Showing papers on "Strain hardening exponent published in 2004"

Mechanical Behavior of Materials

Abstract: 1. Stress and strain 2. Elasticity 3. Mechanical tensile testing 4. Strain hardening of metals 5. Plasticity 6. Strain-rate and temperature dependence of flow stress 7. Slip 8. Dislocation geometry and energy 9. Dislocation mechanics 10. Mechanical twinning 11. Hardening mechanisms 12. Discontinuous and inhomogeneous deformation 13. Ductility and fracture 14. Fracture mechanics 15. Viscoelasticity 16. Creep and stress rupture 17. Fatigue 18. Residual stresses 19. Ceramics 20. Polymers 21. Composites 22. Mechanical working Appendix I. Miller indices Appendix II. Stereographic projection.

Strain hardening, strain rate sensitivity, and ductility of nanostructured metals

Abstract: This paper presents an overview of the strain hardening and strain rate hardening behavior of nanostructured and ultrafine-grained metals. The experimental findings obtained in our laboratory are summarized, with some recent data for ultrafine-grained Cu presented as a model case. Due to the diminishing strain hardening capacity and inadequate strain rate hardening, plastic instabilities in the form of inhomogeneous and localized deformation such as necking and shear banding often contribute to the low ductility of nanostructured and ultrafine-grained metals at room temperature (RT). The observed grain size dependence of the strain rate sensitivity is also discussed in terms of its implications for new deformation mechanisms when the grain size is in the nanocrystalline (nc) and ultrafine regime.

Strain hardening and large tensile elongation in ultrahigh-strength nano-twinned copper

Abstract: A high density of growth twins in pure Cu imparts high yield strength while preserving the capacity for efficient dislocation storage, leading to high strain hardening rates at high flow stresses, especially at 77 K. Uniform tensile deformation is stabilized to large plastic strains, resulting in an ultrahigh tensile strength of similar to1 GPa together with an elongation to failure of similar to30%. (C) 2004 American Institute of Physics.

Strain hardening in polypropylenes and its role in extrusion foaming

Abstract: Extensional viscosity of several polypropylene polymers and their blends was measured and the foam processing of these blends using carbon dioxide blowing agent was studied. Foaming was carried out on a co-rotating twin-screw extrusion line, with a gear pump to build pressure. A linear isotactic polypropylene and two branched polypropylenes were considered. The uniaxial extensional viscosity was quantified and the foam characterized based on bulk density, cell size, and cell concentration. The linear polymer exhibits no strain hardening, while both branched polymers show pronounced strain hardening. Blends of low concentrations of branched polymer in the linear polypropylene show significant strain hardening down to 10-wt% branched polypropylene. Strain hardening is expected to prevent cell coalescence and lead to higher cell concentrations. The branched polymers were found to have a lower cell concentration than the linear polymer. Yet blends of linear and branched polypropylenes attained a cell concentration higher than either of the neat polymers. This suggests that even small amounts of branched polypropylene blended in linear polypropylene can improve the foaming process. Polym. Eng. Sci. 44:2090–2100, 2004. © 2004 Society of Plastics Engineers.

Structure, Deformation, and Failure of Flow-Oriented Semicrystalline Polymers

Abstract: This study deals with the influence of processing induced crystalline orientation on the macroscopic deformation and failure behavior of thin samples of polyethylene and polypropylene. Distribution and structure of flow-induced orientations were characterized by optical microscopy, X-ray diffraction techniques, and transmission electron microscopy. Hermans' orientation functions were either determined from the flat plate wide-angle X-ray diffraction patterns or calculated from full pole figures. The deformation behavior of the oriented samples was studied in both impact and tensile testing conditions and was found to be strongly anisotropic and related to the oriented structure. For all polymers studied, an increase of extended chains (shish) in the loading direction is proposed to cause an increase in the yield stress, and a lamellar structure oriented perpendicular to loading direction leads to an increase in strain hardening. In the extruded samples, where a low level of extended chains and a high level of oriented lamellae were found, the resulting combination of yield stress and strain hardening leads to homogeneous deformation. Brittle-ductile transitions in impact toughness of the molded samples could also be explained from differences in yield stress and strain hardening. Toughness enhancement was found to be most efficient with increasing strain hardening, and the effect was less pronounced in the polypropylene samples.

Intrinsic Deformation Behavior of Semicrystalline Polymers

Abstract: The influence of crystallinity and lamellar thickness on the intrinsic deformation behavior of a number of semicrystalline polymers is studied: a poly(ethylene terephthalate) and two different molecular weight grades of polyethylene and polypropylene. The crystallinity and lamellar thickness are altered by varying the rate of crystallization from the melt and by cold crystallization (annealing) at elevated temperatures above Tg but below the melting point. Crystallinity and lamellar thickness are determined by wide-angle X-ray diffraction and small-angle X-ray scattering measurements. Uniaxial compression tests are performed to obtain the large strain intrinsic deformation behavior, e.g., yield stress, strain softening, and strain hardening modulus. The yield stress is found to be proportional to lamellar thickness, whereas the strain hardening modulus is shown not to depend on crystallinity or lamellar thickness. Over the strain range experimentally covered, the strain hardening modulus appears to be well described by a simple neo-Hookean relation and appears to be related to the chain entanglement density. An affirmation for this relation arises from the observation that slowly melt crystallized samples exhibit a lower strain hardening, resulting from a lower chain entanglement density, which is expected to be caused by reeling in of the molecular chains in such a slow crystallization process. The similarity in the results observed on all polymers tested supports the conclusion that the crystalline phase does not contribute to strain hardening, which is primary controlled by the chain entanglement density.

Strengthening via the formation of strain-induced martensite in stainless steels

Abstract: The strengthening that results from the low-temperature formation of strain-induced martensite in austenitic stainless steel was studied. Specifically, the work hardening behaviour was characterized, as well as the spatial distribution of the martensite as a function of prior strain. Neutron diffraction measurements revealed the degree of elastic strain partitioning between the austenite and martensite. It was found that a sufficiently high initial dislocation density leads to a localization of the martensite transformation in the form of a Luders front. The martensite acts as an elastic reinforcing phase as it supports a higher stress than the austenite tensile loading, even though the martensite co-deforms plastically with the austenite. A model was developed that predicts the volume fraction of martensite formed as a function of plastic strain. © 2004 Elsevier B.V. All rights reserved.

Finite element analysis of the plastic deformation zone and working load in equal channel angular extrusion

Abstract: A comprehensive finite element (FE) study is conducted to analyze the formation of the plastic deformation zone (PDZ) and evolution of the working load with ram displacement during a single pass of equal channel angular extrusion (ECAE) with intersection angle 90°. This study explores systematically the coupled effects of material response, outer corner angle (Ψ = 0°, 45°, or 90°), and friction on ECAE deformation, which can be effectively analyzed through two key characteristics of the PDZ alone. These characteristics, the morphology and strain-rate distribution within the PDZ, are largely responsible for the heterogeneity in strain that develops in the sample at the end of a single pass. Strain hardening, Ψ, and friction were all found to have some effect on the PDZ, though under their combined influence, one tends to dominate over the others. Strain hardening tends to produce asymmetry in the strain-rate distribution within the PDZ, resulting in corner gaps and a more heterogeneous strain distribution than an ideal perfectly plastic material. In cases in which the material fills the die, the PDZ shape is largely governed by the die geometry, i.e. Ψ, independent of material response and friction. In this respect, friction does however help to reduce the free surface gaps that form between a strain hardening material and the die, but to further increase the degree of heterogeneity. The distinct stages that are present in the load versus displacement curves are defined and associated with those in sample deformation, some of which depend on Ψ and others on material properties. Effective strain calculations are compared with various analytical models and the one that directly accounts for the PDZ tends to perform better. To date, most of the cases studied here have not been modeled analytically; however, a stronger connection between analytical modeling and actual ECAE deformation can be made by the guidance of these FE studies on the interactive influence of processing and material variables.

Effect of long branches on the rheology of polypropylene

Abstract: In order to study the rheology of long chain branched polymers, branches have been added on linear polypropylene precursors in varying amounts using reactive modification with peroxydicarbonates. The branched polypropylene samples show distinct strain hardening, something absent from the linear melt; this considerably improves the melt strength of the modified polymer. The zero shear viscosity and the elasticity measured by the relaxation spectrum also increase with the number of branches per molecule. Two models are applied to describe strain hardening of the viscosity during the course of elongation. The model parameters were found to vary systematically with the degree of branching and, therefore, their values can be used as a measure of this. Consequently, fluidity, elasticity, strain hardening, and melt strength are all related to the degree of long chain branching.

Strain-hardening due to Dispersed Cementite for Low Carbon Ultrafine-grained Steels

Abstract: Strain(work)-hardening in tensile tests was examined for low carbon steels with various ferrite grain sizes ranged from 0.4 to 16 μm. The steels had microstructures composed of ferrite grains and dispersed cementite particles. They were fabricated through warm caliber bar-rollings with an accumulative area reduction of 93%. Strain-hardening rate at a given strain increased with an increase in volume fraction of cementite particles. The balance of yield strength and uniform elongation for ultrafine-grained structures could be improved by the dispersion of cementite particles. Effects of the cementite dispersion and the ferrite grain size on the strain-hardening rate can be roughly explained by the work-hardening model with GN-dislocation density. Strain-hardening design using dispersed cementites was proved to be effective in controlling ductility of the ultrafine-grained steels.

The effect of long chain branching on the processability of polypropylene in thermoforming

Abstract: Linear polypropylene was modified by reaction with peroxydicarbonates in a twin screw extruder to obtain varied degrees of long chain branching. The melt strength and the elasticity of the modified polymers were found to increase with the modification. The processability in foaming and thermoforming processes improved with branching and showed an optimum, beyond which higher degrees of long chain branching appeared not to help any further. The branched PP samples showed distinct strain hardening in the elongational viscosity, which was absent from the original linear melts. Melt strength, elasticity and strain hardening increased with the increase of the number of long chain branches on the main chain. The effect of molecular weight and molecular weight distribution of the precursor on the improvement of the processability of the polymer was examined. Polym. Eng. Sci. 44:973–982, 2004. © 2004 Society of Plastics Engineers.

Quasi-static and dynamic axial crushing of thin-walled circular stainless steel, mild steel and aluminium alloy tubes

Abstract: Quasi-static and dynamic axial crushing tests have been performed on circular thin-walled sections made of three materials: 304 stainless steel, aluminium alloy 6063-T6, and mild steel. The tests were arranged to investigate the mode transitions during the impact crushing of thin-walled tubes and the three materials were chosen for their distinctive individual characteristics, such as strain rate sensitive properties, pronounced strain hardening, etc. The stainless steel, aluminium alloy and mild steel shells have moderate diameter-to-thickness ratios, 2R/H, of 22, 33 and 26, respectively, and were examined over a range of different axial lengths that encompassed both classical progressive buckling and the global bending modes of failure. The tests were conducted at a standardised energy of 9 kJ, approximately, with a few tests repeated at a higher energy of 18 kJ. The shells were impacted at velocities up to 13.4 m/s with masses up to 502 kg. Standard collapse modes developed in the tubes and the associated energy absorbing characteristics have been examined and compared with previous studies on mild steel. Quasi-static and dynamic tensile test results on the materials are also reported and the critical slenderness ratios at the transition between the two principal modes of failure are identified. The effects of strain hardening, strain rate as well as inertia effects due to the individual characteristics of the three materials are explored.

Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models

Abstract: The deformation of a composite made up of a random and homogeneous dispersion of elastic spheres in an elasto-plastic matrix was simulated by the finite element analysis of three-dimensional multiparticle cubic cells with periodic boundary conditions. “Exact” results (to a few percent) in tension and shear were determined by averaging 12 stress–strain curves obtained from cells containing 30 spheres, and they were compared with the predictions of secant homogenization models. In addition, the numerical simulations supplied detailed information of the stress microfields, which was used to ascertain the accuracy and the limitations of the homogenization models to include the nonlinear deformation of the matrix. It was found that secant approximations based on the volume-averaged second-order moment of the matrix stress tensor, combined with a highly accurate linear homogenization model, provided excellent predictions of the composite response when the matrix strain hardening rate was high. This was not the case, however, in composites which exhibited marked plastic strain localization in the matrix. The analysis of the evolution of the matrix stresses revealed that better predictions of the composite behavior can be obtained with new homogenization models which capture the essential differences in the stress carried by the elastic and plastic regions in the matrix at the onset of plastic deformation.

Dislocation mechanics-based constitutive equations

Abstract: A review of constitutive models based on the mechanics of dislocation motion is presented, with focus on the models of Zerilli and Armstrong and the critical influence of Armstrong on their development. The models were intended to be as simple as possible while still reproducing the behavior of real metals. The key feature of these models is their basis in the thermal activation theory propounded by Eyring in the 1930’s. The motion of dislocations is governed by thermal activation over potential barriers produced by obstacles, which may be the crystal lattice itself or other dislocations or defects. Typically, in bcc metals, the dislocation-lattice interaction is predominant, while in fcc metals, the dislocation-dislocation interaction is the most significant. When the dislocation-lattice interaction is predominant, the yield stress is temperature and strain rate sensitive, with essentially athermal strain hardening. When the dislocation-dislocation interaction is predominant, the yield stress is athermal, with a large temperature and rate sensitive strain hardening. In both cases, a significant part of the athermal stress is accounted for by grain size effects, and, in some materials, by the effects of deformation twinning. In addition, some simple strain hardening models are described, starting from a differential equation describing creation and annihilation of mobile dislocations. Finally, an application of thermal activation theory to polymeric materials is described.

Banded Microstructure in 2024-T351 and 2524-T351 Aluminum Friction Stir Welds: Part II. Mechanical Characterization

Abstract: A series of micro-mechanical experiments have been performed to quantify how the friction stir welding (FSW) process affects the material response within the periodic bands that have been shown to be a common feature of FSW joints. Micro-mechanical studies employed sectioning of small samples and micro-tensile testing using digital image correlation to quantify the local stress–strain variations in the banded region. Results indicate that the two types of bands in 2024-T351 and 2524-T351 aluminum FSW joints (a) have different hardening rates with the particle-rich bands having the higher strain hardening exponent, (b) exhibit a periodic variation in micro-hardness across the bands and (c) the individual bands in each material have the same initial yield stress.

High strain rate response of aluminum 6092/B4C composites

Abstract: Aluminum 6092/B 4 C p (boron carbide) metal-matrix composites (MMC) fabricated by two different powder consolidation routes, extrusion and sintering/hot isostatic-pressing (HIPing), were made and tested over a wide range of strain rates (10 −4 to 10 4 s −1 ). The strength of these MMCs increases with increasing volume fraction of particulate reinforcement. Strain hardening is observed to increase with increasing volume fraction of reinforcement at lower strains ( 5 μm) considered. Finally, the Li–Ramesh model captures the observed high-rate behavior exhibited by these powder-consolidated composites.