Shear Traction Research Articles

On the tractive rolling nanocontact of an exponentially graded coating-substrate structure

This paper studies the tractive rolling nanocontact occurring between an exponentially graded coating-substrate structure and a circular rigid indenter. Employing the framework of Steigmann–Ogden surface elasticity, it models the surface effects inherent in the nanocontact of graded coatings. The contact area is assumed to comprise a central stick zone bounded by two distinct slip zones. Central to the investigation is the utilization of the nonclassical Flamant solution, which serves as the foundational framework for deriving integral equations governing the continuity of both vertical and tangential displacement gradients. Utilizing Gauss–Chebyshev quadratures, the paper discretizes and collocates these integral equations, along with the force equilibrium conditions and shear traction smooth condition at the leading side stick/slip transition point. An iterative algorithm is then developed to tackle the resultant algebraic system, particularly concerning the discretized contact pressure and friction traction. The paper rigorously validates its proposed solution method and numerical algorithm against existing literature results, showcasing their accuracy and reliability. Moreover, it conducts extensive parametric studies to unravel the effects of various parameters, such as surface material properties, coefficient of friction, inhomogeneity index, and thickness of the exponentially graded coating. These analyses uncover the significant role of surface effects in shaping contact pressure, frictional traction, stresses, subsidence distributions, and stick–slip zones. Notably, the inclusion of surface effects is found to reduce maximum stress and subsidence while inducing a shift of the stick region towards the rolling direction. The parametric exploration of graded coating properties also offers insights into tailoring nanocontact responses for gradient nanostructures.

NUMERICAL SIMULATIONS OF ELASTIC-PLASTIC CONTACT CONSIDERING FRICTION

The solution of the elastic-plastic contact is of major importance in contact mechanics because contact damage and wear are responsible for the failure of many machine elements subjected to contact load. In many situations including gears and bearings, the load is transmitted through a small contact region, i.e. a concentrated contact, and the resulting high gradients of stress often exceed the plastic yield limit of the softer material. Plastic flow is initiated at a certain depth, resulting in modification of contact geometry and of the stress state that can lead to crack inception and propagation. Understanding the contact behaviour in the presence of plastic strains is fundamental for predicting the contact resistance. Considering the mathematical model complexity for the contact between bodies of arbitrary boundary, as well as the dissipative nature of plasticity, an analytical solution for the elastic plastic contact problem is hard to accomplish. Alongside finite element analysis, semi-analytical methods are the only existing simulation tools for the elastic-plastic contact problems. This paper extends a previously reported elastic-plastic contact solver developed by the same author, by considering friction. In the previous solver iteration, residual displacements were calculated only in the normal contact direction, thus assuming that the shear displacements are small enough to be neglected, in other words, the contact was assumed frictionless. By considering friction, a slip-stick contact process is introduced, adding a new iterative loop in which the contact pressure and shear stresses are iterated until convergence is reached. The new computer simulation tool is expected to give more realistic predictions for the elastic-plastic contact between materials with dissimilar elastic properties, in which case the shear tractions disturb the stress and displacements fields calculated for the frictionless contact case. The results are expected to contribute to a better understanding of the contact processes in the presence of both plastic strains and friction.

Disturbance range characterization and reinforcement design method of concealed bedding slope

The concealed bedding slopes exhibit sudden and extensive failure characteristics, harboring significant safety hazards. It is crucial to employ rapid and accurate methods to determine excavation disturbance ranges and reinforcement forces to prevent such slope disasters. This paper first analyzes the failure characteristics of slope excavation to reveal the mechanism of slope failure. Secondly, a novel method was proposed to calculate excavation disturbance ranges and solve for active reinforcement forces. Thirdly, the rationality of the method was validated through numerical simulation experiments. Finally, the method was applied to engineering. The results are as follows:(1) Excavation induces plastic shear failure of structural planes first, and the strength of the structural plane will be reduced, resulting in extrusion shear deformation of the rock mass at the foot of the slope under greater unidirectional load along the structural plane, forming a shear sliding surface. (2) From both strength and deformation perspectives, a method for calculating disturbance ranges in excavated slopes is proposed. This method determines key indicators for analyzing two disturbance range factors: ultimate height and disturbance thickness. The disturbance range is divided into shear plastic zones and traction sliding zones. (3) An active reinforcement design method is proposed considering the timing, scope, and force of reinforcement. The disturbance thickness is used to determine the reinforcement range, while the ultimate height is used to determine the timing of reinforcement. Active reinforcement forces are calculated based on the equilibrium of forces and deformation amounts. (4) A comparison with the Finite Element Method (FEM) shows that during excavation, the disturbance ranges and reinforcement forces calculated using this method are slightly larger than those obtained from the FEM. The calculations are fast, and as the excavation height approaches the limit slope height, the disturbance thickness and horizontal deformations closely match the FEM results, ensuring safety. It can provide monitoring, early warning and reinforcement guidance for bedding slope construction.

Estimation of fatigue life of TiN coatings using cyclic micro-impact testing

We studied the behaviour of a thin titanium nitride (TiN) coating (1.5 µm thick) on a tool steel substrate under dynamic and cyclic impacts through an approach combining experimental testing and computational modelling. Dynamic impact testing was used to investigate the load-dependent dynamic hardness and assess the energy-dissipation capabilities of the coating system. In cyclic impact tests, the coating-substrate system experienced permanent plastic deformation in each cycle, ultimately leading to coating failure. Chemical analysis identified an interlayer between the coating and the substrate that influenced the coating response, while cross-sectional analysis revealed the extent of coating damage due to cycling and impact load. A three-dimensional map was constructed, connecting the acceleration load, sensed depth, and cycles to the coating failure, and an empirical equation was used to characterise the relationship between the depth and cycles to failure. The computational model examined the traction component distribution during loading and unloading, focusing on normal and shear tractions. These findings suggested the potential significance of normal traction in the interfacial fatigue failure due to impact.

Dynamical Modeling of Fault Slip Rates at the New Zealand Plate Boundary Indicates Fault Weakness

AbstractWe construct a thin‐sheet dynamical model of the New Zealand plate boundary that includes faults. Our model fits fault slip rates, style of distributed deformation, and is constrained by relative plate boundary motion. We assume a pseudo‐plastic rheology and achieve a best fit to slip rate observations with a deviatoric stress magnitude of 20 MPa. Modeled local forces are significant at Puysegur and Hikurangi subduction zones, and smaller forces are related to mantle downwelling beneath South Island and Havre Trough mantle upwelling. Modeled tractions on faults are mostly 5–20 MPa, similar to or slightly smaller than stress magnitudes adjacent to faults. Modeled shear tractions are generally 2–10 MPa, comparable to stress drops during earthquakes. Modeled stress orientations and fault dips suggest that many faults are not optimally oriented for their style of faulting. Notably small traction magnitudes of <5 MPa and shear tractions of <0.5 MPa are modeled for faults in the central North Island Dextral Fault Belt (NIDFB), which we infer to be very poorly oriented. Friction coefficients on faults (ratio of shear stress to effective normal stress) are in the range 0.1–0.3 for major crustal faults such as the Alpine Fault and Marlborough faults, but subduction zones and the NIDFB have values <0.1. We propose that low values of long‐term fault strength, shear stress resolved onto the fault, and overall magnitudes of deviatoric stress in the crust are a consequence of dynamic weakening of faults during fault slip.

Density of Micropillar Array Influences Shear Traction of Individual Pillars on Soft Substrates

Density of Micropillar Array Influences Shear Traction of Individual Pillars on Soft Substrates

Deep neural network aided cohesive zone parameter identifications through die shear test in electronic packaging

AbstractThe die shear test is a feasible and conventional method to characterize the shear strength of die‐attaching layer materials in electronic packaging. A new method for determining cohesive zone model (CZM) parameters using deep neural networks (DNN) and die shear tests is proposed, different from classical fracture framework or lap shear test‐based methods. With the sintered nano‐silver die shear test, the results show that the bilinear CZM inversion results agree well with the experimental results. It is found that the DNN model has high accuracy in predicting and identifying the maximum shear traction strength τmax, separation displacement of the interface δf, and the interface stiffness k1 of CZM parameters for sintered nano‐silver adhesive layer through die shear test load versus displacement curves. The presented DNN‐aided inverse identifying method through the die shear test in this paper could provide an alternative and convenient method for extracting CZM parameters of various kinds of adhesive materials in electronic packaging.

A numerical model to simulate the transient frictional viscoelastic sliding contact

Sliding motion has always been one of the major concerns when it comes to the analysis of viscoelastic contact problems. A new model simulating the transient sliding contact of smooth viscoelastic surfaces is developed in this paper. By taking the dry contact friction and the coupling between shear tractions and normal pressure into account, the effect of the early partial slip period, which is often neglected in the study of viscoelastic sliding contact problems, is investigated numerically. Compared with solutions based on the frictionless assumption, the steady-state pressure profile is found to be slightly different under the effect of the partial slip regime, including a lower peak pressure and the shift of the contacting region in the direction opposite to the sliding motion. Furthermore, the time required for the viscoelastic contact to reach its steady state is delayed owing to the partial slip period preceding the global sliding motion.

Edge Changes in Contacts and Joints to Reduce High Localized Shear Traction, Microslip, and Fretting

Contacts and joints in structures, mechanisms, and dynamic systems often exhibit high localized interface shear at their edges, leading to edge microslip and fretting wear and fatigue. This introduces complexity, nonlinearity, and multiscale friction phenomena. This paper presents a novel approach to address this issue by introducing geometrical changes near contact edges. Two-dimensional contact models are developed and analyzed using asymptotic, closed-form, and numerical methods to study the effect of edge changes on pressure and shear traction. The results show that geometric changes near contact edges can effectively reduce contact edge shear, thereby inhibiting edge microslip and the resulting fretting wear and fatigue in contacts that occur under dynamic conditions. This approach has implications for reduced complexity in contacts and joints for improved capability in modeling, analysis, and measurement characterization.

Numerical modeling of stresses and deformation in the Zagros–Iranian Plateau region

Abstract. The Zagros orogenic system resulted due to collision of the Arabian plate with the Eurasian plate. The region is characterized by ocean–continent subduction and continent–continent collision, and the convergence velocity shows variations from east to west. Therefore, this region shows the complex tectonic stress and a wide range of diffuse or localized deformation between both plates. The in situ stress and GPS data are very limited and sparsely distributed in this region; therefore, we performed a numerical simulation of the stresses causing deformation in the Zagros–Iran region. The deviatoric stresses resulting from the variations in lithospheric density and thickness and those from shear tractions at the base of the lithosphere due to mantle convection were computed using thin-sheet approximation. Stresses associated with both sources can explain various surface observations of strain rates, SHmax, and plate velocities, thus suggesting a good coupling between lithosphere and mantle in most parts of Zagros and Iran. As the magnitude of stresses due to shear tractions from density-driven mantle convection is higher than those from lithospheric density and topography variations in the Zagros–Iranian Plateau region, mantle convection appears to be the dominant driver of deformation in this area. However, the deformation in the east of Iran is caused primarily by lithospheric stresses. The plate velocity of the Arabian plate is found to vary along the Zagros belt from the north–northeast in the southeast of Zagros to the northwest in northwestern Zagros, similarly to observed GPS velocity vectors. The output of this study can be used in seismic hazards estimations.

Numerical method for quasi-static adhesive elastic contact subjected to tangential loading

This paper presents a three-dimensional (3D) numerical model for simulating the adhesive contact with linear isotropic elasticity considering the interaction between normal and tangential loads. The model is based on the Boussinesq-Cerruti integral equations for elasticity, the Maugis-Dugdale (MD) model for adhesion, and the friction/adhesion interaction theory in the McMeeking model; it uses the Coulomb's law of friction to identify the occurrence of local microslip. Efficient and accurate determination of the contact behavior, together with adhesive and stick/slip regions, uses the iterative conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) algorithm. The model analyzes adhesive-contact pressure, shear traction, and subsurface stress fields. It is used to study the effects of increasing tangential loading on the variations of stick/slip zones and adhesive-energy dissipation, as well as the influence of sinusoidal roughness on surface adhesion behavior. Compared with most theoretical models, the proposed numerical model has no restrictions on surface geometry and roughness of contact bodies, and it should have a wider range of applications.

Experimental investigation of the effects of load path on the life of fretting fatigue contacts

Slip and changes to stresses within a load cycle both contribute to damage in fretting contacts. By considering conditions for slip in normal-bulk loaded fretting contacts, experiments were performed wherein the contact slip varied, whilst changes to stress were modest. This was achieved by keeping the load endpoints constant but altering the load path. Experiments showed stark contrast in life between tests permitting slip and those prohibiting it. FE models were used to plot slip and stress components, revealing that the differences in life were due to a combination of slip and changes in shear traction. A method is presented by which the crack position can be measured, by adding a feature to the pad to produce a datum mark.

Geometric nonlinear analysis of slender layered non-prismatic beams with interlayer slip

This paper presents a novel model that, for the first time, simultaneously captures the effects of variable cross-section and interlayer slip on the geometrically nonlinear response of slender symmetrically layered beams within the framework of a beam theory. While the central layer has a constant cross-section along its length, the height of the two outer layers can vary arbitrarily. A nonlinear axial strain–displacement relationship captures the influence of moderately large deflections for immovably supported beams. The kinematic hypothesis of the Euler–Bernoulli theory is applied layerwise. The relationship between the interlaminar shear tractions and the interlayer slips is assumed to be linear. The Galerkin method is used to solve the derived initial–boundary value problem. Several application examples demonstrate the influence of the interlayer slip, the variable cross-section, and the geometrically nonlinear formulation of the equations of motion on the static and dynamic response. The results of comparative analyses with a numerically much more computational expensive finite element model discretized by plane stress continuum elements are in excellent agreement with the outcomes of the presented theory.

Experimental and numerical study on the fretting wear-fatigue interaction evolution in press-fitted axles

Fretting fatigue in press-fitted axles is closely related to fretting wear. However, most studies have been limited to the effect of fretting wear on crack initiation, neglecting the interaction influence between fretting wear, crack initiation, and propagation. In this study, interrupted fretting fatigue tests of press-fitted axles were conducted. The evolution of the surface damage and fretting cracks with the number of test cycles was observed and measured. Then, based on numerical simulations, the fretting wear-fatigue interaction evolution was investigated. The results indicated that the stress redistribution resulting from fretting wear led to fretting crack initiation within the fretted wear scar. Due to fretting wear, the compressive stress within the press-fitted region was released and the stress field surrounding the crack tip was enhanced, promoting the propagation of fretting cracks, especially those close to the contact surface. Fretting crack propagation resulted in the loss of stiffness of the axle and locally prevented the transmission of bulk stress to the inner side of the contact surface. The shear traction and slip range were redistributed, alleviating the fretting wear near the wear boundary and increasing the surface damage within the region close to the right-hand side of the crack.

On the structure of poroplastic constitutive relations

The paper discusses from first principles all aspects relevant to the plasticity of porous materials. Emphasis is laid on unhomogeneous yielding, defined as the process of yielding and plastic flow under gradient-free macroscopically nonuniform deformation. The nonuniformity is represented by strain localization in one or more bands of finite thickness. A universal feature of all intrinsic yield criteria is their dependence upon the normal and shear tractions resolved on the band. When specialized to isotropy, a Mohr–Coulomb criterion and a Rankine–Tresca criterion emerge as two extremes. The latter is an ideal that typifies the yield behavior of porous materials under arbitrary loadings. The general theory stands for a finite number of bands or yield systems. Its overall structure bears some features of crystal plasticity, but with dependence upon the resolved normal stress. The evolution of microstructural parameters can be given in general terms, being solely based on the kinematic constraints of unhomogeneous yielding and matrix incompressibility. Throughout the paper, the competition with homogeneous yielding, heretofore taken for granted, is analyzed with or without strain and strain-rate hardening effects. We close by discussing the thermodynamic consistency of this new class of constitutive relations and a link to strain-gradient theories.

The deep-learning-based evolutionary framework trained by high-throughput molecular dynamics simulations for composite microstructure design

The interfacial shear behavior, including the elastic deformation stage, the debonding stage and the sliding stage, is of critical importance in determining the overall performance of a composite. Here a deep-learning-based framework that integrates the generative adversarial network (GAN) and the genetic algorithm (GA) is proposed to establish a bidirectional mapping between the interfacial microstructure and the interfacial shear behavior of SiC fiber reinforced SiC composite (SiCf/SiC). High-throughput molecular dynamics (MD) simulations are carried out to collect the strain–stress curves of the SiCf/SiC interfaces under shear tractions, considering the exhaustive variations in the interfacial microstructure and the temperature. The well-trained GAN model can predict the shear strain–stress curve of an arbitrarily given interfacial microstructure with excellent robustness and accuracy. In the reverse direction, the GA is utilized to infer the interfacial microstructure given desired shear properties. We demonstrate that the proposed GAN-GA protocol can enhance the physical modeling of conventional continuum-scale simulation and efficiently identify the microstructure leading to optimal mechanical properties. Such capability can greatly facilitate the demand-oriented development of composite materials, thereby contributing to intelligent manufacturing.

A Cohesive-Zone-Based Contact Mechanics Analysis of Delamination in Homogeneous and Layered Half-Spaces Subjected to Normal and Shear Surface Tractions

AbstractA contact mechanics analysis of interfacial delamination in elastic and elastic-plastic homogeneous and layered half-spaces due to normal and shear surface tractions induced by indentation and sliding was performed using the finite element method. Surface separation at the delamination interface was controlled by a surface-based cohesive zone constitutive law. The instigation of interfacial delamination was determined by the critical separation distance of interface node pairs in mixed-mode loading based on a damage initiation criterion exemplified by a quadratic relation of the interfacial normal and shear tractions. Stiffness degradation was characterized by a linear relation of the interface cohesive strength and a scalar degradation parameter, which depended on the effective separation distances corresponding to the critical effective cohesive strength and the fully degraded stiffness, defined by a mixed-mode loading critical fracture energy criterion. Numerical solutions of the delamination profiles, the subsurface stress field, and the development of plasticity illuminated the effects of indentation depth and sliding distance on interfacial delamination in half-spaces with different elastic-plastic properties, interfacial cohesive strength, and layer thickness. Simulations yielded insight into the layer and substrate material property mismatch on interfacial delamination. A notable contribution of the present study is the establishment of a computational mechanics methodology for developing plasticity-induced cumulative damage models for multilayered structures.

Effect of Fiber–Matrix Interface Friction on Compressive Strength of High-Modulus Carbon Composites

Carbon-fiber-reinforced polymers (CFRPs) enable lightweight, strong, and durable structures for many engineering applications including aerospace, automotive, biomedical, and others. High-modulus (HM) CFRPs enable the most significant improvement in mechanical stiffness at a lower weight, allowing for extremely lightweight aircraft structures. However, low fiber-direction compressive strength has been a major weakness of HM CFRPs, prohibiting their implementation in the primary structures. Microstructural tailoring may provide an innovative means for breaking through the fiber-direction compressive strength barrier. This has been implemented by hybridizing intermediate-modulus (IM) and HM carbon fibers in HM CFRP toughened with nanosilica particles. The new material solution almost doubles the compressive strength of the HM CFRPs, achieving that of the advanced IM CFRPs currently used in airframes and rotor components, but with a much higher axial modulus. The major focus of this work has been understanding the fiber-matrix interface properties governing the fiber-direction compressive strength improvement of the hybrid HM CFRPs. In particular, differences in the surface topology may cause much higher interface friction for IM carbon fibers compared to the HM fibers, which is responsible for the interface strength improvement. In situ Scanning Electron Microscopy (SEM)-based experiments were developed to measure interface friction. Such experiments reveal an approximately 48% higher maximum shear traction due to interface friction for IM carbon fibers compared to the HM fibers.

Quantifying stiffness and forces of tumor colonies and embryos using a magnetic microrobot.

Stiffness and forces are two fundamental quantities essential to living cells and tissues. However, it has been a challenge to quantify both 3D traction forces and stiffness (or modulus) using the same probe in vivo. Here, we describe an approach that overcomes this challenge by creating a magnetic microrobot probe with controllable functionality. Biocompatible ferromagnetic cobalt-platinum microcrosses were fabricated, and each microcross (about 30 micrometers) was trapped inside an arginine-glycine-apartic acid-conjugated stiff poly(ethylene glycol) (PEG) round microgel (about 50 micrometers) using a microfluidic device. The stiff magnetic microrobot was seeded inside a cell colony and acted as a stiffness probe by rigidly rotating in response to an oscillatory magnetic field. Then, brief episodes of ultraviolet light exposure were applied to dynamically photodegrade and soften the fluorescent nanoparticle-embedded PEG microgel, whose deformation and 3D traction forces were quantified. Using the microrobot probe, we show that malignant tumor-repopulating cell colonies altered their modulus but not traction forces in response to different 3D substrate elasticities. Stiffness and 3D traction forces were measured, and both normal and shear traction force oscillations were observed in zebrafish embryos from blastula to gastrula. Mouse embryos generated larger tensile and compressive traction force oscillations than shear traction force oscillations during blastocyst. The microrobot probe with controllable functionality via magnetic fields could potentially be useful for studying the mechanoregulation of cells, tissues, and embryos.

Pore pressure evolution in bed sediment overridden by debris flow: A general formulation

AbstractDebris flows can grow dramatically in volume and mobility as they override bed sediment due to the reduction in bed friction resistance caused by high pore fluid pressure (PP). However, the mechanisms that control PP evolution in overridden bed sediment are still unclear. Here, a new mathematical model clarifies how diverse styles and magnitudes of PP evolution can result from regulation of the flow diffusion and shear contraction of bed sediment. Normalization of the model equations shows that the propensity for PP generation depends on timescales of PP diffusion and deformation of the bed grains. The PP of saturated bed sediment under immobile conditions is equal to the fluid pressure at the bottom of the flow due to a non‐flux basal boundary. However, the PP of unsaturated bed sediment is lower than that of the overlying flow. PP diffusion from a debris flow into an unsaturated bed increases with the bed’s permeability and water content. The shear deformation behavior changes from undrained to drained with increasing permeability or decreasing shear velocity of the saturated bed sediment, leading to a reduced magnitude of pore pressure. By contrast, the shear deformation transitions from drained to undrained behavior with increasing permeability and water content of unsaturated bed sediment. The entrainment rate and erosion pattern of bed sediment are closely related to the PP evolution and liquefaction ratio of the bed sediment due to Coulomb‐friction shear tractions. Our models can be used to interpret the feedback of PP on the flow momentum during debris flow entrainment.