A generic rock mass database consisting of nine parameters is compiled from 225 studies. The nine parameters are the deformation modulus, elastic modulus, dynamic modulus, rock quality designation, ...rock mass rating, Q-system, geological strength index of a rock mass, as well as intact-rock Young’s modulus and intact-rock uniaxial compressive strength. This generic database, labeled as ROCKMass/9/5876, consists of 5876 rock mass cases. The goal of this paper is to examine how an existing transformation model such as deformation modulus versus rock mass rating can be made more unbiased and more precise for a specific site by combining sparse site data with ROCKMass/9/5876 in a manner sensitive to site-specific differences. The outcome is a quasi-site-specific transformation model. Four methods are studied to construct a quasi-site-specific transformation model for the deformation modulus of a rock mass: probabilistic multiple regression (current state of practice), hybridization method, hierarchical Bayesian model, and similarity method. The results from two case studies in Turkey show that the hierarchical Bayesian model is the most effective.
This paper presents the finite-element (FE) block shear failure (BSF) deformation-to-fracture analysis. FE analysis reveals the following: BSF begins with bolt – bolt hole contact point compressive ...yielding and not the tensile or shear yielding reported in the literature. BSF does not result from the combination of the gauge tensile plane tensile deformation and the shear plane pure shear deformation alone as reported in the literature and codes. BSF results from compressive deformation of the bolt – bolt hole contact points, tensile deformation of bolt hole portions not in contact with the bolts, gauge tensile plane and edge distance tensile plane deformations in combination with pure shear deformation and a combined shear and tensile bending deformation of the portions of the shear planes near to and remote from the bolt – bolt hole contact points, respectively. This study provides a better understanding of the BSF mechanism, BSF total load-bearing areas, and various resistances to deformation that contribute to the block shear capacity.
Electrically-assisted (EA) deformation has shown promising effects in increasing formability and reducing springback in sheet metal forming. This work experimentally and analytically investigated the ...influence of non-uniform and transient Joule heating on the plastic flow stress of titanium which evolved nonlinearity with time and deformation. Three-stage constitutive analysis was carried out in the present study. First, the pure influence of non-uniform Joule heating was investigated in terms of linear elastic thermal expansion, which then explained the measured drops in stress. Second, the Johnson-Cook model was adopted to interpret a plastic thermal-mechanical behavior of the material loaded at a constant quasi-static deformation rate under the uniaxial tension combined with a single pulse of electric current. Finally, it was revealed that the sudden change in strain rate and rapid heating rate due to an electric current pulse could give rise to the transient occurrence of dynamic strain aging (DSA) in materials. This resulted in an accumulated plastic strain as well as transient high-temperature strain hardening, which estimated the experimentally measured data well. The DSA contribution revealed in this work could help to explain many observations in the past studies in the field of EA deformation.
•The model incorporates the non-uniform Joule heating.•Modeled the response from a single electrical pulse, paved the foundation for future multi-pulse cases.•Dynamic strain aging due to rapid change in strain rate and heating rate in the case of single-pulse case is modeled.•Fine experimental measurement of strain change in the single-pulse case is presented.
Lamellar stack in semicrystalline polymers composed of alternatively arranged lamellar crystal and amorphous layers is one of the typical hard-soft laminated nano-composites. Considering the Poisson ...contraction effects during uniaxial tensile deformation along the normal direction of layers, microbuckling instability of lamellar stacks is first proposed as a new deformation mechanism to trigger the nonlinear mechanical behaviors in semicrystalline polymers. Based on the non-equilibrium process of crystallization and experimental observations, a three-phase structure with lamellar stack (crystal and interlamellar amorphous) and the amorphous matrix is proposed as a deformation unit in semicrystalline polymers. Based on the three-phase model and the proposition of buckling with shear mode, we deduce the theoretical critical strain for the sinusoidal microbuckling through linear stability analysis method. Taking hard-elastic isotactic polypropylene as an example, the theoretically calculated critical strain is in a good agreement with the experimental critical strain at temperatures below α relaxation temperature Tα. These results suggest that elastic microbuckling is indeed a possible mechanism to trigger the nonlinear instability, which is different from current plastic deformation models with crystal destruction around yield in semicrystalline polymers.
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•Microbuckling is first proposed as a possibility to trigger nonlinear instability in semicrystalline polymer.•Linear stability analysis is used to calculate theoretical critical strain for microbuckling.•A perfect agreement between experimental and theoretical critical strain of microbuckling is obtained.
Twin-thickness-controlled plastic deformation mechanisms are well understood for submicron-sized twin-structural polycrystalline metals. However, for twin-structural nanocrystalline metals where both ...the grain size and twin thickness reach the nanometre scale, how these metals accommodate plastic deformation remains unclear. Here, we report an integrated grain size and twin thickness effect on the deformation mode of twin-structural nanocrystalline platinum. Above a ∼10 nm grain size, there is a critical value of twin thickness at which the full dislocation intersecting with the twin plane switches to a deformation mode that results in a partial dislocation parallel to the twin planes. This critical twin thickness value varies from ∼6 to 10 nm and is grain size-dependent. For grain sizes between ∼10 to 6 nm, only partial dislocation parallel to twin planes is observed. When the grain size falls below 6 nm, the plasticity switches to grain boundary-mediated plasticity, in contrast with previous studies, suggesting that the plasticity in twin-structural nanocrystalline metals is governed by partial dislocation activities.
As emerging and revolutionary alloy materials, high entropy alloys (HEAs) have been extensively studied because of their unique composition, microstructures and excellent mechanical properties and ...performances. However, there have been limited studies on the deformation behaviors and mechanisms of HEA single crystals at the micro/nanoscale. Here, we fabricated single-crystalline CoCrFeNi HEA pillars with typical orientations of , and and diameters ranging from 272 nm to 1,253 nm and then conducted in situ uniaxial compression tests on these fabricated micro/nanopillars inside a scanning electron microscope. The in situ compression tests showed pronounced size effects on yield and flow stresses in the -, - and -oriented micro/nanopillars, i.e., both yield and flow stresses follow a scaling law with pillar diameter. The scaling exponents of - and -oriented micro/nanopillars are approximately -0.60, which is close to those of face-centered cubic (FCC) pure metallic micro/nanopillars. However, the -oriented pillars, having a scaling exponent of -0.32∼-0.17, exhibit weaker size effects on yield and flow stresses compared with the - and -oriented micro/nanopillars. Combining observations and analyses using transmission electron microscopy, and large-scale atomistic simulations, we revealed that the nucleation and slip of full dislocations dominate the plastic deformation in the - and -oriented micro/nanopillars, while deformation twinning is a governing mechanism in the -oriented micro/nanopillars. These underlying deformation mechanisms are responsible for the size effects of single-crystalline HEA micro/nanopillars. Large-scale atomistic simulations further reveal that twin nucleation in -oriented pillars is initiated by the slip of pre-existing partial dislocations from an internal source. By considering the free energy change during partial slip, we used a theoretical model to predict the scaling law for the size effects of -oriented micro/nanopillars. The predicted scaling exponent for the size effect of -oriented micro/nanopillars is consistent with our experimental results. Our current study sheds light on the underlying deformation mechanisms in FCC HEA single crystals at the micro/nanoscale, which provides a guide for the design and fabrication of HEAs with high strength and remarkable plasticity.
The book offers a careful introduction to modern non-linear mechanics. The used mathematical tools, such as tensor algebra and analysis are given in detail. The general theory of mechanical behaviour ...is particularized for the broad and important classes of elasticity and plasticity. It is intended to bring the reader close to the fields of today's research activities. A list of notations and an index help the reader to find specific topics. The book is based on three decades of teaching experience in this field.
In the conventional spinning of metal sheets, the deformation mode and wall thickness variation have a critical effect on forming stability, quality, and accuracy. Although it is widely accepted ...there is near-constant wall thickness during conventional spinning, there is actually a certain degree of variation in wall thickness during this process. The nature of this variation has yet to be fully understood, which makes it difficult to precisely control wall thickness during conventional spinning. In this study, we investigated and predicted the deformation mode and wall thickness variation in the conventional spinning of a 1060 aluminium alloy plate. It is found that there are three deformation modes that change sequentially in conventional spinning: shear deformation, compression-shear deformation, and tension-shear deformation. These modes correspond, respectively, to the wall thickness variation of (a) sine-law reduction, (b) a reduction intermediate between sine-law reduction and no reduction, and (c) wall thickening. These dynamic changes in deformation mode and wall thickness variation are caused by a decrease in stress triaxiality in the forming region, which is induced by a decrease in the constraint from the flange region to the forming region. We quantified this constraint by calculating the bending rigidity of the flange region, which represents the resistance to the elastic bending deformation that occurs once the flange loses its stability. Then, we developed a formula with the bending rigidity of the flange region as an independent variable to predict the deformation mode and wall thickness variation that occurs during the conventional spinning of 1060 aluminium alloy. Moreover, we determined the effects of the processing parameters on the deformation, and then used a process-related correction factor to incorporate these effects into the above predictive model. By this model, the effects of processing parameters on the change in the deformation mode during spinning were revealed. The model was also used to modify the traditional flange wrinkling model, in which the wall thickness is assumed to be constant. This modified wrinkling model considers the actual variation in wall thickness, which enabled us to accurately determine the maximum circumferential compressive stress on the flange. Thus, the predictive accuracy and applicability of the modified wrinkling model for characterizing the conventional spinning of 1060 aluminium alloy was far superior to that of the traditional wrinkling model. These results increase the understanding of deformation behavior in conventional spinning, thereby providing important guidance for improved processing design and forming accuracy.
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•Mechanism investigation and modelling of deformation mode and wall thickness variation in conventional spinning were conducted.•Sequential changes of shear, compression-shear and tension-shear deformation modes and the generated different thickness variations are identified.•The changes of deformation mode and thickness variation are induced by the decreasing stress triaxiality in forming region, while the decreasing stress triaxiality is generated by the weakening constraint from flange region.•A model for prediction of deformation mode and thickness variation was developed based on the constraint from flange region.•The thickness variation model was embedded to the traditional wrinkling model to improve the prediction accuracy and application in conventional spinning.
Fractional derivative models, which are expressed by combining standard dashpots, fractional dashpots and elastic springs in series or parallel, are often utilized to account for the behaviors for ...viscoelastic materials. Even with the models extended to finite deformation, the precise definition of objective fractional derivative remains challenging. The proposed fractional derivative model is expressed by the combination of an elastic spring in series with two parallel fractional dashpots. We extend the fractional derivative model to finite deformation through a new approach without defining an objective fractional derivative and assuming the decomposition of the deformation rate into the elastic and inelastic parts. This proposed model can be reduced to the Maxwell model for finite deformation. Such reduction results in a model that stands in between the two existing Maxwell models in which the objective rate of the Cauchy stress is taken as the material corotational rate and the relative corotational rate respectively. The proposed model is applied to the simple shear deformation.
The twinning behavior and kinking behavior of a commercial purity Ti subjected to room temperature dynamic plastic deformation (DPD) has been studied. Three types of deformation twins, {101¯2}, ...{112¯2} and {112¯1}, have been observed. It is found that a considerable fraction of the {112¯1} twin crystals were encompassed by the twin boundary segments in connection with kink band boundaries with much lower misorientation angles. A close investigation on the crystallographic nature of these deformation twins revealed that the {112¯1} twin boundaries have evolved from deformation kink band boundaries through accumulative slip of single basal-〈a〉 dislocations. This mechanism for the formation of twin boundaries is different from the known mechanisms through deformation twinning in metals, for which the twin orientation relationship has been achieved once the twin embryo is nucleated. The mechanism for the formation of kink band, the transformation from kink band boundary to deformation twin boundary and the further evolution of twin boundaries during DPD have been discussed in terms of Schmid factors of various dislocation slip systems.
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