Complete Slip Research Articles

Small Loosening of Bolt-Nut Tightening System due to Micro Bearing-Surface Slip: Finite Element Method Study

Bolt-nut tightening systems are widely used in mechanical structures since the disassembly for maintenance is easy without much cost. However, vibration induced loosening has been unsolved subject. In this paper, we have paid attention to the mechanisms of small loosening process due to micro bearing-surface slip in the framework of the three-dimensional finite element method (FEM). Results show good agreement with Kasei’s experimental results. It was found that early-stage nut rotation obtained by the experiments originates from bolt-nut simultaneous rotation induced by tightening torsion of bolt and does not correspond to the loosening rotation. Therefore, loosening rotation must be defined by the relative rotational angle of nut with respect to bolt. It was also found that the small loosening initiates when the vibrational force reaches about 50 to 60 % of that bearing-surface slip occurs. It is necessary to pay attention to the contact state of both bearing surface and thread surface for the consideration of loosening of bolt-nut tightening systems. Contact states are classified into three kinds of states, that is, complete slip involving no sticking region, micro slip involving no ever-sticking region over a vibration cycle, and localized slip involving ever-sticking region over a vibration cycle. A total of nine kinds of contact states are defined by the combination of the bearing surface and thread surface. It is also found that loosening rotation can proceed when micro slip or complete slip occurs at both thread and bearing contact surfaces.

Three-dimensional Finite Element Analysis on Tightening and Loosening Mechanism of Bolted Joint

Bolted joints are widely used in mechanical structures since the disassembly for maintenance is easy without much cost. However, vibration induced loosing due to dynamic loading has been unsolved subject over past six decades. In this paper, we have investigated the mechanisms of bolted-joint tightening process and loosening process due to shear loading in the framework of the three-dimensional finite element method (FEM). Results are compared with the previous theory based on the material mechanics and experimental results. We found some new aspects for bolted-joint theory. Previous theory overestimates the tightening torque in the relation between axial forces and tightening torque. Since the previous theory ignores the extrusion of bolt from nut and the stiffness of jointed material, the load distribution of 1st pitch decreases and that of 4th pitch turns to be minimum. Good qualitative agreement is observed between FEM and experiments with respect to behavior of loosening process subjected to shear loading, such as hysteresis loop of transverse displacement and transverse load and critical slipping distance for gross slip at the head contact surface. It is found that loosening has started when complete thread contact slip has occurred prior to the gross slip at the head contact, which has been considered as an initiation point of loosening. Therefore, the modification of the design of bolted joint is needed.

Three-dimensional finite element analysis of tightening and loosening mechanism of threaded fastener

Threaded fasteners are widely used in mechanical structures largely because the disassembly for maintenance is easy and low cost. However, vibration-induced loosening due to dynamic loading has remained problematic over the past six decades. In this report, we investigated the mechanisms of the tightening process and the loosening process due to shear loading using the framework of the three-dimensional finite element method (FEM). Results are compared with those of conventional theories based on material mechanics and with experimental results. We found some new aspects of threaded fastener theory. Previous theory overestimates the tightening torque in the relation between preload and tightening torque. Because we modeled the protrusion of bolt from nut and the stiffness of the clamped component unlike previous theory, the load distribution of 1st pitch decreases and that of 4th pitch turns to be the minimum. Good qualitative agreement was observed between FEM and experiments with respect to the behavior of loosening under conditions of shear loading such as hysteresis loop of transverse displacement and shear load and critical slip width for complete bolt-head slip. It was found that loosening is initiated when complete thread slip has occurred prior to head slip, which has previously been considered the initial point of loosening. Therefore, modification of the design of the threaded fastener is needed.

Modeling of fatigue crack closure in inclined and deflected cracks

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, Smax/σ0. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45 ◦ inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from 'complete slip before opening' to 'opening in mode I before mode II shear offset'. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks.

A method based on asymptotics for the refined solution of almost complete partial slip contact problems

A refined semi-infinite contact solution, for a punch possessing a rounded edge and under conditions of partial slip is derived. This is applied, as an example, to the D-shaped punch. It permits the addition of a lot of detail to a sharp, locally adhered solution, and the technique is of general applicability.

Analytical modeling of ultra-thin-film bearings

We develop an analytical model based on kinetic theory of gases and we apply this to thin-film bearings that are frequently encountered in data storage systems. This model incorporates the effects of the higher-order stress tensor and temperature gradient in the governing equations and it can be used for a wide range of Knudsen numbers covering the complete slip regimes. The corresponding modified Reynolds equation is obtained and the flow rate is plotted versus the inverse Knudsen number. Pressure distributions along the air bearing at various Knudsen numbers, bearing numbers, Mach numbers and pitching angles are presented and the load carrying capacities are also obtained. The results are compared with the first-order and second-order slip models. It is observed that the current work is in very good agreement with solutions obtained from the linearized Boltzmann equation and direct simulation Monte Carlo results.

Three-dimensional finite element analysis of threaded fastener loosening due to dynamic shear load

The two most widespread causes of failure of threaded fasteners subjected to dynamic loads are fatigue and vibration induced loosening. This paper presents results of a study on failure of threaded fasteners by vibration induced loosening caused due to dynamic shear loads. Previous experimental work has revealed that fastener loosening occurs as a result of complete or localized slip at the thread and head contact surfaces. A three-dimensional finite element (FE) model is used to study details of four different loosening processes that are characterized by either complete or localized slip at the head and thread contacts. The FE model is found to be capable of adequately modeling factors that influence slip and predicting the different loosening processes. Primary factors that influence slip at fastener contacts are discussed. The results show that loosening can occur at relatively low shear loads due to the process of localized slip.

Investigation of the Temperature Field Induced in the Process of Friction of a Wheel against a Rail

The solution of the Ling thermal problem of friction is integrated to obtain expressions for the contact temperature and temperature field formed in the process of sliding of a wheel over a rail. The distribution of contact pressure is regarded as elliptic. The proposed model is true only under the conditions of complete slip of the wheel in the course of its translational motion. We also study the elevation of temperature caused by the partial slip (creep) of the wheel along the rail.

Crust‐mantle decoupling by flexure of continental lithosphere

Mechanical decoupling between the crust and upper mantle has been proposed as an explanation for anomalously low effective elastic thicknesses (<20 km) locally associated with thermally mature (∼1 Ga) continental lithosphere. The processes and consequences of crust‐mantle decoupling are investigated with a fully dynamic elastic‐viscous‐plastic (EVP) finite element model of orogenic loading and foreland basin subsidence. The basic dependencies of continental flexure on lithospheric thermal state, crustal thickness, and load magnitude are determined and are characterized by the best fit elastic thickness for the simulated deflections. Additional variables such as loading rate, viscoelastic stress relaxation, the boundary condition at the underthrust edge of the plate, and the lithospheric rheology also influence the flexural signature, and these sensitivities are likewise defined by EVP simulations. Decoupling can result in substantial reductions in the effective elastic thickness‐up to a factor of 2 for lithosphere with a thermal age of 1 Ga. Elastic‐viscous‐plastic models show that lower crustal weakening occurs by locally enhanced creep driven by high shear stresses in the middle lithosphere at the load margin. Crust‐mantle decoupling in these models is fundamentally controlled by the temperature and the rheological contrast at the Moho. Previous studies of flexural decoupling have employed simplified multilayered elastic or elastic‐plastic methods, the latter using a yield strength envelope with aprescribed strain rate and an assumption of complete slip at the Moho. However, lithospheric rheology is inherently stress and time dependent, with the deformation rate varying both spatially and temporally. Comparison of elastic‐plastic solutions to the EVP simulations indicates that the former method is satisfactory for oceanic and coupled continental lithosphere but performs poorly with decoupled lithosphere. The EVP model is marginally successful at achieving effective elastic thicknesses <20 km for ∼l‐Ga lithosphere; additional reductions in the thickness may be achieved by a more thorough treatment of the thermal evolution of underthrust continental lithosphere.

Representation of crack-tip plasticity in pressure sensitive geomaterials

This paper presents a model based on dislocation theory for representation of crack tip plasticity in a pressure sensitive material. The basic equations are derived from a simple model of the crack tip plasticity which represents the plasticity by superdislocations placed at the effective centres of the complete slip process distributed around the crack tip. The positions and strengths of the superdislocations are determined by imposing the following conditions: (i) the total stress-intensity factor at the crack tip is zero (ii) the total stress minus the self stress of the superdislocation acting at the superdislocation position is just equal to the friction stress due to the Mohr-Coulomb yield criterion and (iii) the total crack opening displacement produced by the model is maximized. Condition (iii) enables the angle of the slip band on which the superdislocation lies to be determined. The results are presented in a dimensionless form allowing the discussion of particular cases and the recognition of the dominant parameters. A series of parametric studies are carried out to demonstrate that the model can capture the essentials of the crack tip plasticity.

Dogtails versus rainbows: Synthetic earthquake rupture models as an aid in interpreting geological data

Abstract Geologists have been collecting, for decades, information from historical and paleoearthquakes that could contribute to the formulation of a “big picture” of the earthquake engine. Observations of large earthquake ruptures, unfortunately, are always going to be spotty in space and time, so the extent to which geological information succeeds in contributing to a grander view of earthquakes is going to be borne not only by the quantity and quality of data collected but also by the means by which it is interpreted. This article tries to understand geological data more fully through carefully tailored computer simulations of fault ruptures. Dogtails and rainbows are two types of fault rupture terminations that can be recognized in the field and can be interpreted through these models. Rainbows are concave down ruptures that indicate complete stress drop and characteristic slip. Rainbow terminations usually coincide with fault ends or strong segment boundaries. Dogtails are concave up ruptures that indicate incomplete stress drop and noncharacteristic slip. Dogtail terminations can happen anywhere along a fault or fault segment. The surface slip pattern of the magnitude 6.6, 1979 Imperial Valley, California, earthquake shows both dogtail and rainbow terminations. The rainbow confirms the presence of a strong fault segment boundary 6 km north of the international border that had been suggested by Sieh (1996). The dogtail implies that the displacement observed in 1979 is not characteristic. By combining paleoseismic information with the surface slip patterns from this event and the magnitude 7.1, 1940 Imperial Valley earthquake, I develop a quantitative Imperial fault model with northern, central, and southern segments possessing 50, 110, and 50 bar strength, respectively. Both the 1940 and 1979 events caused 1-m amplitude dogtailed ruptures of the northern segment; however, characteristic slip of the segment is more likely to be about 3 m. To illustrate the full spectrum of potential rupture modes, models were run forward in time to generate a 2000 year rupture “encyclopedia.” Even with well-constrained segmentation and strengths, modest changes in two friction law parameters produce several plausible histories. Further discrimination awaits analysis of the extensive paleoseismic record that geologists believe exists in the shore deposits of the intermittent lakes of the Salton Trough.

Wall friction and slip of highly filled suspension

Failure and slip on the wall in the straight pipe were studied for highly filled suspension (HSF) of kaolin‐water including additives. To visualize the deformation of HFS, red mark lines were inserted. Complete slip between HSF and solid wall was observed. It was confirmed that Coulomb’s criterion was valid for the failure between flat wall and HSF, and was different from that in the bulk suspension. The equilibrium equation between the failure shear stress at the wall and the extrusive pressure by piston was derived on the assumption that the extrusive pressure was equal to the axial stress at the wall. The prediction, which showed the variation of extrusive pressure along the axial direction, was in good agreement with the experimental result. It was also shown that the increase of wall stress with slip flow velocity after the failure was equal to the superposed friction resistances of motion to the static failure stress.

Fault slip evolution determined from crack-seal veins in pull-aparts and their implications for general slip models

Most observations of fault slip history are limited to a short period of a fault's lifetime (usually less than five major earthquake cycles) and are therefore not representative of long-term slip behaviour. A new approach to determine more complete slip histories on small inactive faults is outlined, where calcite-filled veins produced by individual slip events are measured. Two normal faults are described from the south Bristol Channel area, near Kilve, north Somerset, U.K. Fault 1 had a variable slip evolution, with variable slip magnitudes through time, but a smooth and fairly constant cumulative increase in displacement. Fault 2 also has a variable slip history but with temporary repetition of similar-sized (characteristic) slip events which were limited to a maximum of eight successive increments. Each set of temporary characteristic events was followed by a period of variable slip. On both faults there were no significant changes in slip increments immediately preceding or following the larger slip events. The average amount of cumulative slip per event at different localities was either constant, accelerated, or decelerated during the fault growth history. The two faults show a slip pattern where the total displacement along the fault varies smoothly, and magnitude of slip increment at any point is highly variable through time. The data from Fault 2 suggests that the central area, where displacement was a maximum, resulted from larger slip for each event rather than more frequent events of similar magnitude, whereas Fault 1 suggests more frequent slip events occurred in the centre of the fault to produce the displacement maximum.

Partial Wall Slip in Polymer Flow

Recently a great deal of attention has been given to the slip of polymers on the walls of containing channels. We discuss the question of where slip begins in a plane stick-slip flow when the pressure gradient far upstream is insufficient to cause complete slip. Some experimentally verifiable results are produced using the J-integral method

Wall Friction and Slip of Highly Filled Suspension

Failure and slip on the wall in the straight pipe were studied for highly filled suspension (HSF) of kaolin‐water including additives. To visualize the deformation of HFS, red mark lines were inserted. Complete slip between HSF and solid wall was observed. It was confirmed that Coulomb’s criterion was valid for the failure between flat wall and HSF, and was different from that in the bulk suspension. The equilibrium equation between the failure shear stress at the wall and the extrusive pressure by piston was derived on the assumption that the extrusive pressure was equal to the axial stress at the wall. The prediction, which showed the variation of extrusive pressure along the axial direction, was in good agreement with the experimental result. It was also shown that the increase of wall stress with slip flow velocity after the failure was equal to the superposed friction resistances of motion to the static failure stress.

Comment on "Characterization of Interfacial Properties in Fiber-Reinforced Cementitious Composites"

Modeling the process of pullout of a fiber from a matrix is a fundamental problem that has received great attention among researchers, as indeed shown by the review presented in the paper by Z. Li, B. Mobasher, and S. I? Shah.' However, a number of recent studies have also addressed the specific problem of fiber pullout from a cementitious matrix and, as discussed below, contribute significantly to extending the current state of knowledge.2 In these references a fundamental study of the bond stress-slip relationship between steel fibers and cement composites is presented and correlated with the pullout problem. The analysis consists of a primal problem, whereby a complete pullout load versus slip curve can be predicted from an assumed (or experimental) bond stress versus slip relationship, and, a dual problem, in which the bond stress versus slip relationship is obtained from an experimental pullout curve. The solution presented is most general. The main purpose of this comment is to show first that the model developed by Li et al.' is a subset of the general model developed by Naaman et ~1.~~ and second that, because of simplifying assumptions, it may be quite limited in scope.

On the Role of Elastic Constants in Multiphase Contact Problems

For a plane composite body consisting of an arbitrary number of different linearly elastic constituents under conditions of plane deformation or plane stress, the minimum number of required elastic constants describing the stress field is determined. For conditions in accordance with the assumptions of Michell and Dundurs, i.e., for prescribed surface tractions and no net forces on internal boundaries, the state of stress in a body involving N different phases is found to be determined by only 2N-2 combinations of the elastic constants. This result holds for conditions of complete adhesion and frictionless slip at the interfaces of the materials.

Theoretical modelling of the effects of grain size on the threshold for fatigue crack growth

The dependence of the threshold for fatigue crack growth, ΔK th grain size has been modelled theoretically using fundamental micromechanistic processes of crack extension in polycrystalline materials. Near threshold, fatigue cracks generally propagate along slip bands piled up at the grain boundary. The effect of grain size on ΔK th principally comes through the increase in the intrinsic fatigue threshold, ΔK eff,th due to larger degree of crack deflection in coarse grained structures and the accompanying high levels of crack closure as a consequence of zig-zag crack growth. Using Minakawa and McEvily's description of roughness induced crack closure, the magnitude of closure stress intensity at threshold, K cl,th is quantified. A strong pile-up is formed at the grain boundary before the crack attempts to propagate inside a grain. It is assumed that dislocations pile-up in the forward loading and are largely irreversible during unloading. By assuming a continuously distributed dislocation configuration, the number of dislocations which are in equilibrium with the resolved shear shear long the slip plane can be calculated. The grain boundary sustains the pile-up until the shear stress in the slip band reaches a critical value required for nucleating slip in the adjacent grain. Assuming complete slip irreversibility during unloading, the magnitude of crack flank disregistry due to the interference of asperities just behind the crack tip can be obtained in terms of the number of dislocations and the Burger's vector of the operative slip system. The magnitude of K cl,th can then be expressed in terms of slip length or grain size, macroscopic yield stress, critical resolved shear stress and the angle between slip plane and crack plane. Theoretically predicted closure levels as a function of grain size have been shown to be in good agreement with the experimentally obtained data. The magnitude of ΔK eff,th as a function of grain size can be derived by considering the piled-up slip band as a kinked crack with the length of the kink being equal to the slip band length. The crack propagation is assumed to occur incrementally along the slip band. The intrinsic crack growth resistance is then formed by two contributions, one is the stress intensity necessary to maintain a critically stressed pile-up and the other is that required to incrementally cleave the slip band in each cycle. By assuming K cl,th and ΔK eff,th, ΔK th can be expressed as a function of grain size. A comparison of the theoretically predicted trend with the experimental data for a variety of alloy systems indicate good agreement. The factors responsible for the deviations are discussed.

Inversion for seismic slip rate history and distribution with stabilizing constraints: Application to the 1986 Andreanof Islands Earthquake

We develop and present a method of inverting seismograms, including their absolute amplitudes, to obtain the complete seismic slip time history and distribution, using the method of linear programming. A rectangular fault is discretized into cells and the source duration into time steps. The inversion for the slip rate distribution on the fault as a function of time reduces to the solution of a system of linear equations. The influence on the solution of constraining different source parameters such as the sign of the slip rate and the seismic moment is investigated. It is found that the constraint of positiveness of slip rate and the constraint that the seismic moment determined from, the solution should be close to that obtained from the centroid moment tensor (CMT) solution are very strong constraints and are essential to obtaining a physically reasonable solution. Since the inverse problem is unstable, instead of presenting only one particular solution we examine several solutions equally well fitting the data for all practical purposes. We find that when both constraints are applied the solution becomes quite stable. The method is applied to a data set consisting of the vertical component of available digitally recorded teleseismic P waves at stations within a chosen distance window for the 1986 Andreanof Islands earthquake (Mw = 8.0). The preferred solution is the one in which the slip rate is constrained to be positive and the moment is set to the CMT value. The average rupture speed in the 90‐km segment to the east of the hypocenter was ≈ 3.2 km/s and in the 190‐km section to the west was ≈ 2 km/s. The maximum slip in the area of large moment release to the west was ≈ 5 m and the maximum slip rate, which occurs in the same place as the maximum slip, was ≈ 6.5 m/s. The slip distribution on the fault shows a corrugated pattern with the long axis in the direction of the plate convergence, rather than normal to the arc, which was the slip vector direction for the earthquake, with most of the slip occurring pn a region of the fault to the west of the rupture nucleation zone. This region continued to slip for about 55 s, the total source duration being about 80 s. The results of this analysis suggest that the long‐term motion on this portion of the Aleutian arc is indeed in the direction of plate convergence.

Yielding in the contact zone of bodies interacting by dry friction

A model is developed to describe the yield process in the contact zone of an elastic body and a half-space, which interact at local contacts by dry friction. The constitutive relation of the local contacts account for the difference between static and dynamic dry friction. Various processes in the contact zone for lateral external loading of the body are shown to occur by use of the wave equation and the constitutive relation of the contacts. These processes include the yield process in the contact zone, the restoration of equilibrium and rest at the contacts between each additional slip and the prestressing of the body. A closed-form analytical solution is derived for the complete slip of the contact zone by means of Laplace transforms. The solution shows that the slipping body has a velocity at the moment that the last contact yields. The upper bound of this velocity is proportional to the difference between the maximum static and dynamic fractional forces. The model further shows the occurrence of high frequency energy radiation at low frequency body excitation.