Mode 2 fracture mechanics

Current development of high-performance rolling element bearings for aircraft engines (up to 3 million DN, where DN is the product of shaft diameter in millimeters and speed in revolutions per minute) has aroused concern about fatigue crack growth in the inner bearing race that leads to catastrophic failure of the bearing and the engine. A failure sequence was postulated by Srawley, and an analytical program was undertaken to simulate fatigue crack propagation in the inner raceway of such a bearing. A fatigue specimen was developed at NASA by which fatigue data may be obtained relative to the cracking problems. The specimen may be used to obtain either mode 2 data alone or a combination of mixed-mode (1 and 2) data as well and was calibrated in this regard. Mixed-mode fracture data for M-50 bearing steel are presented, and a method for performing reversed-loading tests is described

Accelerated fatigue crack growth behavior of PWA 1480 single crystal alloy and its dependence on the deformation mode

An investigation of the fatigue crack growth (FCG) behavior of PWA 1480 single crystal nickel base superalloy was conducted. Typical Paris region behavior was observed above a delta K of 8 MPa sq rt of m. However, below that stress intensity range, the alloy exhibited highly unusual behavior. This behavior consisted of a region where the crack growth rate became essentially independent of the applied stress intensity. The transition in the FCG behavior was related to a change in the observed crack growth mechanisms. In the Paris region, fatigue failure occurred along (111) facets; however, at the lower stress intensities, (001) fatigue failure was observed. A mechanism was proposed, based on barriers to dislocation motion, to explain the changes in the observed FCG behavior. The FCG data were also evaluated in terms of a recently proposed stress intensity parameter, K sub rss. This parameter, based on the resolved shear stresses on the slip planes, quantified the crack driving force as well as the mode I delta K, and at the same time was also able to predict the microscopic crack path under different stress states

Optimum interface properties for metal matrix composites

Due to the thermal expansion coefficient mismatch (CTE) between the fiber and the matrix, high residual sresses exist in metal matrix composite systems upon cool down from processing temperature to room temperature. An interface material can be placed between the fiber and the matrix to reduce the high tensile residual stresses in the matrix. A computer program was written to minimize the residual stress in the matrix subject to the interface material properties. The decision variables are the interface modulus, thickness and thermal expansion coefficient. The properties of the interface material are optimized such that the average distortion energy in the matrix and the interface is minimized. As a result, the only active variable is the thermal expansion coefficient. The optimum modulus of the interface is always the minimum allowable value and the interface thickness is always the maximum allowable value, independent of the fiber/matrix system. The optimum interface thermal expansion coefficient is always between the values of the fiber and the matrix. Using this analysis, a survey of materials was conducted for use as fiber coatings in some specific composite systems

Reliability-based failure analysis of brittle materials

The reliability of brittle materials under a generalized state of stress is analyzed using the Batdorf model. The model is modified to include the reduction in shear due to the effect of the compressive stress on the microscopic crack faces. The combined effect of both surface and volume flaws is included. Due to the nature of fracture of brittle materials under compressive loading, the component is modeled as a series system in order to establish bounds on the probability of failure. A computer program was written to determine the probability of failure employing data from a finite element analysis. The analysis showed that for tensile loading a single crack will be the cause of total failure but under compressive loading a series of microscopic cracks must join together to form a dominant crack

Reliability based analysis of contact problems

The Batdorf model is modified to include the reduction in shear due to the effect of compressive stresses on the crack face. This new formulation was used to obtain the probability of failure of ceramic components under contact stress conditions. The combined effect of the surface and volume flaws are included in the analysis. Due to the nature of the fracture of brittle materials under compressive loading, the component is modeled as a series system in order to establish bounds on the probability of failure

Modeling of crack bridging in a unidirectional metal matrix composite

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

Fatigue crack growth in unidirectional metal matrix composite

The weight function method was used to determine the effective stress intensity factor and the crack opening profile for a fatigue tested composite which exhibited fiber bridging. The bridging mechanism was modeled using two approaches; the crack closure approach and the shear lag approach. The numerically determined stress intensity factor values from both methods were compared and correlated with the experimentally obtained crack growth rates for SiC/Ti-15-3 (0)(sub 8) oriented composites. The near crack tip opening profile was also determined for both methods and compared with the experimentally obtained measurements

Numerical calibration of the stable poisson loaded specimen

An analytical calibration of the Stable Poisson Loaded (SPL) specimen is presented. The specimen configuration is similar to the ASTM E-561 compact-tension specimen with displacement controlled wedge loading used for R-Curve determination. The crack mouth opening displacements (CMOD's) are produced by the diametral expansion of an axially compressed cylindrical pin located in the wake of a machined notch. Due to the unusual loading configuration, a three-dimensional finite element analysis was performed with gap elements simulating the contact between the pin and specimen. In this report, stress intensity factors, CMOD's, and crack displacement profiles are reported for different crack lengths and different contacting conditions. It was concluded that the computed stress intensity factor decreases sharply with increasing crack length, thus making the SPL specimen configuration attractive for fracture testing of brittle, high modulus materials

Failure Maps for Rectangular 17-4PH Stainless Steel Sandwiched Foam Panels

A new and innovative concept is proposed for designing lightweight fan blades for aircraft engines using commercially available 17-4PH precipitation hardened stainless steel. Rotating fan blades in aircraft engines experience a complex loading state consisting of combinations of centrifugal, distributed pressure and torsional loads. Theoretical failure plastic collapse maps, showing plots of the foam relative density versus face sheet thickness, t, normalized by the fan blade span length, L, have been generated for rectangular 17-4PH sandwiched foam panels under these three loading modes assuming three failure plastic collapse modes. These maps show that the 17-4PH sandwiched foam panels can fail by either the yielding of the face sheets, yielding of the foam core or wrinkling of the face sheets depending on foam relative density, the magnitude of t/L and the loading mode. The design envelop of a generic fan blade is superimposed on the maps to provide valuable insights on the probable failure modes in a sandwiched foam fan blade

Back-Face Strain for Monitoring Stable Crack Extension in Precracked Flexure Specimens

Calibrations relating back-face strain to crack length in precracked flexure specimens were developed for different strain gage sizes. The functions were verified via experimental compliance measurements of notched and precracked ceramic beams. Good agreement between the functions and experiments occurred, and fracture toughness was calculated via several operational methods: maximum test load and optically measured precrack length; load at 2 percent crack extension and optical precrack length; maximum load and back-face strain crack length. All the methods gave vary comparable results. The initiation toughness, K(sub Ii) , was also estimated from the initial compliance and load.The results demonstrate that stability of precracked ceramics specimens tested in four-point flexure is a common occurrence, and that methods such as remotely-monitored load-point displacement are only adequate for detecting stable extension of relatively deep cracks