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Molecular dynamics simulations are used to investigate the mechanical behavior of Cu nanowires (NWs) with planar defects such as grain boundaries (GBs), twin boundaries (TBs), stacking faults (SFs), etc. To investigate how the planar defects affect the deformation and fracture mechanisms of naowires, three types of nanowires are considered in this paper: (1) polycrystalline Cu nanowire; (2) single-crystalline Cu nanowire with twin boundaries; and (3) single-crystalline Cu nanowire with stacking faults. Because of the large fraction of atoms at grain boundaries, the energy of grain boundaries is higher than that of the grains. Thus, grain boundaries are proved to be the preferred sites for dislocations to nucleate. Moreover, necking and fracture prefer to occur at the grain boundary interface owing to the weakness of grain boundaries. For Cu nanowires in the presence of twin boundaries, it is found that twin boundaries can strength nanowires due to the restriction of the movement of dislocations. The pile up of dislocations on twin boundaries makes them rough, inducing high energy in twin boundaries. Hence, twin boundaries can emit dislocations, and necking initiates at twin boundaries. In the case of Cu nanowires with stacking faults, all pre-existing stacking faults in the nanowires are observed to disappear during deformation, giving rise to a fracture process resembling the samples without stacking fault. [ABSTRACT FROM AUTHOR]

While tissue engineering holds significant potential to address current limitations in reconstructive surgery of the head and neck, few constructs have made their way into routine clinical use. In this review, we aim to appraise the state of head and neck tissue engineering over the past five years, with a specific focus on otologic, nasal, craniofacial bone, and laryngotracheal applications. A comprehensive scoping search of the PubMed database was performed and over 2000 article hits were returned with 290 articles included in the final review. These publications have addressed the hallmark characteristics of tissue engineering (cellular source, scaffold, and growth signaling) for head and neck anatomical sites. While there have been promising reports of effective tissue engineered interventions in small groups of human patients, the majority of research remains constrained to in vitro and in vivo studies aimed at furthering the understanding of the biological processes involved in tissue engineering. Further, differences in functional and cosmetic properties of the ear, nose, airway, and craniofacial bone affect the emphasis of investigation at each site. While otolaryngologists currently play a role in tissue engineering translational research, continued multidisciplinary efforts will likely be required to push the state of translation towards tissue‐engineered constructs available for routine clinical use. Level of Evidence: NA. [ABSTRACT FROM AUTHOR]

With few exceptions, intermediate-depth seismicity is associated with active subduction. In the Alboran slab, which is located just east of the Gibraltar Strait in the westernmost Mediterranean, although evidence suggests subduction is no longer active, tens to hundreds of M < 5.0 earthquakes are observed every year at depths of ~80 km. In this paper, we relocated 58 such events recorded by the PICASSO temporary network using a 3-D velocity model and implementing a grid-search approach to minimize the normalized misfit between observed and predicted P and S wave arrival times. Meanwhile, we relocated 908 events recorded by the Spanish national network using the double-difference method and gave a high-precision picture of seismicity distribution within the slab. Relocation results reveal five clusters in this region separated by small gaps. Jointly considering relocation results and a 3-D tomography model indicates one cluster is at a shallower depth above the northern, E-Woriented arm of the Alboran slab, while the other four are aligned from north to south, parallel to the strike of the slab and near its core. Larger events are generally shallower and more scattered, while the deeper, more clustered events tend to have smaller magnitudes. Clusters further to the north show concentrated seismicity on narrow zones that dip ~45° to the south. We suggest this seismicity is associated with active necking and break-off of the Alboran slab, which is progressing from north to south. Shear instability is likely to be the failure-enabling mechanism for the occurrence of these earthquakes. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract This paper aims to estimate and analyze both the necking and fracture based path-independent forming limit criteria during two-stage forming of anisotropic sheet materials. In this context, in-house experimental setups were fabricated to impart pre-strain along three distinct strain paths viz. equi-biaxial, plane strain and uniaxial in different automotive grade sheet materials namely EDD, AA5052 and DP600. Uniaxial tensile and stack compression tests were conducted, and the test results were used to evaluate the eight anisotropic coefficients of Yld2000-2d yield model. The predicted evolutions of the yield loci and both the strength and plastic strain ratio (r -value) directionalities of the pre-strained materials were calibrated with experimental data. In the second stage of deformation, all pre-strained sheet materials were stretch formed up to the onset of necking and further until the initiation of fracture. Correspondingly, the forming limit diagram (ε -FLD) and fracture forming limit diagram (ε -FFLD) were experimentally evaluated. The necking and fracture limit of as-received materials was theoretically predicted incorporating calibrated Yld2000-2d yield model in the geometrical imperfection based Marciniak-Kuczynski (MK) model and ductile fracture based Bao-Wierzbicki (BW) damage model, respectively. It is noteworthy that the dynamic shifting of pre-strained ε -FLDs and ε -FFLDs has been recorded in principal strain space (ε 1 , ε 2) depending on the type and amount of pre-strain. Hence, the polar effective plastic strain (PEPS) based necking (PEPS-FLD) and fracture (PEPS-FFLD) limits were estimated using Yld2000-2d anisotropy plasticity theory, and it was observed that the shift of the limiting strains was restricted successfully. It was found that the maximum absolute error during necking and fracture dome height prediction of pre-strained materials was restricted up to 5% and 6%, respectively, when PEPS based failure limits were used as damage model in FE simulation. [ABSTRACT FROM AUTHOR]

Highlights • High-purity α -titanium flat tensile specimens subjected to dynamic loading. • Effect of plastic orthotropy and tension-compression asymmmetry on necking instabilities. • Specimen orientation plays a key role in the location and characteristics of the necks. • For three specimen orientations the necks contain two identical localization bands. • For other orientations, the bands have different inclinations, and grow at different speeds. Abstract In this paper we study, using finite element simulations, the combined effect of plastic orthotropy and tension-compression asymmmetry on the formation of necking instabilities in high-purity α -titanium flat tensile specimens subjected to dynamic loading under a wide range of impact velocities. To this end, the material behaviour is described using the constitutive model developed by Nixon et al. (2010a), which accounts for these specific features of the plastic response of hexagonal-close-packed materials. While numerical studies have shown the effect of material properties and loading conditions on the formation and development of necking instabilities in dynamically loaded tensile specimens, none of them, to the best of our knowledge, has considered the plastic orthotropy and tension-compression asymmmetry of the material. The finite element simulations show that the orientation of the specimen with respect to the in-plane symmetry axes of the material plays a key role in the location and characteristics of the neck(s) formed in the sample. Moreover, the results indicate that only for three specimen orientations the main neck formed in the sample contains two localization bands, equally inclined with respect to the specimen axis, which grow at equal speed. For all other orientations, the localization bands have different inclinations, and one grows faster than the other one. [ABSTRACT FROM AUTHOR]

Highlights • A one-dimensional nonlocal model is proposed to address the necking problem. • Spectral analysis of the model is presented to examine mathematical regularization. • The tangent operator is derived for the proposed nonlocal formulation. • The proposed model effectively characterizes the post-necking behavior. Abstract In modeling necking in steel bars subjected to uniaxial tension using a classical one-dimensional elastoplastic continuum, numerical results exhibit strong mesh dependency without convergence upon mesh refinement. The strain localization and softening with respect to necking in structural steels is induced by hybrid material and geometric nonlinearities rather than material damage. A one-dimensional nonlocal model is proposed to address these numerical difficulties and to provide an enhanced numerical representation of necking-induced localization in structural steels for the potential implementation in fiber-based formulations. By introducing a characteristic length and a nonlocal parameter to the standard constitutive model, the enhanced nonlocal continuum provides a well-posed governing equation for the necking problem. The finite element calculations based on this one-dimensional nonlocal model give rise to objective solutions, i.e., numerical results converge under mesh refinement. In addition, the size of the necking region also exhibits mesh-independence. The characteristic length and nonlocal parameter significantly influence the post-necking response and the dimension of the necked region. Comparison of the local and global response of necking between one-dimensional analysis and 3D simulations demonstrates that the proposed model is capable of accurately characterizing the post-necking behavior. Relationships between characteristic length for the nonlocal model and the diameter of a cylindrical bar are examined. The novel contributions of the paper are: (1) providing a transparent link between the nonlocal formulation and the physics of the necking phenomenon, and (2) providing a mathematical basis for the necessity of the "over-nonlocal" formulation. [ABSTRACT FROM AUTHOR]

Abstract Volcanic seismicity during silicic spine eruptions often involves recurrent excitation of similar sources at stationary depth just beneath the crater. The mechanics of volcanic spine extrusion may be compared to those of high-temperature, industrial metal working. We thus use slip-line field theory to assess stress, strain and faulting in ascending magma, which, although hot, behaves as a solid. Earthquake fault-plane solutions during the 09/2004–08/2005 eruptions of Mount St. Helens are generally consistent with shrinking of magma rising across a conduit "bottle-neck". Among 215 fault plane solutions, thrust and vertical fault planes prevail, with fewer normal or strike-slip faults. Constriction across the neck and vertical shear along the conduit walls thus predominate. Dynamic Discrete Element Modeling reproduces repetitive nucleation and growth of thrust faults within such a neck. The pressure drop across the neck's core (secondary tension) boosts crack opening and hence gas extraction. Such natural "fracking" could promote full magma degassing, contributing to the typically low explosivity of silicic spine extrusion. Highlights • Stationary thrusting beneath extruded Mount St. Helens' spines. • Accounting magma constriction across a conduit bottle-neck. • Magma degassing related to necking and fracking process. [ABSTRACT FROM AUTHOR]

Highlights • Dynamic weakening produces a necking instability and detachment of a subducted slab. • The characteristic timescale is governed by the damage law and rheology. • Slab decoupling may provide an explanation of abrupt tectonic events. • A new method solves the evolution and advection of grainsize using tracer particles. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a non-destructive method for detecting necking defects in bored piles using electromagnetic waves. Small-scale laboratory experiments are conducted with a defective model pile with diameter of 0.6 m and length of 1.0 m. Four artificial necking defects are introduced on three different sides of the model pile. One necking defect is introduced at the upper position on one side of the model pile, another one is introduced at the lower position on other side of the model pile, and the other two are introduced at both the upper and lower positions on the same side of the model pile. Electrical wires are installed alongside the main rebars of a reinforcement cage to configure a two-conductor transmission line. Electromagnetic waves are generated and detected using a time domain reflectometer. The experimental results indicate clear detection of the reflected electromagnetic waves at the necking defects and pile end. In addition, the calculated defect locations are similar to the actual locations. This study demonstrates that electromagnetic waves can be effective in detecting necking defects at various positions in bored piles. [ABSTRACT FROM AUTHOR]

Highlights • Considère criterion has been revisited using Estrin–Mecking approach for tempered martensitic steels. • For 9% Cr steels, the interrelationship between true uniform plastic strain and dynamic recovery parameter has been established. • Strong influence of dynamic recovery restricts the work hardening ability in tempered martensitic steels. Abstract Considère criterion accounting for necking instability has been examined in terms of dislocation density based approach for tempered martensitic 9% Cr steels. The critical dislocation density as well as the critical strain at which instability sets-in has been predicted from the dislocation dynamics approach. The parameters associated with the approach such as mean free path of dislocations and dynamic recovery have been the key for developing microstructural based necking instability criterion. The interrelationship between true uniform plastic strain and dynamic recovery parameter has been established from the present formulation for tempered martensitic 9% Cr steels. The increase in dynamic recovery with decreasing mean free path and increasing temperature strongly influences the work hardening ability of tempered martensitic 9% Cr steels. [ABSTRACT FROM AUTHOR]

Highlights • Τhree areas of research in nonlinear science are considered that G. Maugin defined in collaboration with the third author. • Necking in cold drawing, spinodal decomposition in diffusive phase transformations and energy transfer in neuronal microtubules. • In all three the common ingredient is the introduction of higher order gradients of deformation in a variational formalism. Abstract This is a modest contribution in memory of Gérard Maugin-a contemporary French scholar of Paris who inspired many young scientists in Greece and maintained special ties with Aristotle University and Thessaloniki. It introduces three particular areas of research in nonlinear science that he defined in collaboration with the third author and presents preliminary one-dimensional results mainly due to previous work of the first author. These pertain to the phenomena of necking in cold drawing, spinodal decomposition in diffusive phase transformations and energy transfer in neuronal microtubules. The common ingredient in all three is the introduction of higher order gradients of deformation in a variational formalism, in order to describe solitary waves and pattern formation that emerge from uniform states when the system enters its nonconvex free energy regime. [ABSTRACT FROM AUTHOR]

Highlights • Circular and oval hole expansion of high strength steel sheets (HSS) were examined. • An anisotropic hardening (AH) model was constructed for large strain range. • Strain localization was strongly influenced by the anisotropy evolution of HSSs. • The AH model well described the HSSs’ anisotropy evolution. • The AH model successfully simulated the strain localization and necking. Abstract The circular and oval hole expansion behaviors of JSH440W and JSH590R high-strength steel sheets were investigated based on experiments and finite element (FE) simulations using three types of anisotropic yield functions: Hill48- r , Yld2000-2d, and 6-poly models. The effects of anisotropy evolution were specifically examined by performing FE simulation using the 6-poly anisotropic hardening (AH) model. Sheet-direction dependent workhardening characteristics were determined by using an in-plane stretch-bending technique. From this work, it was found that hole expansion behavior was strongly affected by anisotropy and its evolution. Thus, it is concluded that the use of AH model is essential for the accurate simulation of hole expansion processes. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper deals with the implementation of thermomechanically coupled gradient-enhanced elastoplasticity at finite strains. The presented algorithmic formulation heavily relies on the variational structure of the considered initial boundary value problem. Consequently, such a variational structure is elaborated. While variational formulations are well-known in the case of isothermal plasticity theory, thermomechanically coupled gradient-enhanced plasticity theory has not been considered before. The resulting time-continuous variational principle allows the computation of all unknown variables jointly and naturally from the stationarity condition of an incremental potential. By discretization of this time-continuous potential in time, a discrete approximation is obtained which represents the foundation of the algorithmic formulation. As a matter of fact, stationarity of the respective potential again defines all unknown variables — now in a time-discrete fashion. Within this paper, the necessary condition associated with stationarity – a vanishing first gradient – is solved numerically by means of Newton’s method. Hence, the first as well as the second derivatives of the incremental potential are required. They are computed by numerical differentiation based on hyper-dual numbers. By considering a perturbation with respect to hyper-dual numbers, the first as well as the second derivatives are computed in an exact manner without introducing any numerical errors. Although numerical differentiation based on hyper-dual numbers is numerically more extensive than real-valued perturbations, it is shown that the scalability of the resulting parallel finite element implementation is not dominated by this effect for sufficiently large problems. [ABSTRACT FROM AUTHOR]

In this study, strain hardening and strain rate sensitivity behavior of commercial DP1000 dual phase steel have been examined in detail at temperatures of 25 °C, 100 °C, 200 °C and 300 °C, at strain rates of 0.0016 s−1 and 0.16 s−1. As the strain rate has increased, the yield strength has increased but no significant change in tensile strength and strain hardening coefficient has been observed. As the temperature has increased, the yield and tensile strength has decreased in between 25 and 200 °C but it has showed an increase at 300 °C. The strain hardening coefficient has increased in parallel with temperature increase. It has been seen that the strain rate sensitivity has not been affected by temperature. No significant difference in the hardening rate has appeared in between 25 and 200 °C, but the highest value has been calculated at 300 °C. It has been determined that the fracture behavior has occurred earlier and load carrying capacity on necking has reduced with the increase of strain rate and not significantly affected by temperature. [ABSTRACT FROM AUTHOR]

This study investigates the influence of physical aging on the tensile deformation behaviors of poly(ethylene terephthalate)-glycol. The polymers are subjected to a quenched and an annealed heat treatment, followed by deformation in tension. The digital image correlation (DIC) is used to capture the surface strain. The DIC results show that the deformation localization occurs in the post-yield strain softening region. The quenched and annealed polymers exhibit different localization types, representing as necking for quenched polymers and shear banding for annealed polymers. With the help of the DIC, the nucleation and propagation of the localization zones are fully captured. The DIC results show that the reference location with the maximum strain does not change with the deformation. At the same strain level, the maximum strain in the shear bands is much larger than that in the necks, which explains the failure strain of the annealed polymers is smaller than the quenched polymers. The stretch rate also has a strong effect on the localization behaviors. A larger stretch rate results in a stronger localization due to an increase in the amount of strain softening. [ABSTRACT FROM AUTHOR]

This paper proposes a metal transfer model describing the dynamic growth and detachment process of the molten drop at the electrode tip in gas metal arc welding under an Ar-rich shielding gas. The proposed model simulates the metal transfer including the growth of the molten drop as well as the formation and break-up of the liquid bridge between the electrode tip and the molten drop based on the forces exerted on the molten and the second order displacement equation. The tapering effect occurring at the side of the electrode tip is considered to enhance the prediction performance in the high-current region above the transition current. Simulation results are compared with experimental results reported in the available literatures and they show good agreement from the low to high current region. [ABSTRACT FROM AUTHOR]

A novel sheet metal forming process, by manufacturing parts in a single sheet with varying thickness, has been employed in this work. It combines hot forming and cold-die quenching, also known as HFQ®, and the use of aluminium tailor welded blanks (TWBs) into a hybrid process. A series of hot stamping tests on the AA6082 TWBs were performed to investigate the deformation behaviour and failure features. Two failure modes, i.e. circumferential necking and parallel weld necking have been observed in the formed parts depending on the forming speed and thickness ratio of the TWBs. An advanced forming limit prediction model has been developed and further integrated into finite element simulation via a cloud-based multi-objective platform 1 1 All the models presented in this paper are available as open access numerical modules at www.smartforming.com, an online knowledge-based cloud platform. to investigate the failure/necking features of AA6082 TWBs. The model incorporates the theories of Hosford yield function, the anisotropic nature of plastic deformation in sheet metals and the Marciniak-Kaczynski (M-K) theory. According to the theories, the incremental work per unit volume ratio ( d ε ¯ B ∙ σ ¯ B / d ε ¯ A ∙ σ ¯ A ) between Zone B (thickness imperfect zone) and Zone A (the remainder of the material) is a key parameter determining the formability, by which the complex failure features have been fundamentally studied. The transition of failure mode in a TWB was attributed to the joint effects of temperature, strain rate and loading path changes. Strain rate could accelerate the development of localised necking in the TWBs when the failure mode was in transition from the circumferential mode to parallel mode. [ABSTRACT FROM AUTHOR]

In this paper we assess, using finite element calculations performed with ABAQUS/Explicit, the influence of porosity in the development of necking instabilities in flat metallic samples subjected to dynamic tension. The mechanical behaviour of the material is described with the Gurson–Tvergaard–Needleman [6, 22, 23] constitutive model pre-implemented in the finite element code. The novelty of our methodology is that we have included in the gauge of the specimen various non-uniform distributions of initial porosity which, in all cases, keep constant the average porosity in the whole sample. This has been carried out assigning random values of initial porosity (within specified bounds) to some nodes and zero to the others. Therefore, the larger the percentage of nodes with non-zero initial porosity, the smaller their initial value of porosity. The goal is to provide an idealized modelling of the distributions of void nucleating particles which in many structural metals nucleate early in the deformation process and lead to material porosity. The key point of this paper is that, following this methodology, we reproduce the experimentally-observed asymmetric-growth of the pair of necking bands which define the localization process in flat tensile samples subjected to dynamic loading [25]. [ABSTRACT FROM AUTHOR]

In this paper, the conditions for the occurrence of diffuse and localized necking in thin sheet metals are investigated. The prediction of these necking phenomena is undertaken using an elastic–plastic model coupled with ductile damage, which is then combined with various plastic instability criteria based on bifurcation theory. The bifurcation criteria are first formulated within a general three-dimensional modeling framework, and then specialized to the particular case of plane-stress conditions. Some theoretical relationships or links between the different investigated bifurcation criteria are established, which allows a hierarchical classification in terms of their conservative character in predicting critical necking strains. The resulting numerical tool is implemented into the finite element code ABAQUS/Standard to predict forming limit diagrams, in both situations of a fully three-dimensional formulation and a plane-stress framework. The proposed approach is then applied to the prediction of diffuse and localized necking for a DC06 mild steel material. The predicted forming limit diagrams confirm the above-established theoretical classification, revealing that the general bifurcation criterion provides a lower bound for diffuse necking prediction, while the loss of ellipticity criterion represents an upper bound for localized necking prediction. Some numerical aspects related to the prestrain effect on the development of necking are also investigated, which demonstrates the capability of the present approach in capturing the strain-path changes commonly encountered in complex sheet metal forming operations. [ABSTRACT FROM AUTHOR]

The effect of the arrangement of two artificial voids on void growth and coalescence mechanisms is studied in flat specimens made of nodular graphite cast iron via in situ 3D laminography imaging and digital volume correlation for bulk displacement measurement. Two configurations of machined holes are studied (i) 90° with respect to the loading direction to mimic internal necking, and (ii) 45° to attempt to trigger a void sheeting mechanism between the artificial voids. The machined holes play the role of primary voids, the graphite nodules that of secondary voids. At a lower scale there is a smaller third population of voids. The 45° void orientation successfully causes a shear band between the primary voids. However, the growth and coalescence mechanisms of voids from graphite nodules are similar for the two configurations. Internal necking is found for nodules that are close to each other and void sheeting for large ferrite ligaments between nodules. Strain fields in the region between machined holes show necking for both cases as well as volume increase, i.e., positive trace of the strain tensor, confirmed by image analysis. The strain to failure in this inter-void region is evaluated in the bulk and also locally, between nodules and for different coalescence configurations. Similar levels are observed in both cases. [ABSTRACT FROM AUTHOR]

The casing serving in the marine gas reservoir is often squeezed by the collapse pressure from salt rock creeps. The combined action of acid corrosion media and high temperature result in necking deformation and even fracture. However, it is difficult the traditional design method of casing safety factor to deal with the randomness of the structural and load factors. The designed strength is either too high or too low. To face the challenges, the reliability evaluation method for the casing collapsing strength in marine gas reservoirs is developed based on the standard of collapsing strength and the load-strength interference model. The distribution of casing collapsing strength is firstly simulated by Monte Carlo sampling. The reliability calculation model of casing under different working conditions is obtained. Then, the quantitative relationship between the target reliability and the safety factor is explored by backward derivation. Four kinds of casing used in marine gas reservoir are evaluated. The result shows that the collapsing strength obeys a Gaussian distribution. The bigger the variation coefficient of casing parameters, the more dispersed the strength distribution. Based on the failure probability, the target reliability can be set and the safety factor can be calculated. The collapse pressure from creep is a key factor to control reliability. With the change of layer groups, the load distribution curve is gradually close to the intensity distribution curve until the interference failure occurs. The reliabilities of casings in some layer groups are < 50%. The corrosion defects and temperature are important factors to casing strength. The reliability and the life expectancy are greatly reduced with time, which leads to premature failure of some casings. [ABSTRACT FROM AUTHOR]

In this paper, an analytical path-dependent instability model is proposed for the thin substrate composite plates, considering the nonlinear reinforced layer effects. The model is introduced by extending a modified maximum force criterion (MMFC) and the vertex criteria to predict diffuse and localized necking, respectively, for the thin substratesupported plates. The MMFC considers the strain hardening on the diffuse necking as well as the loading conditions. The vertex criteria presented by St€ore n and Rice are usually based on the J2 deformation theory of classical plasticity, which explores the localized necking through the rate discontinuity assumption at the necking band. Both models will be combined with the strain path effect through a linear adoption of an equivalent strain. It will be investigated by applying a pre-strain in the major and minor directions. Moreover, a dependent to yield criterion (DYC) angle is used for prediction of the necking band angle in the vertex theory. Also, a nonlinear neo-Hookean reinforced layer is considered to make a sensible delay at plastic deformation. Since the reinforcing layers are the materials with high stretchability, the effects of material properties and thickness values will be studied for supporting metal layers. Also, it is assumed that the incompressibility condition remains for corresponded elastomer and metal layer strains. Finally, the quadratic Hill criterion is used to investigate the anisotropy effect. The model is verified by experimental and other theoretical results. [ABSTRACT FROM AUTHOR]

The flow and acoustic characteristics of underwater gas jets exhausted from large vertical nozzles are experimentally investigated in this work with gas flow rates of 30–150 m3/h, nozzle widths of d = 10 mm, 20 mm, 30 mm, and 40 mm. A high-speed digital video camera is used to examine bubble behavior and flow regimes. Sound pressure is measured by two hydrophones and recorded by a digital audio tape recorder. The audio and video signals are synchronized to find out the relationship between sound and gas behavior. Experimental results indicate that the general behavior of gas exhausted into water is of periodical necking and expansion. Sound pressure peaks are mostly excited by necking in two ways: pinch-off and redial expansion. Necking itself is a kind of low frequency behavior, corresponding to strong low frequency sounds. Moreover, necking can force the growing bubble to oscillate and emit broadband sound. As the gas velocity increases, necking would happen more frequently, and gas jets would grow into larger volume in shorter time, and then the sound radiated from the gas jets would have higher frequency and larger amplitude. [ABSTRACT FROM AUTHOR]

At high strain rates, the fragmentation of expanding structures of ductile materials, in general, starts by the localization of plastic deformation in multiple necks. Two distinct mechanisms have been proposed to explain multiple necking and fragmentation process in ductile materials. One view is that the necking pattern is related to the distribution of material properties and defects. The second view is that it is due to the activation of specific instability modes of the structure. Following this, we investigate the emergence of necking patterns in porous ductile bars subjected to dynamic stretching at strain rates varying from 103 s-1 to 0.5 × 105 s-1 using finiteelement calculations and linear stability analysis. In the calculations, the initial porosity (representative of the material defects) varies randomly along the bar. The computations revealed that, while the random distribution of initial porosity triggers the necking pattern, it barely affects the average neck spacing, especially, at higher strain rates. The average neck spacings obtained from the calculations are in close agreement with the predictions of the linear stability analysis. Our results also reveal that the necking pattern does not begin when the Considère condition is reached but is significantly delayed due to the stabilizing effect of inertia. [ABSTRACT FROM AUTHOR]

Duplex stainless steels are characterized by oriented microstructures, in which its constituent phases, ferrite ( α ) and austenite ( γ ) form layered or fibrous phase arrangements depending on forming operations (e.g. rolling). These microstructures have the potential to induce anisotropy in the macroscopic mechanical properties of the material. A very interesting phenomenon related to this microstructurally-induced anisotropy is the subject of investigation in the present work: a sample submitted to tensile testing, which presents a regular initial geometry (either circular or square transverse sections), exhibits an anisotropic necking zone after fracture (with the transverse section becoming, respectively, elliptical and rectangular). The phenomenon is most surprising since the region of the specimen which remains homogeneously strained (that is, outside the necking zone) remains regular. This result suggest that this anisotropy develops due to the cavitation damage orientation in the necking zone. Present results confirm that the lamellar microstructure, typical of these steels, is responsible for the observed anisotropy. Observation of fracture surfaces clearly demonstrate that cavities align according to the underlying microstructure and a model is introduced to explain the observed anisotropy in elongation observed in samples extracted parallel or perpendicular to the rolling direction in rolled plates. [ABSTRACT FROM AUTHOR]

Cu/Ni laminated composites with the same total thickness of 128 µm, but different modulation wavelength λ (the sum of monolayer thickness of constituent layers) of 32 µm and 3 µm, respectively were prepared using a dual-bath electrodeposition technique. The tensile testing results and the quantitative characterization of strain gradient in the post-necking region of the composites reveal that the λ = 3 µm composites have the higher tensile strength and the better strain hardening ability, as well as the stronger resistance to post-necking compared with the λ = 32 µm ones. A high density of layer interfaces in the ultrathin laminated composite may play a key role in delaying the development of unstable plastic deformation along the layer thickness direction through periodical strain gradient and a number of geometrically necessary dislocations near the interfaces. Thus, the fatal localized plastic deformation along the through thickness direction has to be spread over along the loading direction, leading to the large neck breadth in the ultrathin laminated composites. [ABSTRACT FROM AUTHOR]

The paper describes limitations in the process of cross wedge rolling (CWR). The problem of necking (rupture) of a shaft step is discussed in detail. In addition, the paper also overviews the state of the art of modelling the cross wedge rolling process by the finite element method-based software, Deform-3D. Next, the paper presents methods for increasing effectiveness in two types of CWR: cross wedge rolling where axial flow of metal is blocked and cross wedge rolling with upsetting. The proposed rolling methods are then verified numerically by Deform-3D. Finally, the presented solutions are verified in experimental tests of a rolling process for producing a lever (with blocked axial flow of metal) and for an upset rolling process for producing a driving shaft. [ABSTRACT FROM AUTHOR]

Subaqueous volcanic eruptions are natural events common under the world's oceans. Here we report results from bench-scale underwater explosions that entrain and eject particles into a water tank. Our aim was to examine how particles are transferred to the water column and begin to sediment from it, and to visualize and interpret evolution of the ‘eruption’ cloud. Understanding particle transfer to water is a key requirement for using deposit characteristics to infer behaviour and evolution of an underwater eruption. For the experiments here, we used compressed argon to force different types of particles, under known driving pressures, into water within a container, and recorded the results at 1 MPx/frame and 1000 fps. Three types of runs were completed: (1) particles within water were driven into a water-filled container; (2) dry particles were driven into water; (3) dry particles were driven into air at atmospheric pressure. Across the range of particles used for all subaqueous runs, we observed: a) initial doming, b) a main expansion of decompressing gas, and c) a phase of necking, when a forced plume separated from the driving jet. Phase c did not take place for the subaerial runs. A key observation is that none of the subaqueous explosions produced a single, simple, open cavity; in all cases, multiphase mixtures of gas bubbles, particles and water were formed. Explosions in which the expanding argon ejects particles in air, analogous to delivery of particles created in an explosion, produce jets and forced plumes that release particles into the tank more readily than do those in which particles in water are driven into the tank. The latter runs mimic propulsion of an existing vent slurry by an explosion. Explosions with different particle types also yielded differences in behaviour controlled primarily by particle mass, particle density, and particle-population homogeneity. Particles were quickly delivered into the water column during plume rise following necking, with minor transfer along initial-jet margins, and for breaching explosions additional delivery from splashdown of tephra jets. Plume rise after necking also draws upward and re-entrains some groups of particles. Most delivered particles participate in initiating vertical sediment-gravity flows, some of which reached the tank floor and began lateral flow within the short duration of our experiments. Particles transferred from plume margins locally were sufficiently well-separated to settle independently from suspension. [ABSTRACT FROM AUTHOR]

This paper describes implementation of anisotropic damage mechanics in the material point method. The approach was based on previously proposed, fourth-rank anisotropic damage tenors. For implementation, it was convenient to recast the stress update using a new damage strain partitioning tensor. This new tensor simplifies numerical implementation (a detailed algorithm is provided) and clarifies the connection between cracking strain and an implied physical crack with crack opening displacements. By using 2 softening laws and 3 damage parameters corresponding to 1 normal and 2 shear cracking strains, damage evolution can be directly connected to mixed tensile and shear fracture mechanics. Several examples illustrate interesting properties of robust anisotropic damage mechanics such as modeling of necking, multiple cracking in coatings, and compression failure. Direct comparisons between explicit crack modeling and damage mechanics in the same material point method code show that damage mechanics can quantitatively reproduce many features of explicit crack modeling. A caveat is that strengths and energies assigned to damage mechanics materials must be changed from measured material properties to apparent properties before damage mechanics can agree with fracture mechanics. [ABSTRACT FROM AUTHOR]

In this study, a total of 26 tests were conducted to investigate the post-fire mechanical and ductile fracture performances of high strength structural steel (HSSS) Q690. The purpose of this experimental research is to evaluate the residual strength and residual ductility of the HSSS Q690 after a fire. Tensile coupons obtained from the HSSS Q690 sheets were heated to various temperatures up to 900℃, and then were cooled down in air to ambient temperature. Tensile coupon tests were carried out to obtain their post-fire nominal stress-nominal strain curves, post-fire true stress-true strain curves, corresponding mechanical properties (including yield stress, ultimate strength, Poisson’s ratio, elastic modulus and elongation), and ductile fracture behaviors. Test results showed that the HSSS Q690 can keep the unchanged mechanical performances after it experiences temperatures up to 600℃. And then a set of prediction equations are obtained to evaluate the post-fire mechanical performances of such high strength steels. The results presented in this experimental study are expected to lead to accurate assessing the post-fire performances, including mechanical performances and ductility performances, of the HSSS Q690. [ABSTRACT FROM AUTHOR]

The paper focuses on the assessment of so-called complete solutions for the problem of diffuse necking in sheet metal. The assessment is based on a virtual tensile test generated with the aid of a finite element model using a reference strain hardening behavior. The resulting displacement fields within the diffuse neck are then used to numerically deform a speckle pattern. Subsequently, the deformed images are post-processed using DIC software to acquire displacement fields and strain fields. The identification of the strain hardening behavior is based on the virtual force-elongation curve, the displacement fields and associated strain fields within the diffuse neck. [ABSTRACT FROM AUTHOR]

One of the most important tasks in sheet metal forming is the prediction of formability. The common criterion for ductile fracture in industrial application is the evaluation of the so-called Forming Limit Curve (FLC). The determination of FLCs is standardized in the international standard 12004-2 by two different experimental methods, the Marciniak- and the Nakajima-test. Several effects, for example bending or contact pressure, are leading to biaxial pre-forming and to a slightly non-linear load path. This results in inaccuracies of the FLC. The so-called Generalized Forming Limit Concept (GFLC) is a phenomenological approach, which was introduced to predict the local necking of non-linear load paths. The accuracy and robustness of the GFLC has already been shown in several papers. In this investigation the GFLC was used to compensate the biaxial pre-forming and to calculate a linear FLC. Input parameters are the Marciniak- and Nakajima-FLCs of the material HC340LA. [ABSTRACT FROM AUTHOR]

Finite element model updating is an inverse method which enables to arrive at a complete solution for the diffuse necking of a thick tensile specimen. The method relies on the characterization of a phenomenological strain hardening model. Therefore, the method’s accuracy is limited due to the predefined character of the analytical function. Consequently, identifying a generic strain hardening model is proposed in this work. First, different possible generic functions to characterize the actual strain hardening behaviour of a material have been scrutinized. Next, the optimal identification procedure has been examined whereof finally, the flexibility of the model has been probed. [ABSTRACT FROM AUTHOR]

A plastic instability model is extended to predict evolution of a bounded deformation in necking phenomenon. There are several studies to predict the plastic instability such as the vertex model proposed by Stören and Rice, which considers strain and stress rate discontinuities in the necking band. Here, the model is established on the J 2 deformation theory of classical plasticity. Effect of stress triaxiality is investigated on the localization in bifurcation analysis. Also, a modified maximum force criterion is applied to predict diffuse necking considering loading conditions. Although considering the effect of strain rate hardening plays an important role to give accurate results, usually imposing it leads to emerging relatively the main complex constitutive equations. Therefore, a delicate bridge between the diffuse and localized models is made using the maximum force assumption to overcome on the complexity of the problem. Also, by investigating the strain rate behavior on the plastic instability, the forming limit diagrams are obtained illustrating more accurate results than other existing models. The anisotropy effect is studied by application of a quadratic Hill's criteria. The necking band angle will be investigated per different conditions through extending the vertex model coupled with the angle-dependent yield criterion. [ABSTRACT FROM AUTHOR]

The maximum force criteria and their derivatives, the Swift and Hill criteria, have been extensively used in the past to study sheet formability. Many extensions or modifications of these criteria have been proposed to improve necking predictions under only stretching conditions. This work analyses the maximum force principle under stretch-bending conditions and develops two different approaches to predict necking. The first is a generalisation of classical maximum force criteria to stretch-bending processes. The second approach is an extension of a previous work of the authors based on critical distance concepts, suggesting that necking of the sheet is controlled by the damage of a critical material volume located at the inner side of the sheet. An analytical deformation model is proposed to characterise the stretch-bending process under plane-strain conditions. Different parameters are considered, such as the thickness reduction, the gradient of variables through the sheet thickness, the thickness stress and the anisotropy of the material. The proposed necking models have been successfully applied to predict the failure in different materials, such as steel, brass and aluminium. [ABSTRACT FROM AUTHOR]

In this work, three numerical necking criteria based on finite element (FE) simulations are proposed for the prediction of forming limit diagrams (FLDs) for sheet metals. An elastic-plastic constitutive model coupled with the Lemaitre continuum damage theory has been implemented into the ABAQUS/Explicit software to simulate simple sheet stretching tests as well as Erichsen deep drawing tests with various sheet specimen geometries. Three numerical criteria have been investigated in order to establish an appropriate necking criterion for the prediction of formability limits. The first numerical criterion is based on the analysis of the thickness strain evolution in the central part of the specimens. The second numerical criterion is based on the analysis of the second time derivative of the thickness strain. As to the third numerical criterion, it relies on a damage threshold associated with the occurrence of necking. The FLDs thus predicted by numerical simulation of simple sheet stretching with various specimen geometries and Erichsen deep drawing tests are compared with the experimental results. [ABSTRACT FROM AUTHOR]

In this paper we explore the inception and development of multiple necks in incompressible nonlinear elastic bars subjected to dynamic stretching. The goal is to elucidate the role played by a spatial-localized defect of the strain rate field in the necking pattern that emerges in the bars at large strains. For that task, we have used two different approaches: (1) finite element simulations and (2) linear stability analyses. The finite element simulations have revealed that, while the defect of the strain rate field speeds up the development of the necking pattern in the late stages of the localization process, the characteristic (average) neck spacing is largely independent of the defect within a wide range of defect amplitudes. The numerical results have been rationalized with the linear stability analyses, which enabled to explain the average spacing characterizing the necking pattern at high strain rates. Moreover, the numerical calculations have also shown that, due to inertia effects, the core of the localization process occurs during the post-uniform deformation regime of the bar, at strains larger than the one based on the Considère criterion. This phenomenon of neck retardation is shown to have a meaningful influence on the necking pattern. [ABSTRACT FROM AUTHOR]

In this paper, forming limit diagrams (FLDs) for an aluminum alloy are predicted through numerical simulations using various localized necking criteria. A comparative study is conducted for the FLDs determined by using the Lemaitre damage approach and those obtained with the modified Gurson-Tvergaard-Needleman (GTN) damage model. To this end, both damage models coupled with elasto-plasticity and accounting for plastic anisotropy have been implemented into the ABAQUS/Explicit software, through the user-defined subroutine VUMAT, within the framework of large plastic strains and a fully three-dimensional formulation. The resulting constitutive frameworks are then combined with four localized necking criteria to predict the limit strains for an AA6016-T4 aluminum alloy. Three of these necking criteria are based on finite element (FE) simulations of the Nakazima deep drawing test with various specimen geometries, while the fourth criterion is based on bifurcation theory. The simulation results reveal that the limit strains predicted by local criteria, which are based on FE simulations of the Nakazima test, are in good agreement with the experiments for a number of strain paths, while those obtained with the bifurcation analysis provide an upper bound to the experimental FLD. [ABSTRACT FROM AUTHOR]

Due to their good mechanical and technological performances, thin substrate-supported metal layers are increasingly used as functional components in flexible electronic devices. Consequently, the prediction of necking, and the associated limit strains, for such components is of major academic and industrial importance. The current contribution aims to numerically investigate the respective and combined effects of strain rate sensitivity of the metal layer and the addition of an elastomer layer on localized necking in substrate-supported metal layers. To this end, strain rate-dependent forms for the flow theory of plasticity and the deformation theory counterpart are used to describe the mechanical behavior of the metal layer. As to the substrate layer, it is made of elastomer material whose mechanical response is described by a neo-Hookean hyperelastic model. The two layers are assumed to be perfectly adhered. Necking limit strains are predicted by the Marciniak-Kuczynski (M-K) imperfection approach. Various numerical results, corresponding to freestanding metal layers as well as substrate-supported metal layers, are presented and extensively discussed in this paper. The significant effect of strain rate sensitivity on the retardation of localized necking is first emphasized. Then, the combined and positive influence of strain rate sensitivity of the metal layer and characteristics of the elastomer layer (thickness and stiffness) on the enhancement of the ductility of the whole bilayer is analyzed and discussed. [ABSTRACT FROM AUTHOR]

Ductile fracture is a local phenomenon, and it is well established that fracture strain levels depend on both stress triaxiality and the resolution (grid size) of strain measurements. Two-dimensional plane strain post-necking models with different model sizes are used to predict the grid-size-dependent fracture strain of a commercial dual-phase steel, DP980. The models are generated from the actual microstructures, and the individual phase flow properties and literature-based individual phase damage parameters for the Johnson-Cook model are used for ferrite and martensite. A monotonic relationship is predicted: the smaller the model size, the higher the fracture strain. Thus, a general framework is developed to quantify the grid-size-dependent fracture strains for multiphase materials. In addition to the grid-size dependency, the influences of intrinsic microstructure features, i.e., the flow curve and fracture strains of the two constituent phases, on the predicted fracture strains also are examined. Application of the derived fracture strain versus model size relationship is demonstrated with large clearance trimming simulations with different element sizes. [ABSTRACT FROM AUTHOR]

An unusual necking behavior was found in twinning-induced plasticity (TWIP) steels during tensile tests, which is quite different from that observed on most ductile metals. A sharp drop of the strain-hardening rate (Θ) arises before necking initiation, rather than after it, leading to the premature necking of TWIP steels. Through carefully examining the evolution of macroscopic defects at various tensile strains using three-dimensional X-ray tomography (3D-XRT), this premature necking behavior was attributed to the multiplication of macroscopic voids during plastic deformation. Combining with the previous theories and present characterizations on the evolution of macroscopic voids, the mechanism of the unusual necking behavior in TWIP steels was quantificationally revealed. [ABSTRACT FROM AUTHOR]

We perform linear stability analysis and nonlinear slender filament simulations of extensional necking in complex fluids and soft solids, during the stress relaxation process following an interrupted strain ramp. We start by deriving analytical criteria for necking within a highly simplified and generalised scalar constitutive model. Within this, we find two different possible modes of necking: one associated with an upward curvature in the stress relaxation function on a log-linear plot, and another related to a carefully defined ‘elastic’ derivative of the tensile force with respect to an imagined sudden strain increment. We showed these two criteria to agree fully with simulations of the Oldroyd B and Giesekus models of polymeric solutions, and with the Rolie-Poly model of more concentrated polymeric solutions and melts, without polymer chain stretch. With chain stretch included, we find a slightly more complicated analytical criterion for necking during the stress relaxation, although with key ingredients that closely mirror counterpart ingredients of the simpler criteria obtained within the scalar model. We show this criterion to agree fully with slender filament simulations of the Rolie-Poly model with chain stretch, and with the scenario discussed by the Copenhagen group in [1,2] . In particular, we see delayed necking after strain ramps with an accumulated strain exceeding ϵ ¯ ≈ 0.7 , for ramp rates exceeding the inverse chain stretch relaxation timescale. We discuss finally an analogy between this delayed necking following an interrupted extensional strain ramp and delayed shear banding following an interrupted shear strain ramp [3]. This work provides the counterpart, for interrupted extensional strain ramps, to earlier papers giving criteria for necking in the protocols of constant imposed Hencky strain rate [4]  and of constant imposed tensile stress or constant imposed tensile force [5] . [ABSTRACT FROM AUTHOR]

The implementation of recent progress on stress state dependent ductile fracture models is inhibited by the break-down of shell element solutions whenever through-thickness necking occurs. The concept of the Domain of Shell-to-Solid Equivalence (DSSE) is therefore introduced to capture the onset of localized necking with shell element meshes. As long as the elasto-plastic loading paths lie inside the DSSE, ductile fracture may be predicted with shell elements using exactly the same models as for solid elements. A simple criterion describing the boundary of the DSSE is proposed based on the results from Marciniak-Kuczynski type of localization analysis. It is combined with the stress triaxiality and Lode angle dependent Hosford-Coulomb (HC) fracture initiation model and implemented as a user material subroutine for explicit finite element analysis. The combined DSSE-HC model is validated for a DP780 steel for notched tension, hemispherical punch loading, stretch bending, and V-bending of strips. [ABSTRACT FROM AUTHOR]