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Showing papers on "Paris' law published in 1994"


Journal ArticleDOI
TL;DR: In this article, a new model was proposed to rationalize the observed variations in the fatigue crack threshold with load ratio, which is based on a requirement for two critical stress intensity parameters, namely ΔK th ∗ and K max ∗, that must be satisfied simultaneously as the crack tip driving forces for fatigue crack growth.
Abstract: Published fatigue crack closure mechanisms are reviewed in the context of the following five ideas that have been developed over the past twenty years to explain the closure effects on near-threshold crack growth behaviour: (1) oxide, (2) asperity, (3) plasticity, (4) phase transformation and (5) viscous fluids. The first three have been considered as more important than the last two. Our analysis indicates that (a) there can be no contribution from plasticity to crack closure, (b) the crack closure contribution can be significant only if it is closed fully, which is reflected as an infinite slope in the load-displacement curve, (c) formation of oxide asperities from a fretting action is a random process and not a deterministic one, and therefore cannot explain the deterministic behaviour of the effect of load ratio on the threshold, and (d) the closure contribution from the asperities resulting from oxides or corrosion products,or surface roughness, it is less than 20% of what has been deduced based on the change in the slope of the load-displacement curves. Thus the analyses show that crack closure can exist, but its magnitude is either small or negligible. The critical evaluation of the literature data on (1) the threshold stress intensity variation with load ratio on many materials, and (2) and examination of the experimentally observed load-displacement curves confirm the above conclusions. Hence to rationalize the observed variations in the fatigue crack threshold with load ratio, we have proposed a new model. It postulates a requirement for two critical stress intensity parameters, namely ΔK th ∗ and K max ∗ , that must be satisfied simultaneously as the crack tip driving forces for fatigue crack growth. This requirement is fundamental to fatigue, since an unambiguous description of cyclic loads requires two independent load parameters. Several experimental results from the literature are presented in support of this postulation. Using these two critical parameters, the entire functional relationship between Kmax, ΔKth and R is explained without invoking an entrinsic factor, namely crack closure. In addition, for a given material and its crack tip environment, a unique relationship between ΔKth and Kmax exists that is independent of test methods used in determining thresholds. Finally, because of this two parameter requirement, all fatigue crack growth data need to be represented in terms of three-dimensional plots involving da/dN, ΔK and Kmax. For a two-dimensional representation, the data need to be transformed correctly, defining the net driving force involving both ΔK and Kmax parameters. The concepts presented are independent of whether crack closure exists or not, or even whether cracks exist or not.

301 citations


Journal ArticleDOI
TL;DR: In this paper, a new mode of electric-field-induced fatigue crack growth was identified, and fracture mechanics concepts were applied to interpret the observed cracking, and an experimental procedure for characterizing crack extension from preexisting flaws in such materials subject to high-amplitude, alternating electric fields was described.
Abstract: When subjected to large alternating electric fields, ferroelectric ceramics may experience cracking and mechanical degradation. This article describes an experimental procedure for characterizing crack extension from preexisting flaws in such materials subject to high-amplitude, alternating electric fields. A new mode of electric-field-induced fatigue crack growth is identified. Fracture mechanics concepts are applied to interpret the observed cracking.

238 citations


Book
01 Jan 1994
TL;DR: Theoretical models and numerical methods for fracture parameters calculation for fatigue crack propagation in metals have been proposed in this paper, where the three-dimensional boundary element method has been applied to quasistatic and fatigue cracks propagation.
Abstract: Volume 1. Introductory Section. Failure criteria for anisotropic bodies (P.S. Theocaris). Introduction to fracture mechanics of fatigue (H. Kitagawa). Numerical methods for fracture parameters calculation (G.J. Tsamasphyros). Fatigue Behaviour of Metallic Materials. Fatigue of steels for concrete reinforcement and cables (M. Elices et al). Fatigue crack growth and crack shielding in a Fe-C-Cu sintered steel (Y-W. Mai et al). Fatigue and fracture properties of aerospace aluminium alloys (R.J.H. Wanhill). Fatigue crack propagation in titanium alloys (J.K. Gregory). Theoretical Models and Numerical Methods. Mechanical model for fatigue crack propagation in metals (X.-L. Zheng). Application of the three-dimensional boundary element method to quasistatic and fatigue crack propagation (M.H. Aliabadi, Y. Mi). Method of damage mechanics for prediction of structure member fatigue lives (X. Zhang et al.). Stochastic fatigue crack propagation (J.H. Yoon, Y.S. Yang). A fracture mechanics approach to the optimum design of cracked structures under cyclic loading (Z. Knesl). Fundamental Aspects of Fatigue Crack Propagation Phenomenon. Stable and unstable fatigue crack propagation in metals (V.T. Troshchenko). Fatigue crack growth from stress concentrations and fatigue life prediction in notched components (C.S. Shin). Propagation of surface cracks under cyclic loading (A. Carpinteri). Growth behaviour of small fatigue cracks and relating problems (H. Nisitani et al). Analytical and experimental study of crack closure behaviour (D.-h. Chen). Studies of fatigue crack closure (D. Francois). Fatigue threshold of metallic materials - a review (A. Hadrboletz et al). Mechanics of fatigue crack growth as a synthesis of micro-and macro-mechanics of fracture (V.V. Bolotin). Random material non-homogeneity effects on fatigue crack growth (K. Dolinski). Volume 2. Influence of Loading Conditions. Fatigue crack growth under variable amplitude loading (J. Dominguez). Mixed mode fatigue crack propagation (L.P. Pook). Numerical and. experimental study of mixed mode fatigue crack propagation (A.S. Kobayashi, M. Ramulu). Crack growth behaviour under repeated impact load conditions (T. Tanaka et al). Influence of Environmental Conditions. Influence of ambient atmosphere on fatigue crack growth behaviour of metals (J. Petit et al). Influence of hydrogen-containing environments on fatigue crack extension resistance of metals (V.V Panasyuk et al.). Fatigue crack propagation in aqueous environments (Y. Nakai). Application of fatigue crack growth data to low cycle fatigue at high temperature (L. Remy). Creep-fatigue interaction under high-temperature conditions (R. Ohtani, T. Kitamura). Fatigue crack propagation in metals at low temperatures (X.-L. Zheng, B.-T. Lu). (Part contents).

221 citations


Journal ArticleDOI
TL;DR: In this article, an application of dual boundary element method to the analysis of three-dimensional mixed-mode crack growth is presented, where the crack growth processes are simulated numerically with an incremental crack-extension analysis based on the minimum strain energy density criterion and a fatigue crack growth law.

175 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the presence of corner point singularities in the vicinity of a corner point where a crack front intersects a free surface and derived the stress intensity factors for three-dimensional mixed mode configurations.

149 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the effects of matrix resin and fibers on the mechanisms and mechanics of delamination fatigue crack growth in unidirectional CFRP laminates and found that the fracture toughness does not fully contribute to the fatigue crack resistance.

119 citations


Journal ArticleDOI
TL;DR: In this article, a correlation between acoustic emission and the stress intensity factor was derived which allows prediction of the ΔK from acoustic emission measurements, at very low values of ΔK, corresponding to the onset of fatigue crack growth, was expected that acoustic emission would detect this event.

89 citations


Journal ArticleDOI
TL;DR: In this article, the results of fatigue crack growth rate tests conducted in the presence of residual stresses are discussed with reference to experimental trends, in order to clarify the predictive capabilities of the method and aspects needing further investigation.
Abstract: — The paper discusses the results of fatigue crack growth rate tests conducted in the presence of residual stresses. Three different residual stress distributions, obtained by laser welds, were employed in order to characterize the crack propagation behaviour under different conditions, producing either an increase or a reduction of the stress intensity factor due to external loads. Test results are analysed by means of a non-linear numerical model (based on the weight function method) and a knowledge of the fatigue crack growth properties of the base material, free from residual stresses. The results of the analysis are discussed with reference to experimental trends, in order to clarify the predictive capabilities of the method and aspects needing further investigation.

73 citations


Book ChapterDOI
01 Jan 1994
TL;DR: In this paper, a model of fatigue crack initiation is discussed based on the concepts of continuum damage mechanics as well as the assumption that fatigue crack nuclei form Poissonian sets distributed in a body.
Abstract: Fatigue life prediction problems are discussed from the viewpoint of probabilistic mechanics of solids and structures. A survey of random factors in damage and fracture is presented with a special emphasis on the statistical scatter of mechanical properties of materials and/or structural components. A model of fatigue crack initiation is discussed based on the concepts of continuum damage mechanics as well as the assumption that fatigue crack nuclei form Poissonian sets distributed in a body. To describe macroscopic fatigue crack propagation, the theory proposed by author that takes into account the interaction between the microdamage accumulation along the crack trajectories and the global balance of forces, energy, etc. in the cracked body under loading is used. Various approaches to the modeling of material property fields are considered, and the influence of random factors from different sources on fatigue life is studied by means of numerical simulation. Discussion of alternative probabilistic approaches to modeling of fatigue damage is presented.

54 citations


Journal ArticleDOI
TL;DR: In this paper, a two-dimensional, weight-function-based, non-linear elastic-plastic analytical model has been developed for considering fatigue crack propagation in a pre-existing residual stress field.

49 citations


Journal ArticleDOI
TL;DR: In this paper, the authors modeled fatigue crack growth in fiber-reinforced metal-matrix composites based on a crack tip shielding analysis, where the fiber/matrix interface is assumed to be weak, allowing interfacial debonding and sliding to occur readily during matrix cracking.
Abstract: Fatigue crack growth in fiber-reinforced metal-matrix composites is modeled based on a crack tip shielding analysis. The fiber/matrix interface is assumed to be weak, allowing interfacial debonding and sliding to occur readily during matrix cracking. The presence of intact fibers in the wake of the matrix crack shields the crack tip from the applied stresses and reduces the stress intensity factors and the matrix crack growth rate. Two regimes of fatigue cracking have been simulated. The first is the case where the applied load is low, so that all the fibers between the original notch tip and the current crack tip remain intact. The crack growth rate decreases markedly with crack extension, and approaches a “steady-state”. The second regime occurs if the fibers fail when the stress on them reaches a unique fiber strength. The fiber breakage reduces the shielding contribution, resulting in a significant acceleration in the crack growth rate. It is suggested that a criterion based on the onset of fiber failure may be used for a conservative lifetime prediction. The results of the calculations have been summarized in calibrated functions which represent the crack tip stress intensity factor and the applied load for fiber failure.

Journal ArticleDOI
TL;DR: In this article, the effects of preexisting glass phase on elevated temperature fatigue and fracture are examined, and the creep crack growth behavior of Si3N4-based ceramics is compared with that of oxide-based Ceramics.
Abstract: Experimental results are presented on subcritical crack growth under sustained and cyclic loads in a HIPed Si3N4 at 1450°C and a hot–pressed Si3N4–10 vol% SiCw composite in the temperature range 1300°–1400°C. Static and cyclic crack growth rates are obtained from the threshold for the onset of stable fracture with different cyclic frequencies and load ratios. Fatigue crack growth rates for both the monolithic and SiCw-reinforced Si3N4 are generally higher than the crack growth velocities predicted using static crack growth data. However, the threshold stress intensity factor ranges for the onset of crack growth are always higher under cyclic loads than for sustained load fracture. Electron microscopy of crack wake contact and crack–tip damage illustrate the mechanisms of subcritical crack growth under static and cyclic loading. Critical experiments have been conducted systematically to measure the fracture initiation toughness at room temperature, after advancing the crack subcritically by a controlled amount under static or cyclic loads at elevated temperatures. Results of these experiments quantify the extent of degradation in crack–wake bridging due to cyclically varying loads. The effects of preexisting glass phase on elevated temperature fatigue and fracture are examined, and the creep crack growth behavior of Si3N4–based ceramics is compared with that of oxide-based ceramics.

Journal ArticleDOI
Kim Chung-Youb1, Song Ji-Ho1
TL;DR: In this paper, the effects of random load spectrum and history length on the behavior of crack closure and growth are discussed, and a relatively simple method is proposed to predict crack growth under random loading.

Journal ArticleDOI
TL;DR: In this article, the growth behavior of small fatigue cracks has been studied in both fine and coarse-grained versions of a pure titanium under axial loading at stress ratio, R, of −1.

Journal ArticleDOI
TL;DR: In this article, the effects of compressive excursions on fatigue crack growth have been investigated on both smooth bars and cracked specimens with intermittent negative R ratio loadings, and the results indicated that the effects are not negligible.

Journal ArticleDOI
TL;DR: In this article, the characteristics of plastic zone development and the relationship between PZS and crack growth rate have been studied through periodic plastic zone size measurement of growing small fatigue cracks.
Abstract: Small fatigue crack growth has been studied in two 7000 series aluminium alloys possessing different grain sizes. As it has been suggested that the relatively large plastic deformation associated with small fatigue cracks may explain thier fast growth rates compared to long cracks, the work focused on experimental measurement of the plastic zone size (PZS) accompanying small cracks. The characteristics of plastic zone development and the relationship between PZS and crack growth rate have been studied through periodic plastic zone size measurement of growing small fatigue cracks. It was found that small fatigue crack growth is indeed accompanied with comparatively large plastic zone sizes. It is suggested that this is mainly due to a near surface effect. It was also found that an exponential relation exists between small crack growth rates and their plastic zone sizes for a given material.

Journal ArticleDOI
TL;DR: In this article, the role of the interface in redistributing stress around cracks in multilayered ceramic/metal composites is investigated, focusing on the different effects of interfacial debonding or of plastic slip in the metal phase adjacent to strongly bonded interfaces.
Abstract: The role of the interface in redistributing stress around cracks in multilayered ceramic/metal composites is investigated. The emphasis is on the different effects of interfacial debonding or of plastic slip in the metal phase adjacent to strongly bonded interfaces. The experiments are conducted on alumina/aluminum multilayered composites. Monotonic loading precracked test pieces causes plastic shear deformation within the aluminum layer at the tip of the notch without debonding. However, interfacial debonding can be induced by cyclic loading, in accordance with a classical fatigue mechanism. Measurements of the stress around the crack demonstrate that debonding is much more effective than slip at reducing the stress ahead of the crack.

Journal ArticleDOI
TL;DR: In this paper, the effects of cyclic frequency, hold time, and stress-intensity factor range (ΔK) on rates of fatigue crack growth in air at 500°C and 700°C have been studied for the direct-aged version of the nickel-based superalloy 718.
Abstract: — The effects of cyclic frequency, hold time, and stress-intensity factor range (ΔK) on rates of fatigue crack growth in air at 500°C and 700°C have been studied for the direct-aged version of the nickel-based superalloy 718. The main effects were similar to those observed for Waspaloy (Part I), namely: (i) small effects of cyclic frequency and hold time at 500°C, (ii) higher rates of crack growth at lower cyclic frequencies at high ΔK at 700°C, and (iii) lower rates of crack growth at low ΔK (and higher ΔK thresholds) for longer hold times at 700°C. For DA 718, there was no increase in crack growth rates with increasing hold times (0–60 s) at high ΔK at 700°C (unlike the large increases reported for standard processed Alloy 718). Metallographic and fractographic observations showed that crack growth was predominantly transgranular at 500°C, and predominantly intergranular at 700°C except at 2 Hz at high ΔK. The precise intergranular crack path, extent of branching, and fracture-surface appearance depended on ΔK, wave-form and cycle-period. The mechanisms responsible for the observed effects, and possible explanations for the different behaviour of DA 718 and standard processed Alloy 718, are discussed.

Journal ArticleDOI
TL;DR: In this paper, a high-strength Si{sub 3}N{sub 4} with elongated {beta}-Si{sub 2]N{ sub 4} and equiaxed {alpha}{prime}-sialon was tested in cyclic and static fatigue at 1400 C. The pullout process of the elongated grains was enhanced, which suppressed the crack growth.
Abstract: A high-strength Si{sub 3}N{sub 4} with elongated {beta}-Si{sub 3}N{sub 4} and equiaxed {alpha}{prime}-sialon was tested in cyclic and static fatigue at 1400 C. At low stress intensity factors and high frequencies, the pullout process of the elongated grains was enhanced, which suppressed the crack growth. This provides a possible explanation for the increased lifetime under cyclic loading conditions reported for ceramics by several investigators. While crack-healing by high-temperature annealing was found to greatly reduce the subsequent static fatigue crack growth rate, it had only a modest effect on cyclic fatigue and none at high frequencies.

Journal ArticleDOI
TL;DR: In this article, the authors demonstrated a 1:1 correlation between striations and stress cycles, which can aid greatly in understanding conditions associated with the fracture, including the number of stress variations that produced the fracture.

Journal ArticleDOI
TL;DR: In this paper, a finite element analysis and fatigue crack growth studies are made of dovetail joints in aeroengine compressor discs, where critical geometrical features and interface conditions of different dovetail configurations are examined.
Abstract: — A finite element analysis and fatigue crack growth studies are made of dovetail joints in aeroengine compressor discs. Three aspects are examined: the first deals with the finite element stress analysis of the critical geometrical features and interface conditions of different dovetail configurations, thus enabling an assessment to be made of the critically loaded regions in the disc. The second deals with the prediction of the direction of potential fatigue cracks, which were allowed to initiate in the finite element model at the regions where fretting damage is most likely to occur, using an incremental crack tracking criterion. The third is concerned with the verification of the above modelling techniques with fatigue tests on a uniaxial back-to-back arrangement, which attempts to simulate the stress fields of a rotating disc.

Journal ArticleDOI
TL;DR: In this paper, the effects of cyclic frequency, hold time, and stress-intensity-factor range (δK) on rates of fatigue crack growth in air at 500-700°C have been studied for Waspaloy.
Abstract: — The effects of cyclic frequency, hold time, and stress-intensity-factor range (δK) on rates of fatigue crack growth in air at 500-700°C have been studied for Waspaloy—a nickel-based superalloy used for gas-turbine engine discs. The main effects observed were: (i) higher rates of crack growth for lower cyclic frequencies at high δK at 600 and 700°C. and (ii) lower rates of crack growth at low δK (and higher δK thresholds) for longer hold times at 700°C, compared with those at a baseline frequency of 2 Hz. Metallographic and fractographic observations suggested that the effects of cyclic frequency and hold time could be rationalised in terms of the competing effects of enhancement of cracking due to creep and inhibition of cracking caused by oxide-induced crack closure, fracture-surface-roughness induced crack closure, and crack-branching/deflection. Possible mechanisms for promoting intergranular and transgranular cracking at low cyclic frequencies or long hold times are discussed.

Journal ArticleDOI
TL;DR: In this article, a fatigue crack growth model for high temperature complex loading and application to turbine disc conditions is proposed based on an extensive experimental study performed on Astroloy at 650°C, which comprises fatigue with or without hold times, special tests with holds at intermediate loads, fastslow or slow-fast triangular waves, sequence tests, etc.

Journal ArticleDOI
R. Hermann1
TL;DR: In this paper, the authors studied mode I fatigue crack growth in notched specimens of 7017-T651 aluminium alloy subjected to fully compressive cyclic loads and found that the fracture growth was confined to a region of tensile cyclic stress within the residual stress field.
Abstract: — Mode I fatigue crack growth has been studied in notched specimens of 7017-T651 aluminium alloy subjected to fully compressive cyclic loads. The specimens were first subjected to a deliberate compressive preload which causes plastic deformation at the notch tip. On unloading, this region developed a residual tensile stress field and on subsequent compressive cyclic loading in laboratory air, a fatigue crack was nucleated at the notch and grew at a diminishing rate until it stopped. The final crack length increased with an increase in the value of the initial compressive preload and with an increase in the negative value of the applied cyclic mean load. To gain a better understanding of crack growth in residual stress fields, the magnitude and extent of residual stress induced from compressive preloads have been analysed. This was achieved when extending the notch by cutting while recording the change in the back face strain. From residual strain models it was found that the fatigue crack growth was confined to a region of tensile cyclic stress within the residual stress field. The effective stress intensity range was investigated at selected mean loads and amplitudes, for correlating purposes, using both the compliance technique and by invoking the crack growth rate behaviour of the alloy. Finally, a brief discussion of the fracture morphology of cracks subjected to cyclic compression is presented.

Journal ArticleDOI
TL;DR: In this paper, three different methods for determining the threshold value for fatigue crack growth were applied to a high-strength aluminium alloy, including load shedding, stepwise increase of load amplitude on specimens precracked in cyclic compression, and decrease of stress intensity range at a constant maximum stress intensity.

Journal ArticleDOI
TL;DR: In this article, a straightforward method of calculating local Schmid factors in front of small crystallographic fatigue crack tips as they approach and cross grain boundaries has been developed, based on an analysis of the stress distribution ahead of a crack, in conjunction with two further factors: the bulk Schmid factor and the crystallographic misorientation across the grain boundary.
Abstract: Small fatigue crack growth is often characterized by anomalous acceleration and deceleration growth patterns due to the presence of microstructural barriers such as grain boundaries. A straightforward method of calculating local Schmid factors in front of small crystallographic fatigue crack tips as they approach and cross grain boundaries has been developed. The method is based on an analysis of the stress distribution ahead of a crack, in conjunction with two further factors: the bulk Schmid factor and the crystallographic misorientation across the grain boundary. The crystallographic features of small crack growth and their influence on deceleration when a crack approaches a grain boundary were determined experimentally. It was found that the difference between the Schmid factors of the slip system containing the crack and the most favourably oriented slip system in the neighbouring grain plays an important role in crack growth retardation as the crack approaches the grain boundary. The experimental results also indicated that cracks prefer to propagate along slip systems with high Schmid factors when transferring from one grain to another. The predictions of the analysis are compared with experimental observation and good agreement is achieved.

Journal ArticleDOI
TL;DR: In this article, a finite element method (FEM) based on the theory of linear elasticity is presented for the plane-strain problem and two small singular elements are installed at the crack tip to compute the singular field.

Journal ArticleDOI
TL;DR: Fatigue crack propagation tests under mixed mode loading conditions were conducted on center-cracked tension specimens machined from extruded blocks of sterilized polyethylene in an attempt to determine how fatigue cracks change direction in this material.
Abstract: Analytical studies of the stresses on and within ultra high molecular weight polyethylene joint components suggest that damage modes associated with polyethylene fatigue failure are caused by a combination of surface and subsurface crack propagation. Fatigue crack propagation tests under mixed mode loading conditions were conducted on center-cracked tension specimens machined from extruded blocks of sterilized polyethylene in an attempt to determine how fatigue cracks change direction in this material. Cyclic testing was performed using a sinusoidal wave form at a frequency of 5 Hz and an R-ratio (minimum load/maximum load) of 0.15. Specimens had the notch oriented perpendicular to the direction of applied load and at angles of 60 degrees and 45 degrees to the loading direction. Numerical analyses were used to interpret the experimental test and to predict the fatigue behavior of polyethylene under mixed mode conditions. It was found that all cracks eventually propagated horizontally, regardless of the initial angle of inclination of the notch to the direction of applied cyclic load. In fact, the extent of the curvilinear crack growth was quite limited. An effective range of cyclic stress intensity factor was calculated for correlation with the rate of crack growth. The results followed a Paris relation, with crack growth rate linearly related to a power of the range of stress intensity, for all three crack orientations. The numerical analyses adequately modeled the experimental fatigue crack growth results.

Journal ArticleDOI
TL;DR: In this paper, a single edge notched geometry with clamped ends is used for fracture toughness and fatigue crack growth testing of composites, and closed form expressions for the stress intensity factor and the compliance are developed using finite element analysis.

Journal ArticleDOI
TL;DR: In this paper, a model for transgranular fatigue-crack growth in highly textured materials was developed, which takes the form of the Paris relationship with a power law exponent of 3, and the material texture is shown to strongly influence the proportional factor.
Abstract: A series of fatigue-crack growth rate (FCGR) tests was carried out on 8090 Al-Li plate to examine the effects of specimen orientation on fatigue-crack growth. The directionality of fatigue fracture behavior is found to be related to the strong {110}〈112〉 texture in this alloy. Based on a previously developed transgranular FCGR model using restricted slip reversibility (RSR) concepts, [1] a mechanistic model is developed for transgranular fatigue-crack growth in highly textured materials. The model takes the form of the Paris relationship with a power law exponent of 3, and the material texture is shown to strongly influence the proportional factor. The effect of texture on FCGR is related through a geometric factor cos2 ϕ, where ϕ defines the angle between the load axis and the normal of the favorable slip plane. The effect of specimen orientation on FCGR in 8090 Al-Li alloy is shown to be related to a combination of its anisotropic mechanical properties and the variation of angleϕ with specimen orientation. The model further predicts that fatigue-crack growth rates will be slower in many textured materials than texturefree materials becauseϕ > 0 and cos2 ϕ < 1.