Analysis of cyclic crack growth in high strength roller bearings

The lives of ball and roller bearings and raceways depend on the number of rolling contacts consumed by 3 stages of the failure process: (i) the preinitiation; (ii) crack initiation, and (iii) crack growth stages. This paper employs fracture mechanics analyses to estimate the portion of the bearing life residing in the crack growth stage. Rough estimates of: (a) the Mode II, ΔK_II driving force for small cracks below the rim surface subjected to repeated 2-dimensional, pure rolling contacts, (b) the corresponding crack growth rates, and (c) the number of contacts to failure, are obtained as a function of the peak contact pressure, initial flaw size and other variables. Factors influential to the growth stage are identified. Finally, the comparisons with measured total lives provide insights into the validity of the analysis and the importance of growth relative to the preinitiation and crack initiation stages.     

Influence of indenter geometry on half-plane with edge crack subjected to fretting condition

An edge crack is analyzed to study fretting failure. A flat punch with rounded corners and a half-plane are regarded as an indenter and a substrate, respectively. Plane strain condition is considered. Contact shear traction in the case of partial slip is evaluated numerically. It is assumed that an initial crack is extended to the point of minimum strain energy density in the half-plane from the trailing edge of contact. Dislocation density function method is used to evaluate K_I and K_II. The variations of K_I and K_II during crack growth are examined in the case of indentation by a punch with different ratio of the flat region (l) to the punch width (L). Sih's minimum strain energy density theory [1] is also applied to predict the propagation direction of the initial crack. The direction evaluated is similar to that found in the experiment. Stress intensity factor ranges (ΔK_I and ΔK_II) are examined during cyclic shear on the contact. For the design of contacting bodies, a suggestible geometry of punch for alleviating cracking failure is studied.     

Near threshold fatigue behaviour of flake graphite cast irons microstructures

This paper describes the influence of material toughness degradation, through reversed temper embrittlement (RTE) and mean stress on the near threshold fatigue crack growth characteristics of a CrMoV turbine bolting steel at ambient and elevated temperatures. It was established at ambient temperatures that strong effects of R-ratio and material condition (toughness) were observed on near threshold fatigue crack growth characteristics. At elevated temperatures it was shown that for the non-embrittled material that only under low R-ratio conditions did increased temperature increase the level of threshold stress intensity ΔK_th, by some 20%. In the case of embrittled material, increasing the temperature increased ΔK_th levels by around 30% and decreased near threshold growth rates by an order of magnitude at low to intermediate R-ratio levels.The effects of R-ratio on ΔK_th for all material and mechanical testing conditions could be simply expressed by the difference between ΔK_th at R = O and a constant B multiplied by R.Quantitative fractographic observations indicated that, generally, the incidence of intergranular failure prevalent in embrittled and non-embrittled steels exhibited a maximum at some specific ΔK level. Also in embrittled steels large effects of environmental assisted crack (EAC) growth were observed at near threshold fatigue crack growth rates. It was suggested that this was the result of the much reduced material cohesive strength which was caused by the presence of both impurity and hydrogen atoms.     

Effect of residual surface stress on the fracture of nanoscale materials

The problem of a mode I crack in nanomaterials under a remote mechanical load is investigated. The effect of the residual surface stress on the crack surface is considered and the solutions to the crack opening displacement (COD) and the stress intensity factor (K_I) are obtained. The results show that the surface effect on the crack deformation and crack tip field are prominent at nanoscale. Moreover, COD and K_I are influenced by the residual surface stress not only on the surface near the crack tip region but also on the entire crack surface.     

Effect of humidity and R-ratio on the near threshold fatigue crack growth of two granular bainitic microstructures

The present report has shown that in ferrite-martensite microstructures, the relative humidity of an air environment can affect both the near threshold fatigue crack growth behaviour and the intermediate Stage II fatigue characteristics. The magnitude of the threshold stress intensity, ΔK_th, was not affected by relative humidity and the significant effect of R-ratio on ΔK_th was suitably demonstrated.The relative humidity affected the nature of both the subcritical static failure mode and the final stage III static failure mode. A direct relationship between the degree of fatigue crack growth enhancement and the extent of transgranular cleavage was evidenced.     

Failure modes of specimens containing surface flaws under cyclic torsion

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such a torsional loading may initiate yielding at the outer radius of the shaft or in the fillets. The methods for predicting turbine-shaft fatigue life due to transient loading depent upon the mode of crack growth from an undetected crack. The most common location for the existence of a crack is the fillets or shoulders of the shaft. Specimens were designed from AISI 4340 steel with two diametrically opposed flat surfaces. Initial defect orientations of 0 deg, 45 deg and 90 deg with respect to the sepcimen axis on the fillet were studied. The specimens were subjected to cyclic torsion with zero mean torque and with a torque amplitude necessary to cause yielding at the outer radius of the specimen. When initial defects were aligned with a plane of maximum shear stress (0 deg and 90 deg), the cracks propagated along that plane. For 45-deg defects (aligned to a plane of maximum tensile stress) the crack still propagated along the plane of maximum shear. However, the number of cycles to initiate and to propagate the crack to failure for 45-deg defects were (two to three times) larger than those for 0-deg and 90-deg defects. Mode II and Mode III crack-growth rates were measured from specimens containing 0-deg and 90-deg defects. It was found that the crack-growth rate in Mode II was higher than in Mode III. However, all the specimens failed due to reduction of the net cross section, mostly attributed to Mode III crack growth. Similar results were obtained from specimens of turbine-shaft material (A469 steel), and 2024 aluminum with different rolling directions. Fatigue-crack-growth rates in Mode III were measured from circumferentially notched bar. They were found to be a unique function of ΔK _III alternating stress intensity in Mode III. It was found that the mechanism of crack growth is produced by the formation and linkage of elongated cavities at the crack tip.     

Stress intensification in cracked shank of tightened bolt

Defects or cracks in the shank of bolts can degrade their load carrying capacity. The ways with which loading and residual stress intensify the crack border stress field can be reflected through the stress intensity factor quantity as defined in the linear elastic fracture mechanics theory. Use is made of the stiffness derivative method where quarter-point singular finite elements are used in the numerical calculation. Improved accuracy is achieved by considering the displacements not only of the main nodes but also of those quarter-point nodes in plane normal and adjacent to the crack.Numerical results are obtained for a semi-elliptical shaped crack in the bolt shank owing to tension, bending, residual stress and stress caused by tightening of the bolt. Maximum value of the Mode I stress intensity factor K_a due to tension or bending could prevail either at the deepest point on the crack border or at the root of the shank where the crack border terminates depending on the aspect ratio of the ellipse. In general, K₁ at the deepest point of crack penetration is larger than that at the free surface for tension and bending for a fixed crack depth with reference to the bolt diameter. Tightening of the bolt tends to increase K₁ at the free surface if the crack depth is small. The opposite is obtained for deeper cracks. Assumed residual stress effect obtained from experimental data is found to have negligible influence on the stress intensity factor when compared with that arising from tensile load.     

Non-self-similar crack growth in elastic-plastic finite thickness plate

This work is concerned with non-self-similar crack growth in medium strength metal plates while the loading step, plate thickness and material properties are altered. The three-dimensional elastic-plastic finite element stress analysis is combined with the strain energy density criterion for modeling the material damage process from crack initiation to final global instability including the intervening stage of slow crack growth. Both inelastic deformation and crack growth are accounted for each increment of loading such that the redistribution of stresses and strains are made for each new crack profile. Numerical results are obtained for the center cracked plate configuration under uniform extension with twenty-seven (27) different combinations of specimen thickness, loading step and material type. The fracture toughness S_c being related to K_1c for three different materials are predicted analytically from the corresponding uniaxial tensile test data. Effective strain energy density factor and half crack length are defined so that the results can be compared with their two-dimensional counterparts. Crack growth resistance curves (R-curves) are constructed by plotting as a function of . The condition is found to prevail during slow crack growth. Translation and/or rotation of the lines can yield results other than those calculated and serve a useful purpose for scaling component size and test time. The minimum thickness requirement for the ASTM valid K_1c test is also discussed in connection with predictions based on the strain energy density criterion. The corresponding K_1c for smaller specimens that exhibit moderate ductility and nonlinearity can also be obtained analytically. In such cases, the influence of loading step can be significant and should not be neglected. Notwithstanding the shortcomings of the theory of plasticity, the qualitative features of non-self-similar crack growth are predicted by the strain energy density criterion. Any refinements on the analytical modeling of the material damage process would only affect the results qualitatively, a subject that is left for future investigation.     

Damage accumulation and crack growth in bilinear materials with softening: Application of strain energy density theory

A pseudo-elastic damage-accumulation model is developed by application of the strain energy density theory. The three-point bending specimen is analyzed to illustrate the crack growth characteristics according to a linear elastic softening constitutive law that is typical of concrete materials. Damage accumulation is accounted for by the decrease of elastic modulus and fracture toughness. Both of these effects are assessed by means of the strain energy density functions in the elements around a slowly moving crack. The rate of change of the strain energy density factor S with crack growth as expressed by the relation dS/da = constant is shown to describe the failure behavior of concrete. Results are obtained for different loading steps that yield different slopes of lines in an S versus a (crack length) plot. The lines rotate about the common intersect in an anti-clockwise direction as the load steps are increased. The intersect shifts upward according to increase in the specimen size. In this way, the combined interaction of material properties, load steps and specimen geometry and size are easily analyzed in terms of the failure mode or behavior that can change from the very brittle to the ductile involving stable crack growth. An upper limit on specimen or structural size is established beyond which stable crack growth ceases to occur and failure corresponds to unstable crack propagation or catastrophic fracture. The parameters that control the failure mode are the threshold values of the strain energy density function (dW/dV)_c and the strain energy density factor S_c.     

Influence of mean stress on the fatigue crack growth characreristics of CrlMo steel tube at elevated temperature

The fatigue crack growth characteristics of CrlMo steel have been investigated at 861 K over the R-ratio range 0.1–0.7 utilising a dwell time of 10 min. at maximum load. All tests were conducted under load control in a laboratory air environment. It was established that the R-ratio significantly affected the fatigue crack extension behaviour inasmuch that with increasing R-ratio, the critical ΔK level for the onset of creep fatigue interactive growth, ΔK^IG, decreased from 20 to 7 MPa√m and the threshold stress intensity, ΔK_th, decreased from 9 to about 3 MPa√m. At intermediate ΔK levels, i.e. between ΔK_th and ΔK^IG, the fatigue crack extension rates, for all R-ratio values, resided on or slightly below the CTOD line, which represents the upper bound for contrnuum controlled fatigue crack growth. Creep fatigue interactive growth was typified by crack extension rates that reside above the CTOD line with a ΔK^IG dependence; the attainment of some critical creep condition or crack linkage condition which causes the abrupt change in crack extension behaviour at ΔK^IG; and crack extension occurs almost exclusively in an intergranular manner. The R-ratio and ΔK^IG followed a linear relation. A literature review concerning the effect of temperature on the threshold fatigue crack growth characteristics of low alloy ferritic steels demonstrated powerful effects of temperature; the magnitude of these effects, however, were dependent upon the testing temperature regime and R-ratio level. The effect of R-ratio on ΔK_th was greatest at temperatures >400°C, significant at ambient temperatures and least in the temperature range 90°C to <300°C. The relationship between temperature and ΔK_th, at a given R-ratio, exhibited a through and a minimum ΔK_th value was observed in the temperature range 200–250°C. The magnitude of the temperature effects on ΔK_th decreased with increasing R-ratio. Such effects of temperature and R-ratio on ΔK_th was reasonably explained in terms of crack closure effects. Finally, the present elevated temperature fatigue crack growth data exhibited massive crack extension enhancement values when compared to ambient near-threshold fatigue crack growth data for CrlMo steel. Such large enhancement values were the combined effects of temperature (environment) and frequency.     

Effect of stress ratio and specimen thickness on fatigue crack growth of CK45 steel

Presented are the effect of stress ratio and thickness on the fatigue crack growth rate of CK45 steel according to DIN 17200. Test results are obtained for constant amplitude load in tension with three stress ratios of R=0, 0.2 and 0.4 and three specimen thicknesses of B=6, 12 and 24 mm. Microgauge crack opening values were used to calculate ΔK_eff values from which the da/dN − ΔK_eff curves are obtained. Crack closure can be applied to explain the influence of mean stress and specimen thickness on the fatigue crack growth rate in the second regime of the two-parameter crack growth rate relation. An empirical model is chosen for calculating the normalized load ratio parameter U as a function of R, B and ΔK and, for correlating the test data.     

Simultaneous measurements of stress intensity and toughness for fast-running cracks in steel

Simultaneous measurements of the dynamicstress-intensity factorK _I ^dyn and the dynamic-fracture toughnessK _ID were made in a high-strength steel to investigate the relation between energy delivered to and energy absorbed by rapidly propagating cracks. Values ofK _I ^dyn were obtained intermittently during the propagation history by the shadow optical method of caustics from high-speed photographs of the moving crack tips. Values ofK _ID were calculated from temperature maxima recorded by thermocouples near the crack path. The results indicate that for fast-running cracks, the change in energy available at the crack tip can be significantly less than the energy absorbed in crack extension, suggesting that currently used dynamic-energy-balance methods for determining dynamic-fracture toughnesses may provide erroneous values.     

Unsteady Dynamic Crack Propagation in a Brittle Polymer

Dynamic crack propagation in a brittle polymer, poly(methyl-methacrylate) (PMMA), was studied using the method of caustics in combination with a Cranz–Schardin high-speed camera. Four different types of specimen geometry and loading method were employed to achieve the crack acceleration, deceleration, and/or reacceleration processes in one fracture event. The dynamic stress intensity factor K _ID and crack velocity were obtained in the course of the crack propagation and the corresponding relationship was determined. The effect of the crack acceleration and deceleration on the K _ID-velocity relationships was as follows: (1) the variations of K _ID and the velocity were strongly influenced by the specimen geometry and loading method; (2) the velocity change was qualitatively in accord with K _ID; (3) K _ID for a constant crack velocity was larger when the crack decelerated than it was when the crack accelerated or reaccelerated; (4) K _ID for an acceleration-free crack was uniquely related to the velocity; and (5) K _ID could be expressed as two parametric functions of the velocity and acceleration.     

Stable growth of a crack interacting with a circular inclusion

The problem of failure of a plate containing a circular inclusion and a crack is studied. The crack is oriented along a diameter of the inclusion and the plate is subjected to a remote uniaxial stress perpendicular to the crack axis. The process of slow stable crack growth from initiation to termination is studied by the strain energy density theory. The crack growth is simulated by predicting finite increments of crack extension when material elements near the crack tip absorb a critical amount of strain energy density level, . Unstable crack growth occurs when the strain energy density factor S reaches a critical value where r_c is the critical size of the final crack increment prior to instability. The stress at crack initiation and the critical stress and crack length at failure are determined. The influence of the mechanical properties of the plate and the inclusion, the relative position of the inclusion and the crack and the crack length on the characteristic quantities of stable crack growth is analyzed. The dependence of the stable crack growth process on the loading rate is also investigated. Results are displayed in graphical form.     

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, K_I, K_II, and K_III.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of K_I, K_II, and K_III are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.     

An Experimental Study of Mixed Mode Crack Initiation and Growth in Functionally Graded Materials

Quasi-static mixed mode crack initiation and growth in functionally graded materials (FGMs) was studied through fracture experiments on polymer-based FGMs manufactured by selective ultraviolet irradiation poly(ethylene carbon monoxide)—a photo-sensitive copolymer that becomes more brittle and stiffer under ultraviolet irradiation. The objective of the study was to determine whether crack kinking criteria for homogeneous materials, e.g., maximum hoop stress criterion, also hold for FGMs. Single edge notched tension specimens with different spatial variations of Young's modulus, failure stress and failure strain, were tested. Near tip mode mixity was introduced either by inclining the crack to the remote loading direction, as in the case of homogeneous materials, or to the direction of material gradient, or both. A full-field digital image correlation technique was used to measure in real-time the displacement field around the crack tip while it propagated through the graded material, and to extract the fracture parameters of stress intensity factor K _I and K _II , and the T-stress. It was found that the nonsingular T-stress term in the asymptotic expansion for stresses plays a very important role in accurately measuring fracture parameters. It was also found that the maximum tangential stress criterion can be applied to the case of FGMs to predict crack kinking provided that the effect of the T-stress is accounted for and the process zone size is small compared to the intrinsic material gradient length scale. However, for accurate crack path prediction at a length scale comparable to the material gradient, detailed material property information is required. In general, the crack will propagate towards a region that exhibits less fracture toughness, but, unlike the case of homogeneous materials, along a path where K _II is not necessarily equal to zero.     

Fatigue crack growth studies in rail steels and associated weld metal

Fatigue crack growth studies in rail steels and associated weld metal have shown that (a) deformed rail steel exhibited fatigue crack growth rates that are slightly faster than undeformed rail steel and (b) weld metal growth data are appreciably faster than rail steel growth results and exhibit growth rate plateaux that reside above the upper bound reported for rail steel fatigue crack growth.In rail steel microstructures at low ΔK levels fatigue crack extension occurred by a ductile striated growth mechanism. However at K_max values approaching 40 MPa √m transgranular cleavage facets initially formed and their incidence increased with K_max until final fast fracture. The average cleavage facet size agreed well with pearlite nodule dimensions of 60–100 μm.The weld metal microstructure was much coarser than the rail steel and contained highly directional columnar grain growth. At all ΔK levels the dominant fracture mode was transgranular cleavage containing small isolated regions of ductile striated fatigue crack growth. The cleavage facet size varied from 150 to 600 μm; such a large variation was explained by the fact that in general crack extension tended to occur in association with the proeutectoid ferrite phase.     

钢轨表面剥离掉块路径预测研究

轮轨滚动接触下,钢轨表面会产生典型的鱼钩形剥离掉块,其形成机理目前暂未明确.为了探究轮轨滚动接触下钢轨表面裂纹扩展机理,基于最大周向拉应力准则,建立轮轨滚动接触疲劳计算模型,提出裂尖扩展路径预测方法,并对不同初始角度裂纹的扩展路径进行预测.结果表明,钢轨表面微裂纹为Ⅰ-Ⅱ复合型裂纹,随着裂纹长度增加,KⅠ先增加后减小,...     

Kinking of a crack emanating from the free surface of a beam under pure bending

A perturbation technique developed by Karihaloo et al. is employed to obtain the stress intensity factors at the tip of a kinking crack that emanates from the free surface of a beam under pure bending. Under the condition that the kink extends in the direction of vanishing K₁₁ the crack path is obtained as well as a path stability condition. From conditions on K₁ a material parameter r^* akin to that of Ramulu and Kobayashi's r_c is obtained. By analysis of the slope of the kinking crack a stability condition is obtained corroborating the stability condition from consideration of vanishing K₁₁. It is shown that for a beam in pure bending the nonsingular remote stress term T must be greater than some positive critical value for kinking to occur confirming the results of Sayir and Schindler.     

Dynamic Crack Growth Past a Stiff Inclusion: Optical Investigation of Inclusion Eccentricity and Inclusion-matrix Adhesion Strength

Interactions between a dynamically growing matrix crack and a stationary stiff cylindrical inclusion are studied optically. Test specimens with two different bond strengths (weak and strong) and three crack-inclusion eccentricities (e = 0, d/2 and 3d/4, d being inclusion diameter) are studied using reflection mode Coherent Gradient Sensing (CGS) and high-speed photography. These variants produce distinct dynamic crack trajectories and failure behaviors. A weaker inclusion-matrix interface attracts a propagating crack while a stronger one deflects the crack away. The former results in a propagating crack lodging (‘key-hole’) into the inclusion-matrix interface whereas in the latter the crack tends to circumvent the inclusion. When the inclusion is in the prospective crack path, the maximum attained crack speed is much higher in the weakly bonded inclusion cases relative to the strongly bonded counterparts. For a crack propagating towards a weakly bonded inclusion, the effective stress intensity factor (K _e) value remains constant for each inclusion eccentricity considered. But these constant K _e values increase with increasing eccentricity. A distinct drop in K _e occurs when the crack is near the inclusion. In strongly bonded inclusion cases, on the other hand, monotonically increasing K _e before the crack reaches the inclusion is observed. A drop in K _e is seen just before the crack reaches the inclusion. The mode-mixity estimates are of opposite signs for weakly and strongly bonded inclusions in case of the largest eccentricity studied, confirming the observed crack attraction and deflection mechanisms.