Statistical Fracture Modeling: Crack Path and Fracture Criteria With Application to Homogeneous and Functionally Graded Materials

Analysis has been performed onfractu# initiation near a crack in a brittle material with strength described by Weibu# statistics. This nonlocal fractul model allows for a direct correlation between near crack-tip stresses and failuz# Predictions are made for both thetou)((') and average fractub initiation angle of a crack uack mixed-mode loading. This is pertinent for composites and is especially interesting forfufiGzYYb-)j graded materials (FGMs), where the stress and strength fields vary from thehomogeneou form away from the crack tip. Both analytic and finite element analyses of FGMs reveal that gradients inWeibuI scaling stress r 0 yubu(b lead to a dramatic decrease of initiationfractut toutionb moreover, gradients normal to the crack resub in a crack growing toward the weaker material. When comparing FGMs with gradients inYouYG( moduG( in the direction of the crack path, Ex, and the same stress-intensity factor K, the crack growing into the steeper negative gradient will betouz)jfi if m, theWeibufi moduufi is low; with growth in the sti# direction, the e#ect is opposite. These e#ects o#set the higher-stress intensity for cracks growing into more compliant material, and the crack-tip shielding when growing into a sti#er material baseduse expectations for the applied load. Perpendicu-G gradients inmoduj# cancaufi a far-field mode I loading toproduY mixed-mode loading of the crack tip and other asymmetric adjuetricb in the stress field; the gradientinduen non-coplanar cracking that depends strongly on m

Time dependent debonding of aluminum/alumina interfaces under cyclic and static loading

The structural integrity of oxide/metal interfaces is important in many applications

Determining worst-case fatigue thresholds for grain-bridging ceramics

A method for determining worst-case cyclic fatigue thresholds in grain-bridging ceramics by quantifying the role of bridging is demonstrated for a model alumina. Crack-growth properties for both long and short (< 2 mm) cracks emanating from machined notches (root radii, (rho) ~; 15 - 150 (mu)m) were investigated. When compared as a function of the applied stress-intensity range (delta K), growth rates (da/dN) were far higher and fatigue thresholds (Delta)KTH were markedly lower with short cracks, with growth being observable at the lowest driving forces for short cracks emanating from razor micronotches ((rho)is approximately equal to 15 (mu)m). For growth rates < 10-8 m/cycle, da/dN vs. (delta)K data for short cracks merged with the steady-state data for long cracks after ~;2 mm of extension

A micromechanical basis for partitioning the evolution of grain bridging in brittle materials

A micromechanical model is developed for grain bridging in monolithic ceramics. Specifically, bridge formation of a single, non-equiaxed grain spanning adjacent grains is addressed. A cohesive zone framework enables crack initiation and propagation along grain boundaries. The evolution of the bridge is investigated through a variance in both grain angle and aspect ratio. We propose that the bridging process can be partitioned into five distinct regimes of resistance: propagate, kink, arrest, stall, and bridge. Although crack propagation and kinking are well understood, crack arrest and subsequent "stall" have been largely overlooked. Resistance during the stall regime exposes large volumes of microstructure to stresses well in excess of the grain boundary strength. Bridging can occur through continued propagation or reinitiation ahead of the stalled crack tip. The driving force required to reinitiate is substantially greater than the driving force required to kink. In addition, the critical driving force to reinitiate is sensitive to grain aspect ratio but relatively insensitive to grain angle. The marked increase in crack resistance occurs prior to bridge formation and provides an interpretation for the rapidly rising resistance curves which govern the strength of many brittle materials at realistically small flaw sizes

Pain perception and brain evoked potentials in patients with angina despite normal coronary angiograms.

OBJECTIVE: To evaluate the role of nociception in patients with angina despite normal coronary angiograms and to investigate whether any abnormality is confined to visceral or somatosensory perception. METHODS: Perception, pain threshold, and brain evoked potentials to nociceptive electrical stimuli of the oesophageal mucosa and the sternal skin were investigated in 10 patients who had angina but normal coronary angiograms, no other signs of cardiac disease, and normal upper endoscopy. Controls were 10 healthy volunteers. The peaks of the evoked potential signal were designated N for negative deflections and P for positive. Numbers were given to the peaks in order of appearance after the stimulus. The peak to peak amplitudes (P1/N1, N1/P2) were measured in microV. RESULTS: (1) Angina pectoris was provoked in seven patients following continuous oesophageal stimulation. (2) Distant projection of pain occurred after continuous electrical stimulation of the oesophagus in four patients and in no controls. (3) Patients had higher oesophageal pain thresholds (median 16.3 mA v 7.3 mA, P = 0.02) to repeated stimuli than controls, whereas the values did not differ with respect to the skin. There were no intergroup differences in thresholds to single stimuli. (4) Patients had substantially reduced brain evoked potential amplitudes after both single oesophageal (P1/N1, median values: 7.2 microV, controls: 29.0 microV; N1/P2: 16.5 microV, controls: 66.0 microV; P < 0.001 for both) and skin (N1/P2: 13.5 microV; controls: 76.0 microV; P < 0.001) stimuli despite the similar pain thresholds. CONCLUSION: Central nervous system responses to visceral and somatosensory nociceptive input are altered in patients who have angina despite normal coronary angiograms