Slip Criterion Research Articles

A new approach to the calculation of variable tangent bending stiffness for helical strands

As the cross-section of the helical strand increases, the effect of its nonlinear bending characteristics becomes significant. To accurately simulate the response of helical strands under such conditions using the finite element method, determining the tangent bending stiffness of helical strands is indispensable. However, the approach of calculating the tangent bending stiffness of helical strands based on the stick-slip state of wires is not universally applicable across all strand models. In this study, we propose an approach for calculating the tangent bending stiffness of strands based on two mechanical models of helical strands. This proposed approach uses the ratio of the “actual increment” to the “theoretical maximum increment” of the nonlinear component of the wire axial force to calculate the contribution of one wire to the tangent bending stiffness of the strand. Significantly, this approach can be applied to different strand models, each of which may adopt different slip criteria. By comparing the results with the numerical solutions, we validate the effectiveness of the proposed approach for calculating the tangent bending stiffness of helical strands on different strand models. Furthermore, it is pointed out that the analytical results of wire sliding may vary significantly depending on the adopted slip criteria.

SLIP‐RESISTANT CONNECTIONS. COMPARISON OF FRICTION AREAS IN SLIP FACTOR TEST SPECIMENS ACCORDING TO INTERNATIONAL CODES

AbstractThere are differences in the slip factor tests used in international codes. In many cases, different slip factors have been obtained for almost the same surfaces. The existing literature confirmed that the discrepancies could be due to different slip criteria, preload levels, measurement methods, etc. However, the specimens used in each test have not been dimension‐ally compared. An analytical comparative study has been carried out comparing the friction disc of seven international codes. It has been verified if the differences found can be compensated with the different preloads indicated in each test. The results confirm that they are not, and that geometric differences are important in explaining the different slip factors.

On the mechanistic driving force for short fatigue crack path

The growth of fatigue cracks at the microstructural level is significant for many engineering industries. The multifarious nature of crack propagation at microstructure length scales necessitates the use of advanced modelling techniques to predict fatigue life accurately. A key contributor to this is the path of the crack, which also remains challenging to predict; the maximum slip criterion has been used widely in the literature but is not fully adequate. This paper tests the hypothesis that for short crystallographic cracks, there is some other factor responsible for guiding their extension on a particular plane. With this, using a crystal plasticity finite element modelling framework, two new energy-based methods are developed: a microstructure-sensitive maximum energy release rate criterion, and a maximum normal stored energy density criterion. Results demonstrate, for the two cases studied, both methods offer a significant improvement over the maximum slip criterion when applied to real microstructures. In particular, the maximum normal stored energy method gives closest agreement with experiments, while maximum energy release rate offers new insights into a mechanism for crack bifurcation.

On the numerical homogenization of real polycrystalline microstructures

AbstractThe FE2 method, cf. [1], a direct micro‐macro homogenization approach, has become a standard procedure for scale‐transition applications. Therein, the modeling of a micro‐heterogeneous material described by a representative volume element (RVE) based on realistic microstructures can give rise to a barely unmanageable computational effort. Alternatively, statistically similar RVEs (SSRVEs) can be used, which are constructed based on morphological information of the real microstructure and lead to a reduction of computational cost, see [2]. In their construction, a least‐square functional is used to minimize the deviation of statistical properties, such as volume fraction, spectral density and lineal‐path function, of the SSRVE and the real microstructure. The application of SSRVEs has been shown to lead to an adequate representation of the mechanical behavior of the real microstructure. The first part of the talk will give an overview on the construction of SSRVEs and present examples of multiscale analyses using the FE2 approach with simplified microstructures in different engineering applications of steel material.The paper also focusses on the details of the microstructure and discusses crystal plasticity models, see e.g. [3], in order to account for the material anisotropy induced by the texture of the crystalline structure of steel. It is well known that for rate independent single crystal plasticity, the ambiguity of the choice of active slip systems and linear dependency of slip criteria may cause instabilities in the algorithm. Classical perturbation methods are often used to solve the problem as well as rate dependent algorithms which model the rate independent case as the limit of vanishing viscosity. However, this leads to stiff constitutive equations and thus requires small time increments. In [4], an alternative approach has been proposed recently which is based on handling the constrained optimization problem in the framework of infeasible primal‐dual interior point methods (IPDIPM). We modify the original constrained optimization problem using slack variables in order to stabilize the algorithm and allow for temporary violation of the constraints. Numerical examples are presented for crystalline structures with face centered cubic properties.

Investigation on Mechanism of Coal Burst Induced by the Geological Weak Surface Slip in Coal Seam Bifurcation Area: A Case Study in Zhaolou Coal Mine, China

Abstract The coal seam bifurcation area (CSBA) exists widely in coal measure strata, where the geological weak surface (GWS) slip in overburden structure is easy to induce coal burst. The coal mass of coal face shows overall instability failure and high-speed throwing characteristics during the coal burst, seriously threatening the safe and efficient coal mine production. In order to understand the GWS-induced coal burst caused by the slip in CSBA and find the main controlling factors of GWS slip, the GWS slip criterion in CSBA was established based on the coal burst case analysis of overburden structure in CSBA of 1305 coal face (1305CF) in Zhaolou Coal Mine. The case study showed that the angle and range of CSBA are the main controlling factors affecting GWS slip. The FLAC3D numerical model of CSBA was established to analyze the influence effect of main control factors. The results show that the increase of angle and range of CSBA will increase the influence scope and degree of coal face mining, improving coal face burst risk. However, the peak point region of abutment pressure will not be affected, gradually reaching its peak within 0 m ~10 m from the coal seam merging area. With the increase of the angle of CSBA, the integrity of the triangular wedged rock mass along the GWS slip will be enhanced, aggravating the dynamic disturbance to the coal mass. With the increase of the range of CSBA, the slip of triangular wedged rock mass along GWS gradually changes from integral slip to phased slip, which will intermittently disturb the coal mass of the coal face. The research results have certain theoretical significance and practical value for preventing and controlling coal bursts in CSBA.

Determination and application of posture adjustable domain under constraints of placement quality

This paper defines the adjustable domain of placement posture during automatic fiber placement process and determines the critical size of the adjustable domain under the constraints of placement quality. The influence of the posture deflection on the placement quality is analyzed first, and compaction and slippage of tows are determined as the main constraints. Simulation models of tow compaction under variable deflection angles are established, and the influence of deflection angle and direction on tow compaction is analyzed. The friction coefficient is measured by experiments to characterize the friction behavior of the tow, and a tow slip criterion was established to avoid unacceptable defects. Combining the above constraints, posture adjustable domain is obtained and the influence of various parameters is analyzed. A searching method is established to calculate the collision-free posture in the adjustable domain and applied on a complex mold surface. The results show that the posture adjustable domain can effectively ensuring the placement quality when the placement head is deflected to avoid collision.

A semi-infinite edge dislocation model for the proportionality limit stress of metals under high strain rate

Micromechanics of strain rate dependent elastic response, within the proportionality limit in metals is investigated, on the basis of dislocation kinetics. It is postulated that, the strain rate dependence of proportionality limit stress is dominated by inertia of dislocations, over drag controlled mechanisms. Subsequently, kinetic energy of accelerating edge dislocation at its incipient motion, is expressed. The proposed, inertia-dominated model is non dissipative in nature when compared with that of Frank-Read dislocation nucleation-based model and dislocation-drag mechanism-based model at high strain rates. Using Hamiltonian formalism, a new rate dependent slip criterion with corresponding threshold shear stress is derived. Experimental data on FCC samples, Aluminium-1100-0 and Oxygen free Copper; and BCC samples, pure Iron and mild steel, within a benchmark strain rate of 104 s−1, are used to validate the model prediction. Reported theory on dislocation drag controlled model is compared with the proposed inertia-based theory, using published experimental data.

Micromechanical Modelling of the Influence of Strain Ratio on Fatigue Crack Initiation in a Martensitic Steel-A Comparison of Different Fatigue Indicator Parameters.

Micromechanical fatigue lifetime predictions, in particular for the high cycle fatigue regime, require an appropriate modelling of mean stress effects in order to account for lifetime reducing positive mean stresses. Focus of this micromechanical study is the comparison of three selected fatigue indicator parameters (FIPs), with respect to their applicability to different total strain ratios. In this work, investigations are performed on the modelling and prediction of the fatigue crack initiation life of the martensitic high-strength steel SAE 4150 for two different total strain ratios. First, multiple martensitic statistical volume elements (SVEs) are generated by multiscale Voronoi tessellations. Micromechanical fatigue simulations are then performed on these SVEs by means of a crystal plasticity model to obtain microstructure dependent fatigue responses. In order to account for the material specific fatigue damage zone, a non-local homogenisation scheme for the FIPs is introduced for lath martensitic microstructures. The numerical results of the different non-local FIPs are compared with experimental fatigue crack initiation results for two different total strain ratios. It is concluded that the multiaxial fatigue criteria proposed by Fatemi-Socie is superior for predicting fatigue crack initiation life to the energy dissipation criteria and the accumulated plastic slip criteria for the investigated total strain ratios.

Analysis of the First Cracks Generating Between Two Holes Under Incremental Static Loading with an Innovation Method by Numerical Modelling

The application of Non-Explosive Expansion Materials (NEEM) has recently been increased in hard rock quarry mining, especially in granitic rocks. The most important mention in the quarry mining methods is determination of hole pattern, because it relates to cost of exploitation of the rock blocks, directly. It needs to predict the rock fracture process which it depends on the length of the first cracks and the growing to join together. A new algorithm has been suggested to evaluate of the first crack length by the linear elastic fracture mechanics (LEFM) theory. It requires determining a stress concentration factor which an experimental model has been utilized. A case study has been selected to verify of the numerical results which it is a granite mine in Iran. Numerical modeling has been applied to illustrate of rock fracture process and crack path and the results showed if the size of elements near the crack tip equal to grain size of the rock material or the ratio of the element length per diameter of the hole is selected about one per fifty, accuracy of the crack path prediction can be acceptable. On the other hand selection of an adequate rock slip criterion for crack planes is important, because of friction between two planes of a crack, plays an important role to predict of the crack growth. Also this research showed that Mohr-Coulomb criterion without cohesion is a suitable model for crack’s elements and Hoek-Brown failure criterion is an adequate model for rock substance.

A nonlinear cohesive/friction coupled model for shear induced delamination of adhesive composite joint

This paper originally proposes a nonlinear cohesive/frictional contact coupled model for the mode-II shear delamination of adhesive composite joint based on a modified Xu and Needleman’s exponential cohesive model. First, the friction is assumed to increase nonlinearly at the delamination interface when the tangential cohesive softening appears. Second, a non-associative plasticity model based on the Mohr–Coulomb frictional contact law is proposed, which includes a frictional slip criterion and a slip potential function. Third, a return mapping algorithm based on the non-associative plasticity theory is proposed to solve the updated normal and tangential tractions and stiffnesses. It is shown the tangential cohesive traction and stiffness depend on the friction and dilatancy of the delamination interface. Finally, the proposed theoretical model is implemented using three-dimensional finite element analysis by ABAQUS-UEL (user element subroutine) and demonstrated by comparing the finite element results with the analytical results for the $$[0^{\circ }]_{6}$$ , $$[\pm 30^{\circ }]_{5}$$ , $$[\pm 45^{\circ }]_{5}$$ end-notched flexure adhesive composite joints with the mode-II shear delamination. The effects of the friction coefficient, cohesive strength, normal contact stiffness and mesh size on the load–displacement curves and delamination mechanisms of composites are studied. Numerical results show the shear delamination growth is governed by the transition from the decreased tangential cohesive traction to the increased tangential friction, and the frictional effect becomes distinct after unstable delamination for angle-ply laminates.

(110)シリコンの高温下のすべりと破壊に及ぼす引張軸方位の影響

Tensile testing of single crystal silicon microstructures was performed along tensile axes of <110> and <111> at 500 °C in a vacuum to investigate crystallographic effects on their slip occurrences and fracture behaviors at the high temperature. Specimens with parallel portions 120 μm long, 2 μm wide, and 5 μm thick, were designed along the two tensile axes on (110) wafers, and were fabricated from SOI (silicon-on-insulator) wafer using UV lithography and deep RIE (reactive ion etching) processes. The specimens were subjected to tensile testing at 500 °C in a vacuum, which exhibited linear stress increments until their fractures at 3.2 GPa on <110> and at 4.0 GPa on <111>. Contrary to the obtained linear nominal stress increments, fractured specimens possessed surface steps due to slip along {111}. The fracture surfaces exhibited large planes oriented mostly along {111} indicating cleavage fracture behaviors. Stress concentration around the surface step was analyzed employing finite element method to discuss effect on the surface step on decrease in nominal tensile strength at a high temperature, and criteria for slip were discussed based on maximum shear stress along the slip system.

TR method (TRM): A separation and stress inversion method for heterogeneous fault-slip data driven by Andersonian extensional and compressional stress regimes

The recently proposed TR method (TRM) which uses the slip preference of the faults to separate heterogeneous fault-slip data in extensional and compressional Andersonian stress regimes, is enhanced so as to determine stress tensors with the use of the Wallace–Bott slip criterion. Published natural fault-slip data from the extensional region of Tympaki, Crete, Greece and artificial fault-slip data modeled from the Chelungpu thrust, activated during the 1999 Chi–Chi earthquake in Taiwan, have been used as case studies. In the first case, the fault-slip data previously considered as homogeneous might actually be of heterogeneous origin as they determine two distinct stress tensors that both fit well with the neotectonic faulting deformation of the region. In the second case, where the fault-slip data belonging to three different subsets are of low diversity, the TRM succeeds in defining the driving stress tensors. The Misfit Angle minimization criterion can adequately separate the fault-slip data between two subsets when the percentage of the “Stress Tensor Discriminator Faults” is higher than approximately 70%.

Simulation Research of Anti-Sliding Control of Urban Rail Brake System Based on AMESim and Simulink

Anti-sliding control of urban rail brake can effectively improve the adhesion utilization rate of the train, shorten braking distance and prevent wheel scratches. This paper takes differential velocity plus slip rate and speed reduction plus its differential as slip criterion, using logic threshold control method to establish Single wheel anti-slip control system. Pneumatic model, mechanical model and control model are built in AMESim and Simulink to implement co-simulation. Simulation results show that the comprehensive model can effectively achieve the anti-slide function. And by taking wheel glide distance as evaluation index, the merits of the two kinds of antiskid criterion are analyzed. The results show that deceleration and deceleration differential criterion as sliding criterion effect is better.

Wheel Torque Distribution Criteria for Electric Vehicles With Torque-Vectoring Differentials

The continuous and precise modulation of the driving and braking torques of each wheel is considered the ultimate goal for controlling the performance of a vehicle in steady-state and transient conditions. To do so, dedicated torque-vectoring (TV) controllers that allow optimal wheel torque distribution under all possible driving conditions have to be developed. Commonly, vehicle TV controllers are based on a hierarchical approach, consisting of a high-level supervisory controller that evaluates a corrective yaw moment and a low-level controller that defines the individual wheel torque reference values. The problem of the optimal individual wheel torque distribution for a particular driving condition can be solved through an optimization-based control-allocation (CA) algorithm, which must rely on the appropriate selection of the objective function. With a newly developed offline optimization procedure, this paper assesses the performance of alternative objective functions for the optimal wheel torque distribution of a four-wheel-drive (4WD) fully electric vehicle. Results show that objective functions based on the minimum tire slip criterion provide better control performance than functions based on energy efficiency.

Concurrent atomistic and continuum simulation of strontium titanate

This paper presents a concurrent atomistic–continuum methodology (CAC) to simulate the dynamic processes of dislocation nucleation and migration as well as crack initiation and propagation in complex crystals. The accuracy and efficiency of the method is tested with respect to the molecular dynamics (MD) method through simulations of the dynamic fracture processes in strontium titanate under a combination of tension and shear loading and the dislocation behavior under nanoindentation. CAC simulation results demonstrated a smooth passage of cracks and dislocations through the atomistic–continuum interface without the need for additional constitutive rules or special numerical treatment. Although some accuracy is lost in CAC simulations as a consequence of a 98.4% reduction in the degrees of freedom, all the CAC results are qualitatively and quantitatively comparable with MD results. The stacking fault width and nanoindentation hardness measured in the CAC simulations agrees well with existing experimental data. Criteria for cleavage and slip in ionic materials are verified. The need to include the internal degrees of freedom of atoms in concurrent atomistic–continuum methods for polyatomic crystalline materials is confirmed.

Boundary velocity slip of pressure driven liquid flow in a micron pipe

The velocity slip of gas flow in a micron channel has been widely recognized. For pressure driven liquid flow in a macro pipe, the minute velocity slip at the wall boundary is usually neglected. With a decreasing scale in the cross section of the flow passage, the effect of velocity slip on flow and heat transfer behaviors becomes progressively more noticeable. Based on the three Hamaker homogeneous material hypotheses, the method for calculating the acting force between the solid and liquid molecular groups is established. By analyzing the forces exerted on the liquid group near the pipe wall, it is found that the active force arising from the rough solid wall can provide the component force to resist the shearing force and keep the liquid group immobile. Based on this a velocity slip criterion is proposed. Considering the force balance of a slipping liquid group, the frictional force caused by the solid wall can be obtained and then the velocity of the liquid group can be calculated using the derived coefficient of friction. The investigation reveals that, in a micron pipe, a small velocity slip may occur when the flow pressure gradient is relatively large, and will cause errors in the pipe flow estimates.

Conditions for thrust faulting in a glacier

Dipping, arcuate bands of debris‐rich ice outcropping near the margins of glaciers are often interpreted as thrust faults, assumed to originate in zones of longitudinal compression. Identification of thrusts is typically based either on the geometry and sedimentology of the debris bands or on the crystal fabric of surrounding ice, but the physical processes necessary to generate thrusts are rarely evaluated. Herein, we combine a numerical model of compressive ice flow near a glacier margin with theoretical stress and strain rate criteria for ice fracture and stress criteria for frictional slip to determine the conditions necessary for thrust faulting in glaciers. This model is applied to two different glaciological settings where longitudinal compression has been documented: (1) the transition between warm‐based and cold‐based ice near the terminus of Storglaciären, Sweden, and (2) the downglacier extent of the 1983 surge front of Variegated Glacier where surging ice encountered stagnant ice. Simulations representing the margin of Storglaciären indicate that peak compressive strain rates are six orders of magnitude too small to induce fracture, whereas at Variegated Glacier, strain rates were an order of magnitude too small for compressive fracture. In both groups of simulations, preexisting fractures governed by Coulomb friction are susceptible to slip if they span the ice thickness, are oriented close to the optimal fracture angle, and, in the case of Storglaciären, are subject to water pressures that are a large fraction of ice overburden pressure. Variations about the optimal fracture orientation, low or zero water pressure, high sliding friction coefficient, and limited vertical or lateral fracture extent each tend to suppress thrusting.

軸直角方向外力を受けるボルト締結体挙動の解析的モデルの構築 : 第1報,荷重変位関係のモデル化

An Analytical model for describing the mechanical behavior of a bolted joint subjected to a transverse load has been theoretically formulated. This paper focuses on the load-displacement relation. The transverse displacement is separated into five factors: (a) bolt bending due to a transverse force acting on the thread surface, (b) bolt bending due to the thread-surface reaction moment, (c) inclination of the bolt head, (d) thread surface slip, and (e) bearing surface slip. Contact force and slip displacement are newly modeled in order to describe (d) and (e). Contact surfaces are discretized into meshes. The contact force acting on each mesh is formulated by taking into account the helical profile of the thread. The slip criterion is judged according to the Coulomb friction law. In order to maintain a mechanical equilibrium, the contact force and contact state are calculated in a self-consistent manner. As for the interaction between the thread and bearing surfaces, torque induced on the thread surface is transmitted to the bearing surface in a model of bolt torsion, relevant to the loosening rotation. The mechanism by which the reaction moment, which affects (b) to (e), is induced on the thread and bearing surfaces is also investigated. We found that the inclination of the bolt affects the reaction moment during localized thread-surface slip, while the transverse displacement of the bolt affects that during the complete thread-surface slip. The reaction moment is formulated to be proportional to the stiffness of the thread and bearing surfaces. Finally, our analytical model is applied to an M16 bolted joint and confirmed that our model agree well with the FEM result.

Analytical Modelling of the Mechanical Behavior of Bolted Joint Subjected to Transverse Loading

An analytical model for describing the mechanical behavior of a bolted joint subjected to a transverse load has been theoretically formulated. This paper focuses on the load-displacement relation. The transverse displacement is separated into five factors: (a) bolt bending due to a transverse force acting on the thread surface, (b) bolt bending due to the thread-surface reaction moment, (c) inclination of the bolt head, (d) thread surface slip, and (e) bearing surface slip. Contact force and slip displacement are newly modeled in order to describe (d) and (e). Contact surfaces are discretized into meshes. The contact force acting on each mesh is formulated by taking into account the helical profile of the thread. The slip criterion is judged according to the Coulomb friction law. In order to maintain a mechanical equilibrium, the contact force and contact state are calculated in a self-consistent manner. As for the interaction between the thread and bearing surfaces, torque induced on the thread surface is transmitted to the bearing surface in a model of bolt torsion, relevant to the loosening rotation. The mechanism by which the reaction moment, which affects (b) to (e), is induced on the thread and bearing surfaces is also investigated. We found that the inclination of the bolt affects the reaction moment during localized thread-surface slip, while the transverse displacement of the bolt affects that during the complete thread-surface slip. The reaction moment is formulated to be proportional to the stiffness of the thread and bearing surfaces. Finally, our analytical model is applied to an M16 bolted joint and confirmed that our model agree well with the FEM result.

Development of an objective determination of a slip with a portable inclineable articulated strut slip tester (PIAST)

A portable inclineable articulated strut slip tester (PIAST) is a slipmeter that is widely used in the USA to measure coefficient of friction (COF) at the shoe sole and floor interface. A determination of a slip at the measurement interface, which is currently judged subjectively by operators, plays a crucial role in deciding the outcomes of a PIAST measurement. The goal of this study was to develop an objective determination of a slip based on the movement of the weight used by the slipmeter. The displacement of the weight and the time duration of consecutive strikes in a measurement were used to derive the objective slip criterion. Various footwear materials, floor materials and surface conditions were used to cover a wide range of COF values. The results of the regression analysis indicated that the objective COF predicted by the method developed in the current study was significant ( R 2 = 0.997, β = 0.991, p < 0.001) in predicting the subjective COF determined by the operator.