We approximate the fracture surface energy functional based on phase-field method with smooth local maximum entropy (LME) and second-order maximum entropy (SME) approximants. The higher-order continuity of the meshfree methods such as LME and SME approximants allows to directly solve the fourth-order phase-field equations without splitting the fourth-order differential equation into two second-order differential equations.We will first show that the crack surface functional can be captured more accurately in the fourth-order model with smooth approximants such as LME, SME and B-spline. Furthermore, smaller length scale parameter is needed for the fourth-order model to approximate the energy functional.We also study SME approximants and drive the formulations. The proposed meshfree fourth-order phase-field formulation show more stable results for SME compared to LME meshfree methods.
The engine must operate properly with the accessory drive and mounting attachments loaded. Each engine accessory drive and mounting attachment must include provisions for sealing to prevent contamination of, or unacceptable leakage from, the engine interior. A drive and mounting attachment requiring lubrication for external drive splines, or coupling by engine oil, must include provisions for sealing to prevent unacceptable loss of oil and to prevent contamination from sources outside the chamber enclosing the drive connection. The design of the engine must allow for the examination, adjustment, or removal of each accessory required for engine operation.
To return your old rebuildable core (no cracks or holes & not burned up from lack of oil), use the original shipping container & foam provided. The transfer case must be completely drained. Shipping companies may stop shipment of boxes showing signs of leakage. [read more...]
All Perfect, Pro-Compe and New Winner bodies can be identified by the stout two-notch freewheel-remover fitting, and by the flange at the back, with four notches corresponding to the four splines on the larger sprockets. The bodies also are labeled on the outer ring.
SunTour Perfect sprockets are bronze-colored, Pro-Compe sprockets are gold, sometimes silver, and New Winner sprockets, silver. These freewheels use four-spline large sprockets, and threaded smaller ones. The teeth are 2mm thick. Exception: sprockets from the earlier-model Winner are black or gold, some are slightly thinner, and some have eight splines rather than four. The photo below is of the sprockets and spacers for the common 5-speed Perfect freewheel.
Except for the 16-tooth sprockets, in two widths with integral spacers, all four-spline sprockets are interchangeable, though Perfect sprockets have slightly deeper, rounded splines which may have to be filed before they will fit a Pro Compe or New Winner body. Most 44mm threaded sprockets are fully interchangeable too. 14-tooth sprockets came with two widths of integral spacers, as indicated in the table. Using an outermost 14-tooth 44mm-threaded sprocket for 5.5mm spacing on an Ultra-spaced freewheel works OK except on the New Winner 6- and 7-speeds, where it would reduce the spacing to the next outer sprocket.
The next photo shows a Perfect body with three splined sprockets and two spacers in place. The red arrow points to one of the splines. The rightmost splined sprocket overhangs the larger-diameter section of the freewheel body, as shown, so that the spacer behind the next, threaded sprocket can secure the splined sprockets.
Perfect and Pro-Compe bodies designed for the narrower Ultra (nominally 5mm) spacing have a splined section to accommodate three or four sprockets and their narrower spacers. With some Ultra-spaced freewheels, paper-thin shims are needed in addition to the regular spacers so that the rightmost splined sprocket overhangs the splines and the threaded sprockets secure the splined ones.
With Ultra (nominally 5mm) spacing, the second-largest sprocket does not overhang the splines of the New Winner body, and so a special 0.9mm thick spacer allows the threaded sprockets to secure the splined ones, as shown in next photo. To engage this narrow spacer, the leftmost threaded sprocket has to have a wide flange.
The New Winner body takes only two splined sprockets, and threaded sprockets were sold only in sizes up to 21 teeth, requiring a big jump in size between sprockets if the splined sprockets are large. An aftermarket adapter to allow a splined sprocket in the third position was available once -- no longer -- but there is a workaround. The 15-tooth threaded sprocket's flange fits neatly into the opening in a splined sprocket with flat-top splines, and can be tack-welded onto the inside face of the larger sprocket (the side where the teeth are shorter), also serving as a spacer. The welds must not extend higher than the face of the smaller sprocket. Grind the welds down if necessary.
A dished sprocket will move the other sprockets 2 mm farther to the right, and can allow a body which was designed for 5.5 mm sprocket spacing to accommodate an additional sprocket in 5 mm (Ultra) spacing. Dishing a sprocket requires the use of a machinist's tool -- an arbor press -- and a forming template of 1/8\" or 3 mm sheet metal with a round hole in the middle. The part of the sprocket which is to be bent should first be heated red hot to soften it and allowed to cool slowly, otherwise the hardened steel may crack. Avoid overheating the teeth.
The lifetime of most engineering structures and components is known to depend on the presence of defects, such as holes, cracks or voids usually introduced during a manufacturing process. In many cases, the crack growth, extension and propagation within a body, still remains a challenging problem in fracture mechanics. The present paper proposes an extended analytical model based on a section method to predict the fracture direction and compute the stress intensity factors for a cracked shaft under mixed-mode loading conditions. The advantage of the present formulation is mainly related to its capability of predicting the direction of crack propagation within a shaft under coupled longitudinal, flexural and torsional loading conditions. The analytical results are straightforwardly compared with the theoretical expressions available from the handbooks and the numerical solutions found with the extended finite element method. The present approach agrees quite well with the theoretical and numerical results already proposed in the literature, thus confirming its potentials for accurate computations of the crack propagation and stress intensity factors for arbitrary configurations.
The accurate modeling of 3D cracks in continuum bodies remains a challenging problem in computational mechanics. The importance of computing the fracture parameters and simulating the crack growth in engineering components, stems from the widespread use of numerical fracture mechanics for static and fatigue problems. Fatigue or static failure usually occurs due to the initiation and propagation of single or multiple cracks with different shapes of multiphysical nature along surfaces or nearby them [1, 2]. Despite the large effort by the scientific community for the study of the main factors controlling the crack paths within materials, the results are still not satisfactory. The works by Pook [3, 4] provide an interesting overview
of the active research on several crack path topics of current interest, e.g. fatigue cracking in aircraft structures, fracture toughness testing, fractography, mixed mode fatigue thresholds, crack path stability, failure of laminated and generally jointed structures. A linear elastic study of cracked bodies, crack paths and a collection of some realistic cases can be also found in Pook  to study the fatigue crack paths within metallic materials. A large variety of crack path topics, however, makes a useful generalization of the problem within standards and codes quite difficult.
Within a linear elastic fracture mechanics (LEFM) framework, the propagation of a crack is mainly governed by the singular behavior of the stress field in the vicinity of its crack tip. For a 2D quasi-static crack, this behavior is generally governed by
describing the angular variation of the stress field, and KI and Kn are the stress intensity factors (SIFs). Thus, except for the cases where higher order terms are required to characterize the crack paths, SIFs usually play an important role for a correct characterization of the mechanical properties of cracked materials. The state of art for the stress analysis of cracks, based on the fracture mechanics concept of the SIF, was already reviewed in 1965 by Paris and Sih . Many 2D theoretical solutions of the SIF available from the literature still represent basic formulations for many engineering applications, design procedures, standards and failure assessment codes [7-10].
However, the simplified analyses based on 2D theories, are largely recognized to ignore the 3D effects, including the effects of the plate thickness , vertex singularities , and coupling of fracture modes I, II and III on the stress and strain fields near the crack front [13-15]. Thus, an accurate computation of the SIFs for 3D surface cracks would be required for practical applications, which is based on the implicit assumption of continuity along a crack front. The understanding of 3D effects has long been recognized as the most important and challenging problem in fracture mechanics, and the increasingly powerful computers have made the numerical investigation possible, especially in the vicinity of corner points. In the last decades, a large amount of theoretical and experimental information about the 3D effects has been discussed by several researchers, as it can be seen in the overview provided by Pook , or other recent works from the literature [17-21].
There is an important class of crack problems, which involve the surface