Showing papers on "Paris' law published in 1987"
TL;DR: In this article, a mathematical model that describes the fatigue crack growth evolution and associated scatter in polycrystalline solids is presented, based on the analogy that an analogy exists between a particular discontinuous Markovian stochastic process, namely the general pure birth process, and the crack propagation process.
132 citations
TL;DR: In this article, the authors investigated the fatigue crack growth behavior, the length of the arrested cracks and the shape of the crack front for cyclic compression under different load amplitudes and load ratios.
Abstract: The fatigue crack growth behaviour, the length of the arrested cracks and the shape of the crack front were investigated for cyclic compression. Specimens with deep sharp notches were used. The experiments were performed for different load amplitudes and load ratios under conditions of small scale yielding. The material used was ARMCO-iron. The growth rate and length of the arrested cracks were estimated and compared with the experimental results. The crack growth rate of very short cracks is determined by the stress intensity and is independent of the stress ratio. The length of the arrested cracks depends on the stress ratio and is bounded by the size of the cyclic and the monotonic plastic zones.
113 citations
TL;DR: In this paper, the fracture toughness of a mechanically alloyed aluminum alloy reinforced with SiC particles has been investigated and the contribution to fracture toughness from work done within the plastic zone and in formation of the void sheet has been computed using analytical models.
Abstract: Subcritical crack growth and rapid fracture of the mechanically alloyed aluminum alloy IN-9052* reinforced with SiC particles have been investigated. Fatigue crack growth rates for the composite exceed those of the unreinforced alloy, except that the threshold stress intensity for growth is higher for the composite. Fracture toughness of the composite is about 9 MPa√m compared to a (reported) value of 29 MPa√m for the unreinforced alloy. The contributions to fracture toughness from work done within the plastic zone and in formation of the void sheet have been computed using analytical models. Fracture toughness is shown to result almost entirely from work done within the plastic zone of the growing crack. The matrix microstructure and the particulate characteristics are found to account for the elastic and fracture properties of this composite.
90 citations
TL;DR: In this paper, a power law relationship between da/dN and the cyclic variation in the energy release rate ΔGI was found for both pure mode I and mixed mode II.
Abstract: Delamination fatigue crack growth experiments were carried out on unidirectional T300/914 C Graphite/Epoxy laminates. Both mode I and mixed mode (mode I and mode II in combination) situations were investigated for the stress ratios R = 0.1, 0.3 and 0.5. Double Cantilever Beam (DCB) specimens were used for the pure mode I tests and Cracked Lap Shear (CLS) specimens were used for the mixed mode tests. The initial delaminations were produced by inserting 0.03 mm thick PTFE films during laminate layup. The cyclic loading of the specimens was carried out at a frequency of 5 Hz and with a constant stress ratio maintained throughout the test. It was found that the mode I cyclic crack growth rate yielded a power law relationship between da/dN and the cyclic variation in the energy release rate ΔGI. This relation was virtually independent of the stress ratio, at least for 0.1 < R < 0.5. The mixed mode results showed a similar power law relation between da/dN and Δ(G I + GII). Here a small stress ratio dependence w...
84 citations
TL;DR: In this article, a model for the fatigue crack propagation is developed which incorporates the bulk cyclic and low-cycle fatigue properties of the material and predicts the R-ratio effects on the fatigue cracks growth at low and intermediate stress intensities.
72 citations
TL;DR: In this article, the authors examined fracture surfaces of short glass fiber-reinforced polymers to gain insight into the mechanisms of cyclic damage and fatigue-crack propagation in these materials, and several distinctly different features were noted between fracture surfaces generated by stable fatigue crack growth and those produced by monotonic or unstable fracture.
Abstract: Fatigue-crack profiles and fracture surfaces of several short glass fibre-reinforced polymers were examined to gain insight into the mechanisms of cyclic damage and fatigue-crack propagation in these materials. Several distinctly different features were noted between fracture surfaces generated by stable fatigue crack growth and those produced by monotonic or unstable fracture. Among the most significant differences were the higher degree of single and multiple fibre fracture generally observed on stable fatigue-crack growth fracture surfaces, and the variations in the interfacial failure site in well-bonded systems. While the former effect is attributed to the occurrence of crack closure and the build-up of compressive stresses in the crack-tip damage zone during unloading, the differences in the interfacial failure mode are related to the adverse effect of fatigue loading on the interfacial bond strength. No features could be identified that would allow a quantitative correlation between the applied stress intensity factor level or the crack growth rates and characteristic fracture surface details.
68 citations
TL;DR: In this paper, the fatigue deformation resulted in the formation of slip bands which were longer for coarse-grained microstructures and typically spaced farther apart and more planar for large γ micro-structures.
Abstract: The fatigue crack growth rates of four Alloy 718 microstructures comprising a two-by-two matrix of grain size and γ" precipitate size were determined in air at 427 °C and 033 Hz For a stress ratio of 005, slower Region II rates were obtained for coarse-grained microstructures, independent of γ" size, and microstructures with large γ", independent of grain size In the near-threshold regime, the coarse-grained microstructures again showed slower growth rates (higher ΔKth), whereas the effect of γ" size was mixed Deformation modes were studied using scanning and transmission electron microscopy Fatigue deformation resulted in the formation of slip bands which were longer for coarse-grained microstructures and typically spaced farther apart and more planar for large γ micro-structures The concepts of dislocation reversibility and slip band strain localization were used to explain the microstructural effects Fatigue morphologies and cyclic constitutive behavior were con-sistent with the observed deformation modes For a stress ratio of 075, the effects of grain size and γ" size were essentially identical to those observed for a stress ratio of 005 This indicated that roughness-induced closure had a minimal influence on the differences that were observed in fatigue crack growth behavior
67 citations
TL;DR: In this article, a model expressed by the J-integral was proposed assuming that the crack growth is determined by the linear summation of relations of pure Mode I and II crack-tip deformation.
65 citations
TL;DR: In this paper, the effects of crystallographic orientation on the fatigue crack growth behavior of MAR-M200* single crystals were examined using compact-tension specimens tested at 20 Hz.
Abstract: The effects of crystallographic orientation on the fatigue crack growth behavior of MAR-M200* single crystals were examined. Using compact-tension specimens tested at 20 Hz, fatigue crack growth rates were determined at ambient temperature at minimum stress to maximum stress ratios,R, of 0.1 and 0.5. In most cases, subcritical crack growth occurred either along a single {111} slip plane or a combination of {111} planes. The mode of cracking was generally mixed and contained mode I, II, and III components. Considerable crack deflection and branching were also observed. Some fracture surfaces were found to contain a significant amount of asperities and, in some specimens, black debris. Based on Auger spectroscopic analyses and the fracture surface appearance, it appears that the black debris represented oxides formed due to rubbing of the fracture surfaces. Using stress intensity solutions obtained based on the Boundary-Integral-Equation technique, an effective ΔK was successfully used for correlating the crack growth rate data. The results indicate that the effect of crystallographic orientation on crack growth rate can be explained on the basis of crack deflection, branching, and roughness-induced crack closure.
64 citations
TL;DR: In this paper, the fatigue crack growth behavior of small part-through cracks in 1045 steel and Inconel 718 subjected to biaxial loading has been investigated.
Abstract: — The fatigue crack growth behavior of small part-through cracks in 1045 steel and Inconel 718 subjected to biaxial loading has been investigated. Experiments were performed on thin-wall tubular specimens loaded in tension, torsion and combined tension torsion. Crack sizes analyzed ranged from 20 μm to 1 mm and growth rates ranged from 10-7 to 10-4 mm/cycle for 1045 steel and from 10-5 to 10-2 mm/cycle for Inconel. Nucleation and the early growth of cracks occurs on planes of maximum shear strain amplitude for both of these materials even in tensile loading. An equivalent strain based intensity factor was employed to correlate the crack growth rate under mixed mode loading conditions In loading conditions other than torsion, a transition from mode II to mode I was observed for 1045 steel. Principal strains were used to analyze mode I cracks. Cracks in Inconel 718 grow in mode II for the majority of the fatigue life. The maximum shear strain amplitude and the tensile strain normal to the maximum shear strain amplitude plane were used to calculate the strain based intensity factor for mixed mode loading.
64 citations
TL;DR: In this article, the authors investigated the transition from short cracks to long cracks in ARMCO-iron with very small notch radius (between 1.5 and 4 μm) and found that the fatigue crack growth rate was measured as a function of the crack length.
Abstract: The fatigue crack growth rateda/dN of short cracks and the transition to long crack behavior were investigated for ARMCO-iron. Deep notched specimens with very small notch radius (between 1.5 and 4 μm) were used. The experiments were performed with constant stress intensity ranges for various stress ratios; the fatigue crack growth rate was measured as a function of the crack length. The results permit a discussion of the mechanisms responsible for the different behavior of “short” and “long” cracks.
TL;DR: In this paper, a constitutive formulation is presented to determine the "driving force" for Mode I fatigue crack growth in notched plates of brittle solids stressed in uniaxial cyclic compression.
Abstract: A constitutive formulation is presented to determine the “driving force” for Mode I fatigue crack growth in notched plates of brittle solids stressed in uniaxial cyclic compression. For the particular case of a microcracking medium, it is demonstrated that residual tensile stresses are induced ahead of the notch during unloading from the maximum far-field compressive stress. We propose that it is this region of residual tensile stresses at the notch-tip which promotes fatigue crack growth in ceramics along the notch plane in a direction normal to the compression axis. The predictions of the analysis are compared with new experimental results on compression fatigue in brittle solids. Specifically, it is shown that the numerical estimates of the near-tip tensile zone size for microcracking ceramics compare favorably with the experimentally measured distance of stable Mode I fatigue crack growth after the first compression cycle. Experimental information on the threshold stress for microcracking, transition stress for the inducement of residual tension during unloading, and the effect of mean stress on fracture, as well as direct observations of microcracks and crack growth in compression fatigue, corroborate the assumptions and implications of the analysis.
TL;DR: In this paper, the authors examined the growth behavior of MAR-M200 single crystals at 982 °C and determined the growth rates as functions of crystallographic orientation and the stress state by varying the applied shear stress range-to-normal stress ratio.
Abstract: The fatigue crack growth behavior of MAR-M200 single crystals was examined at 982 °C. Using tubular specimens, fatigue crack growth rates were determined as functions of crystallographic orientation and the stress state by varying the applied shear stress range-to-normal stress range ratio. Neither crystallographic orientation nor stress state was found to have a significant effect on crack growth rate when correlated with an effective ΔK which accounted for mixed-mode loading and elastic anisotropy. For both uniaxial and multiaxial fatigue, crack growth generally occurred normal to the principal stress direction and in a direction along which ΔK
II vanished. Consequently, the effective ΔK was reduced to ΔKI and the rate of propagation was controlled by ΔK
I only. The through-thickness fatigue cracks were generally noncrystallographic with fracture surfaces exhibiting striations in the [010], [011], and [111] crystals, but striation-covered ridges in the [211] specimen. These fracture modes are contrasted to crystallographic cracking along slip bands observed at ambient temperature. The difference in cracking behavior at 25 and 982 °C is explained on the basis of the propensity for homogeneous, multiple slip at the crack tip at 982 °C. The overall fracture mechanism is discussed in conjunction with Koss and Chan’s coplanar slip model.
31 Mar 1987
TL;DR: In this paper, the authors compared the constant amplitude fatigue crack growth properties of five batches of aluminium alloy 2024 in the naturally aged T3 and T351 conditions and paid particular attention to crack growth curve transitions in the near-threshold regime.
Abstract: Constant amplitude fatigue crack growth properties of five batches of aluminium alloy 2024 in the naturally aged T3 and T351 conditions are compared. Particular attention is paid to crack growth curve transitions in the near-threshold regime. These transitions correspond to monotonie or cyclic plane strain plastic zone dimensions becoming equal to characteristic microstructural dimensions. Changes in fracture surface topography are associated with the transitions also. From the observations an explanation of the shape of the low stress intensity fatigue crack growth curve and the transitions is given.
TL;DR: In this article, the fracture toughness and R-curves for ceramics can be determined in bending (or tension) after pre-cracking notched specimens in uniaxial cyclic compression to produce a controlled and through-thickness fatigue flaw.
Abstract: Experimental observations of stable Mode I fatigue crack growth at room temperature in notched plates of brittle solids subjected to fully compressive far-field cyclic loads have recently been reported. !n this paper, we outline an experimental procedure whereby the fracture toughness and R-curves for ceramics can be determined in bending (or tension) after pre-cracking notched specimens in uniaxial cyclic compression to produce a controlled and through -thickness fatigue flaw. The capability of this technique to provide reproducible fracture toughness values in illustrated with the aid of experimental results obtained for coarse-grained and fine-grained aluminium oxide.
Book•
01 Jun 1987
TL;DR: In this article, a systematic review of the current achievement by each author with the emphasis on important points is presented, where the elaborated experimental techniques and theoretical approaches, some of which are quite unique, are introduced by respective authors to make clear the difficulty arising in the observation of small cracks and analysis of data.
Abstract: This first volume of CJMR (Current Japanese Materials Research), contains thirteen chapters concerning the above three themes of fatigue cracks. Each chapter is not a single paper as appearing in many academic journals and transactions, but a systematic review of the current achievement by each author with the emphasis on important points. The common feature is that the elaborated experimental techniques and theoretical approaches, some of which are quite unique, are introduced by respective authors to make clear the difficulty arising in the observation of small cracks and analysis of data. Theoretical models are proposed from the viewpoint of fracture mechanics to link the two thresholds of fatigue limit and crack growth, and intensive discussions are made for further development of the theory. Threshold stress intensity factors and the growth rate of medium and long sized cracks are also discussed, together with their opening behavior. The influencing factors are plastic zone size, the stress ratio and residual stress distribution occurring in welded joints. Mode II crack growth is of great significance since the initial fatigue cracks propagate mainly in shear mode. The problems of fatigue crack growth in corrosive environment is highly important since its retardation and enhancement take placemore » in structural steels affected by the variety of factors. Life prediction in such environments poses another important problem. These are systematically discussed in this book.« less
TL;DR: In this article, a d-c electric potential system for measuring crack length under thermal/mechanical fatigue-crack-growth (TMFCG) test conditions is described.
Abstract: The paper describes a d-c electric potential system for measuring crack length under thermal/mechanical fatigue-crack-growth (TMFCG) test conditions. A programmable d-c current supply and precision multimeter produce reliable electric-potential readings. H.H. Johnson's formula is used to calculate crack length from electric potential for the center-crack-tensionM(T) geometry. Calibration constants for the formula are determined from an initial optical crack-length measurement. The resolution of the system is 1.0 microvolt which corresponds to a crack extension of approximately 0.002 mm for the center-crack-tension geometry using a current of 10.00 amps. Good crack-length accuracy and low data scatter are achieved by taking special precautions to minimize or eliminate errors in potential measurement due to thermal effects. Material resistivity changes are identified as the cause of short and long term changes in the measured electric potential for uncracked specimens. Crack-length accuracy is discussed in terms of short-term scatter and longterm drift.
TL;DR: In this article, the near threshold fatigue behavior of a nickel base superalloy and a wrought 2024 aluminum alloy is examined as a function of specimen geometry, and the observed discrepancies are given in terms of the near field crack tip stress distribution and deformation behavior of the material affecting crack advance.
Abstract: — The near threshold fatigue behavior of a nickel base superalloy and a wrought 2024 aluminum alloy is examined as a function of specimen geometry. Experimental results revealed that for a given value of ΔK in Region I, crack growth rates were observed to increase as the specimen loading became more symmetric with respect to the load line. Compact tension type specimens exhibited lower crack growth rates than the more symmetrically loaded center cracked tension specimens. Consideration of the observed discrepancies is given in terms of the near field crack tip stress distribution and deformation behavior of the material affecting crack advance.
TL;DR: In this article, the concept of cyclic Jintegral (ΔJ) is considered, and equations for estimating its value are given for estimating Fatigue crack growth rate data for an alloy steel using ΔJ and rough crack closure measurements.
TL;DR: In this paper, the effect of phase continuity on the low cycle fatigue and fatigue crack growth behavior of a Fe-C-Mn dual-phase steel has been investigated, and two microstructures, one consisting of continuous ferrite and the other continuous martensite, were examined.
Abstract: The effect of phase continuity on the low cycle fatigue and fatigue crack growth behavior of a Fe-C-Mn dual-phase steel has been investigated. Two microstructures, one consisting of continuous ferrite and the other continuous martensite, were examined. Although there was no difference in the low cycle fatigue lives between the two microstructures, the continuous martensite structure exhibited an extremely high fatigue threshold value of 20 MPa m1/2, compared to 16 MPa m1/2 for the continuous ferrite microstructure. A major effect of phase continuity has also been found in the crack closure levels during fatigue crack propagation studied over three decades of crack growth rates. The continuous martensite microstructure exhibited much higher closure levels due to the martensite constraining the plastic deformation in the ferrite and bearing a larger portion of the applied cyclic load. This effect is similar to the extrinsic toughening phenomenon cited in the literature. After accounting for the closure levels the intrinsic or effective fatigue crack growth rates are similar for the two microstructures. These intrinsic thresholds are predicted by employing experimentally obtained low cycle fatigue parameters and the ferrite grain size.
TL;DR: In this article, the authors investigated the effects of mixed-mode loading on aluminum alloys on crack initiation and growth in a precrack under mixed mode loading and showed that the direction of shear mode crack growth approaches the plane in which K I decreases and K II increases towards the maximum with crack growth.
TL;DR: In this paper, stress intensity levels at the tip of cracks approaching and growing past second-phase particles have been computed using finite element methods and it is predicted that particles having a lower modulus than the matrix attract and accelerate cracks growing into their vicinity, whereas hard particles deflect them and retard local growth.
Abstract: Stress intensity levels at the tip of cracks approaching and growing past second-phase particles have been computed using finite element methods. It is predicted that particles having a lower modulus than the matrix (i.e. ‘soft’ particles) attract and accelerate cracks growing into their vicinity, whereas ‘hard’ particles deflect them and retard local growth. A reverse, but weaker, effect is indicated once the crack has extended past a particle. Using a ferrite matrix with either spheroidized cementite or spheroidal graphite as the second phase, these predictions have been largely verified experimentally. An apparent anomaly is the cross-over in the growth rate curves of the cast iron and the totally ferritic microstructure. However, this may be explained by the requirement for the crack to reinitiate following its interaction with each graphite particle, during which decohesion of the particle/matrix interface occurs.MST/417
Book•
01 Aug 1987
TL;DR: In this paper, the fractographic analysis of fracture surfaces in composites and metals is discussed in reviews and reports of recent theoretical and experimental investigations, including fracture-surface micromorphology in engineering solids, SEM fractography of pure and mixed-mode interlaminar fractures in graphite/epoxy composites, determination of crack propagation directions, and the fracture surfaces of irradiated composites.
Abstract: The fractographic analysis of fracture surfaces in composites and metals is discussed in reviews and reports of recent theoretical and experimental investigations. Topics addressed include fracture-surface micromorphology in engineering solids, SEM fractography of pure and mixed-mode interlaminar fractures in graphite/epoxy composites, determination of crack propagation directions in graphite/epoxy structures, and the fracture surfaces of irradiated composites. Consideration is given to fractographic feature identification and characterization by digital imaging analysis, fractography of pressure-vessel steel weldments, the micromechanisms of major/minor cycle fatigue crack growth in Inconel 718, and fractographic analysis of hydrogen-assisted cracking in alpha-beta Ti alloys.
TL;DR: In this article, the authors reviewed the literature pertaining to small cracks in nickel-base superalloys and the consequences of this behaviour upon the lifetime prediction of gas turbines are evaluated for a typical case.
01 Jan 1987
TL;DR: In this article, the fracture propagation analysis is used for the design and life prediction of fatigue critical structures, such as airframes, gas turbine engine components, and helicopter structures, just to mention a few.
Abstract: From the fracture mechanics standpoint, fatigue failure of a metallic component results from the propagation of a dominant crack to its critical size. Hence, the crack propagation analysis is one of the major tasks in the design and life prediction of fatigue-critical structures, such as airframes, gas turbine engine components, and helicopter structures, just to mention a few. Durability and damage tolerance are two major design requirements for aircraft structures, in which the prediction of fatigue crack growth damage accumulation is one of the most important subjects (e.g., MIL-, 1974, 1975; Rudd, 1984; Tiffany, 1978; Manning and Yang, 1984).
TL;DR: In this article, the growth characteristics of small fatigue cracks were investigated under rotary bending in a high tensile strength steel, and the critical crack length above which linear elastic fracture mechanics (LEFM) is applicable was evaluated systematically from the results of the present study and previous studies in which two steels having different microstructures and strengths were used.
Abstract: — The growth characteristics of small fatigue cracks were investigated under rotary bending in a high tensile strength steel, and the critical crack length above which linear elastic fracture mechanics (LEFM) is applicable was evaluated systematically from the results of the present study and previous studies in which two steels having different microstructures and strengths were used. It is found that the critical crack length extends over two regions each exhibiting different growth mechanisms. These regions of microstructurally small cracks and mechanically small cracks are found to be a unique function of the microstructural unit size and the yield strength of the materials, respectively. Therefore, using these relationships, it is possible to estimate the critical crack length for a given material.
TL;DR: In this paper, the authors compared the crack growth behavior in terms of the closure-free component of the threshold stress intensity range, ΔKth,eff while a systematic variation in the absolute threshold stress intensities with yield strength was observed.
Abstract: Near threshold fatigue crack growth behavior of a high strength steel under different tempered conditions was investigated. The important aspect of the study is to compare the crack growth behavior in terms of the closure-free component of the threshold stress intensity range, ΔKth,eff While a systematic variation in the absolute threshold stress intensity range with yield strength was observed, the trend in the intrinsic ΔKth or ΔKth,eff exhibited a contrasting behavior. This has been explained as due to the difference in fracture modes during near threshold crack growth at different temper levels. It is shown that in a high strength and high strain hardening microstructure, yielding along crystallographic slip planes is difficult and hence it exhibited a flat transgranular fracture. In a steel with low strain hardening characteristics and relatively low strength, a tendency to crystallographic planar slip is observed consequently resulting in high ΔKth. Occurrence of a predominantly intergranular fracture is shown to reduce intrinsic ΔKth drastically and increase crack growth rates. Also shown is that crack closure can occur in high strength steels under certain fracture morphologies. A ‘transgranular planar slip’ during the inception of a ‘microstructure sensitive’ crack growth is essential to promote intergranular and faceted fracture. The occurrence of a maximum in the fraction of intergranular fracture during threshold crack growth corresponds to the ΔK value at which the cyclic plastic zone size becomes equal to the prior austenitic grain size.
TL;DR: In this article, the effects of load ratio and environment on crack growth rate properties were investigated in four gaseous environments; laboratory air, wet hydrogen, dry hydrogen and dry helium.
TL;DR: In this article, a review of several statistical and probabilistic approaches to the problem of fatigue crack growth is presented, showing that many Markov models are equivalent in that they express the probability density of the crack length at time t as solutions of the Kolmogorov, or Fokker-Plank, equations.
TL;DR: In this article, the authors construct models depicting the comparative rate of fatigue crack growth of a variety of steels under the influence of liquefied gases and the temperatures required by them.
Abstract: The authors construct models depicting the comparative rate of fatigue crack growth of a variety of steels under the influence of liquefied gases and the temperatures required by them. The relationship of the rate parameter and the stress intensity factor at the crack tip is represented by kinetic fatigue failure diagrams which are used to determine the cyclic crack resistance of the steels.