Deformation Path Research Articles

Misorientation-dependent transition between grain boundary migration and sliding in FCC metals

Grain boundaries (GBs) play a crucial role in the mechanical behaviors of nanocrystalline materials. The dynamics of GBs depend on a variety of intrinsic and extrinsic factors, including GB misorientation, inclination, curvature, metal type and loading history. Controlling GB geometry and deformation behavior thus provides effective means to tailor the mechanical properties of nanostructured materials. However, the relationship between deformation mechanism and GB geometry is still lacking, largely due to the vast amount of metastable GB structures and deformation paths. Here, the relation between GB misorientation (θ, a critical degree of freedom for GB structure) and GB deformation mechanisms was studied by large-scale molecular dynamic simulation in face-centered cubic (FCC) metals. With increasing GB misorientation, the GB deformation mechanism transitions from migration to sliding and further to migration again. The critical transition thresholds (critical misorientations) vary with metal types. An energetic model that links deformation mechanism with GB structure was further developed with a focus on predicting the critical GB misorientation at which GB sliding supersedes GB migration. The influence of metal type on the transition threshold is well captured. We finally extend this model to general GBs with complex atomic structures and compare the theoretical predictions with data reported in the literatures and obtained from the present work. Our findings shed lights on the misorientation-dependent GB deformation mechanisms and can be utilized in GB engineering that pursues high-performance nanocrystalline metals.

An Overview of Deformation Path Shapes on Equal Channel Angular Pressing

In recent years, research on ultra-fine grain materials has gained attention. While attempts have been made to improve the properties of the material, it has also become increasingly important to decrease the costs. Studies on improving material properties have revealed new production methods or have required the revision of existing production methods. In this direction, severe plastic deformation methods have come to the fore as a good alternative, and by improving the methods with new variations, materials with grain sizes below 1 µm have been obtained. In addition, this method positively affects the mechanical properties of the material. In this study, the Equal Channel Angular Pressing (ECAP) method, one of the severe plastic deformation methods, which has attracted great attention among researchers, was examined and the development stages of the method were investigated according to recent studies. The effective parameters in the method were examined and the effects of these parameters on the grain structure and mechanical properties of the material were discussed. Channel shapes, which are open to innovation and increase the efficiency of the ECAP method, were kept in the foreground among the prominent parameters in the ECAP process, and the results of the design changes made with new variations were examined.

Inelastic Deformation of Coronary Stents: Two-Level Model.

This study describes the internal structure of materials used to produce medical stents. A two-level elastoviscoplastic mathematical model, which sets the parameters and describes the processes at the grain level, was developed and numerically implemented. A separate study was conducted to identify the most dangerous deformation modes in the balloon-expandable stent placement using the finite-element method in COMSOL Multiphysics. As a result, the challenging strain state type required for setting the kinematic loading on a representative macrovolume in the two-level model was obtained. A yield surface for different deformation paths in the principal deformation space for stainless steel AISI 316L was obtained and the effect of grain size on the deformation behavior of this material was explored using the developed model.

Evolution of Thin-Film Wrinkle Patterns on a Soft Substrate: Direct Simulations and the Effects of the Deformation History.

Surface wrinkling instability in thin films attached to a compliant substrate is a well-recognized form of deformation under mechanical loading. The influence of the loading history on the formation of instability patterns has not been studied. In this work, the effects of the deformation history involving different loading sequences were investigated via comprehensive large-scale finite element simulations. We employed a recently developed embedded imperfection technique which is capable of direct numerical predictions of the surface instability patterns and eliminates the need for re-defining the imperfection after each analysis step. Attention was devoted to both uniaxial compression and biaxial compression. We show that, after the formation of wrinkles, the surface patterns could still be eliminated upon complete unloading of the elastic film–substrate structure. The loading path, however, played an important role in the temporal development of wrinkle configurations. With the same final biaxial state, different deformation histories could lead to different surface patterns. The finding brings about possibilities for creating variants of wrinkle morphologies controlled by the actual deformation path. This study also offers a mechanistic rationale for prior experimental observations.

Procedure to implement shear evolution in fast rolling models with online capability on the example of an aluminum flat rolling process

The rolling process induces a heterogeneous deformation over the rolling stock height. The causes are the frictional shear stress between the contacting surfaces and the roll gap geometry. They induce a complex material flow within the rolling stock describable by the shear evolution. The shear evolution has a significant impact on rolling values like grain size and crystallographic texture and therefore on the final material properties of the rolled product. Industry and academia use fast rolling models for flat rolling processes to predict the material properties due to their short computation time. The time advantage enables online applicability to adapt processes in real time or to evaluate the influence of different process conditions several times within seconds. However, these models have a limitation regarding the shear evolution. They do not consider all relevant influences or apply simplifying assumptions, valid only for specific rolling cases. This work presents a general approach to extend fast rolling models to consider the shear evolution without any restrictions to specific rolling cases. The approach derives the shear evolution as shear angle alpha evolution based on FE simulations. The shear angle alpha is a geometrical description and not influenced by rotations, which occur during the rolling process. This enables an enhanced and simple analysis of the material flow. The outcome is an extended model that completely describes the deformation along a deformation path and enables the calculation of each desired deformation value (strain, deformation gradient, velocity gradient, etc.).

EVALUATION OF DEFORMABILITY OF MATERIAL DURING PLANTING OF ELEMENTS OF PREPARATIONS BY ROLLING STAMPING METHOD

The article presents the results of development and research of technological schemes of planting flanges on tubular (ring) workpieces by stamping by rolling cylindrical and conical rolls. It is shown that the achievement of significant dimensions of the various elements of the workpiece is possible by providing a directed flow of metal by changing the relative position of the roll and the workpiece. Planting of external flanges is one of the most effective operations of stamping by rolling, as it allows you to form a wide range of products with advanced geometric elements. To assess the technological capabilities of the flange landing operation, the most dangerous from the destruction positions of the workpiece zone was identified and the analysis of the stress-strain state of the material using the method of grids, hardness measurement and microstructural analysis. According to the results of the research, the ways of deformation of the particles of the material of the peripheral surface of the flange in the coordinates "intensity of deformations - an indicator of the stress state" are schematically constructed. These deformation paths are given against the background of curves of ultimate deformations of steels, which are built on the results of uniaxial compression and torsion of cylindrical specimens and using tested approximations. A mathematical model of deformation trajectories is constructed, for which a one-parameter function is taken as a basis, which is "glued" from the elementary function of the sine and tangent to it at some point in the line. To determine the used plasticity resource, a damage summation model with a power approximation of the damage function was adopted. As a result, we have for the first time described the general expression of the linear damage summation model for the case of the parametric deformation path problem. The graphical representation on the constructed model of accumulation of damages in material of a dangerous zone of a flange at landing by a method of SHO is resulted. Based on the constructed model, it is possible to model the accumulation of damage by changing the values of the model parameters for different materials and deformation paths, which, in turn, depend on the relative geometric parameters of the workpiece and its location relative to the rolling roll.

The evolution of Hooke’s law under finite plastic deformations for fiber-reinforced materials

When an elastoplastic material undergoes large plastic deformations, the elastic law and particularly the stiffness tetrad will evolve. This evolution is strongly dependent on the particular material. In the present paper, we consider a fiber-reinforced composite with fibers in different distinct directions. These directions introduce the anisotropy into the material behavior, particularly into the elastic law. Under plastic deformations, these directions are deformed together with the material (in contrast to crystal plasticity). This effect is called material plasticity and gives the basis for our new method. It consists of superimposing transversely isotropic stiffnesses for each fiber direction at any stage of the deformation process. A comparison for different composites and deformation paths shows the range of applicability of this method.

A new ductile failure criterion for micro/meso scale forming limit prediction of metal foils considering size effect and free surface roughening

For the establishment of reliable micro/meso scale forming processes, it is essential to accurately predict the forming limits of metal foils under different deformation paths. However, existing uncoupled ductile failure criteria cannot accurately forecast the micro/meso scale forming limits of metal foils affected by size effect in the whole strain path range of forming limit curve (FLC). To deal with the issue, a new ductile failure criterion is proposed in this paper based on the theoretical analyses of size effect affected void nucleation, growth, and coalescence, as well as free surface roughening affected critical damage of metal foils. A method for identifying the material parameters of the proposed ductile failure criterion coupled with a modified Yld2000 yield criterion is provided, and the size effect on micro/meso scale FLCs forecasted by the proposed ductile failure criterion is discussed. In addition, the forming limit strains of SUS304 and pure copper foils with different thicknesses and grain sizes are employed to reveal the prediction capability of the new ductile failure criterion. Comparisons between the experimental results and the FLCs constructed by the proposed failure criterion demonstrate that the proposed failure criterion can accurately predict the forming limits of metal foils affected by size effect between uniaxial tension (UT) and equi-biaxial tension (EBT). To further show the prediction capability of the proposed failure criterion in actual micro/meso scale forming processes, the limit drawing ratio of a SUS304 foil and local maximum forming heights in micro-channel hydroforming for pure copper foils are predicted using the new failure criterion combined with the finite element method, and the predicted results are compared with experimental results. Comparative research demonstrates that the proposed ductile failure criterion can accurately forecast the forming limits of metal foils affected by size effect in actual micro/meso scale forming processes.

Three-dimensional stress rotation and control mechanism of deep tunneling incorporating generalized Zhang–Zhu strength-based forward analysis

Deep rock tunneling exhibits a significant three-dimensional (3D) space effect. The complex stress path and extrusion deformation during excavation are the most significant and decisive factors in the stability and construction safety of a deep tunnel. 3D and forward numerical analyses based on generalized Zhang–Zhu (GZZ) strength criterion are performed to investigate the principal stress rotation behavior and active control mechanism during deep tunneling. The surrounding rock element experiences significant stress rotations because of the sharply increased shear stress (τry) near the tunnel face. A dimensionless stress index (τry/I1) is proposed to quantitatively evaluate the principal stress rotation during excavation. τry/I1 increases with increasing buried depth, and the deep tunnel presents significant principal stress rotation that reaches a large τry/I1 value. The mechanical behavior of the advanced core rock is primarily affected by the strengthening parameter, geological strength index (GSI). Strengthening of the core rock can greatly improve the stress conditions and mechanical behavior, increase the strength of the rock mass, and reduce the stress rotation. The pre-extrusion deformation of the core rock and pre-convergence of the surrounding rock are discovered to follow a consistency law, which suggests that the pre-convergence deformation and surrounding rock stability near the tunnel face depend on the extrusion deformation of the tunnel face. The GZZ strength-based 3D forward analysis and stress control method proposed in this study can enhance the design and construction of deep and ultra-deep tunnels by weakening the 3D space effect (e.g., tunnel face extrusion and stress rotation) and exerting the strength potential (self-bearing capacity) of a rock mass.

Saturation and periodic self-stress in geometric auxetics

The auxetic structures considered in this paper are three-dimensional periodic bar-and-joint frameworks. We start with the specific purpose of obtaining an auxetic design with underlying periodic graph of low valency. Adapting a general methodology, we produce an initial framework with valency seven and one degree of freedom. Then, we describe a saturation process, whereby edge orbits are added up to valency 16, with no alteration of the deformation path. This is reflected in a large dimension for the space of periodic self-stresses. The saturated version has higher crystallographic symmetry and allows a precise description of the deformation trajectory. Reducing saturation by adequate removal of edge orbits results in vast numbers of distinct auxetic designs which obey the same kinematics.

Schelkunoff Formulation of the Sommerfeld Integral for the Hertzian Dipole Located in the Vicinity of Cylindrical Structures

AbstractA numerical integration of the Sommerfeld integral is performed using the Schelkunoff formulation for cylindrical media. The Schelkunoff kernel for cylindrical media involves higher order modified Bessel functions with azimuthal summation over higher order modes. As such, the convergence characteristics of the cylindrical integral kernel are strongly dependent on complex linear combinations of higher order Bessel/Hankel/modified Bessel functions, compared to the case of the planar media where only a single Bessel/modified Bessel function of zeroth order is present. Two cylindrical configurations are analyzed using the new formulation, viz. a conducting cylinder and a dielectric‐coated conducting cylinder. The branch‐point singularity in the first configuration is removed using the angular transformation for the Sommerfeld/Schelkunoff formulations. A path deformation technique is used for the second configuration to address the problem of poles and branch‐point singularities on the real axis of integration. The in‐depth analysis of the cylindrical kernels and the integrals with variation in the location of the observation point clearly bring out the relative merits of both formulations for the cylindrical configurations, with the TE/TM coupling for the coated cylinder considered.

Possibility of Deformation of Billet with Various Internal Structure in KOBO Extrusion

The potential of KOBO unconventional extrusion of metallic materials based on phenomenon of changing the path of plastic deformation with use of cyclic oscillation of the die by given angle and frequency has been presented in this paper. This process is used to change material properties by fragmentation of grains without preheating the billet and press parts with significantly lower extrusion force in comparison to conventional process. Various types of billets (various metallic materials in the form of: solid initial material, condensed chips, layered composite material) were used during the experimental tests to analyze the plastic flow of the material and the possibility of plastic deformation of various metallic materials such as aluminum alloys, magnesium alloys and copper in order to obtain a product with a complex shape in the KOBO process, using dies with different geometries. Mechanical properties, microstructure, scheme of plastic flow and extrusion force were examined during experimental work. KOBO extrusion can be considered as a more cost-effective process than conventional extrusion.

Impact of Depressurizing Boreholes on Energy Dissipation in Deep Roadway

Depressurizing borehole drilling is an effective approach to control the large deformation of deep roadway. It can transfer the high stress in the proximity of the roadway into the deep stable rock masses. However, it should be noted that the borehole drilling will inevitably cause the secondary damage to roadway. To determine the parameters of depressurizing boreholes, the degree of the secondary damage must be evaluated properly. Given that the rock mass failure is an unstable phenomenon driven by energy, it is of great use to reveal the disturbing impact of depressurizing boreholes on the roadway stability from the angle of energy dissipation. This is much more consistent with the failure nature of rock mass. Hence, an integrated method of laboratory test, numerical simulation, and theoretical analysis was used to study the disturbing effect of depressurizing boreholes on roadway energy dissipation. The equations of elastic energy and dissipated energy of rock cell grid were derived based on the energy principle and finite-difference algorithm, which was implemented into FLAC3D software by the FISH language. The numerical stress-strain and dissipated energy-strain curves of rock samples were verified by experimentally obtained data, and the whole deformation path from roadway excavation to instability was back-analyzed by the dissipated energy evolution. Based upon the energy model, the ratio of borehole diameter D to row spacing R ( D / R ) was selected as the variable to analyze the influence of borehole parameters on the depressurizing effect. The varying D / R leads to three depressurizing states: insufficient depressurization, sufficient depressurization, and overdepressurization. Increasing D / R will make the roadway transfer from insufficient depressurization to sufficient depressurization and finally to overdepressurization. The sufficient depressurizing state could be realized by adjusting the borehole D / R value, which is of great use to the roadway control. The D / R values of 1 : 6 to 1 : 2 were proposed for the test roadway, and D / R = 1 : 6 was applied in the field test, which achieved a well roadway control effect.

Superimposed structures, incremental strain and deformation path from field data to modelling: A case study from the Alpi Apuane metamorphic core complex (NW Tuscany, Italy).

In this study, superimposed folds and antitaxial strain fringes are investigated to unravel the deformation path of the core zones of the Alpi Apuane metamorphic complex (northwest Tuscany Italy). Detailed field mapping combined with microstructural analyses is used together with computer-modelling of a complex strain fringe system to disclose the main steps of the Alpi Apuane syn-metamorphic deformation history. A comparison between natural investigated fibres and those produced by paraffine wax experiments provides details of the relative core-object-fringe rotation allowing new insight on the growth kinematics of strain fringes. The results of our analyses show that our composite fringe system is characterized by a first set of fibres to be related with the main composite axial planar foliation of regional scale isoclinal non-cylindric folds. This first set of fibre fringes records a local non-coaxial strain with an absolute core-object rotation (relative to an external reference frame represented by the main foliation) of 140° and a calculated shear strain (γ) of about 4. The second set of fringes, developed after the tilting of the main foliation and the first fringe-set in a sub-vertical orientation, records a lower absolute rotation of the core-object (25°), a lower shear strain (γ) of about 1.4 and a coaxial strain associated with the vertical shortening. This part of the composite fringe system and the related structures may relate to the switch from the crustal scale contractional regime to the extensional one, which characterized the development of the inner northern Apennines orogen.

Asymmetric multi-stability from relaxing the rigid-folding conditions in a stacked Miura-ori cellular solid

Traditionally, origami has been categorized into two groups according to their kinematics design: rigid and non-rigid origami. However, such categorization can be superficial, and rigid origami can obtain new mechanical properties by intentionally relaxing the rigid-folding kinematics. Based on numerical simulations using the bar-hinge approach and experiments, this study examines the multi-stability of a stacked Miura-origami cellular structure with different levels of facet compliance. The simulation and experiment results show that a unit cell in such cellular solid exhibits only two stable states if it follows the rigid origami kinematics; however, two more stable states are reachable if the origami facets become sufficiently compliant. Moreover, the switch between two certain stable states shows an asymmetric energy barrier, meaning that the unit cell follows fundamentally different deformation paths when it extends from one state to another compared to the opposite compression switch. As a result, the reaction force required for extending this unit cell between these two states can be higher than the compression switch. Such asymmetric multi-stability can be fine-tuned by tailoring the underlying origami design, and it can be extended into cellular solids with carefully placed voids. By showing the benefits of exploiting facet compliance, this study could foster multi-functional structures and material systems that traditional rigid origami cannot create.

Continuous and Discrete Deformation Modes of Mechanical Metamaterials With Ring-Like Unit Cells

Structures with multiple deformation paths provide a promising platform for robotics and reprogrammable mechanical and thermal deformation materials. Reconfigurations with a multi-path can fulfill many tasks (e.g., walking and grasping) and possess multiple properties (e.g., targeted Poisson’s ratio and thermal expansion coefficient). Here, we proposed a new ring-like kirigami structure and theoretically and experimentally found that for a basic unit, there are four discrete deformation patterns and a continuous shearing deformation pattern; thus, there are a large number of discrete deformation patterns for a multi-unit combination with geometrical compatibility coupled with a shearing deformation mode. Moreover, targeted Poisson’s ratios (either + or -) in the x- and y-directions can be realized by inversely designing the geometrical parameters for a certain deformation path. Additionally, we showed the capability of constructing 2D and 3D cellular structures in various patterns with the proposed ring-like units. The multiple deformation modes demonstrated here open up avenues to design new reprogrammable materials and robots across various scales.

Dating Low‐Grade Deformation: Role of Lithology and Strain Partitioning on Ar Isotope Records in the Alpi Apuane of Northern Apennines (Italy)

AbstractThe Alpi Apuane (northern Apennines) represent a key area for understanding the processes related to the Apennines building and geodynamic evolution of the central Mediterranean, but the timing of tectono‐metamorphic events is still debated. White mica from cover rocks of the Massa and Apuane units was investigated by the40Ar‐39Ar in situ and step‐heating techniques. Samples recorded several episodes of deformation developed under low‐grade conditions and resulting in a D1 composite schistosity followed by a variably developed D2 retrograde crenulation. In the Massa Unit, D2 crenulation was accompanied by replacement of muscovite‐phengite by paragonite, whereas the composition of phengite from the Apuane Unit does not vary noticeably, irrespective of whether phengite is aligned along D1 or D2 schistosities. Both units exhibit a significant intrasample scatter of in situ ages and variably discordant age spectra from step‐heating data, due to partial reequilibration of white mica along a deformation path lasting ≥10 Ma, with dates approaching the time of younger events as retrogression becomes more pervasive. The onset of deformation has a minimum age of ∼20 Ma, as documented by40Ar‐39Ar data for the composite D1 foliation in the Massa Unit. D2 deformation shows a common temporal evolution at the scale of the region and is recorded for at least ∼2.5 Ma, starting not after ∼12.5 Ma and ending at ∼10.5 Ma. Results highlight the importance of a detailed microscale characterization and of a careful preselection of samples, as compositionally different domains a few millimeters apart may yield different results because of compositionally driven strain partitioning.

Shear zone fabrics and their significance in curved, inverted basin-derived thrust systems

In this study, we report how criteria inferred from structural and kinematic analysis of shear zone fabrics can be instrumental in deciphering events of positive or negative inversion tectonics. Mesoscopic structural and kinematic analyses are performed on well-exposed brittle-ductile thrust shear zones within curved thrust systems in the Central-Northern Apennines of Italy.The structural and kinematic features of thrust-related tectonites make it possible to outline a history of positive inversion. S/C- and S-tectonites/fabrics are distinctive of frontal or oblique thrust ramps, respectively. In particular, S-fabrics result from selective transpressional-reactivation of pre-thrusting normal faults. By contrast, more complex composite fabrics, characterized by folded cleavage, reveal a history of negative inversion tectonics. Mesocopic cleavage folding is ascribed to shear-sense reversal along the shear surfaces during extensional reactivation of pre-existing thrusts; or to synthetic reactivation by listric foreland-dipping normal faults, merging downwards on former thrust surfaces during protracted episodes of gravitational collapse.Shear zone fabrics identification criteria, here illustrated from thrusts of different size, if systematically used, may be diagnostic of different deformation paths, and hence provide useful tools to elucidate the tectonic history of curved thrust systems in orogens that have experienced multiple episodes of inversion.

Experiments on forming behaviour of the aluminium alloy AA6016

Investigation of the sheet metal formability is an important issue in the design of components. During metal forming different deformation histories occur which may cause various damage and failure mechanisms on the micro-level affecting the quality of products. Therefore, description of the material characteristics by means of a linear limit change curve is not sufficient because the remaining formability and the fracture processes also depend on deformation history. For this purpose the aluminium alloy AA6016 is systematically investigated in order to obtain their forming capability as well as the damage and fracture behaviour after complex deformation paths. Different uniaxial tests with various initially unloaded and preloaded specimens have been performed to identify the effect of the forming history, the loading direction and the stress state on the formability and the mechanical parameters of the investigated material. The results can be used to propose a critical ratio between the pre-strain and the change in loading direction from which on shear failure occurs instead of necking behaviour leading to the loss of formability.

Crystal plasticity algorithm based on the quasi‐extremal energy principle

AbstractThe direct incremental energy minimization in rate‐independent plasticity does not account for the skew‐symmetric part of the tangent stiffness matrix. In crystal plasticity, this corresponds to neglecting the asymmetry of the matrix of interaction moduli for active slip‐systems. This limitation has been overcome in the recently proposed quasi‐extremal energy principle (QEP) applicable to nonpotential problems. In the present article it is shown how to extend QEP to finite increments in the backward‐Euler computational scheme. A related constitutive algorithm is proposed which enables automatic selection of active slip systems using an energetic criterion, along any path of large deformation of a rate‐independent single crystal with a nonsymmetric slip‐system interaction matrix. Numerical examples have been calculated for a fcc single crystal subjected to simple shear or uniaxial tension. The slip system activity predicted by using the QEP algorithm has been found to be more reliable in describing the actual plastic response of metal crystals than conventional rate‐dependent modeling in cases where the selection of active slip‐systems is essential.