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In automotive suspension, a control arm is a hinged suspension link between the chassis and the suspension or hub that carries the wheel. The chassis end of a control arm usually rubber busing, is attached by a single pivot. It controls the position of the tyre end in only a single degree of freedom, maintaining the radial distance from the chassis mount. The single bushing does not control the arm from moving back and forth; this motion is constrained by a separate link or radius rod. Wishbones are triangular and have two widely spaced chassis bearings, which constrain the tyre end of the wishbone from moving back and forth, controlling two degrees of freedom, and without requiring additional links. Most control arms form the lower link of a suspension with few designs using them as the upper link, usually with a lower wishbone. The lower arm should be sturdy, in many cases reported by the users of a particular vehicle, fluttering noise heard over the humps. This paper calculates the forces acting on the lower arm of a four-wheeler with critical loading conditions as the Finite Element Analysis carried for the McPherson type suspension system. The static analysis performed to determine the location of maximum deflection and stress distribution while the vehicle is stationary and moving over the hump at different speeds. The free-free and constrained modal analysis performed on the suspension arm to find the natural frequency. The fatigue analysis performed to find the life of the arm. Further, by performing topological optimization leads to reduction in the weight.

Dynamic capacity, defined as the load under which rolling element bearing raceways will survive for 1 million revolutions with 90% probability of survival, is commonly used in bearing life-rating standards. This term was introduced by Lundberg and Palmgren to simplify life prediction equations, and was derived using the elastic Hertzian-theory of contact mechanics for earlier, relatively impure bearing materials. Modern ultra-clean steels with fewer impurities can survive for multi-millions of contact stress cycles, even under elastic-plastic loading conditions. Under such conditions, elastic-plastic stresses are significantly different from the elastic Hertz contact stresses. Current experimental and finite-element study, shows accounting for plastic deformation of the material necessitates significant correction in the material parameters used in the expressions for dynamic capacity calculations.

Modern bearing steels are critically important ultra-high strength structural materials used in a multitude of industrial systems, and subject to the highest loading conditions for billions of cycles . They are unique among structural materials because of the localized nature of rolling contact fatigue (RCF) loading, leading to extreme sensitivity of fatigue life to microstructural attributes. The complex phenomena displayed by RCF from nanometer to millimeter length scales make reliable bearing life prediction in the gigacycle regime difficult. A comprehensive review is provided for cyclic fatigue loading experienced by the subsurface volume of RCF-affected material. Microstructural evolution in the subsurface region is presented. Traditional empirical probabilistic approaches to subsurface-initiated bearing life prediction, and their limitations are discussed. Reasons why modern ultra-clean bearing steels can exhibit life in the gigacycle regime are outlined, including the important effects of compressive mean stress. Quantifying material property changes in the subsurface and computation of evolving stress fields are discussed. Refinements to material-specific bearing life prediction in the gigacycle regime using microstructure-sensitive elasto-plastic stress fields are discussed.

The load-life exponents used in the modified life rating equation for rolling element bearings were determined by statistical analysis of the experimental data generated in the 1940s, following Lundberg and Palmgren's seminal work. Based on fracture mechanics arguments, the fatigue life is known to be inversely proportional to the square root of the size of the nonmetallic inclusions. However, modern high-performance vacuum induction melt–vacuum arc remelt (VIMVAR) bearing steels are clean and nonmetallic inclusions are no longer the weak link. Fatigue life predictions (L10 life) for modern bearings using the modified load-life relations greatly underpredict observed life. Hence, there is a need to update parameters of these equations using more recent life data. Based on the endurance data reported in Harris and McCool (1), validation analysis of the modified life rating equation was performed to reevaluate the values of load-life exponent for both ball and cylindrical roller bearings. The results from t...

The analytical expressions currently available for Hertzian contact stresses are applicable only for homogeneous materials and not for case-hardened bearing steels, which have inhomogeneous microstructure and graded elastic properties in the subsurface region. Therefore, this article attempts to determine subsurface stress fields in ball bearings for graded materials with different ball and raceway geometries in contact. Finite element models were developed to simulate ball-on-raceway elliptical contact and ball-on-plate axisymmetric contact, to study the effects of elastic modulus variation with depth due to case hardening. Ball bearings with low, moderate, and heavy load conditions are considered. The peak contact pressure for case-hardened steel is always more than that of through-hardened steel under identical geometry and loading conditions. Using equivalent contact pressure approach, effective elastic modulus is determined for case-carburized steels, which will enable the use of Hertz equations for different gradations in elastic modulus of raceway material. Nonlinear regression tools are used to predict effective elastic modulus as a weighted sum of surface and core elastic moduli of raceway material and design parameters of ball–raceway contact area. Mesh convergence study and validation of equivalent contact pressure approach are also provided. Implications of subsurface stress variation due to case hardening on bearing fatigue life are discussed.

Compressive residual stresses provide a well-known advantage to the fatigue life of bearing materials under rolling contact fatigue (RCF), but the stresses change under fatigue loading and may later contribute to failures. Previous measurements of the depth-wise distribution of residual stresses in post-fatigue bearings with X-rays involved the time consuming process of etching to determine subsurface stresses and only in limited locations. By contrast, the contour method determines the 2D residual stress map over a full cross section. The method involves the sectioning of the part using Electrical Discharge Machining, measuring the out of plane displacements of the exposed cross section, and using the afforded field as boundary conditions on a finite element model of the component to back calculate the causative residual stress. For this investigation, the residual hoop stresses in the split inner rings of the main shaft bearing assembly of an aircraft jet engine was mapped using the contour method. Prior to measurement, the full-scale bearing made of hardened AISI M50 was subjected to RCF during engine operation. In this talk, the unique challenges of the particular measurements are discussed. The tested bearings showed effectively no residual stresses induced by the RCF, probably because they were conservatively removed from service prior to sufficient cyclic loading. A more highly loaded bearing will be measured in future work.

The influence of strain hardening exponent on two-parameter J–Q near tip opening stress field characterization with modified boundary layer formulation and the corresponding validity limits are explored in detail. Finite element simulations of surface cracked plates under uniaxial tension are implemented for loads exceeding net-section yield. The results from this study provide numerical methodology for limit analysis and demonstrate the strong material dependencies of fracture parameterization under large scale yielding. Sufficient strain hardening is shown to be necessary to maintain J–Q predicted fields when plastic flow progresses through the remaining ligament. Lower strain hardening amplifies constraint loss due to stress redistribution in the plastic zone and increases the ratio of tip deformation to J . The onset of plastic collapse is marked by shape change and/or rapid relaxation of tip fields compared to those predicted by MBL solutions and thus defining the limits of J–Q dominance. A radially independent Q -parameter cannot be evaluated for the low strain hardening material at larger deformations within a range where both cleavage and ductile fracture mechanisms are present. The geometric deformation limit of near tip stress field characterization is shown to be directly proportional to the level of stress the material is capable of carrying within the plastic zone. Accounting for the strain hardening of a material provides a more adjusted and less conservative limit methodology compared to those generalized by the yield strength alone. Results from this study are of relevance to establishing testing standards for surface cracked tensile geometries.

This article contains empirical equations for the K I , K II , and K III stress intensity factors (SIFs) for semi-elliptical surface cracks for brittle materials subjected to rolling contact fatigue (RCF) as a function of the contact patch diameter, angle of crack to the surface, max pressure, position along the crack front, and aspect ratio of the crack. The equations were developed from SIFs calculated by parametric three-dimensional (3D) finite element analysis (FEA) for a range of contact patch radii (1b, 2b, and 3b) and angles of the crack to the surface (0°, 45°, and 60°). Calculating mixed-mode SIFs for surface cracks subject to RCF using 3D FEA is computationally complex because of extreme mesh refinement required at multiple levels to capture steep stress gradients. The comprehensive empirical curve fits presented are accurate to within 0.5% of FE simulations and are useful for component design where contact-initiated surface fatigue damage is important such as in gears, roller bearings, and rail...

Silicon nitride balls, used in hybrid ball bearings, are susceptible to failure from fatigue spalls emanating from preexisting partial cone cracks that can grow under rolling contact fatigue (RCF). We simulate the range of three-dimensional nonplanar surface flaw geometries subject to RCF to calculate mixed mode stress intensity factors to determine the critical flaw size (CFS) or the largest allowable flaw that does not grow under service conditions. The cost of nondestructive evaluation (NDE) methods for silicon nitride balls scales exponentially with decreasing CFS and increasing ball diameter and can become a significant fraction of the overall manufacturing cost. Stress intensity factor variability is analyzed for variations of the location and orientation of the load relative to the crack, the geometry of load, and full-slip traction. The modeling techniques utilized in the creation of a three-dimensional (3D) finite element analysis (FEA) model is discussed and the maximum tensile contact periphery...

Surface crack-tip stress fields in a tensile loaded metallic liner bonded to a structural backing are developed using a two-parameter J–T characterization and elastic–plastic modified boundary layer (MBL) finite element solutions. The Ramberg–Osgood power law hardening material model with deformation plasticity theory is implemented for the metallic liner. In addition to an elastic plate backed surface crack liner model, elastic–plastic homogeneous surface crack models of various thicknesses were tested. The constraint effects that arise from the elastic backing on the thin metallic liner and the extent to which J–T two parameter solutions characterize the crack-tip fields are explored in detail. The increased elastic constraint imposed by the backing on the liner results in an enhanced range of validity of J–T characterization. The higher accuracy of MBL solutions in predicting the surface crack-tip fields in the bonded model is partially attributed to an increase in crack-tip triaxiality and a consequent increase in the effective liner thickness from a fracture standpoint. After isolating the effects of thickness, the constraint imposed by the continued elastic linearity of the backing significantly enhanced stress field characterization. In fact, J and T along with MBL solutions predicted stresses with remarkable accuracy for loads beyond full yielding. The effects of backing stiffness variation were also investigated and results indicate that the backing to liner modulus ratio does not significantly influence the crack tip constraint. Indeed, the most significant effect of the backing is its ability to impose an elastic constraint on the liner. Results from this study will facilitate the implementation of geometric limits in testing standards for surface cracked tension specimens bonded to a structural backing.

Hybrid silicon nitride ball/steel raceway bearings are used in advanced aircraft engines and space propulsion systems. Silicon nitride is a brittle material and partial cone cracks, or c-cracks, originate from contact interactions during manufacturing. These cracks limit the Rolling Contact Fatigue (RCF) life of the balls. Here the authors examine subsurface Hertzian stresses between contacting spheres, using an analytical stress solution, to investigate their applicability to predicting and characterizing crack size and shape. The authors also incrementally develop these cracks through an iterative crack growth procedure using a 3D finite element analysis. Comparisons are then made to experimental images of the flaws in silicon nitride. By varying the initial conditions during the contact interaction of the balls we demonstrate that a wide range of cone and partial cone cracks, observed in practice, can be generated using both the analytical and numerical fracture mechanics approaches. Furthermore, an expression is presented for the impact velocity that induces a cone crack from a maximum radial stress criterion at the contact periphery.

A combined experimental and numerical method is developed to estimate the continuously evolving cyclic plastic strain amplitudes in plastically deformed subsurface regions of a case-hardened M50 NiL steel rod subjected to rolling contact fatigue (RCF) over several hundred million cycles. The subsurface hardness values measured over the entire plastically deformed regions and the elastoplastic von Mises stresses determined from the three-dimensional (3D) Hertzian contact finite element (FE) model have been used in conjunction with Neuber's rule to estimate the evolved cyclic plastic strain amplitudes at various points within the RCF-affected zone. The cyclic stress–strain plots developed as a function of case depth revealed that cyclic hardening exponent of the material is greater than the monotonic strain-hardening exponent. Effective S–N diagram for the RCF loading of the case-hardened steel has been presented and the effect of compressive mean stress on its fatigue strength has been explained using Haigh diagram. The compressive mean stress correction according to Haigh diagram predicts that the allowable fatigue strength of the steel increases by a factor of two compared to its fatigue limit before mean stress correction, thus potentially allowing the rolling element bearings to operate over several hundred billion cycles. The methodology presented here is generalized and can be adopted to obtain the constitutive response and S–N diagrams of both through- and case-hardened steels subjected to RCF.

The effect of notch orientation on the evolution of slip bands in double-notched tensile samples of a single crystal superalloy loaded in a 〈0 0 1〉 orientation was experimentally investigated and compared to the results of a three-dimensional linear elastic anisotropic finite element analysis (FEA). The analysis was conducted for two orientations with notches parallel to a 〈0 1 0〉 and a 〈1 1 0〉 orientation, respectively. The observed slip traces agreed well with the predicted dominant slip systems based on the FEA. The experimental results suggest that the dominant slip planes activated at low load levels persist at higher load levels and the activation of other slip bands within a domain is initially inhibited.

Single-crystal superalloy turbine blades used in high-pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high-cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes and noncrystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single-crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two- and three-dimensional (3D) subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single-crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii (1963, Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, Inc., San Francisco, pp. 1–40). Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis. Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single-crystal contact problems require extremely refined 3D finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses on the principal slip planes also involves considerable postprocessing work. For these reasons, it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

Metals and their alloys, except for a few intermetallics, are inherently ductile, i.e., plastic deformation precedes fracture in these materials. Therefore, resistance to fracture is directly related to the development of the plastic zone at the crack tip. Recent studies indicate that the fracture toughness of single crystals depends on the crystallographic orientation of the notch as well as the loading direction. In general, the dependence of crack propagation resistance on crystallographic orientation arises from the anisotropy of (i) elastic constants, (ii) plastic deformation (or slip), and (iii) the weakest fracture planes (e.g., cleavage planes). Because of the triaxial stress state at the notch tips, many slip systems that otherwise would not be activated during uniaxial testing become operational. The plastic zone formation in single crystals has been tackled theoretically by Rice and his co-workers [Rice, J. R., 1987, Mech. Mater. 6, pp. 317–335; Rice, J. R., and Saeedvafa, M., 1987, J. Mech. Phys. Solids 36, pp. 189–214; Saeedvafa, M., and Rice, J. R., 1988; ibid., 37, pp. 673–691; Rice, J. R., Hawk, D. E., Asaro, R. J., 1990, Int. J. Fract. 42, pp. 301–321; Saeedvafa, M., and Rice, J. R., 1992, Modell. Simul. Mater. Sci. Eng. 1, pp. 53–71] and only limited experimental work has been conducted in this area. The study of the stresses and strains in the vicinity of a fcc single-crystal notch tip is of relatively recent origin. We present experimental and numerical investigation of three-dimensional (3D) stress fields and evolution of slip sector boundaries near notches in fcc single-crystal PWA1480 tension test specimens and demonstrate that a 3D linear elastic finite element model, which includes the effect of material anisotropy, is shown to predict active slip planes and sectors accurately. The slip sector boundaries are shown to have complex curved shapes with several slip systems active simultaneously near the notch. Results are presented for surface and mid-plane of the specimens. The results demonstrate that accounting for 3D elastic anisotropy is very important for accurate prediction of slip activation near fcc single-crystal notches loaded in tension. Results from the study will help establish guidelines for fatigue damage near single-crystal notches.

Hot section components in high-performance aircraft and rocket engines are increasingly being made of single crystal nickel superalloys such as PWA1480, PWA1484, CMSX-4, and Rene N-4 as these materials provide superior creep, stress rupture, melt resistance, and thermomechanical fatigue capabilities over their polycrystalline counterparts. Fatigue failures in PWA1480 single crystal nickel-base superalloy turbine blades used in the space shuttle main engine fuel turbopump are discussed. During testing many turbine blades experienced stage II noncrystallographic fatigue cracks with multiple origins at the core leading edge radius and extending down the airfoil span along the core surface. The longer cracks transitioned from stage II fatigue to crystallographic stage I fatigue propagation, on octahedral planes. An investigation of crack depths on the population of blades as a function of secondary crystallographic orientation (β) revealed that for β=45+/−15 deg tip cracks arrested after some growth or did not initiate at all. Finite element analysis of stress response at the blade tip, as a function of primary and secondary crystal orientation, revealed that there are preferential β orientations for which crack growth is minimized at the blade tip. To assess blade fatigue life and durability extensive testing of uniaxial single crystal specimens with different orientations has been tested over a wide temperature range in air and hydrogen. A detailed analysis of the experimentally determined low cycle fatigue properties for PWA1480 and SC 7-14-6 single crystal materials as a function of specimen crystallographic orientation is presented at high temperature (75°F–1800°F) in high-pressure hydrogen and air. Fatigue failure parameters are investigated for low cycle fatigue data of single crystal material based on the shear stress amplitudes on the 24 octahedral and 6 cube slip systems for FCC single crystals. The max shear stress amplitude [Δτmax] on the slip planes reduces the scatter in the low cycle fatigue data and is found to be a good fatigue damage parameter, especially at elevated temperatures. The parameter Δτmax did not characterize the room temperature low cycle fatigue data in high-pressure hydrogen well because of the noncrystallographic eutectic failure mechanism activated by hydrogen at room temperature. Fatigue life equations are developed for various temperature ranges and environmental conditions based on power-law curve fits of the failure parameter with low cycle fatigue test data. These curve fits can be used for assessing blade fatigue life.

The failure of a bearing-raceway assembly is governed by the spatial distribution of subsurface stresses at the vicinity of a bearing-raceway contact and the evolution of these stresses during rolling contact fatigue (RCF) loading. In this paper, we propose an experimental methodology that allows one to accurately measure the location and magnitude of the cyclically evolving elastoplastic von Mises stresses in terms of microhardness numbers. An M50NiL steel rod is subjected to RCF by three silicon nitride (Si3N4) balls for over several hundred million cycles at 5.5 GPa contact stress level. Microindentation hardness measurements within the subsurface RCF-affected regions of the rod revealed significant material hardening. A mechanistic methodology to construct a stress-life (S-N) diagram for RCF loading is proposed. S-N diagrams are constructed based on maximum von Mises stress amplitude and volume average von Mises stress amplitude. The effects of elastic modulus and yield strength gradient on stress fields are also considered in this analysis. Comparison of S-N diagrams based on both stress amplitudes indicates that the maximum von Mises stress amplitude overpredicts the fatigue strength of material in S-N diagrams. The experimental results obtained by following this methodology can help construct material hardening models for RCF, which may lead to an improved estimate of bearing fatigue life.

Extraction and testing of miniature compression specimens from localized regions of components affected by rolling contact fatigue loading can provide significant insight into material degradation. Current ASTM standards for compression testing of cylindrical specimens become too stringent and difficult to achieve when specimen size is reduced to around 1 mm in diameter. The tolerances for surface flatness, parallelism of the loading surfaces, and the perpendicularity between the axis and the loading surfaces play crucial roles in the resulting stress-strain curves under uniaxial compression loading. In this manuscript, a systematic study is performed to quantify the influence of the above geometric parameters on the stress-strain response. Based on the analysis, the allowable geometric tolerances of miniature cylindrical specimens for a valid compression tests are recommended. The analysis results are validated and the usefulness of the method is demonstrated on miniature specimens extracted from the rolling contact fatigue affected regions of high strength M50 bearing balls. The yield stress within the rolling contact fatigue affected region is shown to increase by over 12%.

The flutter behavior of a supercritical airfoil is investigated using a panel formulation, which solves the subsonic unsteady linearized small-disturbance integral equations. Linear aerodynamic theories provide good predictions for attached moderately subsonic and supersonic flows but break down in the transonic flow conditions due to the nonlinearities inherent in unsteady transonic flow. These nonlinearities dominate the transonic flutter behavior typically resulting in the so-called transonic dip. Time-domain aeroelastic simulations involving Computational Fluid Dynamics (CFD) are computationally very expensive and are not favored when a large number of simulations are required. It is a common practice to correct the unsteady aerodynamics calculated from linear formulations to account for the flow nonlinearities associated with unsteady transonic flows. A Reduced Order Method (ROM) is presented yielding to complex-valued aerodynamic corrections for vibration modes. This ROM is used in linear frequency-domain flutter analyses.

Single crystal nickel base superalloy turbine blades are being utilized in rocket engine turbopumps and turbine engines because of their superior creep, stress rupture, melt resistance and thermomechanical fatigue capabilities over polycrystalline alloys. Currently the most widely used single crystal nickel base turbine blade superalloys are PWA 1480/1493 and PWA 1484. These alloys play an important role in commercial, military and space propulsion systems. High Cycle Fatigue (HCF) induced failures in aircraft gas turbine and rocket engine turbopump blades is a pervasive problem. Blade attachment regions are prone to fretting fatigue failures. Single crystal nickel base superalloy turbine blades are especially prone to fretting damage because the subsurface shear stresses induced by fretting action at the attachment regions can result in crystallographic initiation and crack growth along octahedral planes. Furthermore, crystallographic crack growth on octahedral planes under fretting induced mixed mode loading can be an order of magnitude faster than under pure mode I loading. This paper presents contact stress evaluation in the attachment region for single crystal turbine blades used in the NASA alternate Advanced High Pressure Fuel Turbo Pump (HPFTP/AT) for the Space Shuttle Main Engine (SSME). Single crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. Blades and the attachment region are modeled using a large-scale 3D finite element (FE) model capable of accounting for contact friction, material orthotrophy, and variation in primary and secondary crystal orientation. Contact stress analysis in the blade attachment regions is presented as a function of coefficient of friction and primary and secondary crystal orientation, Stress results are used to discuss fretting fatigue failure analysis of SSME blades. Attachment stresses are seen to reach peak values at locations where fretting cracks have been observed. Fretting stresses at the attachment region are seen to vary significantly as a function of crystal orientation. Attempts to adapt techniques used for estimating fatigue life in the airfoil region, for life calculations in the attachment region, are presented. An effective model for predicting crystallographic crack initiation under mixed mode loading is required for life prediction under fretting action.

High cycle fatigue (HCF) induced failures in aircraft gas turbine and rocket engine turbopump blades is a pervasive problem. Single crystal nickel turbine blades are being utilized in rocket engine turbopumps and jet engines throughout industry because of their superior creep, stress rupture, melt resistance, and thermomechanical fatigue capabilities over polycrystalline alloys. Currently the most widely used single crystal turbine blade superalloys are PWA 1480/1493, PWA 1484, RENE' N-5 and CMSX-4. These alloys play an important role in commercial, military and space propulsion systems. Single crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. The failure modes of single crystal turbine blades are complicated to predict due to the material orthotropy and variations in crystal orientations. Fatigue life estimation of single crystal turbine blades represents an important aspect of durability assessment. It is therefore of practical interest to develop effective fatigue failure criteria for single crystal nickel alloys and to investigate the effects of variation of primary and secondary crystal orientation on fatigue life. A fatigue failure criterion based on the maximum shear stress amplitude /Delta(sub tau)(sub max))] on the 24 octahedral and 6 cube slip systems, is presented for single crystal nickel superalloys (FCC crystal). This criterion reduces the scatter in uniaxial LCF test data considerably for PWA 1493 at 1200 F in air. Additionally, single crystal turbine blades used in the alternate advanced high-pressure fuel turbopump (AHPFTP/AT) are modeled using a large-scale three-dimensional finite element model. This finite element model is capable of accounting for material orthotrophy and variation in primary and secondary crystal orientation. Effects of variation in crystal orientation on blade stress response are studied based on 297 finite element model runs. Fatigue lives at critical points in the blade are computed using finite element stress results and the failure criterion developed. Stress analysis results in the blade attachment region are also presented. Results presented demonstrates that control of secondary and primary crystallographic orientation has the potential to significantly increase a component S resistance to fatigue crack growth with- out adding additional weight or cost. [DOI: 10.1115/1.1413767]

High cycle fatigue loading of gear webs due to in-plane stresses, caused by forced excitation resulting from centrifugal loading and dynamic tooth loads, has been known to cause radial fatigue cracks. This is especially prevalent in high-speed gears used in aerospace applications, with small web thickness, for weight reduction. Radial cracks have also been observed to originate at the outer edge of lightening holes machined in gear webs for weight reduction. This paper presents an analytical treatment of the in-plane vibration of high-speed gear webs resulting from rotational effects and periodic excitation from dynamic tooth loading. Dynamic tooth loads result from the combined effect of inertia forces of gear wheels which are significant at high speeds, the periodic variation of gear mesh stiffness, and involute tooth profile errors. The gear web is modeled as a thin rotating disc and the governing differential equations of motion and the associated boundary conditions are derived from first principles. The equations are then nondimensionalized which leads to some essential nondimensional parameters. A comprehensive tooth stiffness model for spur gears is used that accounts for periodic variation of mesh stiffness. The dynamic tooth loads are obtained by solving the pertinent equations of motion, using a collocation method, that yields a closed-form expression for the periodic excitation, that is used as an input for the in-plane vibration problem. The in-plane vibration equations are solved by an approximate method of weighted residuals. It is found that the displacement fields and the resulting stresses can be significant under certain speeds and loading conditions. The interaction between the forcing frequencies due to gear teeth dynamics and the in-plane vibration natural frequencies can result in resonances that induce high fatigue stresses in the gear web. The in-plane stresses leading to high cycle fatigue loading, and frequency components of the resulting response are discussed in detail.

Materials with customized spatial gradients in mechanical properties are increasingly used in high performance applications requiring enhanced resistance to contact loads, wear, and fatigue. In many engineering materials, multiple property and microstructural gradients may occur simultaneously with depth. In this manuscript, two case carburized steels are analyzed for their gradient in hardness with depth, emphasizing the resulting variation in surface hardness under increasing indentation loads. A parametric study using finite element analysis is then conducted in order to characterize the influence of individual property gradients on the surface indentation response of graded materials. It is shown that the measured surface hardness value decreases rapidly under increasing surface indentation loads in materials with sharp negative hardness gradients. It is also shown that this trend is independent of the magnitude of the strain hardening exponent of the material, as well as the gradient in strain hardening exponent. Gradients in elastic properties were also shown to have negligible influence on surface hardness trends for a fixed gradient in hardness. Finally, it is revealed that the depth of subsurface plastic deformation increases with sharper gradients in hardness, while being insensitive to changes in strain hardening exponent. For elastically graded materials, a decreasing gradient in elastic modulus limits the depth of plastic deformation.

International audience; Numerical and experimental evolutions of slip fields in notched Ni-Base Single Crystal superalloy tensile specimens are presented as a function of secondary crystallographic orientation. The numerical predictions based on three-dimensional anisotropic elasticity and crystal plasticity are compared with experimental observations. The results illustrate the strong dependence of the slip patterns and the plastic zone size and shape on the secondary orientation of notches, which can have important consequences on crack initiation. Specific orientations or non-symmetric notch geometries lead to non-symmetric patterns on both sides of the sample. The computations show that strongly different plastic zones are expected in the core of the sample and at free surfaces. The ability of the anisotropic elastic model to anticipate the plastic domains, based on identifying dominant slip systems, is confirmed by the crystal plasticity computations, at low load levels. An important observation is that kink shear banding is a real deformation mode operating at crack tips and notches in high strength nickel-based single crystal superalloys for specific orientations.

A framework for aeroservoelastic computations of a typical business jet conguration is presented. The eects of a nonlinear actuator model on control surface stability under various actuator failure scenarios are examined. The various failures result in the actuator dynamics becoming highly nonlinear in both amplitude and frequency. Unsteady Generalized Aerodynamic Force (GAF) matrices are obtained from MSC/Nastran at various Mach numbers and reduced frequencies. The GAF’s and the structural modal data are then used in ZAERO to generate state-space models of the aeroelastic system comprising the complete aircraft conguration at various ight conditions. These state-space models are then coupled with a nonlinear actuator model in the Matlab/Simulink environment. Free-play in the actuator and its linkages can also be simulated with this framework. The response of the control surface to various initial conditions is examined in the presence of free-play and/or the nonlinear actuator, including the variation of internal actuator parameters subject to normal production tolerance ranges. Limit Cycle Oscillations (LCO) are observed at various ight conditions. The paper highlights some important considerations in aeroservoelastic modeling and simulation of a typical business jet conguration involving actuator nonlinearities.

Ball and rolling element bearings are perhaps the most widely used components in industrial machinery. They are used to support load and allow relative motion inherent in the mechanism to take place. Subsurface originated spalling has been recognized as one of the main modes of failure for rolling contact fatigue (RCF) of bearings. In the past few decades a significant number of investigators have attempted to determine the physical mechanisms involved in rolling contact fatigue of bearings and proposed models to predict their fatigue lives. In this paper, some of the most widely used RCF models are reviewed and discussed, and their limitations are addressed. The paper also presents the modeling approaches recently proposed by the authors to develop life models and better understanding of the RCF.

A comprehensive fracture-mechanics-based life prediction methodology is presented for fcc single crystal components based on the computation of stress intensity factors (SIFs), and the modeling of the crystallographic fatigue crack growth (FCG) process under mixed-mode loading conditions. The 3D finite element numerical procedure presented for computing SIFs for anisotropic materials under mixed-mode loading is very general and not just specific to fcc single crystals. SIFs for a Brazilian disk specimen are presented for the crack on the {111}) plane in the 101 and 121 directions, which represent the primary and secondary slip directions. Variation of SIFs as a function of thickness is also presented. Modeling of the crystallographic FCG behavior is performed by using the resolved shear stress intensity coefficient, Krss. This parameter is sensitive to the grain orientation and is based on the resolved shear stresses on the slip planes at the crack tip, which is useful in identifying the active crack plane as well as in predicting the crack growth direction. A multiaxial fatigue crack driving force parameter, Krss, was quantified, which can be used to predict the FCG rate and, hence, life in single crystal components subject to mixed-mode fatigue loading. DOI: 10.1115/1.2838990

A comprehensive numerical investigation of plasticity (slip) evolution near notches was conducted at 28°C and 927°C, for two crystallographic orientations of double-notched single crystal nickel base superalloys (SCNBS) specimens. The two specimens have a common loading orientation of and have notches parallel to the (specimen I) and (specimen II) orientation, respectively. A three dimensional anisotropic linear elastic finite element model was employed to calculate the stress field near the notch of these samples. Resolved shear stress values were obtained near the notch for the primary octahedral slip systems ({111} ) and cube slip systems ({100} ). The effect of temperature was incorporated in the model as changes in the elastic modulus values and the critical resolved shear stress (CRSS). The results suggest that the number of dominant slip systems (slip systems with the highest resolved shear stress) and the size and the shape of the plastic zones around the notch are both functions of the orientation as well as the test temperature. A comparison between the absolute values of resolved shear stresses near the notch at 28°C and 927°C on the {111} slip planes revealed that the plastic zone size and the number of activated dominant slip systems are not significantly affected by the temperature dependency of the elastic properties of the SCNBS, but rather by the change in critical resolved shear stress of this material with temperature. The load required to initiate slip was found to be lower in specimen II than in specimen I at both temperatures. Furthermore, at 927°C the maximum resolved shear stress (RSS) on the notch surface was found to be greater on the {100} slip planes as compared with the {111} slip planes in both specimens. The results from this study will be helpful in understanding the slip evolution in SCNBS at high temperatures.

A comprehensive fracture mechanics based life prediction methodology is presented for FCC (Face Centered Cubic) single crystal components, based on computation of stress intensity factors (SIFs), and modeling the crystallographic fatigue crack growth process, under mixed-mode loading conditions. The 3D finite element numerical procedure presented for computing SIFs for anisotropic materials under mixed-mode loading is very general, and not just specific to FCC single crystals. Stress intensity factors for a Brazilian Disc (BD) specimen are presented for the crack on the {111} plane in the 〈101〉 and 〈121〉 directions, which represent the primary and secondary slip directions. Variation of SIFs as a function of thickness is also presented. Modeling of the crystallographic fatigue crack growth (FCG) behavior is performed by using the resolved shear stress intensity coefficient (RSSIC), Krss . This parameter is sensitive to the grain orientation and is based on the resolved shear stresses on the slip planes at the crack tip, which is useful in identifying the active crack plane as well as predicting the crack growth direction. A multiaxial fatigue crack driving force parameter, ΔKrss , was quantified, which can be used to predict the FCG rate and hence life in single crystal components subject to mixed mode fatigue loading.Copyright © 2006 by ASME

Deformation mechanisms and failure modes of FCC (face centered cubic) single crystal components subjected to triaxial states of static and fatigue stress are very complicated to predict, because plasticity precedes fracture in regions of stress concentration, and the evolution of plasticity on the surface and through the thickness is influenced by elastic and plastic anisotropy. The triaxial stress state at regions of stress concentration results in the activation of many slip systems that otherwise would not be activated during uniaxial testing. We recently presented [1] results from a numerical and experimental investigation of evolution of slip systems at the surface of notched FCC single crystal specimens, as a function of secondary crystallographic orientation. Results showed that the slip sector boundaries have complex curved shapes with several slip systems active simultaneously near the notch. We extend our work on slip at the surface to investigating the evolution of slip or plastic deformation through the thickness of the specimen. A single crystal double-edge-notched rectangular specimen of a Ni-base superalloy, under the tensile loading ([001] load orientation and [110] notch direction) is considered. A three dimensional (3-D) finite element model (FEM) including elastic anisotropy is used for the numerical investigation. Results indicate that the stress distribution and slip fields are a strong function of axial location through the thickness. Numerical results are verified by comparing them with experimentally observed slip fields. We demonstrate that inclusion of three dimensional analysis and elastic anisotropy is important for predicting evolution of slip at the surface and through the specimen thickness. The resolved shear stresses (RSS) on the dominant slip systems and the normal stress on the dominant planes are shown to vary significantly from the surface to the midplane of the specimen. Based on the consideration of RSS, normal stress and the number of activated slip systems at each thickness level, it is concluded that fatigue cracks most likely start in the midplane, for the orientation reported here.Copyright © 2006 by ASME

Foam, a cellular material, is found all around us. Bone and cork are examples of biological cell materials. Many forms of man-made foam have found practical applications as insulating materials. NASA uses the BX-265 foam insulation material on the external tank (ET) for the Space Shuttle. This is a type of Spray-on Foam Insulation (SOFI), similar to the material used to insulate attics in residential construction. This foam material is a good insulator and is very lightweight, making it suitable for space applications. Breakup of segments of this foam insulation on the shuttle ET impacting the shuttle thermal protection tiles during liftoff is believed to have caused the space shuttle Columbia failure during re-entry. NASA engineers are very interested in understanding the processes that govern the breakup/fracture of this complex material from the shuttle ET. The foam is anisotropic in nature and the required stress and fracture mechanics analysis must include the effects of the direction dependence on material properties. Material testing at NASA MSFC has indicated that the foam can be modeled as a transversely isotropic material. As a first step toward understanding the fracture mechanics of this material, we present a general theoretical and numerical framework for computing stress intensity factors (SIFs), under mixed-mode loading conditions, taking into account the material anisotropy. We present mode I SIFs for middle tension — M(T) — test specimens, using 3D finite element stress analysis (ANSYS) and FRANC3D fracture analysis software, developed by the Cornell Fracture Group. Mode I SIF values are presented for a range of foam material orientations. Also, NASA has recorded the failure load for various M(T) specimens. For a linear analysis, the mode I SIF will scale with the far-field load. This allows us to numerically estimate the mode I fracture toughness for this material. The results represent a quantitative basis for evaluating the strength and fracture properties of anisotropic foam insulation material.

A method for predicting the tool point frequency response of a tool-holder-spindle system is provided. Receptance coupling is used to analytically combine responses for the tool, holder, and spindle substructures and predict the assembly dynamics. The spindle response is determined using experimental procedures, while the holder and tool are modeled using Timoshenko beams. With the use of this method, predictions may be completed for micro scale end mills where impact testing is inconvenient. Experimental results are provided.Copyright © 2005 by ASME

Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and noncrystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii [1]. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis (FEA). Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single crystal contact problems require extremely refined three-dimensional (3-D) finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses (RSS) on the principal slip planes also involves considerable post-processing work. For these reasons it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

Numerical and experimental investigations of evolution of slip fields in notched Ni-base superalloy single crystal tensile specimens are presented as functions of load and secondary (notch) orientation. Three crystallographic orientations were investigated with the primary (load) orientation fixed along the [0 0 1] direction while the notch directions are parallel to ½ 110� =½1 10 � ; ½ 010 � =½0 10 � , and ½ 310 � =½3 10 � , respectively. A three-dimensional elastic anisotropic finite element analysis (FEA) was used to compute the triaxial stress fields in the neighborhood of the notch. The elastic solution is successful in identifying which slip systems are activated initially. Interestingly this procedure was found to be also successful in predicting slip evolution at higher loads, because of slip localization in the superalloy tested. Based on this analysis, the concept of ‘‘dominant slip system” is introduced and defined as the single slip system that experiences the highest resolved shear stress (RSS) at a given point near the notch. The dominant slip systems are seen to persist with increasing load and inhibit the activation of new slip systems, which implies that when plasticity is initiated in the dominant slip systems, either softening takes place and/ or the rate of increase in RSS on the other slip systems is reduced significantly. The distribution of dominant slip systems in the neighborhood of the notch and on the surface is used to accurately predict the evolution of activated slip sectors and sector boundaries observed experimentally. The activated stress fields are shown to vary strongly through the specimen thickness. Elastic anisotropy governs the development of the elastic stress field and controls which slip systems become initially dominant/activated. Therefore inclusion of elastic anisotropy was found to be important for the prediction of stress field evolution as functions of load and crystal orientation.