Complex Strain History Research Articles

Influence of lateral variations in décollement strength on the structure of fold-and-thrust belts: Insights from viscous wedge models

Fold-and-thrust belts (FTBs) evolve over a mechanically weak basal décollement that separates the overlying intensely deformed rocks from the underlying less deformed ones. Although deformation structures in FTBs commonly show lateral continuity, a closer inspection reveals distinctive variations in structural style (e.g., fold style) along and across mountain belts. This study uses laboratory-scale viscous models to investigate the influence of lateral décollement strength variations on the spatio-temporal evolution of strain patterns in FTBs. These experiments, simulating crustal-scale deformation, show notable changes in the mode of tectonic wedge growth, including the topographic evolution and ductile strain pattern distribution. For example, the deformation front propagates faster over weakly coupled décollement than the laterally adjacent strongly coupled segment, leading to along-strike variations of the topographic slope and curved outline of the deformation front. Constrictional strain, characteristic of regions of weak coupling, is transient and replaced by flattening strain beyond ∼20 % bulk shortening. The latter prevails in regions over strong décollement, whereas complex strain histories mark the transition zone between weak and strong décollements. Based on our modelling results, we propose that variations in décollement strength may cause the segmentation of deformation processes and the development of transverse faults in FTBs.

Residual Strain Monitoring and Dynamic Characteristics of Hybrid Hollow Square Tube with Metal–FRP–Metal Sandwich Walls

In order to design and fabricate a novel hollow square tube (HST) for ram structure in machine tools, the hybrid HST with sandwich walls based on steel skins and unidirectional carbon fiber-reinforced polymer (CFRP) composite core is proposed. A detailed co-cured fabrication method with embedded fiber Bragg grating (FBG) sensors for residual strains/stresses determination in a hybrid metal–composite structure is presented. Results reveal that the hybrid HST has undergone complex residual strain history, and the strain rate is about 10 times the cooling rate. The tensile strains in the dwell stage transform into compressive strains in the cooling stage due to the mismatch of the coefficients of thermal expansion of the steel plates and the CFRP composite. A comparison of the residual strains in the cooling phase obtained by FBG sensors with those obtained by theoretical calculation is carried out. Furthermore, the dynamic characteristics of the hybrid HST and the steel HST are tested. The results showed that the damping of the hybrid HST is 586% higher than that of the steel HST, while the hybrid HST has a lower first natural frequency (4.6% reduction) and mass (15.9% weight reduction). The influence of co-cure temperature and cooling rate on the size and state of the residual strains is analyzed, which might be helpful to guide the manufacturing of sandwich structures in machine tools. This novel hybrid HST may be used for online health monitoring and safety evaluation to build intelligent machine tools structures.

Coal seam failure during primary/enhanced gas production: How failure develops in fields

Coal failure has been observed in many coal seam reservoirs during gas production, which generated significant impacts to coal permeability and to the efficiency of gas recovery. In this paper we develop a flow-geomechanical-coupled numerical approach and use two genuine field examples to discuss the relevant large-scale coal failure behaviours in fields. One example is with the CBM production in Cedar Hill reservoir, San Juan Basin; and the other one is with the CO2-injected ECBM process in Allison Unit, San Juan Basin. Major observations from the present work include: 1) Laboratory tests and analytical analyses based on uniaxial strain conditions may have considerable deviations in prediction of the coal failure during gas production in fields, because such a condition would not hold there because of non-uniform pressure distributions in the field due to gas production/injection. 2) Field-scale coal strength parameters (e.g., the friction angle) should be remarkably weaker than its counterparts measured with core samples because, if otherwise, the coal failure that has been observed would not occur. 3) In CBM processes, coal failure usually occurs first in the immediate vicinity of a wellbore, and then may expand to the whole field with continuing gas depletion. 4) ECBM processes can have complex strain history including inelastic coal failure due to primary production as well as elastic unloading due to CO2 injection.

Work hardening during alternating load directions of 316L SS

Understanding and modelling the plastic behavior of a material are essential for simulation and design of metal forming processes. Cold pilgering of tubes is a process with very complex strain history with alternating loading direction. This makes evaluation of the work hardening challenging. Cold deformation applied in a single direction predominantly exhibit work hardening, while changes of the loading direction may even cause softening in other directions. The influence of alternating loading directions on work hardening has been experimentally investigated for 316L stainless steel (SS). Cubic specimens were cut out from the preform of the tube. The specimens are subjected to uniaxial compressions in alternating directions along two perpendicular axes. From the results, a cyclic elastic-plastic constitutive model based on a Chaboche-type approach is calibrated and implemented in the commercial finite element code MSC.Marc.

Viscous anisotropy of textured olivine aggregates: 2. Micromechanical model

AbstractThe significant viscous anisotropy that results from crystallographic alignment (texture) of olivine grains in deformed upper mantle rocks strongly influences a large variety of geodynamic processes. Our ability to explore the effects of anisotropic viscosity in simulations of these processes requires a mechanical model that can predict the magnitude of anisotropy and its evolution. Unfortunately, existing models of olivine textural evolution and viscous anisotropy are calibrated for relatively small deformations and simple strain paths, making them less general than desired for many large‐scale geodynamic scenarios. Here we develop a new set of micromechanical models to describe the mechanical behavior and textural evolution of olivine through a large range of strains and complex strain histories. For the mechanical behavior, we explore two extreme scenarios, one in which each grain experiences the same stress tensor (Sachs model) and one in which each grain undergoes a strain rate as close as possible to the macroscopic strain rate (pseudo‐Taylor model). For the textural evolution, we develop a new model in which the director method is used to control the rate of grain rotation and the available slip systems in olivine are used to control the axis of rotation. Only recently has enough laboratory data on the deformation of olivine become available to calibrate these models. We use these new data to conduct inversions for the best parameters to characterize both the mechanical and textural evolution models. These inversions demonstrate that the calibrated pseudo‐Taylor model best reproduces the mechanical observations. Additionally, the pseudo‐Taylor textural evolution model can reasonably reproduce the observed texture strength, shape, and orientation after large and complex deformations. A quantitative comparison between our calibrated models and previously published models reveals that our new models excel in predicting the magnitude of viscous anisotropy and the details of the textural evolution. In addition, we demonstrate that the mechanical and textural evolution models can be coupled and used to reproduce mechanical evolution during large‐strain torsion tests. This set of models therefore provides a new geodynamic tool for incorporating viscous anisotropy into large‐scale numerical simulations.

Cracking energy density calculation of hyperelastic constitutive model and its application in rubber fatigue life estimations

ABSTRACTThe finite deformation of rubber under multiaxial stress will finally result in its fatigue failure. The ability to predict the effects of complex strain histories on fatigue life is a critical need. The cracking energy density (CED) distribution characteristics in the finite deformation and rubber fatigue life estimated by the CED criterion are investigated. Then the influences of the crack orientation angle θ and the principal stretch ratio λ on the relationship between CED and strain energy density (SED) are obtained. Finally, the results are used for predicting the fatigue life of rubber material and are compared to experimental values. The results indicate that the ratios of the predicted lives based on the CED damage parameter and measured lives are within two times scatter factor and that of the predicted lives based on the SED damage parameter and measured lives are greatly influenced by the crack orientation angle θ. The rubber fatigue life has great relationship with the angle of the crack plane normal vector and the first principal stretch direction. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 44195.

Crystal plasticity finite element modeling of crystallographic textures in simple shear extrusion (SSE) process

The main objective of this study is characterization and modeling of crystallographic textures in one of the most recent severe plastic deformation methods named as the simple shear extrusion (SSE) technique. In the crystal plasticity finite element (CPFE) models, three polycrystalline aggregates as the representative volumes at the central region of a sample are subjected to deformation that simulates the real deformation histories experienced by the SSE process. The CPFE models capture not only the complex interactions among the constituent individual crystals of the polycrystal, but also they capture the inherent boundary conditions during SSE processing. The experiments confirm the reliability of the predicted textures which acknowledge the accuracy of the used CPFE models to understand the effect of the complex strain history on the texture evolution in the SSE process.

On the use of model alloys as a way to understand the effects of complex deformation conditions on austenite microstructure evolution during hot metal forming processes

During industrial hot metal forming processes, deformed metal undergoes complex strain history that in most cases is non-linear. This very often leads to improper prediction of microstructure evolution and properties of final metal forming products by the computer models that are used currently as in most cases, they are not strain-path sensitive. In the present work, effect of strain path changes on the austenite microstructure evolution has been studied using a special group of model alloys that were designed for this purpose. These alloys are characterised by similar stacking fault energy and flow behaviour to low carbon steels at elevated temperatures, and most of all, by the fact, that austenite in these alloys is stable all the way down to room temperature, what in turn, allows to study its behaviour directly. In the current works, the results of the study of the effects of complex strain path changes on the kinetics of static recrystallisation, strain-induced precipitation process and development of grain boundaries of deformed austenite are shown. Presented results will be very useful as an input data for the computer simulation of metal forming processes towards their improvement in order to take into account full strain path history during deformation processes at elevated temperatures.

Predicting ballistic impact failure of aluminium 6061-T6 with the rate-independent Bao–Wierzbicki fracture model

The main objective of the paper is to exploit a dedicated material calibration to predict an extreme loading condition: the damage of a helicopter tail rotor transmission shaft due to a small arm ballistic impact. A typical material point in the damage area undergoes to complex stress and strain history, starting from a large compressive stresses through shear deformation during crack extension all the way to the tensile fracture of the remaining ligament. The plasticity and the fracture characterization require to perform material tests covering the wide range of stress state. Therefore, a part of the paper is devoted to the description and analysis of plasticity and fracture test of different type of specimens. This includes test on round smooth and notched specimens under combined torsion/tension-compression, flat dog-bone and a curved tensile specimen cut from the wall of the shaft. The test data have been used to calibrate the phenomenological Modified Mohr-Coulomb model and the empirical Bao–Wierzbicki fracture models. The result of the numerical simulation of the projectile impact was then compared with the experiments on the ballistic impact of 7.62 ball projectile against the helicopter shaft. A very good agreement was found for both damage shape and residual velocity.

Time Dependent Behavior of a Dual Cross-Link Self-Healing Gel: Theory and Experiments

Recent experiments have shown that hydrogels with enhanced toughness can be synthesized by incorporating self-healing physical cross-links in a chemically cross-linked gel network. These gels exhibit rate dependent mechanical behavior, suggesting that improved mechanical properties are closely tied to the breaking and reattaching of temporary cross-links in the gel network. In this work, the connection between rate dependent mechanical behavior and kinetics of breaking and reattachment of temporary cross-links is quantified using a three-dimensional finite strain constitutive model. The parameters of the model are fitted using relaxation and constant strain rate tests in uniaxial tension of a model dual-cross-link gel. The stress versus time curves of more complex strain histories, involving loading followed by unloading at different rates, is successfully and quantitatively predicted by our model. Such modeling strategy combining physically based kinetics and three-dimensional large strain mechanics shows great promise for quantitative modeling of soft biological tissues and synthetic counterparts containing dynamic bonds.

Impact against X65 steel pipes – An experimental investigation

Offshore pipelines subjected to accidental loads, such as impacts from trawl gear or anchors, may experience large global displacements from its initial position and large local strains. The axial forces set up during deformation move the pipeline back towards its initial position, thereby creating a complex local stress and strain history that may lead to fracture in the pipeline. In this study, material and component tests have been carried out on an X65 offshore pipeline material to investigate the behaviour during impact, and to observe if fracture occurs. Pipes were first impacted in a pendulum accelerator at varying velocities before they were pulled straight in a tension machine. Fracture was found in the impacted area of all the pipes. Material tests were carried out to determine the characteristics of the X65 pipeline material. A metallurgical investigation was also conducted, revealing that fracture initiated both inside the pipe wall and on the surface.

The behaviour of an offshore steel pipeline material subjected to bending and stretching

Guidelines have been worked out on how to design sub-sea pipelines in fishing-rich areas subjected to the possible interference by trawl gear or ship anchors. One topic of special interest for the offshore industry is pipelines first subjected to impact from an anchor before being dragged along the seabed. After removal of the load, the pipe will be straightened due to rebound and present axial forces. The material in the deformed impact zone will experience a complex stress and strain history, which subsequently can cause cracking, leading to leakage or full failure. To study these topics, full-scale testing is not straightforward and thus a simplified approach is chosen as a first step in the present study. Motivated by the observed local curvature in impacted pipelines, three-point bending tests of plate strips cut from a typical offshore pipeline have been carried out and the strips subsequently stretched to a straight position. One objective of these tests was to investigate whether cracking in the plate strip could occur after such a loading sequence. Material tests with specimens taken in different directions and at different locations in the actual pipe were carried out to calibrate an appropriate constitutive relation (taking anisotropy and kinematic hardening into account) and a simplified fracture criterion. Numerical simulations of the complete loading sequence were finally carried out and the predicted response was validated against the experimental data.

Viscous collision in channel explains double domes in metamorphic core complexes: REPLY

In hot orogens, gneiss domes are a response to upper crustal stretching and lower crustal flow. Two-dimensional thermal-mechanical modeling shows that localization of extension in the upper crust triggers, in the deep crust, oppositely verging horizontal flows that converge beneath the extended region. Upon viscous collision, both flowing regions rotate upward to form two upright domes of foliation (double domes) separated by a steep median high-strain zone. In such systems, horizontal shortening in the infrastructure develops in an overall extensional setting. Dome material follows a complex depth-dependent strain history, from shearing in the deep crustal channel, to contraction upon viscous collision in the median high-strain zone, to extension upon advection into the shallow crust. This depth-dependent strain history is likely a general feature of dome evolution, and is arguably well preserved in double domes such as the Montagne Noire (France) and Naxos (Greece) gneiss domes.

Viscous collision in channel explains double domes in metamorphic core complexes

In hot orogens, gneiss domes are a response to upper crustal stretching and lower crustal flow. Two-dimensional thermal-mechanical modeling shows that localization of extension in the upper crust triggers, in the deep crust, oppositely verging horizontal flows that converge beneath the extended region. Upon viscous collision, both flowing regions rotate upward to form two upright domes of foliation (double domes) separated by a steep median high-strain zone. In such systems, horizontal shortening in the infrastructure develops in an overall extensional setting. Dome material follows a complex depth-dependent strain history, from shearing in the deep crustal channel, to contraction upon viscous collision in the median high-strain zone, to extension upon advection into the shallow crust. This depth-dependent strain history is likely a general feature of dome evolution, and is arguably well preserved in double domes such as the Montagne Noire (France) and Naxos (Greece) gneiss domes.

Influence of Mechanical Loading on Failure of Aircraft Protective Coatings

The degradation and failure of protective coatings (paints and sealants) is a key element influencing the service life of aircraft. Such degradation is influenced by the response of coatings to environmental factors such as high temperatures and exposure to ultraviolet radiation, as well as chemical factors. However, the effect of loading and load history on coating durability has received little attention, despite clearly being a factor in determining failure sites (such as joints) and the rate of degradation. This paper describes the key characteristics of coatings at aircraft joints, and the nature of the strains experienced by coatings in locations influenced by in-service loads. It is first step in assessing the complex strain history at joint strain concentration locations as part of developing a prognostic capability for the service life of aircraft coatings. The configuration of coating layers at different joints is important and this research has considered a simplification of a butt strap joint from a RAAF military aircraft and a generic lap joint; predictions of critical movements/displacements have been made using finite element analysis; the predictions will be tested later as part of an experimental program associated with a full-scale fatigue test.

The structural environment as a factor affecting coating failure in aircraft joints

For critical aircraft structural features such as mechanically fastened joints, coatings which prevent the ingress of moisture are vital for preventing the onset of corrosion which might require costly rectification or, at worst, threaten structural integrity. While aircraft coatings are usually of relatively high quality, they must provide a long service life in a demanding environment, with thermal cycles, high levels of ultraviolet radiation, and mechanical loading. To date, the effect of load history on coating longevity has received little attention, despite clearly being a factor in promoting coating failure at specific sites (such as joints) and the rate of coating degradation. This paper describes the key characteristics of coatings at aircraft joints and also outlines the factors which influence the complex strain history at joints. The research identifies the important regions in a joint and specifically the strain concentration locations where coatings are likely to fail. These regions include exposed sheet ends, shear interfaces and fastener heads. Finite element modelling and experimental testing of a generic joint configuration, which is representative of many light military and civil aircraft structures, is use to predict the sheet end movements under the maximum load capacity of the joint, and to measure critical displacements which would be experienced by a coating layer at the interfaces. This study is part of a larger program developing a prognostic capability for the durability of surface coatings at critical locations.

Peak wavelength interrogation of fiber Bragg grating sensors during impact events

In this paper, we embed fiber Bragg grating (FBG) sensors in graphite fiber–epoxy wovencomposite laminates to detect evolving damage modes. The peak wavelengths of the FBGsensors are interrogated at 625 and 295 kHz, while the laminates are subjected to11.0 J low-velocity impact events. It is demonstrated that 295 kHz interrogation issufficient for accurately collecting the dynamic response of the sensors. The FBGsensors embedded at the laminate midplanes successfully reconstructed the globallaminate response to impact. The maximum and full width at half-maximum(FWHM) for the relative strain histories demonstrated the same trends as themaximum and FWHM of the contact force histories measured from the impactor.More noise was present in the strain histories obtained from the FBG sensorsthan the contact force histories, as the embedded FBGs were sensitive to localperturbations in the stress state. The FBG sensors embedded below the midplane ofthe laminate were closer to the damage regions and measured complex strainhistories. In one case, this strain history revealed the presence of delamination.

“Granite tectonics” revisited: insights from comparison of K-feldspar shape-fabric, anisotropy of magnetic susceptibility (AMS), and brittle fractures in the Jizera granite, Bohemian Massif

In the Jizera granite of the Krkonose–Jizera Plutonic Complex, northern Bohemian Massif, contrasting patterns of magmatic K-feldspar fabrics and brittle fractures characterize different structural levels of the pluton. The uppermost exposed level at ∼800–1,100 m above sea level is dominated by flat foliation that overprints two steep foliations. In contrast, K-feldspar shape-fabric in an underground tunnel (∼660 m above sea level) shows complex variations in orientation and intensity. Magnetic fabric carried by coaxial contributions of biotite, magnetite, and maghemite is homogeneous along the examined section of the tunnel, and is decoupled from the K-feldspar fabric. The Jizera granite is crosscut by two regional sets of subvertical fractures (∼NE–SW and ∼NW–SE) and by near-surface exfoliation joints. The multiple fabrics are inferred to reflect a complex magmatic strain history at different structural levels of the pluton, bearing little or no relationship to the fracture network. In contrast to the original concept of Hans Cloos (“granite tectonics”), we conclude that no simple genetic relationship exists between fabrics and fractures in plutons. An alternative classification of fractures in plutons thus should avoid relationships to magmatic fabrics and should instead consist of cooling, syntectonic, uplift, and post-uplift fractures.

Plastic Behavior of Polycrystalline Aluminum during Biaxial Compression with Strain Path Change

Biaxial compression tests with an abrupt strain path change have been performed on polycrystalline aluminum to investigate the plastic deformation behavior under complex strain histories. Attentions are paid especially to the rapid change in the normal stresses due to the abrupt strain path change. The influences of the prestrain amplitude and the angular relation of sequential strain paths on the stress changes were also studied. The results showed that the transient increase of the normal stresses related to the latent hardening phenomenon with strain path change as well as the plastic anisotropy increase with the pre-straining amplitude. The transient increase in the stress was also affected by the strain histories in the sequential compression tests with the strain path change. The transient stress increment became large to the maximum then decreases with the angle between the sequential paths.

A comprehensive description for shape memory alloys with a two-phase mixture modelincorporating the conventional theory of plasticity

A comprehensive description for the constitutive behavior of polycrystalline shape memoryalloys (SMAs) is proposed based on a two-phase mixture model incorporating theconventional theory of plasticity. An SMA is composed of austenite and martensite phases,and its constitutive behavior should be the combination of the individual behavior of eachof the two phases. In the interested ranges of stress and temperature, the behavior of theaustenite is assumed to be linearly elastic while that of martensite is assumed tobe elastoplastic. The main features of SMAs, such as shape memory effect andpseudoelasticity, can be successfully replicated with the proposed constitutive model. Theconstitutive behavior of SMA Au–47.5 at.% Cd subjected to uniaxial forward and reverseloading and the pseudoelasticity of Cu–Al–Zn–Mn SMA polycrystal subjected toproportional and nonproportional complex stress or strain histories are simulated andcompared with the experimental results.