Effect of varying normal stress on stability and dynamic motion of a spring-slider system with rate- and state-dependent friction

Incorporating rate and state friction laws, stability of linearly stable （i.e., with stiffness greater than the critical value） spring-slider systems subjected to triggering perturbations was analyzed under variable normal stress condition, and comparison was made between our results and that of fixed normal stress cases revealed in previous studies. For systems associated with the slip law, the critical mag- nitude of rate steps for triggering unstable slips are found to have a similar pattern to the fixed normal stress case, and the critical velocity steps scale with a/（b - a） when k = kcr for both cases. The rate-step boundaries for the variable normal stress cases are revealed to be lower than the fixed normal stress case by 7 %-16 % for a relatively large ct = 0.56 with （b - a）/a ranging from 0.25 to 1, indicating easier triggering under the variable normal stress condition with rate steps. The difference between fixed and variable normal stress cases decreases when the α value is smaller. In the same slip- law-type systems, critical displacements to trigger instability are revealed to be little affected by the variable normal stress condition. When k 〉 kcr（V,）, a spring-slider system with the slowness law is much more stable than with the slip law,suggesting that the slowness law fits experimental data better when a single state variable is adopted. In stick-slip motions, the variable normal stress case has larger stress drops than the constant normal stress case. The variable normal stress has little effect on the range of slip velocity in systems associated with the slowness law, whereas systems associated with the slip law have a slowest slip velocity immensely smaller than the fixed normal stress case, by ~ 10 orders of magnitude.

Forces and Stresses During Friction Stir Joining of 2024 Aluminum Alloy

An attempt is made to measure three direction forces using octagonal ring dynamometer in the 2024 aluminum alloy friction stir joining(FSJ)process.A test is made to measure the specific area stress and stress distributions in the specific area of the workpiece are obtained.The workpiece stresses in the FSJ process are analyzed by numerical simulation method.It is found that,in the downward stage of the process,feed force and lateral force in the tool are small,almost zero,and the maximum axial force can reach 12.5kN.In the stable joining stage,the forces acting on the tool become stabilized.Compared with the low speed,high feed speed results in small feed force and small lateral force,but large feed force in the stable joining stage.The stresses in three directions of feed direction,direction that perpendicular to butt face and direction perpendicular to the surface are obtained.The simulation stress value of measure point is obtained.Test and numerical simulation can authenticate each other.Both experimental stress values and numerical simulation stress values are credible.

EFFECT OF BIAS STRESS ON NON-LINEAR INTERNAL FRICTION OF Al-Mg ALLOY

The influence of longitudinal and torsional bias stresses on anomalous amplitude-dependent internal friction was studied.The longitudinal bias stress may always weaken the anomalous amplitude-dependent effect,while the torsional one may induce different effects from differ- ent directions applied.Bias stress effect exhibits only in properly heat treated and cold worked ahoy specimens.The anomalous amplitude-dependent internal friction peaks,P_3,P_2 and P_1, are found to be related closely to slant dislocation kink chains.Thus,the application of bias stress to internal friction would be contributed to the study on dislocation structure.

CONTACT FRICTION ANALYSIS AND STRESS OSCILLATION SUPPRESSION WITH A SIMPLE INTERFACE ELEMENT

A simple interface element for analyzing contact friction problems is developed. Taking nodal displacements and contact stresses as unknowns, this element can simulate frictional slippage, decoupling and re-bonding of two bodies initially mating or having gaps at a common interface. The method is based on the Finite Element Method and load incremental theory. The geometric and static constraint conditions on contact surfaces are treated as additional conditions and are included in stiffness equations. This simple element has the advantages of easy implementation into standard finite element programs and fast speed for convergence as well as high accuracy for stress distribution in interface. Undesirable stress oscillations are also investigated whenever large stress gradients exist over the contact surfaces. Exact integration or the conventional Gauss integration scheme used to evaluate the interpolation function matrix of the interface element is found to be the source of the oscillations. Eigenmode analysis demonstrates that the stress behavior of an interface element can be improved by using the Newton-Cotes integration scheme. Finally, the test example of a strip footing problem is presented.

Study on the distribution of residual stresses in linear friction welds of Ti6AI4V

The linear friction welding process of Ti6Al4 V was modeled and computed ,for obtaining the residual stresses. Temperature, stress and strain fields were simulated, based on which, the residual stresses were also cah＇ulated. Simulated resttlts showed that the longitudinal residual stresses were tensile stresses at the bonding interface, and decreased rapidly with the increase of the distance from the bonding interface until turned into compressive stresses. The compressive stresses decreased slowly as the distance increased, and approached to zero finally. The distribution of the transverse residual stresses was similar to that of the longitudinal residual stresses, but showed much smaller values. The residual stresses in one linear friction weld were measured by an X-ray diffrnctometer. The average valwe of errors between computed and measured results was 14. 5 %.

Using Neural Network to Predict the Interfacial Friction and Flow Stress of Materials via Ring Compression

In this study a neural network approach is proposed to realize an automatic numerical prediction of the interfacial friction factor and the flow stress of materials. Decrease in the inner diameter and reduction in the height of the ring are taken as input

Friction Shear Stress on the Surface of Iron-Based Coating/HSS during Sliding Wear of Pin Disk

With the increasing demand for lightweight and lower fuel consumption and safety of automobile industry, lightweight materials of high strength steel (HSS) are more and more widely used. The hot stamping technology, which is determined by the inherent mechanical properties of high strength steel, makes molds prone to wear failure in the harsh service environments. In this paper, a finite element model is proposed for analyzing the value and distributions law of friction shear stress of contact surface of the pin disk. Through the simulation process of sliding wear, two kinds of different cladding materials of the pin specimens including H13 and Fe65, were experimented under three different loads by using the software ABAQUS. And then the pin-on- disk wear test at elevated temperature was conducted to verify the effectiveness of the simula-tion results. The results showed that the friction shear stress of pin with iron-based cladding and H13 steel was different under different loads, but the distribution was basically the same;the normal friction shear stress increased gradually along the direction of the pin movement, and the tangential shear stress increased gradually from the center of the pin to the outside of the circle;the value of the friction shear stress of the normal joints on the contact surface was periodically fluctuating in the whole dynamic analysis step, while it was basically stable in the tangential direction.

Stress-strain characteristics of linear friction welding of TC11 and TC17 alloys

Abstract Transient stress and strain fields of dissimilar titanium alloys （TCll and TC17 ） joint during linear friction welding （ LFW） were investigated by a two-dimensional model with ABAQUS/Explicit. The results showed that in the X-axis, the maximum compressive stress of 850 MPa occurred in the center zone of friction interface , and the maximum tensile stress of 190 MPa distributed at the flash; in the Y-axis, the maximum compressive stress of 1 261 MPa located at the junction region between the welding fixture and edge of the specimen, and the maximum tensile stress of 320 MPa distributed in the connecting portion between the flash and edge of the specimen. In addition, areas of plastic strain increased gradually during welding process. In the X-axis, tensile strain mainly existed at the heads of the specimens; in the Y-axis, compressive strain mainly occurred at the heads of the specimens.

EFFECT OF SLIP ORIENTATION ON STRESS RESPONSE,INTERNAL FRICTION AND ULTRASONIC ATTENUATION DURING CYCLIC DEFORMATION IN Al SINGLE CRYSTALS

The variation of cyclic stress,internal friction and ultrasonic attenuation during cyclic deformation and relations among them have been investigated with different slip orientation Al single crystals.The results indicate that the value of cyclic stress σ,internal friction Q^(-1)and ultrasonic attenuation △α depend obviously on the slip orientation.There are large differences in above three parameters for different slip orientation Al crystals.In early stage of fatigue life,σ and △α increase and Q^(-1)decreases with cycles N,and △α reached maxi- mum before σ,while Q^(-1)and σ get the valley and the peak,respectively,at same cycles.

Evolution of residual stress field in 6N01 aluminum alloy friction stir welding joint

Based on the characteristics of friction stir welding( FSW) and Coulomb friction work theory,the residual stresses field of FSW joints of 6 N01 aluminum alloy( T5),which was used in high speed train,were calculated by using the ANSYS finite element software. During the FEM calculation,the dual heat source models namely the body heat source and surface heat source were used to explore the evolution law of the welding process to the residual stress field. The method of ultrasonic residual stress detecting was used to investigate the residual stresses field of the 6 N01 aluminum alloy FSW joints. The results show that the steady-state temperature of 6 N01 aluminum alloy during FSW is about 550 ℃,and the temperature mutates at the beginning and at end of welding. The longitudinal residual stress σ_x is the main stress,which fluctuates in the range of-25 to 242 MPa. Moreover,the stress in the range of shaft shoulder is tensile stress that the maximum tensile stress is 242 MPa,and the stress in the outside of shaft shoulder is compressive stress that the maximum compressive stress is 25 MPa. The distribution of the tensile stress in the welding nugget zone( WNZ) is obviously bimodal,and the residual stress on the advancing side is higher than that on the retreating side. With the increasing of the welding speed,the maximum temperature decreased and the maximum residual stress decreased when the pin-wheel speed kept constant. With the increasing of the pin-wheel speed,the maximum temperature of the joint increased and the maximum residual stress increased when the welding speed was constant. The experimental results were in good agreement with the finite element results.

Predictive Models for the Ultimate Tensile and Yield Stresses Occurring in Joints of Untreated Friction Stir Welded 2017AA (ENAW-AlCu4MgSi) Plates

Friction Stir Welding (FSW) processes have been applied in numerous industrial fields and broadly embraced by the research community. In this paper, given three FSW process parameters, namely, the tool rotation speed N (rpm), the tool traverse feed F(mm/min) and the tool pin/shoulder diameters ratio (r%), we purpose to ascertain their impact on joints Ultimate Tensile Stress (UTS) and joints Yield Stress (YS). The FSW has been executed using 6 mm thick rolled plate in 2017AA. For the design of experiments strategy, we conducted a face centered central composite strategy through which 18 trials have been executed. Then, we utilized the RSM technique to formulate the predictive models which are relevant to the (UTS) and (YS) outputs. Accordingly, the study has pointed out the prevalence of the tool rotation speed and the tool diameters ratio factors;however, the tool traverse feed (F) was found trivial and statistically insignificant. Likewise, the sensitivity analysis regarding factors N, F and r% on both (UTS) and (YS) has exhibited the dominance of the tool diameters ratio (r%), indistinctively.

Strip Layer Method for Analysis of the Three-Dimensional Stresses and Spread of Large Cylindrical Shell Rolling

As the traditional forging process has many problems such as low efficiency, high consumption of material and energy, large cylindrical shell rolling is introduced. Large cylindrical shell rolling is a typical rotary forming technology, and the upper and lower rolls have different radii and speeds. To quickly predict the three-dimensional stresses and eliminate fishtail defect, an improved strip layer method is developed, in which the asymmetry of the upper and lower rolls, non-uniform deformation and stress, as well as the asymmetrical spread on the end surface are considered. The deformation zone is divided into a certain number of layers and strips along the thickness and width, respectively. The transverse displacement model is constructed by polynomial function, in order to increase the computation speed greatly. From the metal plastic mechanics principle, the three-dimensional stress models are established. The genetic algorithm is used for optimization calculation in an industrial experiment example. The results show that the rolling pressure, the normal stresses, the upper and lower friction stress distributions are not similar with those of a general plate rolling. There are two relative maximum values in rolling pressure distribution. The upper and lower longitudinal friction stresses change direction nearby the upper and lower neutral points, respectively. The fishtail profile of spread on the end surface is predicted satisfactorily. The reduction could be helpful to eliminate fishtail defect. The large cylindrical shell rolling example illustrates the calculation results acquired rapidly are good agreements with the finite element simulation and experimental values of previous study. A highly effective and reliable three-dimensional simulation method is proposed for large cylindrical shell rolling and other asymmetrical rolling.

Nonlinear regression model for peak-failure strength of rockfill materials in general stress space

A nonlinear regression model for peak-failure strength prediction of rockfill materials is proposed. It is based on the relationship between the peak-failure stress ratio and the normalized confining pressure as well as the relationship between the normalized peak-failure stress ratio and the exponent function of the intermediate principal stress ratio. This model can well predict the variations of the peak-failure stress ratio with the initial confining pressure and the intermediate principal stress ratio for different rockfill materials under different general stress paths. Comparisons of the measured and predicted results show that the peak-failure strength under the constant-p' and constant-b path is larger than that under the constant-σ'_3 and constant-b path. The predictive capacity of the proposed model for the peakfailure stress ratio is better than that for the peak-failure friction angle.

DEFORMATION BEHAVIOR OF AA6063 ALUMINIUM ALLOY AFTER REMOVING FRICTION EFFECT UNDER HOT WORKING CONDITIONS

The hot deformation behavior of AA6063 aluminium alloy has been investigated by means of compression tests at temperatures between 400 and 520℃, and strain rates ranging from 2.5 to 10 s^-1. Owing to the barreling, the theoretical model on the basis of Hills general method is used to calculate the flow stress of a cylindrical specimen under uniaxial simple compression so as to consider the friction effect at the die-specimen interface. A method of evaluating the friction coefficient by combining compression tests with the finite element method is presented. The real flow behavior of AA6063 aluminium alloy can be described with sinh-Arrhenius equation. The hot deformation activation energy Q derived from the corrected stress and strain data is 232. 350 kJ/mol.

WAVE ATTENUATION BY BOTTOM FRICTION IN CURRENTS

In nature, wave attenuation occurs with propagation. In some cases, it is significant and cannot be neglected. In this paper, the attenuation of wave spectra in current by bottom friction is studied. To simplify the calculation, a linearized bottom friction stress formula is introduced, which gives an equivalent energy loss due to bottom friction. Model test data indicate that the authors' method for the calculation of wave attenuation in this paper agrees well with the experimental results.

An improved wall shear stress measurement technique using sandwiched hot-film sensors

In this letter we present a novel wall shear stress measurement technique for a turbulent boundary layer using sandwiched hot-film sensors. Under certain conditions, satisfactory results can be obtained using only the heat generated by one of the hot-film and a calibration of the sensors is not required. Two thin Nickel films with the same size were used in this study, separated by an electrical insulating layer. The upper film served as a sensor and the bottom one served as a guard heater. The two Nickel films were operated at a same temperature, so that the Joule heat flux generated by the sensor film transferred to the air with a minimum loss or gain depending on the uncertainties in the film temperature measurements. Analytical solution of the shear stress based on the aforementioned heat flux was obtained. The preliminary results were promising and the estimated wall shear stresses agreed reasonablywell with the directly measured values （with errors less than 20%） in a fully developed turbulent pipe flow. The proposed technique can be improved to further increase precisions.

A comparative study of stress influence on fracture apertures in fragmented rocks

This study compares the calculated fracture apertures in a fragmented rock layer under different stress scenarios using two different approaches. Approach 1 is a simplified method using a two-dimensional(2 D) mapping of the fracture network and projects the far-field stresses to individual fractures, and calculates the dilation, normal and shear displacements using experimental stiffnesses available in the literature. Approach 2 employs a three-dimensional(3 D) finite element method(FEM) for the mechanical analysis of the fragmented rock layer considering the interaction with the neighbouring rock layers, frictional interfaces between the rock blocks, stress variations within the fragmented rock layer,and displacements, rotations and deformations of rock blocks. After calculating the fracture apertures using either of the approaches, the permeability of the fragmented rock layer is calculated by running flow simulations using the updated fracture apertures. The comparison between the results demonstrates an example of the inaccuracies that may exist in methods that use simplified assumptions such as2 D modelling, ignoring the block rotations and displacements, projected far-field stresses on fractures,and the stress variations within the rock layer. It is found that for the cases considered here, the permeability results based on apertures obtained from the simplified approach could be 40 times different from the results from apertures calculated using a full mechanical approach. Hence, 3 D mechanical modelling implementing realistic boundary conditions, while considering the displacements and rotations of rock blocks, is suggested for the calculation of apertures in fragmented rocks.

Period Doubling Bifurcation of Stress Drop for Stick-slip and Its Physical Implication

It is revealed in frictional experiments on medium-scale samples that period doubling bifurcation of stress drop for stick-slip occurs due to macroscopic heterogeneity of the sliding surface under conditions for typical stick-slip.The observed data show that the period doubling bifurcation of stress drop results from the alternate occurrence of strain release along the whole fault and along part of fault.This implies that complicated nonlinear behavior corresponds to clear physical implication in some cases.

Numerical Analysis of Rolling-sliding Contact with the Frictional Heat in Rail

Thermal damage caused by frictional heat of rolling-sliding contact is one of the most important failure forms of wheel and rail. Many studies of wheel-rail frictional heating have been devoted to the temperature field, but few literatures focus on wheel-rail thermal stress caused by frictional heating. However, the wheel-rail creepage is one of important influencing factors of the thermal stress In this paper, a thermo-mechanical coupling model of wheel-rail rolling-sliding contact is developed using thermo-elasto-plastic finite element method. The effect of the wheel-rail elastic creepage on the distribution of heat flux is investigated using the numerical model in which the temperature-dependent material properties are taken into consideration. The moving wheel-rail contact force and the frictional heating are used to simulate the wheel rolling on the rail. The effect of the creepage on the temperature rise, thermal strain, residual stress and residual strain under wheel-rail sliding-rolling contact are investigated. The investigation results show that the thermally affected zone exists mainly in a very thin layer of material near the rail contact surface during the rolling-sliding contact. Both the temperature and thermal strain of rail increase with increasing creepage. The residual stresses induced by the frictional heat in the surface layer of rail appear to be tensile. When the creepage is large, the frictional heat has a significant influence on the residual stresses and residual strains of rail. This paper develops a thermo-meehanical coupling model of wheel-rail rolling-sliding contact, and the obtained results can help to understand the mechanism of wheel/rail frictional thermal fatigue.

Constraints on rupture speed of the 2001 MS 8.1 West Kunlun Mountain Pass earthquake by co-seismic surface rupture slip displacements based on the slip-weakening mechanism with frictional undershoot involved

With co-seismic surface rupture slip displacements provided by the field observation for the 2001 MS8.1 West Kunlun Mountain Pass earthquake, this paper estimates the rupture speed on the main faulting segment with a long straight fault trace on the surface based on a simple slip-weakening rupture model, in which the frictional overshoot or undershoot are involved in consideration of energy partition during the earthquake faulting. In contrast to the study of Bouchon and Vallée, in which the rupture propagation along the main fault could exceed the local shear-wave speed, perhaps reach the P-wave speed on a certain section of fault, our results show that, under a slip-weakening assumption combined with a frictional undershoot (partial stress drop model), average rupture speed should be equal to or less than the Rayleigh wave speed with a high seismic radiation efficiency, which is consistent with the result derived by waveform inversion and the result estimated from source stress field. Associated with the surface rupture mechanism, such as partial stress drop (frictional undershoot) associated with the apparent stress, an alternative rupture mechanism based on the slip-weakening model has also been discussed.