Tangential Load Research Articles

Exact Solution to Axisymmetric Interface Crack Problem in Magneto-Piezo-Electric Transversely Isotropic Materials

Summary This seems to be the first exact closed-form solution to the problem of a penny-shaped interface crack, subjected to an axisymmetric normal and tangential loading. The crack is located at the boundary between two bonded magneto-piezo-electric transversely isotropic half-spaces, made of different materials. We use the combination of Green’s functions for two different half-spaces and Fourier transform. We derive first the governing equations, which are valid for a crack of arbitrary shape. The usual approach leads to five hypersingular integral equations, we arrive at four integro-differential equations (one of them being complex). While the coefficients of the governing equations in existing publications are presented in terms of the results of the solution of a set of linear algebraic equations and are too cumbersome to be written explicitly in terms of the basic constants, our choice of the basic constants leads to quite elegant explicit expressions for these coefficients and reveals certain symmetry, which was noticed only numerically in previous publications or not noticed at all. In the particular case of axial symmetry, the problem is reduced to just one singular equation, for which an exact closed-form solution is known. We are not aware of any other publication with which our results can be compared.

Finite Element Analysis of Elastoplastic Elements in the Iwan Model of Bolted Joints.

The Iwan model is composed of elastoplastic elements and is widely used to represent the stiffness degradation of bolted joints under mixed-mode loading (normal and tangential loading). The latest static methods of parameter identification established the relationship between the elastoplastic elements and the contact pressure under normal loading. Under mixed-mode loading, the parameters of the Iwan model are dynamic for the evolution of contact conditions. Therefore, static parameter identification methods are not suitable for the dynamic Iwan model. A new technique was proposed to identify the parameters of the elastoplastic elements in this paper. Firstly, several different finite element models were established. The influence of the contact method and the thread structure were analyzed, and a reliable and efficient bolted-joint modeling method was proposed. Secondly, the evolution of contact conditions was studied. The dynamic elliptical contact model and the ellipticity discrete method were proposed. Finally, the residual stiffness of the Iwan model was analyzed to establish the mapping between the residual stiffness and the bending of the screw. The results can provide a technique for identifying the parameters of the dynamic Iwan model.

A Fully Coupled Normal and Tangential Contact Model to Investigate the Effect of Surface Roughness on the Partial Slip of Dissimilar Elastic Materials

By adopting a global search method for all shear tractions in the contacting area and using an alternative convergence criterion regarding load balance in the lateral direction, the newly developed algorithm provides stable solutions to partial-slip problems of elastically dissimilar materials. The model is validated via the comparison between the simulation and literature results for a sphere-on-flat problem under fully coupled conditions. It is then employed to investigate the influence of surface roughness parameters including the root mean square (RMS) roughness and RMS slope on partial-slip solutions under coupled conditions. Since the gross sliding condition is modified under coupling effects, the relationship between the ratio of the stick area to the contacting area (stick ratio) and tangential load in the coupled case, unlike that in the uncoupled one, becomes non-linear for all tested rough surfaces. Under low or medium tangential loads, the surface with a higher RMS gradient or a lower RMS roughness experiences more stick regions within the contacting area. This trend then becomes irregular at higher tangential loads.

Small-Scale Dynamic Behavior of Embedded Beams Under Moving Force in Complex Environments

Forced and free dynamic responses of nanobeams resting on a three-parameter foundation subjected to a moving force in magneto-hygro-thermal conditions are investigated based on the nonlocal strain gradient theory. Also, a detailed parametric study is conducted to identify the impact of slender ratio, axial and distributed tangential loads on the vibration characteristics and dynamic phenomena of the small-scale system. Comparative studies with existing results in the literature are performed to ensure the accuracy of the presented model and solution approach. Analytical and numerical methods are implemented to detect the effects of foundation coefficients, environmental conditions, geometrical and scale parameters on the dynamic amplification factor, critical moving force velocity, cancellation, and maximum free response mechanisms of the system. The outcomes revealed that the critical moving force velocity is enhanced by ascending the slender ratio, elastic, and shear moduli of the foundation. It is found that when the damping factor is considered for the foundation, it is feasible to prevent the occurrence of the cancellation phenomenon. Also, it is concluded that by fine-tuning scale parameters and environmental conditions, unwanted vibration of the system can be suppressed. The attained results of this study can be helpful in the vibration control of nanoscale actuators, switches, and resonators.

Nano-sized single-asperity friction behavior: Insight from molecular dynamics simulations

Friction phenomenon plays an essential role in contact pairs, from macroscale to nanoscale friction. Nano-sized friction behavior is different from macroscopic friction behavior due to discreteness of atoms. Taking α-Fe as paradigm material, single-asperity friction molecular dynamics (MD) simulations are conducted. The MD results show that the multi-slip phenomenon exists during the tangential loading process of nano-sized single asperity. Meanwhile, the macroscopic friction coefficient model is not suitable for nano-sized friction, while the macroscopic Kogut-Etsion (KE) contact radius model can approximately describe nano-sized contact radius. Besides, the Mindlin model can hardly describe the initial tangential stiffness under large normal loadings due to the neglect of plastic deformation. Therefore, it is suggested to modify the macroscopic friction models by considering the plastic deformation mechanism and asperity size effect to improve the full-scale description ability.

Oblique Low-Velocity Impact Response and Damage Behavior of Carbon-Epoxy Composite Laminates.

The low-velocity impact behavior of carbon-epoxy cross-ply composites was numerically investigated, examining the effect of impact angle. A plastic continuum damage model, introducing the cohesive interface to describe delamination damage, was established and was validated by available experimental data. Impact histories, progressive deformation, stress transfer, and impact damage are respectively discussed. The results show that an increase in impact angle intensifies the action of tangential force, and gradually transfers energy absorption from normal plastic deformation to tangential deformation and friction, which dissipates more energy through relatively longer contact duration and larger impactor displacement. The delamination damage to upper layers is more affected by tangential loads, intensifying with the increase of the impact angle, and the damage area to the top interface is increased by 132.1% from 0° impact to 60° impact. Meanwhile, the delamination damage to lower layers is mainly determined by normal loads, weakening with the increasing impact angle overall, and the damage area of the lowest interface decreases by 36.6% from 0° impact to 60° impact.

Analysis of PDC cutter cutting‐broken conglomerate based on the discrete element method

AbstractIt is well known that the magnitude of impact load is one main reason for polycrystalline diamond compact (PDC) cutter failure rapidly when drilling conglomerate formation. However, there are many factors affecting the magnitude of impact load. To assess and mitigate these impacts, the discrete element model of PDC cutting‐broken conglomerate has been established, and the influence law of cementation strength difference (CSD), gravel diameter, and cutting velocity on impact load and gravel fragmentation in the process of cutting broken conglomerate is performed. What is more, the laboratory experiment of rock cutting by different shaped PDC cutters under different CSD and gravel diameters has also been conducted, and the correctness of numerical simulation results is verified by laboratory experiment. Meanwhile, the cutting depth and impact load of different shape PDC cutters under different CSD and gravel diameters have been analyzed. First, the simulation results show that the stripping mode of gravel mainly occurs when the CSD is large, and the corresponding axial and tangential impact load (mean axial peak cutting force [MAPCF]/mean tangential peak cutting force [MTPCF]) is relatively small. As the decrease of CSD, the gravel will be directly broken and the magnitude of the MAPCF/MTPCF will gradually increase, and the probability of impact damage to the cutting cutter will incrementally increase. In addition, larger gravel diameter and cutting velocity will lead to larger MAPCF/MTPCF, and the mode of gravel fragmentation changes gradually from being stripped to being directly broken with the increase of gravel diameter. Second, the laboratory experiment results not only verify the correctness of the simulation results but also find that ridged diamond element cutter has the smallest impact load and the largest cutting depth under different CSD and gravel diameters. This paper can provide a theoretical foundation for the optimization of drilling parameters and PDC bit design in drilling conglomerate formation.

Stress state of the grinding tool loaded with tangential force

Purpose. Determining the interaction mechanism of discrete grains through material that binds them in a tool for abrasive material processing in the case of its loading with a tangentially directed cutting force. Methodology. Development and analytical solution to a mathematical model formulated on the basis of static equilibrium of an abrasive grain as a system element of tool grains bound with a material with excellent mechanical characteristics. Findings. A mathematical model has been developed and an algorithm has been formulated to analytically determine the stress-strain state parameters of a tool for abrasive processing of materials, which is loaded with a discrete cutting force, tangential to its working surface. The nature of the dependence of stresses and deformations on mechanical parameters, the quantity of grains and the material binding them in an abrasive tool, loaded with a unit tangential force, has been determined. Originality. The loading of the extreme grains leads to greater displacements, tangents of the shear angles of the material binding the grains. They decrease with increasing quantity of grain rows in the tool or with increasing quantity of grains to the nearest tool edge. Practical value. The distribution of interaction forces of grains and stresses in the material binding them has been determined. The found distribution allows one in the process of developing the tool and technology, in which it is involved, to comprehensively assess the influence of tangential load value of the tool working grain on its stress state and the material containing the grains. The determined stress state makes it possible to predict the number of loading cycles until the simultaneous rational wear of the grain and the destruction of that part of the material that contains it. The linear formulation of the problem makes it possible to take into account the mutual influence of the tangential loads of several grains on the stress-strain state of the tool as a whole.

Analysis of sliding behavior of coated surfaces under shear traction

The tribological behavior of non conformal coated contacting surface i.e. rigid sphere on the coated flat material surface normal force and shear traction is studied through numerical results. The non-conforming contact is a fundamental problem in the contact mechanics, which has a wide range of applications. Contact is the science behind tribology, the interdisciplinary study of friction, wear and lubrication with major applications in particle handling or friction between contacting rough surfaces, brakes, Bearings and so on. In the present investigation, the contact between the coated flat and the rigid sphere under the combination of normal and tangential loading is analyzed using finite element software ABAQUS. The substrate material is chosen for the analysis High speed steel, Titanium alloy and coating material is TiN (E=305GPa) of 5µm thick with a bonding material is Chromium (379GPa) of 1µm thick at the interface between the coating and substrate is modeled by three dimensional finite element method (3DFEM) in order to optimize coating coated surface and bonding layer to coating fracture. The elastic-perfectly plastic contact is assumed on the flat model. The results obtained from the FEA are used in the understanding of the tribological behavior of the contact pair.

Generation of friction-increasing surfaces by turn-milling

Increasing the coefficient of static friction (COF) in frictional connections can help to respond to current demands such as increasing power density or lightweight design. Turn-milling is used to generate surfaces with protruding microstructures that lead in combination with a surface exhibiting a lower hardness to an increase of the COF. For the investigations, end faces of cylindrical specimens of the steel 1.7225 (42CrMo4) in quenched and tempered heat treatment condition (+QT) are machined using single-edged TiAlN coated cemented carbide end milling cutters. Four tool types varying in terms of the corner geometry are utilised in order to create different profile tip angles (PTAs) αpt of the microstructures: rounded (rε = 0.2 mm), chamfered (0.2 mm × 45°) and two types of sharp corners with different tool included angles of εr = 88° and 75°. The influence of the process parameters feed per tooth fz, radial feed frad and cutting speed vc on the surface topography and the COF are investigated using a 23 full factorial design with centre point for each corner type. The COF is determined with a special torsional test bench using face turned counterbodies made of the steel 1.0503 (C45). The PTA influences the ability of the profile tips to penetrate the surface of the counterbody but also their shear strength under a tangential load. Among the variants studied, microstructures with a PTA αpt = 88° proved to be most effective in regard to an increase in the COF. However, the feed per tooth fz has a strong effect on the surface topography as well as on the COF for all tool types tested, but in particular for this PTA. A slight change of fz in the micrometer range results in strongly differentiated surface patterns. These differences can also be demonstrated by the peak material volume Vmp. This surface parameter shows the best correlation with the COF. The highest mean COF μ¯max=0.69 is achieved with microstructures exhibiting a PTA of αpt = 88° at the feeds frad = 0.2 mm and fz = 0.125 mm.

Mechanical and Tribological Properties of 3D Printed Polyamide 12 and SiC/PA12 Composite by Selective Laser Sintering.

Polymeric matrix composites are important to the advancement of industries such as the automobile and medicine industries. In this study, the silicon carbide (SiC) particle-reinforced polyamide12 (PA12) matrix composites were fabricated by selective laser sintering system as well as the pure PA12. The surface topographies, mechanical, and tribological properties were further examined. The results indicated that the friction and wear resistance of the composite were improved compared with the PA12 matrix. The compressive strength increased about 8.5%, shore D hardness increased about 6%. The friction coefficient decreased about 10%, the specific wear rate decreased 20% after adding silicon carbide 10% weight to PA12. The wear mechanisms were also discussed. The deformed asperities on the worn surface can withstand more tangential load, and therefore resulted in lower specific wear rate. It was found that the content of SiC particles on the surface were reduced after friction tests. According to the analysis of SEM, EDS, and FTIR results, the wear mechanisms were considered to be the abrasive and fatigue mode. This type of PA12 matrix composite might be a promising potential in marine and energy applications.

Elevated temperature contact creep and friction of nickel-based superalloys using machine learning assisted finite element analysis

Nickel-based superalloys with superior thermochemical, mechanical, and tribological properties are highly utilized for critical components in several high temperature applications such as gas turbines and nuclear reactors. Inconel 617, in particular, is considered as one of the main candidate superalloys for tribo-components in very-high-temperature gas-cooled nuclear reactors. Recent findings indicate that this alloy grows unique surface oxide especially in a high-temperature helium environment with distinctive wear, friction, and contact properties. This study investigates the high temperature contact area evolution and frictional behavior of Inconel 617 using finite element simulation and provides predictive models for the contact and friction performance at different normal loads, dwell times, and temperatures. High temperature helium-aged Inconel 617 top surface properties (up to 600 °C) are utilized along with a single asperity-based deformable elastic-plastic contact model under combined normal and tangential loading. Machine learning is used to assist the finite element results and to predict friction coefficient as well as contact area evolution. While a small difference is observed in the instantaneous friction coefficient (no dwell time) for all temperatures, friction coefficient increases considerably with dwell time. This shows that the effect of contact creep for longer dwell times significantly dominants the effect of high temperature variation in basic mechanical parameters such as modulus and yield strength. It is found that increasing temperature and dwell times lead to the friction coefficient increase, yet the dominance of dwell time effects decreases at higher temperatures and loads. While the analysis is presented for Inconel 617, the methodology is easy to be generalized and can be applied to other HT alloys.

Magnetically induced friction damping based on magnetoactive elastomers — A proof of concept

In this work we present a new concept for friction damping which is based on the permanent magnetization and the flexibility of magnetoactive elastomers (MAE). The concept is called “magnetofriction” and is studied on a sandwich structure in the present work. The assembled structure consists of a MAE core and ferromagnetic skins. Due to the magnetization of the MAE, the skins are attracted to the core and the sandwich is assembled without the need of glue or other means of fixation. The magnetic forces generate the normal loading in the contact interfaces between skins and core while a tangential loading is induced by forced vibrations applied to the sandwich beam. Random and harmonic vibration tests reveal the nonlinear dynamic behavior of the sandwich structure and highlight the damping capacity of magnetofriction. The harmonic balance method is used on a nonlinear dynamic model of the system to identify the parameters related to the resonance frequency and damping ratio. The results obtained from the identification state damping ratios up to 9% under harmonic excitation, which is remarkable for friction damping. In addition, a Finite Element-based model of the structure is implemented to study the local contact states in the sandwich. Multi-physical simulations are performed to analyze the magnetic and mechanical loading in the contact interface. The local results are used to evaluate the overall contact states in the interfaces which determine the absence or presence of friction damping. The simulations show that the vibration amplitude changes the contact state.

Influence of Wear Profile Geometry on Critical Plane Fatigue Crack Initiation Criteria in Plane and Axisymmetric Elastic Fretting Contacts

The subsurface elastic stress fields in plane and axisymmetric contacts with friction under oscillating tangential loading are calculated via a very robust, high-precision method, which operates with appropriate superpositions of analytic solutions for the respective Hertzian contact problems. Based on the stress fields, two critical plane fatigue crack initiation criteria—the Smith-Watson-Topper (SWT) parameter and the Findley parameter—are evaluated for three types of contact profile geometries: (unworn) parabolic contact, the partial slip limiting wear profile of an initially parabolic contact, and truncated parabolic contact. Appropriate scaling laws are introduced to formulate a general solution in terms of non-dimensional variables. The crack initiation criteria are determined in the full subsurface loading plane. It is found that the truncated profile—which may originate from sliding wear—has practically the same local distribution of crack initiation criteria as the unworn profile, despite the (weak) stress singularity at the edge of the flat face. The partial slip limiting wear profile, on the other hand, exhibits a strong edge stress singularity at the boundary of the permanent stick zone, the crack initiation criteria are drastically increased (and theoretically infinite). Also, while for the unworn and truncated profiles high values of the crack initiation criteria are extremely localized around “hotspots” at the surface, for the partial slip limiting wear profile they reach much deeper into the subsurface material. This offers a new explanation for the dominance of fatigue failure in the partial slip regime of fretting. The differences between plane and axisymmetric cases are generally small. The SWT parameter is generally more localized than the Findley parameter.

Tangential mechanical properties analysis of cylindric elastoplastic contact model

An elastoplastic contact model of two cylinders is proposed in this paper. The crossing angle of two cylinders axes is introduced into the contact model. An analytical solution including the tangential displacement and tangential load under the axis crossing angles is provided. The finite element method is used to verify analytical solutions. The verification result shows that the analytical solution is in good agreement with the simulation result obtained by the finite element analysis. The stress distribution law of the cylinder contact surface is analyzed based on the contact model. The influence of model parameters on tangential mechanical properties is explored. Results show that tangential mechanical properties of the cylinder are governed by many factors, such as the applied load, material properties, and axis crossing angle. Cylinder contact models with different axis crossing angles can be applied to some engineering structures, such as roller bearings and gear meshing.

Unloading effect of the shear resistance of rock joints

To investigate the stress path dependent of rock joints, a series of tangential loading tests and normal unloading tests were conducted using 32 cement mortar replicas of artificially split rock joints with 4 different joint roughness coefficients (JRC). The critical normal stresses of the unloading tests were recorded, and a comparative study was conducted by referencing the results under different loading paths and joints conditions. The test results indicate that the shear resistance has a distinct unloading effect, which is mainly influenced by the morphologic characteristics, normal stress levels and stress paths. By analyzing the results, it can be concluded that the variation trend of shear/normal stress ratio against the normal stress and JRC of the two test conditions were identical. However, under low normal stress condition, the stress ratio of the joints under normal unloading stress path is the higher one; while under higher normal stress, the relationship becomes converse. Compared to that of the tangential loading condition, shear/normal stress ratio of the unloading stress path reduces rapidly as the increasing of normal stress, and the influence of the morphology is masked under lower normal stress.

Generic self-stabilization mechanism for biomolecular adhesions under load

Mechanical loading generally weakens adhesive structures and eventually leads to their rupture. However, biological systems can adapt to loads by strengthening adhesions, which is essential for maintaining the integrity of tissue and whole organisms. Inspired by cellular focal adhesions, we suggest here a generic, molecular mechanism that allows adhesion systems to harness applied loads for self-stabilization through adhesion growth. The mechanism is based on conformation changes of adhesion molecules that are dynamically exchanged with a reservoir. Tangential loading drives the occupation of some states out of equilibrium, which, for thermodynamic reasons, leads to association of further molecules with the cluster. Self-stabilization robustly increases adhesion lifetimes in broad parameter ranges. Unlike for catch-bonds, bond rupture rates can increase monotonically with force. The self-stabilization principle can be realized in many ways in complex adhesion-state networks; we show how it naturally occurs in cellular adhesions involving the adaptor proteins talin and vinculin.

Fracture Analysis of Ultrahigh-Strength Steel Based on Split Hopkinson Pressure Bar Test

Impact loading is an important cause of fracture failure of ultrahigh-strength steel parts during service. Revealing the fracture mechanism of ultrahigh-strength steel under impact loading has important reference significance for the material preparation, part design, and manufacturing of such steel. Based on the split Hopkinson pressure bar (SHPB) test, the mechanical response characteristics of 45CrNiMoVA steel under impact loading were analyzed, and the true stress–true strain curves under a high strain rate (103 s−1) were obtained. It was found that under the simultaneous action of forward and tangential loading forces, a severe plastic deformation layer with a thickness of 20–30 μm was generated in the near impact-loading end face, which is the main cause for crack initiation and propagation. Under the condition of a high strain rate, the plastic flow stress of 45CrNiMoVA steel was characterized by the equilibrium of strain hardening and strain softening, and its impact fracture toughness decreased by 43.6%, resulting in increased quasi-cleavage fracture. Hence, severe surface plastic deformation during 45CrNiMoVA steel machining should be avoided, as it may lead to early failure.

Tangential elastic contact model of the cylindrical contact with different axis crossing angles.

In this paper, a cylinder contact model with different axis crossing angles is proposed, and the axis crossing angle is introduced into the normal and tangential constitutive equations. This paper uses the method of formula derivation to establish the analytical solution of the tangential elastic contact of the cylinder with different axis cross angles, and gives the relational expression of the tangential load and the tangential displacement. The finite element method (FEM) is used to verify the tangential displacement load curve and the tangential stiffness curve of the two cylinders. The influence of various factors on mechanical properties such as tangential stiffness, tangential displacement and contact area is explored, and the distribution of stress and strain on the contact surface is analyzed. The research results show that the tangential displacement and tangential stiffness of the cylindrical contact model correspond well to the simulation results.

An asperity-based statistical model for the adhesive friction of elastic nominally flat rough contact interfaces

Contact mechanics-based models for the friction of nominally flat rough surfaces have not been able to adequately capture certain key experimentally observed phenomena, such as the transition from a static friction peak to a lower level of sliding friction and the shear-induced contact area reduction that has been observed in the pre-sliding regime especially for soft materials. Here, we propose a statistical model based on physically-rooted contact mechanics laws describing the micromechanics of individual junctions. The model considers the quasi-static tangential loading, up to full sliding, of the contact between a smooth rigid flat surface and a nominally flat linear elastic rough surface comprising random independent spherical asperities, and accounts for the coupling between adhesion and friction at the micro-junction level. The model qualitatively reproduces both the macroscopic shear-induced contact area reduction and, remarkably, the static friction peak without the need to explicitly introduce two different friction levels. It also demonstrates how the static friction peak and contact area evolution depend on the normal load and certain key microscale interface properties such as surface energy, mode mixity and frictional shear strength. “Tougher” interfaces (i.e. with larger surface energy and smaller mode mixity parameter) are shown to result in a larger real contact area and a more pronounced static friction peak. Overall, this work provides important insights about how key microscale properties operating at the asperity level can combine with the surface statistics to reproduce important macroscopic responses observed in rough frictional soft contact experiments.