Showing papers on "Strain hardening exponent published in 1998"

Molecular constitutive equations for a class of branched polymers: The pom-pom polymer

Abstract: Polymer melts with long-chain side branches and more than one junction point, such as commercial low density polyethylene (LDPE), have extensional rheology characterized by extreme strain hardening, while the shear rheology is very shear thinning, much like that of unbranched polymers. Working with the tube model for entangled polymer melts, we propose a molecular constitutive equation for an idealized polymer architecture, which, like LDPE, has multiple branch points per molecule. The idealized molecule, called a “pom-pom,” has a single backbone with multiple branches emerging from each end. Because these branches are entangled with the surrounding molecules, the backbone can readily be stretched in an extensional flow, producing strain hardening. In start-up of shear, however, the backbone stretches only temporarily, and eventually collapses as the molecule is aligned, producing strain softening. Here we develop a differential/integral constitutive equation for this architecture, and show that it predicts rheology in both shear and extension that is qualitatively like that of LDPE, much more so than is possible with, for example, the K-BKZ integral constitutive equation.

Plastic deformation and fracture behaviour of Ti–6Al–4V alloy loaded with high strain rate under various temperatures

Abstract: This study investigates the plastic deformation and fracture behaviour of titanium alloy (Ti–6Al–4V) under high strain rates and various temperature conditions. Mechanical tests are performed at constant strain rates ranging from 5×102 to 3×103 s−1 at temperatures ranging from room temperature to 1100°C by means of the compressive split-Hopkinson bar technique. The material's dynamic stress–strain response, strain rate, temperature effects and possible deformation mechanisms are discussed. Furthermore, the plastic flow response of this material is described by a deformation constitutive equation incorporating the effects of temperature, strain rate, strain and work hardening rate. The simulated results based on this constitutive equation are verified. The fracture behaviour and variations of adiabatic shear band produced by deformation at each test condition are investigated with optical microscopy and scanning electron microscopy. The results show that the flow stress of Ti–6Al–4V alloy is sensitive to both temperature and strain rate. Nevertheless, the effect on flow stress of temperature is greater than that of strain rate. Fracture observations reveal that adiabatic shear banding turns out to be the major fracture mode when the material is deformed to large plastic strain at high temperature and high strain rate.

Strain rate behavior of composite materials

Abstract: The effect of strain rate on the compressive and shear behavior of carbon/epoxy composite materials was investigated. Strain rate behavior of composites with fiber waviness was also studied. Falling weight impact system and servohydraulic testing machine were used for dynamic characterisation of composite materials in compression at strain rates up to several hundred per second. Strain rates below 10 s −1 were generated using a hydraulic testing machine. Strain rates above 10 s −1 were generated using the drop tower apparatus developed. Seventy-two-ply unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions and [(0 8 /90 8 ) 2 /0 8 ] s crossply laminates were characterised. Off-axis (30 and 45°) compression tests of the same unidirectional material were also conducted to obtain the in-plane shear stress–strain behavior. The 90° properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The shear stress–strain behavior, which is also matrix-dominated, shows high nonlinearity with a plateau region at a stress level that increases significantly with increasing strain rate. The 0° and crossply laminates show higher strength and strain values as the strain rate increases, whereas the modulus increases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases the dynamic stress–strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal case and highest in the transverse and shear cases. Unidirectional and crossply specimens with fiber waviness were fabricated and tested. It is shown that, with severe fiber waviness, strong nonlinearity occurs in the stress–strain curves due to fiber waviness with significant stiffening as the strain rate increases.

Deformation of a polydomain, liquid crystalline epoxy-based thermoset

Abstract: Liquid crystalline thermosets (LCT's) were prepared by curing a difunctional LC epoxy monomer, diglycidyl ether of 4,4‘-dihydroxy-α-methylstilbene, with the tetrafunctional cross-linker 4,4‘-methylenedianiline (MDA). A commercial, non-LC epoxy monomer of similar starting molecular weight was also cured with MDA to produce an isotropic thermoset for comparison. Dynamic mechanical analysis revealed reduced glassy moduli, increased stiffness in the rubbery state, and broadened and lowered glass transitions for the LCT's compared to the isotropic thermoset based on the non-LC monomer. At room temperature, the true stress versus true strain curves of the LCT's under uniaxial compression showed no strain softening region, substantial plastic deformation (ef ≈ 50%), and increased strain hardening compared to the isotropic thermoset. LCT's with a smectic type of local order exhibited bulk, homogeneous plastic yielding, which led to slow, stable crack propagation and an increased fracture toughness (GIc = 1.62 kJ/...

Fractal dislocation patterning during plastic deformation

Abstract: During the later stages of plastic deformation, strain hardening of face-centered cubic metals goes along with the formation of cellular dislocation patterns appearing on various scales. The paper presents an analysis of the fractal geometry of these dislocation structures. A theoretical model is presented according to which dislocation cell formation is associated with a noise-induced structural transition far from equilibrium. The observed fractal dimensions are related to the stochastic process of dislocation glide, and implications for quantitative metallography are discussed.

Effects of 'sinking in' and 'piling up' on estimating the contact area under load in indentation

Abstract: The phenomena of the 'piling up' and 'sinking-in' of surface profiles in conical indentation in elastic-plastic solids with work hardening are studied using dimensional and finite-element analysis The degree of sinking in and piling up is shown to depend on the ratio of the initial yield strength Y to Young's modulus E and on the work-hardening exponent n The widely used procedure proposed by Oliver and Pharr for estimating contact depth is then evaluated systematically By comparing the contact depth obtained directly from finite-element calculations with that obtained from the initial unloading slope using the Oliver-Pharr procedure, the applicability of the procedure is discussed

A thermodynamics-based formulation of gradient-dependent plasticity

Abstract: A nonlocal thermodynamic theoretical framework is provided as a basis for a consistent formulation of gradient-dependent plasticity in which a scalar internal variable measuring the material isotropic hardening/softening state is the only nonlocal variable. The main concepts of this formulation are: i) the ‘regularization operator’, of differential nature, which governs the relation between the above nonlocal variable and a related local variable (scalar measure of plastic strain) and confers a unified character to the proposed formulation (this transforms into a formulation for nonlocal plasticity if the regularization operator has an integral nature); ii) the ‘nonlocality residual’, which accounts for energy exchanges between different particles at the microstructural level as a consequence of the hardening/softening diffusion processes within the body; and iii) the (nonambiguous) ‘constitutive’ boundary conditions, which must be satisfied at points of the boundary surface of any (finite) region of the body where an irreversible deformation mechanism takes place (e.g. shear band). The plastic yielding laws for gradient plasticity are established with their domain and boundary equations, and their consistency with the nonlocal Clausius-Duhem inequality is assessed as well. Also, a suitable nonlocal-form maximum intrinsic dissipation theorem is provided, and the response problem of a continuous set of material particles to a given total strain rate field studied. Points of agreement and disagreement between this theory and the related literature are indicated, also via a case-study bar in uniaxial tension for which the analytical solution is worked out.

Experimental Study of Drained Creep Behavior of Sand

Abstract: The experimental techniques pertaining to accurate measurement of creep in sand are explained in detail. Triaxial compression and proportional loading tests were performed in a triaxial setup for which special procedures were developed to maintain constant temperature, constant confining pressure, and constant axial load, whereas the axial and volumetric deformations were measured using two types of mechanical measurement systems, both free of zero drift. Special attention was paid to the avoidance of air and water leakage through the membrane in the long-term tests. The experiments show that the nature of creep strains is similar to that of plastic strains. They may be predicted from the framework provided by the hardening plasticity theory. In particular, the potential surface determined for the prediction of plastic strains may also be used for the prediction of time-dependent creep strains. From the experiments it also appears that the yield surface and the plastic potential surface move out together, and the point at which to evaluate inelastic strain increment directions is at the current location of the yield surface and the accompanying plastic potential surface.

Microstructures and properties of nanocomposites obtained through SPTS consolidation of powders

Abstract: The microstructures and properties of copper- and aluminum-based nanocomposites processed through severe plastic torsional straining (SPTS) consolidation of metallic micrometer powders and ceramic nanopowders were investigated by transmission electron microscopy (TEM), X-ray diffraction (XRD), microhardness and electrical resistivity measurements, and mechanical tests. It was shown that the SPTS consolidation of powders is an effective technique for fabricating metal-ceramic nanocomposites with a high density, ultrafine grain size, and high strength. Copper samples processed under a high pressure of 6 GPa exhibited high failure strength and strain as well as unusual strain hardening. Superplastic-like behavior was found in Al-Al2O3 nanocomposite samples.

Compressive mechanical behavior of nanocrystalline Fe investigated with an automated ball indentation technique

Abstract: Nanocrystalline (nc) iron was produced by mechanical attrition and compacted into near fully dense samples. Isothermal annealing at 800 K resulted in grain sizes between 15 and 24 nm. A newly available Automated Ball Indentation system was used to study the compressive mechanical properties of the samples. The ABI method proved useful in examining the mechanical properties of nc iron on a more quantitative level than previously possible by conventional hardness testing methods. Stress–strain curves were obtained which indicated a compressive behavior similar to that of perfectly plastic materials: low strain hardening at high flow stresses around 3 GPa and a low room-temperature strain-rate sensitivity. The flow stresses were independent of the grain size in the range of the present study. The deformation pile-up around the indentations seems to have formed inhomogeneously, exhibiting intense plastic deformation in localized shear bands.

Nonlinear shear and extensional rheology of long-chain randomly branched polybutadiene

Abstract: We present nonlinear shear and uniaxial extensional measurements on a series of polybutadienes with varying amounts of long-chain, random branching. Startup of steady shear experiments is used to evaluate the damping function of the melts. The damping function is found to show a trend toward decreased dependency on strain with increasing branching content. Interior chains, which are believed to be responsible for changing the damping function, are calculated to comprise less than 3 wt % of the melt. Extensional measurements are used to investigate the role of branching in strain hardening. We show that samples with increased branch contents do show larger deviations of the transient Trouton ratio from the linear viscoelastic limit of three. However, we also show that the extensional data can be fit using parameters determined solely by the shear measurements. Furthermore, we show that the changes in the damping function seen in shear have little impact on extensional behavior. The extensional behavior of the melt is found to be most affected by changes in the relaxation spectra which can result from both branching and increases in the high end of the molecular weight distribution. This statement runs contrary to the often expressed view that strain hardening behavior in extension is exclusively produced by branching.

Tensile superplasticity in a nanocrystalline nickel aluminide

Abstract: Tensile superplasticity has been demonstrated in a nanocrystalline nickel aluminide processed by severe plastic deformation at 650–725°C and a strain rate of 1×10 −3 s −1 . The flow curves exhibit an unusually large strain hardening stage and very high flow stresses as compared to the flow stress of microcrystalline Ni 3 Al alloy of the same composition at typical superplastic strain rate and temperature. It is suggested that the origin of high flow stresses and extensive strain hardening stage is likely to be linked to the role of grain size on slip accommodation during grain boundary sliding. It is proposed that part of the high ductility in nanocrystalline materials processed by severe plastic deformation arises from the `Exhaustion Plasticity' mechanism.

Flexural Behavior of Steel Fiber Reinforced Concrete

Abstract: A constitutive model for steel fiber reinforced (SFR) concrete is proposed, in which the tensile behavior incorporates a bilinear strain softening feature. Composite material properties (fcu, ft), fiber volume concentration (Vf), fiber aspect ratio (L/d), and fiber-concrete matrix bond stress (τd) are used to define the model. The model may also exhibit strain hardening characteristic depending on the magnitude of the variables. Based on the constitutive model, the full history of the flexural moment-curvature relationship for SFR concrete is calculated. Predicted curves are superimposed onto and compared with published experimental data. The results show good overall agreement; the post-cracking softening and post-cracking strengthening response were predicted. In order to facilitate the rapid assessment of the ultimate flexural behavior of SFR concrete, a secondary tensile model is derived from the proposed model. A strain softening parameter (α) is defined for the secondary model and used to evaluate t...

Fem analysis for hysteretic behavior of thin-walled columns

Abstract: Thin-walled steel columns composed of stiffened plate elements are often used in Japan as piers for elevated highway bridges in urban areas, because of their small cross-sectional areas and high earthquake resistance. An accurate finite-element-method-based (FEM-based) analysis to predict the ultimate hysteretic behavior of thin-walled steel columns subjected to seismic loading is presented in this paper. For this purpose, a three-surface cyclic metal plasticity model is developed. The three-surface model includes less material parameters and internal variables for the ease of its implementation in the FEM analysis. This model is characterized by a discontinuous surface inserted between the yield surface and the bounding surface. The discontinuous surface is used to express the yield plateau and the change of hardening coefficient. Most material parameters in the three-surface model can be determined by the tensile coupon test. However, three parameters independent of material types are calibrated by the existing cyclic loading test results of thin-walled steel columns. This is to improve the accuracy of this analysis specifically in the simulation of the localized buckling behavior, which accompanies extremely large plastic strains.

A plasticity model for multiaxial cyclic loading and ratchetting

Abstract: The nonlinear behavior of metals when subjected to monotonic and cyclic non-proportional loading is modeled using the proposed hardening rule. The model is based on the Chaboche [1], [2] and Voyiadjis and Sivakumar [3], [4] models incorporating the bounding surface concept. The evolution of the backstress is governed by the deviatoric stress rate direction, the plastic strain rate, the backstress, and the proximity of the yield surface from the bounding surface. In order to ensure uniqueness of the solution, nesting of the yield surface with the bounding surface is ensured. The prediction of the model in uniaxial cyclic loading is compared with the experimental results obtained by Chaboche [1], [2]. The behavior of the model in multiaxial stress space is tested by comparing it with the experimental results in axial and torsional loadings performed by Shiratori et al. [5] for different stress trajectories. The amount of hardening of the material is tested for different complex stress paths. The model gives a very satisfactory result under uniaxial, cyclic and biaxial non-proportional loadings. Ratchetting is also illustrated using a non-proportional loading history.