Showing papers on "Slip line field published in 2023"

(Synthetic) Data-driven identification of governing equations of aseismicseismic fault slip and frictional heterogeneities

Abstract: Models of fault slip development generally consider interfacial strength to be frictional and deformation of the bounding medium to be elastic. The frictional strength is usually considered as sliding rate- and state-dependent. Their combination, elastic deformation due to differential slip and rate-state frictional strength, leads to nonlinear partial differential equations (PDEs) that govern the spatio-temporal evolution of slip. Here, we investigate how data on fault slip rate and stress can directly discover the complex system (of PDEs) that governs aseismic slip development. We first prepare (synthetic) data sets by numerically solving the forward problem of slip rate and fault stress evolution with models, such as a thin laterally deformable layer over a thick substrate. We now identify the variables, for example, slip rate or friction state variable, and use nonlinearity identification algorithms to discover the governing PDE of the chosen variable. In particular, we use sparse identification of nonlinear dynamics algorithm (SINDy, Brunton et al., 2016) where we solve a regression problem, Ax=y . Here, y is the time derivative of the variable of interest, for example, slip rate. A is a large matrix (library) with all possible candidate functions that may appear in the slip rate evolution PDE. The entries in x , to be solved for, are coefficients corresponding to each library function in matrix A . We update A according to the solutions x so that A ’s column space can span the dynamics we seek to find. To find the suitable column space for A , we encourage sparse solutions for x , suggesting that only a few columns in matrix A are dominant, leading to a parsimonious representation of the governing PDE. We show that the algorithm successfully recovers the terms of the PDE governing fault slip and could also find the frictional parameter, for example, a/b, where a and b, respectively, are the magnitudes that control direct and evolution effects. Moreover, the algorithm can also determine whether the associated state variable evolves as aging- or slip-law types or their combination. Further, with the data set prepared from distinct initial conditions, we show that the SINDy can also determine the problem parameter’s spatial distribution (heterogeneities) from fault slip rate and stress data.

Characterisation of the strain rate sensitivity of basal, prismatic and pyramidal slip in Zircaloy-4 using micropillar compression

Abstract: For polycrystalline deformation in metals such as Zircaloy-4, the slip strength at different strain rates will control mechanical response and strongly influence the anisotropy of plastic deformation. In this work, the slip activity and strain rate sensitivity of the basal, prismatic, and pyramidal slip systems were explored by testing at variable strain rates (1E-4 s^-1 and 125 s^-1) using single crystal micropillar compression tests. These systematic experiments enabled the direct fitting of the strain rate sensitivities of the different slip systems using a simple analytical model to reveal that deformation will be accommodated using different slip systems depending on the strain rate of deformation in addition to the stress state (i.e. Schmid's law). This insight helps inform metal forming and understanding of the mechanical performance of these engineering alloys in the extremes of service conditions.

Analysis of the Failure Area of the Slope Using the Slip Line Method

Abstract: Most geotechnical engineers focus on ground strength and stability. However, when determining stability by analyzing the exact strength of the ground, the failure surface is essential. Nevertheless, limited studies have been conducted on the methods to determine the exact failure surface of the ground. This study shows that the failure surface and plastic area can be analyzed using the slip line method based on the slip line and lower bound analysis. To improve existing studies limited to single ground, we analyzed the failure area of heterogeneous ground conditions. The results of the slip line method were compared and verified through FELM, a finite element analysis method to which a lower limit analysis was applied. As a result, the failure area and maximum internal stress according to the ground properties and the slope angle are presented. In addition, the points of the slip line method and the finite element limit analysis are summarized. Finally, we propose limitations and solutions when applying the slip line method to the slope.

Determination Rule for α, β Directions and φ in Teaching of Slip-Line Theory

Abstract: In the teaching of plastic mechanics and applications of slip-line theory using conventional methods, multivalued results are usually caused by the uncertain direction of the slip line and dip angles. Determination rules for the α and β directions and φ values are proposed to improve slip-line theory according to the particle flow law under the effect of principal stress, and slip lines and dip angles suitable for a typical stress boundary problem are described. The α and β slip lines should simultaneously point to or away from the intersection, and the synthetic direction of the slip lines should point to the first principal stress σ1 or away from the direction of the third principal stress σ3. When the Hencky stress equation of the α line is applied, two points on the α line should maintain the same direction, and the absolute value of the φ difference should be less than or equal to π. Moreover, the α line of two points should simultaneously point to the inner and outer normal direction of the β line when the Hencky stress equation of the β line is used. The average stress and critical load of plastic deformation in the plane lath V-notch tension are solved using slip-line theory. Both the calculated critical stress and the load maintain uniformity using different slip lines and dip angles, and the proposed determination rule reliably avoids multivalued solutions. This is important for students and researchers in correctly understanding and applying slip-line theory.

Analysis of slip transfer behavior of tantalum during quasi in-situ compression

Abstract: This paper reports a quasi in-situ study on the plastic deformation behavior of high purity tantalum, particularly the slip activation and slip transfer, using the electron backscatter diffraction method. We found that the rotation degree of grains is in the range of 0–15°; the rotation axes of slip-activated grains are mainly concentrated in the three corners, while the axes of slip-transfer ones are concentrated near {111} corner in the stereographic triangle. Microstructural parameters including grain size and grain aspect ratio were found to have no apparent relationships with the slip activation or slip transfer process. Most m' factors for the grains underwent slip-transfer are larger than 0.27, and most slip systems involved in the slip-transfer observations are associated with relatively high Schmid factors (SFs), indicating that slip would more easily transfer through the boundaries with large m' factors. In addition, according to the distribution of geometrical necessary dislocation density and the SF of slipping activated grains, we found the slip transfer process is affected by a combination of factors, including the SF, m' factor, and the strain concentration in local regions.

Interface slip models and slip measurement

Abstract: In Chapter 5, we have given the measurement experiments and analysis of non-Newtonian characteristics, especially the limit shear stress. We have mentioned that when the shear stress reaches the limit value, the slip will appear at the fluid solid interface, which has been confirmed by experiments. The unresolved questions are how the slip happens and what the slip is related to. In this chapter, we discuss two interface slip models, they are: the slip length model and the limited shear stress model. The verifications of the two models are analyzed in detail, and how to measure the slip and consider its influencing factors are discussed.

Analytical model for the load-slip relationship of bearing-shear connectors

Abstract: The shear behavior of shear connectors in steel-concrete composite structures mainly depends on its load-slip relationship. The load-slip relationship not only reflects the shear capacity and slip capacity of the shear connectors, but also the degradation of shear stiffness during loading. In this study, fifteen push-out tests were carried out to investigate the load-slip relationship of the novel bearing-shear (B-S) connectors, which consist of pressuring-bearing plates and shear plates. Based on push-out tests, the influence of the shape and height of the pressure-bearing plate, and the shear plate shape on the load-slip relationship of the B-S connectors was analyzed. Then, an effective finite element model, validated by push-out tests, was used to study the influence of the concrete strength, and the thickness and tensile strength of the shear plate on the load-slip relationship of B-S connectors. Finally, based on the push-out tests, numerical analysis and theoretical analysis, an analytical model expressing the load-slip relationship of the B-S connectors was proposed.

Hydrodynamics of a slip-stick sphere with a non-axisymmetric patch

Abstract: We study the low Reynolds number hydrodynamics of a slip-stick sphere suspended in an arbitrary ambient Stokes flow, whose surface is partitioned into two regions with different slip lengths. The fore-aft symmetry of the sphere breaks due to the varied slip length over the surface, which causes translational and rotational motion of the slip-stick sphere. An analytical solution is developed using the double curl method to evaluate Fax\'en's formulae for the hydrodynamic drag and torque exerted on the slip-stick sphere for the sub-cases, namely, (a) cap/strip model and (b) patch model. Subsequently, we compute the flow field, velocity, and rotation rate, which strongly depend on the slip lengths and configuration of the patch. As a specific example, we consider the slip-stick sphere immersed in a Poiseuille flow. For the cap/strip model, we find an optimal configuration for which the velocity of the slip-stick sphere is maximum compared to the slip-stick sphere with uniform slip. We also find configurations for which the velocity is independent of the slip lengths. Subsequently, in the patch model, we obtain the optimal azimuthal angles for the maximum rotation rate of the slip-stick sphere. We observe near-field deviations in streamlines due to the heterogeneous nature of the surface of the slip-stick sphere. These findings help to design efficient artificial passive swimmers with prescribed slip lengths.

(Synthetic) Data-driven identification of governing equations of aseismic/seismic fault slip and frictional heterogeneities

Abstract: Models of fault slip development generally consider interfacial strength to be frictional and deformation of the bounding medium to be elastic. The frictional strength is usually considered as sliding rate- and state-dependent. Their combination, elastic deformation due to differential slip and rate-state frictional strength, leads to nonlinear partial differential equations (PDEs) that govern the spatio-temporal evolution of slip. Here, we investigate how data on fault slip rate and stress can directly discover the complex system (of PDEs) that governs aseismic slip development. We first prepare (synthetic) data sets by numerically solving the forward problem of slip rate and fault stress evolution with models, such as a thin laterally deformable layer over a thick substrate. We now identify the variables, for example, slip rate or friction state variable, and use nonlinearity identification algorithms to discover the governing PDE of the chosen variable. In particular, we use sparse identification of nonlinear dynamics algorithm (SINDy, Brunton et al., 2016) where we solve a regression problem, Ax=y . Here, y is the time derivative of the variable of interest, for example, slip rate. A is a large matrix (library) with all possible candidate functions that may appear in the slip rate evolution PDE. The entries in x , to be solved for, are coefficients corresponding to each library function in matrix A . We update A according to the solutions x so that A ’s column space can span the dynamics we seek to find. To find the suitable column space for A , we encourage sparse solutions for x , suggesting that only a few columns in matrix A are dominant, leading to a parsimonious representation of the governing PDE. We show that the algorithm successfully recovers the terms of the PDE governing fault slip and could also find the frictional parameter, for example, a/b, where a and b, respectively, are the magnitudes that control direct and evolution effects. Moreover, the algorithm can also determine whether the associated state variable evolves as aging- or slip-law types or their combination. Further, with the data set prepared from distinct initial conditions, we show that the SINDy can also determine the problem parameter’s spatial distribution (heterogeneities) from fault slip rate and stress data.

Partial slip problems in contact mechanics

Abstract: In this chapter, we study the mechanics of fretting contacts and, in particular, investigate the problems in which part of the contacting region is in a state of slip. We begin by considering an overview of half-plane theory and wedge theory for incomplete and complete contacts of two elastically similar bodies, and we derive the conditions for full stick to be maintained in the presence of the different possible applied loads, including applied normal and shear forces, an applied moment, and differential bulk tensions. In many incomplete contacts, the conditions of full stick are violated as the loads vary, so that slip zones necessarily initiate at the edges of the contact. We outline the current, state-of-the-art theoretical models that allow us to analyze and understand partial slip problems, in particular giving descriptions of both corrective slip-based and dislocations-based approaches. For the former, there is an extensive range of solutions with all four applied loads varying, provided that the slip zones are of the same sign. Dislocation-based approaches are necessary when the slip zones are of opposite sign, and we describe this methodology for problems in which no varying applied moment is present. If a varying moment is present as well as the slip zones being of opposite sign, we reach the limit of applicability for dislocation-based methods, and we therefore conclude with a brief discussion of the asymptotic and approximate methods that can be used in this regime.

Two-dimensional flow over a smooth depression in a channelwith a slip wall

Abstract: Abstract The effect of slip along a Gaussian-shaped gap deformity, located about a fixed position on the lower wall of a two-dimensional channel, is numerically investigated. Two gap deformations are modelled, with dimensions sufficient to generate localised pockets of reversed flow when the channel walls are fully no-slip. The Reynolds number of the flow, based on the channel half-width, is 4000 for this investigation. The two gap deformations have the same depth, 𝑑, but different widths, 𝜎, leading to a wide gap with an aspect ratio 𝜂 = 𝑑/𝜎 = 0.4 and a narrow gap with an aspect ratio 𝜂 = 0.8. The wide gap establishes a higher intensity region of separated flow within the deformation than the narrow gap. Surface slip with slip length, 𝜆, is modelled via a Robin-type slip boundary condition. Applying the slip condition to the gap concavity reduces the intensity and thickness of the separation bubble within the deformation. Eventually, slip eliminates flow separation altogether for slip lengths 𝜆 = 0.15 and 𝜆 = 0.1 for the wide and narrow gaps, respectively.

A Critical Review of von Mises Criterion for Compatible Deformation of Polycrystalline Materials

Abstract: A von Mises criterion for compatible deformation states that five independent slip systems must operate for polycrystals to deform uniformly and without failure at the grain boundaries, which is supported by the Taylor–Bishop–Hill theory or simply the Taylor model, defining the laws of plastic deformation of polycrystalline aggregates and being one of the key cornerstones of crystal plasticity theory. However, the criterion has fundamental flaws as it is based on an unfounded correlation between phenomenological material flow behaviour in continuum mechanics and crystal structure dependent dislocation slip, and there has been no experimental evidence to show simultaneous operation of five independent slip systems. In this paper, the Von Mises criterion and the Taylor model are revisited and examined critically, and the fundamental issues related to the requirement of independent slip systems for compatible deformation and the selection of the active slip systems are addressed. Detailed analysis is performed of the stress state that eliminates the possibility of the simultaneous operation of five independent slip systems, and of the relative displacement vector due to the dislocation slip which defines the quantity of the strain that can be expressed by a strain tensor, instead of individual strain components. Discussions are made to demonstrate that although three linearly independent slip systems are essentially sufficient for compatible deformation, one slip system, being selected according to Schmidt law, dominates at a time in a characteristic domain as deformation accommodation occurs between grains or characteristic domains rather than at each point.

Higher order lubrication model between slip walls

Abstract: Abstract A higher order lubrication model between slip walls is proposed for predicting the flow fields that cannot be described by the standard lubrication models based on the thin-gap approximation. The analysis shows that when considering the non-negligible pressure gradient in the surface-normal direction, the local pressure can be separated into (i) the base contribution by the modified Reynolds lubrication equation and (ii) the higher order component varying in both longitudinal and wall-normal directions, which takes the form proportional to the longitudinal derivative of the local velocity of the Couette–Poiseuille flow. For both (i) and (ii), the effect of the slip boundaries appears as the apparent displacements of the no-slip solid walls, and for (i) additional terms (to the no-slip case) also appear. The validity of the higher order slip-wall lubrication model is established by comparing the analytical prediction of the pressure with the fully resolved numerical results in a relatively wide region between a no-slip corrugated wall and a flat plate with varying slip length: the contribution of the higher order term is identified as the decreased lubrication pressure due to velocity slip. The model also successfully predicts the trend of pressure change between the varying slip case and a more realistic system with constant slip length for a channel, where the thin-gap approximation does not hold.

Slip-stuck kinematics of fault surfaces in laboratory experiments: implications for heterogeneous slip distributions during earthquake events

Abstract: Combining field observations with analogue laboratory experiments, this study aims to use surface-roughness characteristics as an indicator of the heterogeneous slip partitioning along shear surfaces. We investigated the roughness of shear surfaces in sheared quartzite of the Singhbhum Shear Zone, eastern India, and identified two distinct kinematic domains: slip zone and stuck zone, marked by strong and weak or no roughness anisotropy, respectively. The experiments, run on brittle-ductile models under a pure shear condition suggest the initial inclination (θ) of shear fractures to the compression direction as a crucial factor in determining their competitive development (measured in terms of their relative area coverage) on the shear surface. Using a laser profilometer we constructed 3D topologies of both field and experimental shear surfaces, which are presented to show their distinctive roughness characteristics. The slip and stuck zones differ from each other in the fractal properties of their surface irregularities. ΔD [difference between across- (D⊥) and along- (D∥) slip direction] is calculated to evaluate the degree of roughness anisotropy. This fractal parameter indicates strong anisotropy in slip (ΔD = 0.0787 – 0.2118) zones, which is virtually absent in stuck zones (ΔD = 0.0024 – 0.0603). We thus propose ΔD as an effective parameter to delineate the slip and stuck zones on a shear surface. Finally, the article presents an in-depth discussion of the geological implications, e.g., earthquake event patterns of this slip-stuck roughness study.

Energy approach to the selection of deformation pattern and active slip systems in single crystals

Abstract: The recently introduced quasi-extremal energy principle for incremental non-potential problems in rate-independent plasticity is applied to select the deformation pattern and active slip systems in single crystals. The standard crystal plasticity framework with a non-symmetric slip-system interaction matrix at finite deformation is used. The incremental work criterion for the formation of deformation bands is combined with the quasi-extremal energy principle for determining the active slip systems and slip increments in the bands. In this way, the incremental energy minimization approach has been extended to the non-potential problem of deformation banding in metal single crystals. It is shown that fulfilment of the mathematical criterion for incipient deformation banding in a homogeneous crystal in the multiple-slip case under certain conditions requires non-positive determinant of the hardening moduli matrix. Numerical examples of energetically preferable patterns of deformation bands are presented for Cu and Ni single crystals.