This study brings to readers the generalized formulation of three-variable plate theory and an efficient computational approach for analyzing plates. The theory not only has three degree of freedoms ...(DOFs) per node, which complies with three dimensional space of full plate model as classical plate theory (CPT) but also accounts for the effect of shear deformation without any requirement of shear correction factors (SCF). A complete set of strong forms, weak form as well as classical and non-classical boundary conditions (BCs) for linear and geometrically nonlinear analysis are consistently derived in this paper through a variational approach. The strong forms are sixth order differential equations, resulting in the symmetrical fourth order differential weak form. It is known that Isogeometric Analysis (IGA) arguably outweighs classical finite element method in terms of high continuity and high order differentiability. Thanks to its advantage, an IGA framework for the generalized three-variable plate theory is formulated with completely locking-free and only three DOFs per node. The classical BCs are strongly enforced to system equations as usual whilst the non-classical BCs are weakly imposed by a penalty approach. The new plate theory with only three-variable is thereafter used for static linear and nonlinear analysis of isotropic and functionally graded material (FGM) plates to demonstrate its ability. The reliability and accuracy of the present approach are ascertained by comparing the obtained results with other existing ones. Based on a robust formulation devoted in the paper, the proposed approach can be further extended for numerous problems related to the shear deformable effect in the literature.
•We propose a novel theory and isogeometric implementation for linear and nonlinear analysis of isotropic and FG plates.•The new theory has three variables and captures well shear deformable effect.•Strong form of new theory is of sixth order leading to a fourth order differential weak form.•Isogeometric analysis can effectively handle the high order differentiability of the proposed theory.•The numerical results show the reliability and efficiency of the present method.
In the current study, parallel tubular channel angular pressing (PTCAP), as a severe plastic deformation (SPD) method, was applied on a commercial pre extruded Mg-3Al-1Zn (AZ31) alloy tubes at 300 °C ...to achieve a fine-grained (FG) structure. To study the deformation behavior, tensile testing at different temperatures of 25 °C, 350 °C, 400 °C, and 450 °C was done on the samples processed by multi-pass PTCAP. Also, the strain rate sensitivity exponent (m) is measured for the four-pass PTCAP processed tube, at 350 °C, 400 °C and 450 °C and strain rates of 10−2, 10−3 and 10−4 1/s. The average value of m coefficients was ∼0.3. A higher elongation to failure of ∼281% was achieved at a higher temperature of 450 °C and a lower strain rate of 10−4 1/s, due to grain boundary sliding as a dominant deformation mechanism. After the first pass of PTCAP a bimodal microstructure, with large gains surrounded by many small ones, was observed. The grain refinement and homogeneity of the microstructure was enhanced by applying subsequent passes of PTCAP. Vickers microhardness measurements show that by more grain refinement caused by applying for more PTCAP passes, the value of hardness increased. Fractographic SEM images revealed that predominately ductile fracture occurred in all evaluated samples.
•PTCAP was applied on a pre-extruded Mg-3Al-1Zn (AZ31) alloy tubes.•Strain rate sensitivity and hot tensile deformation behavior of were investigated.•A highest elongation to failure of ∼281% was achieved on the processed tubes.•The average value of m coefficients was ∼0.3.•Tensile behavior of PTCAPed tubes is different from ECAPed rods.
Tensile deformation behavior of the equiatomic CoCrFeMnNi high entropy alloy single crystals were studied along three different crystallographic orientations, i.e. 001, 1¯23, 1¯11, in order to reveal ...the orientation dependence of deformation twinning at room temperature. It was shown that initial yield behavior along these orientations is governed by dislocation slip mechanism and the critical resolved shear stresses for slip are independent of crystal orientation. Twinning starts at different strain levels after slip deformation, depending on the tensile testing orientation: in the 1¯11-oriented crystals, twinning starts after 5% strain while in the 1¯23-oriented crystals, it starts after about 25% strain. Deformation twinning was not detected in the 001-oriented crystals under tensile loading. The critical resolved shear stresses for twinning are determined to be τcrtw = 110–140MPa. Onset of deformation twinning in the 1¯11-oriented crystals at low strain levels, together with multiple active dislocation slip systems, leads to a significantly higher strain hardening coefficient and stress for fracture in comparison with the 001-oriented crystals, where the plastic deformation occurs only by multiple slip systems, and the 1¯23-oriented crystals, in which the deformation mainly occurs by single slip and then twinning in one system at later stages of the deformation.
The mechanical behavior and deformation mechanisms of a body-centered cubic (BCC) Ti29Zr24Nb23Hf24 (at%) high entropy alloy (HEA) was investigated in temperatures and strain rates from 700° to ...1100 °C and 10−3 to 10 s−1, respectively. The HEA exhibits a substantial increase in yield stress with increasing strain rate. The strain rate sensitivity (SRS) coefficient is ~3 times that of BCC alloy Nb-1Zr and even ~3.5 times that of pure Nb. This high SRS is attributed to the high Peierls stress of the HEA, which is about twice the Peierls stress of pure Nb. On the other hand, the flow stress exhibits a tendency from strain softening to strain hardening with the increase of strain rate especially at the relatively low temperatures. This behavior is explained by a change in dislocation motion from climbing to multiple slip with the increase of strain rate. Taking the specimen subjected to 800 ºC for example, dislocation walls formed at the early stage of deformation and at low strain rate of 10−3 s−1. In this case there is sufficient time to activate dislocations climb, which results in discontinuous dynamic recrystallization, and strain softening. However, when the strain rate amounts to 1 s−1, thermally activated processes such as dislocation climb are too sluggish. As a consequence, multiple slip systems are activated, and the dislocation interactions lead to the evolution of deformation bands, leading to strain hardening.
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•Strain-rate dependent mechanical behavior of BCC Ti29Zr24Nb23Hf24 RHEA at elevated temperatures is revealed.•The effect of strain rate on the dynamic recrystallization of BCC RHEA is studied.•The effect of strain rate on the dislocation structure evolution of BCC RHEA is investigated.
High-entropy alloys are a class of materials that contain five or more elements in near-equiatomic proportions
. Their unconventional compositions and chemical structures hold promise for achieving ...unprecedented combinations of mechanical properties
. Rational design of such alloys hinges on an understanding of the composition-structure-property relationships in a near-infinite compositional space
. Here we use atomic-resolution chemical mapping to reveal the element distribution of the widely studied face-centred cubic CrMnFeCoNi Cantor alloy
and of a new face-centred cubic alloy, CrFeCoNiPd. In the Cantor alloy, the distribution of the five constituent elements is relatively random and uniform. By contrast, in the CrFeCoNiPd alloy, in which the palladium atoms have a markedly different atomic size and electronegativity from the other elements, the homogeneity decreases considerably; all five elements tend to show greater aggregation, with a wavelength of incipient concentration waves
as small as 1 to 3 nanometres. The resulting nanoscale alternating tensile and compressive strain fields lead to considerable resistance to dislocation glide. In situ transmission electron microscopy during straining experiments reveals massive dislocation cross-slip from the early stage of plastic deformation, resulting in strong dislocation interactions between multiple slip systems. These deformation mechanisms in the CrFeCoNiPd alloy, which differ markedly from those in the Cantor alloy and other face-centred cubic high-entropy alloys, are promoted by pronounced fluctuations in composition and an increase in stacking-fault energy, leading to higher yield strength without compromising strain hardening and tensile ductility. Mapping atomic-scale element distributions opens opportunities for understanding chemical structures and thus providing a basis for tuning composition and atomic configurations to obtain outstanding mechanical properties.
A single FCC phase 40Fe–25Ni–15Cr–10Co–10V high-entropy alloy was designed, fabricated, and evaluated for potential cryogenic applications. The alloy forms a single FCC phase and exhibits higher ...yield strength, tensile strength, and elongation at cryogenic temperature (77 K) than at room temperature (298 K). The superior tensile properties at cryogenic temperature are discussed based on the formation of deformation twins during the tensile test at cryogenic temperature. In addition, a constitutive model reflecting the cryogenic deformation mechanism (i.e., twinning-induced plasticity) was implemented into the finite element method to analyze this behavior. Experimental results and the finite element analysis suggest that the increase in plastic deformation capacity at cryogenic temperature contributes to the formation of deformation twins.
•We successfully prepared a Cu55.4Zr35.2Al7.5Y1.9 bi-continuous nanoporous metallic glass with ligaments size of ∼20 nm. The mechanical properties and plastic deformation of nanoporous and solid ...metallic glasses have been studied using depth-sensing nanoindentation combined with electron microscopy characterization.•The nanoporous metallic glass has distinct mechanical properties and deformation behavior comparing to solid glass. It fails in transverse fracture under tension but becomes ductile under compression without any noticeable shear banding events. Irreversible plastic deformation has taken place well before the global yield point from partial unload compression.•We discovered a transition of deformation modes at a critical strain near 0.03. The global yielding in this nanoporous metallic glass obeys a universal scaling law of yielding in metallic glasses. The results provide intrinsic relations between classic Gibson-Ashby law and the universal scaling law in metallic glasses.•This nanoporous metallic glass has the highest yield stress comparing to crystalline nanoporous materials and it maintains a high strain hardening index under compression.
The mechanical properties and plastic deformation of a Cu55.4Zr35.2Al7.5Y1.9 nanoporous metallic glass (MG) have been studied using depth-sensing nanoindentation combined with electron microscopy characterization. The nanoporous MG exhibits an initial relative density of 50.9% and a bicontinuous structure with 20.84 ± 1.49 nm-diameter interconnecting ligaments. It is brittle in tension, whereas it has significant homogeneous plasticity under compression. It has a hardness of 0.67 ± 0.06 GPa and Young's modulus of 14.72 ± 0.74 GPa from nanoindentation. While under tensile and compression, it has a yield strength of 0.22 to 0.23 GPa and an effective modulus of 10.37 ± 0.99 GPa. The discrepancy between the moduli is caused by irreversible shear transformation zone (STZ) plasticity that takes place well ahead of the yield point. The deformation in the nanoporous MG begins with both elastic and plastic bending in ligaments and transfers to plastic uniaxial deformation in ligaments at a critical strain near 0.03, at which a significant change in stiffness is observed. The yielding stress follows the universal scaling law predicted by the critical-like behavior in glassy systems. The strength to modulus ratio is well maintained in this nanoporous MG and is higher than the porous crystalline alloys. Our experimental study clarifies the fundamental failure mechanism and deformation behavior in nanoporous MGs.
The effect of cold plastic deformation by multi-directional forging prior to artificial aging treatment on the microstructure and mechanical properties of WE43 alloy was investigated. The results ...show that the pre-deformation produced high density of dislocations and deformation twins. After peak-aging treatment at 200°C, the pre-deformation reduced the average size of fine β″ and β′ precipitates and promoted the formation of β1 phase. Additionally, spheroid–shaped precipitates formed at twin boundaries and the deformation twins were thermally stable during the aging treatment. Mechanical properties reveal that the tensile yield and ultimate strength is significantly enhanced from 191±3MPa to 270±15MPa and 278±5MPa to 320±18MPa, respectively.
A size-dependent sinusoidal shear deformation beam model is developed to investigate the free vibration of nanobeams based on the nonlocal strain gradient theory. The new model contains a nonlocal ...parameter and a material length scale parameter which can capture the size effect. The governing equations and boundary conditions are derived by employing Hamilton's principle. Navier's method is utilized to obtain analytical solutions for natural frequencies of simply supported nanobeams. The results are compared with other beam models and other classical and non-classical theories. Several numerical examples are presented to illustrate the effects of nonlocal parameter, material length scale parameter, slenderness ratio and shear deformation on the free vibration of nanobeams. It is found that natural frequencies predicted by the nonlocal strain gradient theory are higher than those predicted by nonlocal theory and lower than those obtained by strain gradient theory. When the length scale parameter is smaller than the nonlocal parameter, the nanobeam exerts a stiffness-softening effect. When the length scale parameter is larger than the nonlocal parameter, the nanobeam exerts a stiffness-hardening effect. Moreover, it is observed that the effect of shear deformation becomes more significant for nanobeams with lower values of slenderness ratios and for higher modes.
Northeast Japan is a typical island arc related to the Pacific plate subduction. The 2011 M
w
9.0 Tohoku-oki earthquake provided a unique opportunity to analyze crustal deformation with different ...boundary conditions, similar to a gigantic rock deformation experiment. We review findings obtained through various observations and data analyses in Northeast Japan, focusing on the crustal deformation in different timescales. The occurrence of the M9 earthquake solved the ongoing paradox that the geodetic strain rate is an order of magnitude larger than the geologic estimate, showing that the centennial geodetic observation had mainly captured the elastic strain accumulation. Along the localized contraction zone along the Japan Sea coast, a comparison of postseismic and interseismic deformation patterns revealed a significant contribution of inelastic deformation, which plays an essential role in long-term deformation. Along the Pacific coast, rapid interseismic subsidence and unexpected coseismic subsidence were followed by a rapid postseismic uplift, indicating that viscous relaxation in the mantle is of essential importance. These findings advance our understanding of plate interactions and the tectonic evolution of the island arc.
The 2011 Tohoku-oki earthquake provided the most complete crustal deformation data set ever for interseismic, coseismic, and postseismic periods.
The discrepancy between the geologic and geodetic deformation rates in Northeast Japan is attributed to an elastic strain due to interplate locking.
A significant contribution of inelastic deformation in the island arc crust is identified through a comparison of interseismic and postseismic deformations.
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