Fatigue of rubber-modified epoxies: effect of particle size and volume fraction

A change in crack-tip plastic zone/rubber particle interactions induces a transition in the fatigue crack propagation (FCP) behaviour of rubber-modified epoxy polymers. The transition occurs at a specific K level, K _T, which corresponds to the condition where the size of the plastic zone is of the order of the size of the rubber particles. At K>K _T, rubber-modified epoxies exhibit improved FCP resistance compared to the unmodified epoxy. This is because the size of the plastic zone becomes large compared to the size of the rubber particles and, consequently, rubber cavitation/shear banding and plastic void growth mechanisms become active. At K>K _T, both neat and rubber-modified epoxies exhibit similar FCP resistance because the plastic zone size is smaller than the size of the rubber particles and hence, the rubber cavitation/shear banding and plastic void growth mechanisms are not operating. As a result of these interactions, the use of smaller 0.2 m rubber particles in place of 1.5 m rubber particles results in about one order of magnitude improvement in FCP resistance of the rubber-modified system, particularly near the threshold regime. Such mechanistic understanding of FCP behaviour was employed to model the FCP behaviour of rubber-modified epoxies. It is shown that the near threshold FCP behaviour is affected by the rubber particle size and blend morphology but not by the volume fraction of the modifiers. On the other hand, the slope of the Paris-Erdogan power law depends on the volume fraction of the modifiers and not on the particle size or blend morphology.     

ΔK ol level effects on fatigue crack propagation

In order to determine the effects of K _ol level on fatigue life, a single peak load was applied at distinct K levels of 7.8×10.3 and 9.8×10³ p.s.i. in^1/2. Here the K _ol level was defined to be a K level at which overload was applied. Three different overload ratios of 1.5, 2.0, and 2.5 were used to determine the overload ratio effect on the recovery factor. The result showed that the recovery factor, Z, was linearly related to K as Z = qK+Z _o, where q was a function of overload ratio. The value of q decreased as the overload ratio increased in a given K _ol level and seemed to be an important factor as well as retardation cycles in determining the fatigue life. For the same overload ratio, specimens that underwent overload at a smaller K _ol level showed more improved fatigue life.Nomenclature a Crack length - a ^* Overload affected zone size - B Specimen thickness - (da/dN)_ca Crack growth rate due to constant amplitude fatigue load - (da/dN)_ol Crack growth rate after overload is applied - E Young's modulus - K Stress intensity factor - K _min Minimum stress intensity factor - K _max Maximum stress intensity factor - K _ol K level at which overload is applied - N Number of cycles - N _D Number of delayed cycles - N _f Number of cycles needed for a specimen to be completely fractured - r _p Assumed plastic zone size - S Load - _ys Yield stress - W Width - Z Recovery factor     

The significance of RPG load for fatigue crack propagation and the development of a compliance measuring system

In can be postulated that fatigue crack does not grow if no damage occurs in the vicinity of the crack tip. Damage may occur beyond the Re-tensile Plastic zone's Generated load (RPG load) in the vicinity of a crack tip under loading process. We propose an effective stress intensity factor range ( K _RP) corresponding to the period in which the re-tensile plastic zone appears, in place of K _eff proposed by Elber [1], for a fatigue crack propagation parameter.We then consider the small change of compliance for a cracked body under cyclic loading, for the purpose of measuring RPG load as well as crack opening load and crack closing load. Moreover a subtraction circuit which can measure the small change of compliance during fatigue test is developed and an automatic controlled system which can control the adequate values of resistance in the circuit and the output voltage range from strain amplifiers for minimizing relative noise level is also developed. Then fatigue crack propagation tests of CT specimens were carried out with various stress ratios of constant amplitude loadings. Moreover K _th tests with the conditions of constant stress ratio and constant maximum load with increasing stepwise minimum load were also carried out. It becomes clear that the logarithmic curve of K _RP—crack propagation rate appears to be linear in a wide range from the region of very slow growth rate to the region of stable growth rate. On the other hand, threshold phenomenon appears only circumstantially due to the particular loading pattern on K _eff based on the crack opening load and K _eff ^cl based on the crack closing load. Moreover K _RP gives the quantitative effect of stress ratio on fatigue crack propagation rate.     

Testing procedures for fatigue crack propagation and the ΔKeffconcept

Two different procedures are available for the experimental determination of fatigue crack propagation (FCP) velocities da/dN as a function of the loading parameters K. The first procedure is the standardized method in accordance with ASTM E 647 [1] and the second procedure is the so-called K_max-constant method. Both procedures are equivalent, meaning that under the same loading conditions (K, K_max, R) the same FCP velocity (da/dN) is measured. But, the ASTM E 647 method emphasizes the effects of closure (contact of fracture surfaces) in the low K and low K_max regime. It is shown for Al 7075–T7351, the Ni-base alloy Nicrofer 5219 Nb (annealed), the Ti-alloys Ti 6Al 4V (annealed), and Ti 6Al 6V 2Sn that K_eff is the sole driving parameter for FCP.Published in Problemy Prochnosti, No. 7, pp. 13–30, July, 1995.     

An investigation of the micromechanisms of fatigue crack growth in structural gas turbine engine alloys

This paper presents an overview of fatigue fracture modes in selected structural alloys employed in gas turbine engines. These include the mechanisms of fatigue crack growth in the near-threshold, Paris and high-K regimes obtained from Ti-6Al-4V, Inconel 718 and PWA 1472 (a single crystal nickel-based superalloy of similar chemical composition to Inconel 718). Fatigue fracture modes in these materials are shown to be strong functions of the stress intensity factor range, K, and the maximum stress intensity factor, K _max. Fatigue mechanism maps are also presented to show the parametric ranges of K and K _max corresponding to the different fatigue fracture modes.     

The molecular weight dependence of fatigue crack propagation in polycarbonate

Fatigue crack propagation has been studied in polycarbonate as a function of specimen thickness and molecular weight. It was found useful to estimate the relative contribution of the shear lips and the plane strain crazing mode to fatigue crack propagation. In addition to measuring the width of the shear lips, the craze in the central region of the crack tip was examined in an optical microscope. The shear lip contribution was found to be particularly important at high values of the range of the stress intensity factor K, and was appreciable in all but the thickest specimens and the lowest values of K.As in the case of fracture toughness, the fatigue crack propagation behaviour of polycarbonate is greatly affected by the molecular weight of the polymer. This is due to changes in both the shear lip contribution and the plane strain craze contribution. Because of the complicated nature of the failure mode it is suggested that the application of the Paris equation to the fatigue crack propagation of polycarbonate will be of limited significance.     

Double influence of hydrogen on fatigue crack growth in heat-resistant steels

We investigate fatigue crack growth in cast heat-resistant steel pipes of reforming furnaces in a vacuum, in air, and in gaseous hydrogen in the temperature range 20 – 800°C. It is shown that the character and intensity of hydrogen-induced effects depend on temperature and loading amplitude. For the crack resistance threshold, we discovered the phenomenon of temperature inversion of these effects. Namely, the value of K _th in hydrogen increases with temperature up to 400°C and then decreases. Under high-amplitude loading, the influence of hydrogen manifests itself only in the acceleration of crack growth. The ambiguity in the influence of hydrogen on the plastic strain resistance of the material at the crack tip is analyzed on the basis of well-known physical concepts of the influence of hydrogen on the processes of generation and displacement of dislocations. The effects discovered in this work are explained by the realization of different fracture mechanisms and different types of hydrogen-induced effects under different conditions. Thus, at low temperatures (up to 400°C) and high K, one observes a decrease in the tearing strength; the case of low temperatures and low K is characterized by the shear fracture mechanism and the strengthening effect of hydrogen; for high temperatures ( 400°C) and low K, the shear fracture mechanism is combined with a decrease in the plastic strain resistance under the influence of hydrogen.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No, 4, pp. 7–15, July – August, 1994.     

On the generality of discontinuous fatigue crack growth in glassy polymers

Fatigue fracture surface characteristics of five commercially available amorphous polymers [poly(methylmethacrylate) (PMMA), polycarbonate (PC), poly(vinyl chloride) (PVC), polystyrene (PS), and polysulphone (PSF)] as well as bulk-polymerized PMMA prepared over a wide range of molecular weights were studied to determine if common mechanisms of fatigue crack propagation prevail among these glassy polymers. In those polymers with viscosity-average molecular weight ¯M _v2×10⁵, the macroscopic appearance of the fracture surface showed the presence of a highly reflective mirror-like region which formed at low values of stress intensity and high cyclic test frequencies (100 Hz). The microscopic appearance of this region revealed that many parallel bands exist oriented perpendicular to the direction of crack growth and that the bands increase in size with K. In all instances, the crack front advanced discontinuously in increments equal to the band width after remaining stationary for hundreds of fatigue cycles. Electron fractographic studies verified the discontinuous nature of crack extension through a craze which developed continuously with the load fluctuations. By equating the band size to the Dugdale plastic zone dimension ahead of the crack, a relatively constant yield strength was inferred which agreed well with reported craze stress values for each material. At higher stress intensity levels in all polymers and all values of ¯M _v, another series of parallel bands were observed. These were also oriented perpendicular to the direction of crack growth and likewise increased in size with the range in stress intensity factor, K. Each band corresponded to the incremental advance of the crack during one load cycle, indicating these markings to be classical fatigue striations.     

Fatigue behaviour of precipitation-hardening medium C steels containing Cu

The presence of Cu precipitates counteracts the cyclic softening present in ordinary quenched and tempered steels. This is expected to result in an increase in fatigue limit. The fatigue crack propagation rate (dc/dN) at constant K in the Cu-C steels was shown to depend on heat-treatment and carbon content. To maximize yield strength and minimize ¦da/dN¦_K for tempering at 500° C, one must choose a low C content and temper for a short time; ¦da/dN¦_K in 0.28 wt % C-1.45 wt % Cu tempered for 13 min was one-third that for 0.45 wt % C-1.45 wt% Cu tempered for 200 min. There is also an advantage in adding Cu while simultaneously lowering the Ccontent. The dc/dN data are discussed in terms of the yield strength and the energy to form a unit area of fatigue crack, U, which was measured using foil strain gauges. The quantity (¦dc/dN ¦_{K y} ² U) where _y is the cyclic yield stress, was found to be nearly constant. In the 0.28 wt % C-1.45wt % Cu alloy, short ageing times at 500° C resulted in greater resistance to initiation of cracks at notches for low Ks than long ageing times.     

High-temperature cracking resistance in cast steel in reforming oven tubes

Summary Results are given from high-temperature tests (770, 870, 920, and 960°C) to estimate the short-time and cyclic cracking resistance for cast NK-40 steel tubes from reforming ovens in the initial state and after use for 75,400 h. The crack growth resistance in static loading has been determined from the crack resistance limit, and in cyclic loading from the kinetic diagrams for the fatigue failure in terms of the crack growth ratev against the scale of the nominal stress intensity coefficient K. Metallography shows that there are differences in structure in the various states, and material that has been used has pores and microcracks, whose numbers are largest in the inner wall layers. Cyclic tests with constant K show substantial increase in the crack growth rate in the defective material.The cracking stability limit falls as the test temperature rises, while the fatigue crack growth rate increases, particularly above 920°C. Increased asymmetry in the loading cycle (R=–1; –0.5; 0; 0.4) is accompanied by deterioration in the cyclic cracking resistance. There are two opposite trends in the effects of loading frequency (f=0.001–10 Hz) on the failure kinetics: in the high-amplitude loading range, reduction inf increases the crack growth rate, while in the low-amplitude range, there is a decrease. The results are explained in terms of creep and fatigue crack opening.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 2, pp. 68–74, March–April, 1990.     

Influence of Hydrogen on the Formation of Fatigue Thresholds in Structural Steels

We analyze certain phenomena related to the influence of gaseous hydrogen and hydrogen dissolved in a metal on the near-threshold growth of fatigue cracks. The significant decrease in crack growth resistance due to the action of hydrogen as compared with that in vacuum is caused mainly by the adsorption decrease in strength due to adsorption. We established three factors of the ambiguous influence of hydrogen on the effective fatigue threshold K _theff, for which a positive influence is replaced by a negative one, namely: the strength level, temperature of testing, and high-temperature degradation of the metal. The following fractographic peculiarities of the near-threshold growth of cracks in a degraded metal are revealed: the local tunneling along the front of a crack and the presence of fatigue grooves. We propose a mechanism of crack closure due to both roughness and the component of longitudinal shear at the tip of the crack. We analyze the scale effect of fatigue thresholds, determine the conditions for invariance of the parameter K _theff under conditions of plane deformation, and established the dependence of K _theff on the thickness of specimens in the case of tests of a hydrogenated degraded metal.     

Influence of various divalent impurities on dislocation density in KCl:Mg2+, Ca2+, Sr2+ or Ba2+ single crystals

Single crystals of nominally pure KCl and KCl doped with Mg²⁺, Ca²⁺, Sr²⁺ or Ba²⁺ were deformed by compression at 77–254 K; during the tests strain-rate cycling was conducted in association with ultrasonic oscillation. The data were analyzed in terms of strain-rate sensitivity ((/ln)) versus stress decrement (). The curve for KCl doped with the divalent impurities has two bending points and two plateau regions. It is proposed that the variation of strain-rate sensitivity at the second plateau place on the curve with shear strain ((/ln)/) is due to a change in forest dislocation density with shear strain. The forest dislocation density for the specimens seemed to increase by the divalent additions in the compression test on account of the jogs on the screw dislocations. It depended on the concentration of impurities and also on the size of impurity in the specimens at a given temperature. Unfortunately, it was not possible to determine whether a change in the size of impurity influences mobile dislocation density, , from the values of / for KCl doped with Ca²⁺, Sr²⁺ or Ba²⁺.     

Modeling of crack bridging in a unidirectional metal matrix composite

The effective fatigue crack driving force and crack opening profiles were determined analytically for fatigue tested unidirectional composite specimens exhibiting fiber bridging. The crack closure pressure due to bridging was modeled using two approaches; the fiber pressure model and the shear lag model. For both closure models, the Bueckner weight function method and the finite element method were used to calculate crack opening displacements and the crack driving force. The predicted near crack tip opening profile agreed well with the experimentally measured profiles for single edge notch SCS-6/Ti-15-3 metal matrix composite specimens. The numerically determined effective crack driving force, K _eff, was calculated using both models to correlate the measured crack growth rate in the composite. The calculated K _eff from both models accounted for the crack bridging by showing a good agreement between the measured fatigue crack growth rates of the bridged composite and that of unreinforced, unbridged titanium matrix alloy specimens.     

Deformation approach to the evaluation of the period of initiation and growth of fatigue macrocracks

We performed experimental investigation of the opening displacements of the contours of stress concentrators (notches and cracks) for various amplitudes of cyclic loading. On the basis of experimental results, we propose a new deformation parameter _t which is a function of the notch (crack) tip opening displacement , namely, _t /(+d*), where is the radius of the tip of the notch andd* is the characteristic size of the prefracture zone. It is shown that this parameter uniquely determines the number of cyclesN _l to the initiation of a fatigue macrocrack independently of the geometry of the specimens and stress concentrators in elastic and elastoplastic materials, i.e., the dependence of _t onN ₁ is a characteristic of the material. It is experimentally demonstrated that this dependence enables one to quantitatively describe the process of fatigue fracture both in the stage of initiation of macrocracks and their propagation.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 5, pp. 7–21, September – October, 1995.     

Regularities in the Main-Crack Propagation and Dislocation Structure Evolution in the Fracture Zone of VT22 Alloy at Various Frequencies of Cyclic Loading

We have studied the relationship between the dislocation structure in the fracture zone and fractographic features of the main-crack propagation in a Ti–5%Al–5%V alloy tested for cyclic crack growth resistance in symmetrical tension–compression at frequencies of 140, 600, 3000, and 10000 Hz. It is demonstrated that the prevailing Types of dislocation structure are cellular over the near-threshold K range and of band-Type structure for the remaining values of the stress intensity factor range. For these Types of structure of the alloy studied at all loading frequencies, the characteristic micromechanism of fracture is the formation of fatigue striations. In the region of low K values, the above-mentioned Types of substructure, and thus fatigue striations, are most commonly formed along certain crystallographic planes and directions. As the K values grow, the crack sensitivity to crystallographic orientation decreases. The effect of the loading frequency on the regularities and mechanisms of fatigue crack growth is governed by two main factors: the processes of plastic deformation at the crack tip during the pre-fracture period and the interaction between the crack front and the initial and formed structural and substructural elements. The appearance of the brittle-fracture elements with increasing loading frequency is due to a rather high sensitivity of the -phase to the loading rate.     

A two-parameter damage criterion and high-temperature fatigue crack growth in a corrosion-resistant steel

Summary The paper is designed to develop the two-parameter failure criterion for describing the growth of fatigue cracks under conditions of high-temperature fatigue. The criterion can be used with laboratory tests on specimens to construct kinetic diagrams for fatigue failure such as would be given if the requirements of linear failure mechanics were met. The initial data are the v-K_eff fatigue failure diagrams, which are effective ones incorporating crack closure, so one can derive v-K_v theoretical diagrams as conservative characteristics for a material for crack growth under conditions of planar strain.The two-parameter criterion enables one to incorporate the effects of frequency and cycle asymmetry at high K, where there are changes in crack growth rate due to changes in the rate of plastic strain at the crack vertex. At low K, the effects of loading frequency are additionally determined by the crack closure, the blunting, and the physicochemical action of the medium, which restricts the scope for using the two-parameter criterion to construct fatigue-failure kinetic diagrams invariant with respect to frequency.Translated from Fiziko-khimicheskaya Mekhanika Materialov., Vol. 26, No. 5, pp. 9–19, September–October, 1990.     

The unzipping model of fatigue crack growth and its application to a two-phase steel

The unzipping analysis, based on the alternate shear deformation process of two intersecting shear planes at a crack tip, is extended to study fatigue crack growth in a two-phase martensitic-ferritic steel. The unzipping crack increment a _uz is directly related to K and J in the case of small scale yielding. It is preferrable to use a _uz is directly related to K and J in the case of small scale yielding. It is preferable to use a _uz as a physical parameter to correlate with the growth rates of micro-cracks and fatigue cracks in a multi-phase material. In the case of micro-cracks, K is often not applicable because of extensive plastic deformation; and in the case of multi-phase material, neither K nor J is applicable because of material inhomogeneity. The effective K, K _eff, is defined in terms of a _uz. The relations between the endurance limit of a two-phase steel and crack nucleus size, ferrite layer thickness, the constraint by the strong martensite on crack tip deformation in the ferrite domain, and K _th's of the martensite and ferrite are analyzed.

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Résumé Une analyse de rupture progressive et continue des liaisons, basée sur un processus de déformation de cisaillement alterné de deux plants de cisaillement s'intersectant à l'extrémité d'une fissure, a été étendue à l'analyse de la propagation des fissures de fatigue dans un acier martensito-ferritique à deux phases. L'accroissement de la fissure a est directement en relation avec K et J dans le cas de déformation plastique de faible étendue. II est préférable d'utiliser a comme paramètre physique en corrélation avec les vitesses de croissance de microfissures et des fissures de fatigue dans un matériau à phases multiples. Dans le cas de microfissures, K n'est souvent pas applicable en raison de la déformation plastique importante. Dans le cas de matériau multiphase ni K ni J ne sont applicables en raison de l'inhomogénéité du matériau. La valeur effective K _eff est définie en terme de a. Les relations entre la limite d'endurance d'un acier à deux phases et la taille du nodule de fissuration, l'épaisseur de la couche de ferrite, la contrainte qu'exerce une zone martensitique dure sur le domaine ferritique, sur la déformation à l'extrémité de la fissure en domaine ferritique, et les valeurs de K de la martensite et de la ferrite sont analysées.

     

Acoustic emission and fatigue crack growth in rigid polyurethane foam

Compact tension specimens of a rigid polyurethane foam have been tested in fatigue and crack growth has been monitored visually and by means of acoustic emission (AE). During the load cycle it has been found possible to resolve the AE activity into four regions: the crack faces un-sticking, fracture events at or close to peak load, a period of zero AE just after peak load, and AE associated with crack closure lower down the unloading part of the cycle. The fracture AE has been found to increase rapidly with crack length — consistent with a seventh power dependence on K — and to occur during every cycle at high K values, but to be absent in an increasingly greater proportion of cycles as K is decreased below about 40 kPa m^1/2. AE data obtained on samples in which crack growth occurred across the layers of foam, through the high density inter-layer skins, show that the technique is very sensitive to the crack retardation effect associated with these skins well before this retardation is detectable visually.