disilicide: Effects of niobium wire vs particulate reinforcements

Abstract: A study has been made of the fracture toughness/resistance-curve (R-curve) and cyclic fatigue-crack propagation behavior in a molybdenum disilicide composite, ductile-phase toughened with nominally 20 vol pct Nb-wire mesh reinforcements (Nb m /MoSi2); results are compared with monolithic MoSi2 and MoSi2 reinforced with 20 vol pct spherical Nb particles (Nb p /MoSi2). It is found that the high aspect ratio wire reinforcements induce significant toughening in MoSi2, both under monotonic and cyclic fatigue loading conditions. Specifically, the Nb m /MoSi2 composite exhibits R-curve behavior with a steady-state fracture toughness of ∼13 MPa $$\sqrt m $$ , compared to unstable fracture atK c values below 5 MPa $$\sqrt m $$ in unreinforced MoSi2 or Nb p /MoSi2. Such behavior is seen to be associated with extensive crack deflection within the reaction layer between Nb and the matrix, which leads to crack bridging by the unbroken ductile phase. Similarly, resistance to fatigue-crack growth is found to be far superior in the wire-reinforced composite over pure MoSi2 and Nb p /MoSi2. Although crack paths are again characterized by extensive deflection along the Nb/matrix reaction layer, the role of crack bridging is diminished under cyclic loading due to fatigue failure of the Nb. Instead, the superior fatigue properties of the Nb m /MoSi2 composite are found to be associated with high levels of crack closure that result from highly deflected crack paths along the (Nb,Mo)5Si3 reaction layer interface.

Fatigue crack growth under mixed-mode I and II loading

Abstract: Mixed-mode fatigue crack growth has been studied using four point bend specimens under asymmetric loads. A detailed finite element analysis provides the stress intensity factors for curved cracks under different mixed-mode load conditions. Both fatigue crack growth direction and crack growth rate are studied. The maximum tangential stress and the minimum strain energy density criteria were found to provide satisfactory predictions of the crack growth directions. An effective stress intensity factor was used to correlate the fatigue crack growth rates successfully. It is found that the use of mode I fatigue crack growth rate properties results in a conservative crack growth rate prediction for mixed-mode load conditions.

Contribution of the cyclic loading portion below the opening load to fatigue crack growth

Abstract: A simple test procedure involving stress ratio changes at the fatigue threshold is proposed to reveal the role of the lower portion of the loading cycle below Kop in the fatigue crack growth behaviour. It is observed for both Al 2024-T3 and Al 7475-T761 alloys that the initially non-propagating fatigue crack at the fatigue threshold resumes growth upon diminishing Kmin while keeping Kth,max constant. These experimental findings can be interpreted by means of a modified crack closure concept in which the contribution of the lower portion of the loading cycle below Kop (including also a part of compressive loading if R < 0) to the variation in the stress state experienced by the fatigue crack tip is taken into account.

Fatigue Crack Growth

Abstract: Metal fatigue is a major cause for failure of mechanical and structural components. We review the fracture mechanics of fatigue and Paris-Erdogan law for the mean behavior. After a consideration of experimental data reported by Virkler et al. (1979), we propose a continuous semimarkov process to model crack growth. The model accounts for the material randomness and sees crack as a motion in a random field.

Influence of micro structure on acoustic emission behavior during stage 2 fatigue crack growth in solution annealed, thermally aged and weld specimens of AISI type 316 stainless steel

Abstract: Acoustic emission (AE) behavior during fatigue crack growth (FCG) in solution annealed, thermally aged and weld specimens of AISI type 316 austenitic stainless steel is reported in this article. The presence of two substages 2(a) and 2(b) during stage 2 FCG could be distinguished by a change in the AE behavior corresponding to a sharp change in the crack growth rate (da/dn). The transition point in the AE parameter vs. number of cycles (n) plot matches well with that of the (da/dn) vs. ‘n’ plot and is found to occur at a da/dn ≈ 3 × 10−7 m cycle−1 which is in agreement with the reported value. The high AE activity observed during the substage 2(a) is attributed to the extensive cyclic plasticity within the cyclic plastic zone (CPZ) and the increasing size of the CPZ with ΔK under plane strain conditions prevailing during stage 2(a). The low AE activity observed during stage 2(b) is attributed to a reduction in the mean free path for dislocation movement and a decrease in the size of the CPZ under plane stress condition prevailing during stage 2(b). The AE during stage 2(a) is found to have a strong influence on the microstructure. The presence of carbide precipitates in thermally aged specimens reduces the AE activity. The high AE activity in weld specimen is attributed to the combined influence of cyclic plasticity, residual stress induced micro cracking and roughness induced crack closure phenomena.

An introduction to fatigue in metals and composites

Abstract: Preface. Acknowledgement. Introduction. Elements of deformable body analysis. Macroscopic and microscopic features of fatigue. Engineering characterizations of safe life. Fatigue crack growth. Structural integrity of metals. Structural Integrity of polymeric matrix composite laminates. Biomaterials. Appendices. Problems. References. Index.

The application of microstructural fracture mechanics to various metal surface states

Abstract: The fatigue crack initiation period, previously thought to be a necessary precursor to fatigue crack propagation and eventual failure, is considered here to be a negligible phase in the fatigue failure of polycrystalline metals. Rather this period is considered to be the propagation of a defect of microstructural dimensions by a variety of processes. The significance of this alternative view is examined in relation to corrosion fatigue, models of short crack growth, different loading modes, and the enhancement of fatigue resistance by surface shot-peening treatments. In both inert and aggressive environments, the fatigue lifetime of plain steel specimens of various strengths and treatments is predominantly determined by the early propagation of short cracks of microstructural dimensions. Microstructural fracture mechanics, rather than continuum mechanics, can quantify both pit growth and Stage I shear crack growth behavior before the defect reaches the dominant microstructural barrier which controls the fatigue behavior of the material. The important processes that determine lifetime are those that are strongly dependent on the synergism between the aggressive environment and cyclic stresses; these are the pitting, Stage I and the Stage I-to-Stage II crack propagation processes. A model has been produced to quantify these three important stages of lifetime named above. Under torsion loading, where Stage I cracks prefer to propagate along the surface, an intermittent series of deceleration/acceleration events of crack growth occur across the first few grain boundaries until the defect is blocked in its further development by a major microstructural barrier. When this barrier is breached, the environmentally-assisted Stage I crack rapidly becomes a Stage II crack. Under push-pull loading, the Stage I environmentally-assisted crack can propagate faster into the bulk material and, as a consequence, the transition to a Stage II environmentally-assisted crack is rapid thereby eliminating the need for the intermittent process observed under torsion loading. With no environmentally-assisted fatigue processes (i.e., testing in air) reversed torsion and push-pull loading test data can best be correlated by a von Mises criterion. Corrosion fatigue lifetimes can best be correlated by a Rankine (tensile stress) criterion. Shot-peening enhances the corrosion fatigue resistance of polycrystalline metals by inducing residual compressive stresses in the surface and creating numerous and more rapidly formed microcracks. This is probably caused by the presence of variously oriented plastically deformed bands within the surface microstructure and “short crack-short crack” interactions both of which delay the progress of the dominant crack toward its final Stage II phase.

The effect of short carbon fibre reinforcement on fatigue crack growth in PEEK

Abstract: Fatigue crack growth has been investigated in a range of short carbon fibre reinforced composites based on the thermoplastic PEEK. The role of fibre volume fraction and the interdependent parameters of skin-core fibre arrangement, fibre preferred orientation and fibre length were studied. Fatigue crack growth rates in compact tension specimens were found to decrease significantly with increasing fibre fraction when loading was parallel to the mould filling direction but the effect was less marked for loading perpendicular to the mould filling direction. The Friedrich concepts of ‘reinforcing efficiency’ and ‘microstructural efficiency’ were employed to quantity the complex fibre microstructure and clarify the role that the fibre microstructure plays during fatigue fracture in the composites. Post fracture SEM studies of the materials showed evidence of the interaction of static and cyclic mechanisms during fatigue in both unreinforced PEEK and its short fibre reinforced composites.

Transient fatigue crack growth behaviour following single overloads at high stress ratios

Abstract: Fatigue crack growth tests with constant amplitude loading and single overload have been performed on a long mode I crack in 2017-T3 aluminium alloy at various stress ratios from 0 to 0.7. Two crack tip parameters of σ op and σ tt were evaluated using a finite element analysis for a growing crack under these loading conditions. The former is the crack opening stress and the latter is the applied stress level at which the stress at the crack tip becomes tensile. It was found that transient crack growth behaviour following single overloads at high stress ratios was significantly different from that at a low stress ratio : at higher stress ratios, following the application of the overload, there was a rapid retardation which was followed by an acceleration in growth rate and then a faster return to the steady state level at baseline loading. The experimentally observed transient post-overload behaviour is discussed in terms of the two effective stress range ratios of U op and U tt , which are determined from σ op and σ tt , respectively. For the stress ratios and overload ratios studied, the results indicate that the changes in U tt , with crack extension after the overload are reasonably consistent with the crack growth rate trends. The stress distribution at minimum applied stress would account for the transient changes in U tt .

Fatigue Crack Growth Rates in Adhesive Joints Tested at Different Frequencies

Abstract: Mode I fatigue crack growth tests were conducted on joints bonded with a filled adhesive (A) at 20 Hz and 2 Hz and on joints bonded with a filled and toughened adhesive (B) at 20 Hz, 2 Hz, 0.2 Hz and 0.02 Hz. Strain energy release rate, G, and J-integral were evaluated based on elastic and elastoplastic finite element analyses (FEA) of the joints bonded with adhesive A and B, respectively. For the configurations considered, J was found to be path-independent and did not differ much from G. The fatigue crack growth rate (FCGR), da/dN, in the joints bonded with adhesive A was relatively independent of frequency while it increased with decreasing frequency at given δ for the joints bonded with adhesive B. The fatigue processes in both adhesives involved the cracking of the filler particles and subsequent linkage of the resultant microcracks. The process zone in adhesive B is larger than that in adhesive A and it increases with decreasing frequency. It is suggested that this variation in process zone...

Morphological aspects of fatigue crack propagation Part I—Computational procedure

Abstract: In the present paper a simulation method is proposed for the evaluation of paths and lives of fatigue cracks. The simulation is based on an incremental crack extension procedure. At each increment the stress analysis ahead of a crack tip is carried out by the finite element method, and the next incremental crack-growth path is predicted by the first order perturbation method with the use of the local symmetry criterion. From the computational viewpoint, the step-by-step rezoning of finite element mesh subdivision is one of the most difficult processes of the simulation procedure. In order to overcome this difficulty, we shall use the modified quadtree method as an automatic mesh generation technique. Considerations are made for the proper mesh arrangement in the vicinity of a crack tip, where a special fine mesh pattern is embedded so that mixed mode stress intensity factors and the higher order coefficients of the near tip stress field parameters can accurately be obtained. Using the proposed method, we simulate the branched and curved fatigue crack growth in three-point-bending specimens. They show fairly good agreement with the experimental results. The simulation procedure is also applied to biaxially loaded cruciform joints.