Showing papers on "Necking published in 2007"

Tensile ductility and necking of metallic glass

Abstract: Metallic glasses have a very high strength, hardness and elastic limit. However, they rarely show tensile ductility at room temperature and are considered quasi-brittle materials(1,2). Although these amorphous metals are capable of shear flow, severe plastic instability sets in at the onset of plastic deformation, which seems to be exclusively localized in extremely narrow shear bands similar to 10nm in thickness(3-13). Using in situ tensile tests in a transmission electron microscope, we demonstrate radically different deformation behaviour for monolithic metallic-glass samples with dimensions of the order of 100 nm. Large tensile ductility in the range of 23-45% was observed, including significant uniform elongation and extensive necking or stable growth of the shear offset. This large plasticity in small-volume metallic-glass samples did not result from the branching/deflection of shear bands or nanocrystallization. These observations suggest that metallic glasses can plastically deform in a manner similar to their crystalline counterparts, via homogeneous and inhomogeneous flow without catastrophic failure. The sample-size effect discovered has implications for the application of metallic glasses in thin films and micro-devices, as well as for understanding the fundamental mechanical response of amorphous metals.

Ductile crystalline–amorphous nanolaminates

Abstract: It is known that the room-temperature plastic deformation of bulk metallic glasses is compromised by strain softening and shear localization, resulting in near-zero tensile ductility. The incorporation of metallic glasses into engineering materials, therefore, is often accompanied by complete brittleness or an apparent loss of useful tensile ductility. Here we report the observation of an exceptional tensile ductility in crystalline copper/copper–zirconium glass nanolaminates. These nanocrystalline–amorphous nanolaminates exhibit a high flow stress of 1.09 ± 0.02 GPa, a nearly elastic-perfectly plastic behavior without necking, and a tensile elongation to failure of 13.8 ± 1.7%, which is six to eight times higher than that typically observed in conventional crystalline–crystalline nanolaminates (<2%) and most other nanocrystalline materials. Transmission electron microscopy and atomistic simulations demonstrate that shear banding instability no longer afflicts the 5- to 10-nm-thick nanolaminate glassy layers during tensile deformation, which also act as high-capacity sinks for dislocations, enabling absorption of free volume and free energy transported by the dislocations; the amorphous–crystal interfaces exhibit unique inelastic shear (slip) transfer characteristics, fundamentally different from those of grain boundaries. Nanoscale metallic glass layers therefore may offer great benefits in engineering the plasticity of crystalline materials and opening new avenues for improving their strength and ductility.

On the dynamics of necking and fragmentation – I. Real-time and post-mortem observations in Al 6061-O

Abstract: In this series of papers, we investigate the mechanics and physics of necking and fragmentation in ductile materials. The behavior of ductile metals at strain rates of about 10,000 per second is considered. The expanding ring experiment is used as the vehicle for examining the material behavior in this range of strain rates. In the present paper, the details of the experiment and the experimental observations on Al 6061-O are reported. Specifically, the design of the expanding ring experiment is evaluated through an analysis of the electromagnetic and mechanical aspects of the problem. Then, through an innovative use of high-speed, high-spatial resolution imaging we determine the sequence of deformation and failure in the expanding ring. In particular, the high speed photographs reveal that multiple necks nucleate along the circumference of the ring near a critical strain level; this is followed by a sequence of fractures, and eventually the fragments are unloaded and move as a rigid body. The strain at the onset of localized deformation, the time of fracture initiation, and the sequence of fragmentation are~all quantified in these experiments. These experimental results facilitate detailed comparison to analytical and numerical models of the fragmentation process. Following this, quantitative interpretation of the experimental observations is pursued. First, the uniform expansion of the ring is considered; the observed radial expansion is shown to agree well with an analytical solution of the problem based on a strain-rate-independent plasticity model. The evolution of the strain in the specimen and the onset of necking are evaluated quantitatively and shown to exhibit no dependence on the applied strain rate for this material; the strain at final fracture, averaged over the entire ring, is shown to be an inadequate measure of the ductility of the material. The fragmentation process is modeled with finite element analysis, incorporating the concept of the Mott release waves; this simulation provides a detailed numerical characterization of the experimental observations. Finally, the statistics of the necking and fragmentation are evaluated; these are interpreted both with the predictions of the linear perturbation analysis and a Weibull/Mott model of necking and fragmentation. In the sequel, we will explore the effect of material ductility, strain rate dependence, the effect of geometry and constraint, and finally the effect of a compliant cladding or coating on the development of necking and fragmentation.

On the Natural Draw Ratio of Semi-Crystalline Polymers: Review of the Mechanical, Physical and Molecular Aspects

Abstract: Drawing of semi-crystalline polymers generally involves a necking phenomenon, which is often referred to as plastic instability. The draw ratio in the stable neck is called natural draw ratio. A review is made of papers dealing with the phenomenology of necking and endeavors to identify its physical origin. The destruction of the spherulitic structure that consists of chain-folded lamellae involves a strain-softening accompanied with a localization of the plastic deformation. In turn, the fibrillar transition that results from the lamellar fragmentation and subsequent rearrangement of the crystal blocks into microfibrils brings about a strain-hardening, which stabilizes the plastic deformation. These competitive processes give rise to the natural draw ratio. The macromolecular network that consists of both chain entanglements and intercrystalline tie molecules appears to be a major factor of the neck stabilization. Theoretical approaches of the phenomenon are critically reviewed. Finally, the practical usefulness of the natural draw ratio is discussed with regard to predicting the long-term mechanical behavior of high-density polyethylene.

Experimental determination of the true epoxy resin strength using micro-scaled specimens

Abstract: In fibre reinforced composite materials, the matrix is the continuous phase, but the inter-fibre distance is rather small. The strength and the capability of plastic deformation is controlled by the matrix physics properties as well as by the acting stress state and the stressed volume. A new method is explained to produce fibres from epoxy resin. The single fibre strength was measured according to the standard test method for single fibre tests. The measured strength data of these thin epoxy resin fibres is close (60%) to the theoretical strength. The mechanism of fracture was identified by fractographic studies as cohesive failure initiated at pre-existing voids or void nucleation and growth. Before final rupture, the fibres showed necking and plastic deformation, which is a surprising behaviour for a brittle epoxy resin.

Where, and how, does a nanowire break?

Abstract: Using molecular dynamics (MD) simulation, we studied the structural transformation and breaking mechanism of a single crystalline copper nanowire under continuous strain. At a certain strain rate, an ensemble of relaxed initial states of the nanowire can preferentially go through one or more paths of deformation. In each deformation path, disordered atoms can be generated at the specific positions of the nanowire, where necking and breaking take place afterward. Such a breaking position is not predetermined; multiple initial states lead to a strain-rate-dependent, statistical distribution of breaking positions.

Mechanics of polycarbonate during high-rate tension

Abstract: Polymeric materials often undergo large inhomogeneous deformations at high rates during their use in various impact-resistant energy-absorbing applications. For better design of such structures, a comprehensive understanding of high-rate deformation under various loading modes is essential. In this study, the behavior of polycarbonate was studied during tensile loading at high strain rates, using a splitcollar type split Hopkinson tension bar (SHTB). The effects of varying strain rate, overall imposed strain magnitude and specimen geometry on the mechanical response were examined. The chronological progression of deformation was captured with a high-speed rotating mirror CCD camera. The deformation mechanics were further studied via finite element simulations using the ABAQUS/Explicit code together with a recently developed constitutive model for high-rate behavior of glassy polymers. The mechanisms governing the phenomena of large inhomogeneous elongation, single and double necking, and the effects of material constitutive behavior on the characteristics of tensile deformation are presented.

Bending induced rippling and twisting of multiwalled carbon nanotubes

Abstract: We report that a twisting deformation mode emerges with the rippling in bent multiwalled carbon nanotubes via atomistic simulations. This mode arises from the curvature-induced lattice mismatch, and is energetically favorable. For the nanotubes with larger radii, twisting may enhance the local strain relaxation. Under the thermal fluctuation, the nucleation of defects involves bond breaking and reconstruction due to strain localization. The defective inner tubes undergo the cyclic torsion, resulting in unstable necking and even failure. Prior to fracture, a monatomic chain is formed under the combination of bending and twisting.

Simultaneous enhancement of toughness, ductility, and strength of nanocrystalline ceramics at high strain-rates

Abstract: Molecular dynamics simulations of tensile testing have been performed on nc-SiC. Reduction of grain size promotes simultaneous enhancement of ductility, toughness, and strength. nc-SiC fails by intergranular fracture preceded by atomic level necking. Conventionally, high strain-rate deformations of ceramics are limited by diffusion time scales, since diffusion prevents premature cavitation and failure. The authors report a nondiffusional mechanism for suppressing premature cavitation, which is based on unconstrained plastic flow at grain boundaries. Based on the composite’s rule of mixture, they estimate Young’s modulus of random high-angle grain boundaries in nc-SiC to be about 130GPa.

Performance and failure of metal sandwich plates subjected to shock loading

Abstract: The deflection and fracture of metal sandwich plates subjected to intense uniform impulsive pressure loads are studied for plates made of four steels representing a wide range of strength, strain hardening and ductility. Sandwich plates with both square honeycomb cores and folded plate cores are considered. The primary fracture modes of the sandwich plates are necking and subsequent tearing of the face sheets and webs and shear delamination of the core webs from the faces. Plates with square honeycomb cores have higher damage tolerance than those with folded plate cores in that they can withstand much larger loads above those at which the first signs of fracture appear. The trade-off between strength and ductility in plate performance is illustrated.

A numerical study on the influence of the Portevin–Le Chatelier effect on necking in an aluminium alloy

Abstract: The constitutive relation proposed by McCormick (1988 Acta Metall. 36 3061–7) for materials exhibiting negative steady-state strain-rate sensitivity and the Portevin–Le Chatelier (PLC) effect is incorporated into an elastic–viscoplastic model for metals with plastic anisotropy. The constitutive model is implemented in LS-DYNA for corotational shell elements. Plastic anisotropy is taken into account by use of the yield criterion Yld2000/Yld2003 proposed by Barlat et al (2003 J. Plast. 19 1297–319) and Aretz (2004 Modelling Simul. Mater. Sci. Eng. 12 491–509). The parameters of the constitutive equations are determined for a rolled aluminium alloy (AA5083-H116) exhibiting negative steady-state strain-rate sensitivity and serrated yielding. The parameter identification is based on existing experimental data. A numerical investigation is conducted to determine the influence of the PLC effect on the onset of necking in uniaxial and biaxial tension for different overall strain rates. The numerical simulations show that the PLC effect leads to significant reductions in the strain to necking for both uniaxial and biaxial stress states. Increased surface roughness with plastic deformation is predicted for strain rates giving serrated yielding in uniaxial tension. It is likely that this is an important reason for the reduced critical strains. The characteristics of the deformation bands (orientation, width, velocity and strain rate) are also studied.

Prediction of Necking in Tubular Hydroforming Using an Extended Stress-Based Forming Limit Curve

Abstract: This paper presents an extended stress-based forming limit curve (XSFLC) that can be used to predict the onset of necking in sheet metal loaded under non-proportional load paths, as well as under three-dimensional stress states. The conventional strain-based eFLC is transformed into the stress-based FLC advanced by Stoughton (1999, Int. J. Mech. Sci., 42, pp. 1-27). This, in turn, is converted into the XSFLC, which is characterized by the two invariants, mean stress and equivalent stress. Assuming that the stress states at the onset of necking under plane stress loading are equivalent to those under three-dimensional loading, the XSFLC is used in conjunction with finite element computations to predict the onset of necking during tubular hydroforming. Hydroforming of straight and pre-bent tubes of EN-AW 5018 aluminum alloy and DP 600 steel are considered. Experiments carried out with these geometries and alloys are described and modeled using finite element computations. These computations, in conjunction with the XSFLC, allow quantitative predictions of necking pressures; and these predictions are found to agree to within 10% of the experimentally obtained necking pressures. The computations also provide a prediction of final failure location with remarkable accuracy. In some cases, the predictions using the XSFLC show some discrepancies when compared with the experimental results, and this paper addresses potential causes for these discrepancies. Potential improvements to the framework of the XSFLC are also discussed.

Strain hardening of high density polyethylene

Abstract: The introduction of true stress strain measurements, at constant strain rate, has promoted the development of empirical or semiempirical models for large deformations in thermoplastics. One such theory, which proposes that the post yield deformation process can be represented by equations derived from the theories of rubber elasticity, has been successfully applied to several glassy polymers. Unexpectedly, it can also model the post yield deformation of many different grades of polyethylene, even when rubber theory is employed in the simplest Gaussian form. Strain hardening is then represented by the single strain hardening coefficient Gp. Examples are given of this equation, which can be modified to give the true engineering or nominal stress σn and then be differentiated to give dσn/dλ = Gp − Y0 / λ2 + 2Gp / λ3, where Y0 is the yield stress and λ the extension ratio. Negative values of this differential then predict the onset of necking in tension and positive values stabilization of the neck. The relation of Gp to molecular weight is then discussed using literature measurements for polyethylenes of differing molecular weight and similar molecular weight distributions. When these results are then plotted, a strong dependency of Gp on molecular weight is observed. Some implications of these measurements are then considered. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1090–1099, 2007

Strain burst phenomena in the necking of a sheet that deforms by non-associated plastic flow

Abstract: In non-close-packed crystalline lattices, e.g. bcc metals and intermetallics, the stress-state dependence of the Peierls barrier for the motion of a screw dislocation violates Schmid's law and leads to non-associated plastic flow in single crystals and polycrystalline aggregates (Bassani 1994 Adv. Appl. Mech. 30 191–258, Bassani et al 2001 Mater. Sci. Eng. A 319–321 97–101). Plasticity models based upon distinct yield and flow functions are proposed to describe polycrystalline behaviour and specialized to the case of isotropic response. Studies of sheet necking using both a Marciniak–Kuczynski analysis and finite elements predict that non-associated flow has a significant effect on the evolution of inhomogenieties in the sheet. For nearly rate-insensitive response, intermittent bursts of strain arise as a consequence of non-associated flow, particularly for deformations near the plane-strain state. These strain bursts, which are due to instantaneously unstable deformation behaviour, are observed to be sensitive to mesh refinement in the case of a purely local constitutive description. Strain-gradient effects are introduced, which significantly improves convergence.

Plastic Deformation and Failure in A359 Aluminum and an A359-SiCp MMC under Quasistatic and High-strain-rate Tension

Abstract: The deformation and failure (under quasistatic and dynamic tension) of an A359 aluminum alloy and an A359 aluminum alloy reinforced by 20 vol.% SiC particles have been investigated. Tensile strains are measured using the laser occlusive radius detector (LORD) and/or strain gauge in Kolsky bar tests, and using the LORD and/or clip extensometer in quasistatic tests. The influence of the rate of deformation on the tensile stress-strain curves and on the failure strains is determined for these heterogeneous materials. Both composite and matrix behave in a brittle manner with no necking before fracture, and the tensile failure strain is slightly reduced at high strain rates. The fracture surfaces and the microstructure of the tested specimens of each material are examined using scanning electron microscopy and optical microscopy. The tensile failure of the A359 matrix alloy and the composite are controlled by the microcracking of Si particles.