T. N. Farris

Mechanics of fretting fatigue crack formation

Abstract Fretting is a contact damage process arising from surface microslip associated with small-scale oscillatory motion of clamped structural members. The fretting damage process is a synergistic competition among wear, corrosive and fatigue phenomena driven by both the microslip at the contact surface and cyclic fretting contact stresses. Fretting fatigue is one mechanism of the formation of cracks in many common structural members, often leading to multi-site damage in riveted lap joint assemblies in aging aircraft. Thus a criterion for prediction of fretting fatigue crack nucleation is needed. A detailed analysis of the microslip distribution at the contact surface and the subsurface stress field is required for such a prediction. Relevant closed-form solutions for the 2-D elastic stress fields are adapted for reduced loading configurations modeled in a recently constructed fretting fatigue experiment that applies loads relevant to aircraft lap joints. The resulting stress field is combined with a multiaxial fatigue theory that combines strain-life ideas with a maximum normal stress to predict both the initiation site and life of fretting cracks. In particular, the theory predicts formation at the trailing edge of contact—not the location of the maximum shear stress traditionally associated with crack formation in contact fatigue. The fretting fatigue crack nucleation theory is validated through comparison with data in the literature. Once validated, the model is used to investigate the effects of coefficient of friction, load intensity and fatigue properties on life. It is shown that increases in coefficient of friction and surface microslip sharply reduce the number of cycles required to nucleate cracks. Application of the fretting fatigue crack nucleation model to actual loading configurations in common structural members such as riveted lap joints can lead to a tool for evaluating fatigue life of those members.

Observation, analysis and prediction of fretting fatigue in 2024-T351 aluminum alloy

Abstract Fretting is associated with microslip at the interface of contacts experiencing oscillatory loads. One consequence of fretting is the formation and subsequent growth of cracks at the edge of contact, a phenomenon known as fretting fatigue. Fretting fatigue is an important fatigue failure mechanism in aircraft structural lap joints and turbine blade/disk contacts. A well-characterized, integrated fretting test system has been developed in which both normal and cyclic tangential fretting loads are applied and monitored in conjunction with a bulk load on the specimen. The experimental data includes histories of the three applied forces and a detailed record of the evolution of interfacial friction coefficient, an evolution driven by surface microslip. The experimental system has been exercised to observe fretting crack nucleation and growth under a wide range of loading conditions in the context of a statistically-designed test matrix. An extensive multiaxial fatigue analysis based on the stress–strain cycle experienced by each point of the bodies subjected to the fretting loads reveals that the critical location for crack formation is the trailing edge of contact, consistent with observations made in the laboratory. The resulting stress–strain cycles are coupled with strain-life theory and literature values of uniaxial fatigue constants to predict fretting fatigue crack nucleation. The data collected for 2024-T351 aluminum alloy correlates very well with this prediction.

Spectral Analysis of Two-Dimensional Contact Problems

Contact problems can be converted into the spatial frequency domain using Fast Fourier Transform (FFT) techniques. Spectral analysis is used to develop an algebraic relationship between the surface displacement and the contact pressure. This relationship can be used to find the contact pressure or displacement for the contact of smooth surfaces or the complete contact of rough surfaces. In addition to providing rapid, robust solutions to contact problems, the algebraic relationship contains details of the relationship between surface displacement and contact pressure on different length scales. In particular, it is shown that the frequency composition of pressure is similar to that for slope of the surface displacement. Thus, the high frequency content of the surface profile gives rise to high localized contact pressure, in some cases singular pressure for complete contact. However, measurement limitations always lead to the omission of certain high frequency components of the surface profile. Assuming that the high frequency content of the surface profile obeys a power law, spectral analysis is also used to estimate partial contact parameters. This result relates the exponent of the power law to the contact pressure and implied surface integrity. It is concluded that spectral analysis can be combined with the FFT to provide a useful technique for classifying rough surface contacts.

Role of indentation fracture in free abrasive machining of ceramics

Abstract Free abrasive machining (FAM) is widely used for stock removal and surface finishing of ceramics. In FAM, material removal results from mechanical action between the abrasive slurry, which is trapped between the workpiece and a rotating lapping block, and the workpiece. Microscopic observations of the machined surface show that lateral cracking due to indentation by the abrasive particles contributes substantially to material removal. A simple model of FAM is developed which is based on indentation fracture and takes into account the abrasive particle distribution in the slurry. The model is used to predict the number of particles actually involved in the machining process, the distribution of load among these particles, and the depth of the plastically deformed layer on the workpiece surface. Many of the predictions of the model are well supported by experimental observations from the FAM of aluminum oxide, Ni-Zn ferrite, and glass using a silicon carbide slurry.

Stress intensity factors for cracks of arbitrary shape near an interfacial boundary

Abstract Modes I, II and III stress intensity factors for a crack of arbitrary planar shape near a bimaterial interface are calculated. The solution utilizes the body-force method and requires Greens functions for perfectly bonded elastic half-spaces. The formulation leads to a system of two-dimensional singular integral equations whose solutions represent the three modes of crack opening displacement. Numerical examples of a semicircular or semielliptical crack terminating at the interface and circular or elliptical cracks contained in one material are given for both internal pressure and farfield tension.

LINKING RIVETING PROCESS PARAMETERS TO THE FATIGUE PERFORMANCE OF RIVETED AIRCRAFT STRUCTURES

The onset of widespread fatigue damage in riveted aircraft structure has been linked to sharp gradients of stress arising from contact between rivets and rivet holes. In addition, the mechanics of load transfer in lap joint structure (and resulting damage) is influenced by the through-thickness restraint offered by the installed rivet. Finally, the propagation of fatigue cracks at and around the rivet/hole interface is tied to the residual stress field induced during the riveting process. In light of the influence that rivet installation has on the fatigue performance of riveted joints, the aim was to link details of a quasi-static, squeeze force-controlled riveting process as provided by finite element modeling to the resulting residual stress field in a single-lap joint structure. Supporting experiments provide insight into the inelastic response of the rivet material and validation of the model results. These results from the model reveal both a strong through-thickness gradient in residual stresses and a change in the distribution of residual hoop stress near the rivet/hole interface with squeeze force. Comments are also made regarding the relationship between riveting process parameters and trends in observed fatigue failures of riveted lap joint test articles.

Wear in Partial Slip Contact

An analytical method that evaluates the evolution of stress and surface profile in fretting under the partial slip conditions is presented. The repeated slip occurring near the edges of contact generates wear that changes the contact geometry and contact stresses. The method is based on two scales of time: time for one cycle of the oscillating tangential force and time corresponding to the number of cycles. Archards wear law is used to evaluate wear and gap variation within the slip zones during one cycle. The governing integral equations are reduced to calculate the contact pressure after each cycle. Evolution of the contact characteristics (contact pressure and shear stress, contact width, gap and slip functions) in fretting is calculated using a stepwise procedure. It is shown that the size of stick zone does not change in wear process of bodies with similar elastic properties under the constant amplitude load conditions, and that an asymptotic solution corresponding to the number of cycles approaching to infinity exists. Analytical expressions for the asymptotic contact pressure, shear and tensile stress, and the gap function are presented. It is proved that the asymptotic contact pressure and shear stress are singular at the ends of stick zone. Detailed results are given for two initial shapes of elastic indenter contacting with an elastic half-space: for the parabolic cylinder and for the indenter having a flat base with rounded edges.

Modeling interfacial conditions in nominally flat contacts for application to fretting fatigue of turbine engine components

Abstract The area of contact between the blade root and disk in high-performance turbomachinery has been identified as a critical area for the nucleation of fatigue damage leading to premature and often catastrophic component failures. The interaction of small-scale relative displacements or microslip at the contact surfaces and sharp gradients in the near-surface contact stress field drives a damage process known as fretting. This paper presents and compares two computational approaches — one relying on a quasi-analytical formulation and another employing the finite element method — for characterizing the interfacial conditions arising in experimental set-ups used to simulate conditions of fretting in blade/disk contacts. The quasi-analytical formulation provides a computationally efficient approach for analyzing arbitrary contacting profiles. It is also shown that predictions from the analyses compare favorably with interfacial damage observed in an on-going series of fretting fatigue tests of a titanium alloy used commonly in turbomachinery components, Ti–6Al–4V.

Sliding microindentation fracture of brittle materials: Role of elastic stress fields

Abstract An analytical model of the stress field caused by sliding microindentation of brittle materials is developed. The complete stress field is treated as the superposition of applied normal and tangential forces with a sliding blister approximation of the localized inelastic deformation occurring just underneath the indenter. It is shown that lateral cracking is produced by the sliding blister stress field and that median cracking is caused by the applied contact forces. The model is combined with measurements of the material displacement around an indentation to show that the relative magnitude of tensile stresses governing lateral crack and median crack growth varies with the magnitude of the applied load. The model also predicts a range of loads at which the lateral crack will grow only after the indenter is removed from the surface. These predictions are consistent with observations of the different regimes of cracking observed under a sliding pyramidal indenter in soda–lime glass and other brittle solids.

Machining as a Wedge Indentation

A case is made for the consideration of single-point machining of ductile metals as a special type of wedge indentation process. A general-purpose finite element analysis of machining using iterative rezoning is developed based on this analogy. The accuracy of this analysis, which does not incorporate any separation criterion, is limited only by our knowledge of the material properties and the friction conditions at the tool-chip interface. Strain hardening, strain rate effects, and the temperature dependence of the properties of the work material can be taken into consideration. While Coulomb friction is assumed at the chip-tool interface in the present model, it can easily be reformulated to include more complicated frictional interactions such as adhesion. An analysis of the cutting/ indentation of an isotropic work-hardening material at slow speeds under two different friction conditions is presented. It is shown that many of the important features of machining processes are consistently reproduced by the analysis.