Showing papers on "Strain hardening exponent published in 2008"

Dislocation Mean Free Paths and Strain Hardening of Crystals

Abstract: Predicting the strain hardening properties of crystals constitutes a long-standing challenge for dislocation theory. The main difficulty resides in the integration of dislocation processes through a wide range of time and length scales, up to macroscopic dimensions. In the present multiscale approach, dislocation dynamics simulations are used to establish a dislocation-based continuum model incorporating discrete and intermittent aspects of plastic flow. This is performed through the modeling of a key quantity, the mean free path of dislocations. The model is then integrated at the scale of bulk crystals, which allows for the detailed reproduction of the complex deformation curves of face-centered cubic crystals. Because of its predictive ability, the proposed framework has a large potential for further applications.

Microband-induced plasticity in a high Mn–Al–C light steel

Abstract: Room temperature tensile behavior of a high Mn–Al–C steel in the solid solution state was correlated to the microstructures developed during plastic deformation in order to clarify the dominant deformation mechanisms. The steel was fully austenitic with a fairly high stacking fault energy of ∼85 mJ/m 2 . The tensile behavior of the steel was manifested by an excellent combination of strength and ductility over 80,000 MPa% in association with continuous strain hardening to the high strain. In addition, the austenite phase was very stable during deformation. The high stacking fault energy and firm stability of austenite were attributed to the high Al content. In spite of the high stacking fault energy, deformed microstructures exhibited the planar glide characteristics, seemingly due to the glide plane softening effect. In the process of straining, the formation of crystallographic microbands and their intersections dominantly occurred. Microbands consisting of geometrically necessary dislocations led to the high total dislocation density state during deformation, resulting in continuous strain hardening. This microband-induced plasticity is to be the origin of the enhanced mechanical properties of the steel.

Size effect on strength and strain hardening of small-scale [111] nickel compression pillars

Abstract: This study investigates uniaxial compression behavior of focused ion beam (FIB) manufactured [1 1 1] nickel (Ni) small-scale pillars, ranging in diameter from approximately 25 μm to below 200 nm, in order to examine the effect of crystallographic orientation on the mechanical properties. This study is unique from other micro-pillar studies in that the [1 1 1] orientation has a considerably lower Schmid factor, and has multiple slip systems available. The [1 1 1] Ni pillars show a strong increase in yield stress and work hardening with decreasing diameter. The relationship between yield stress and diameter (σy ∝ d−0.69) matches well with previous small-scale pillar studies. Strain hardening, which has been inconsistently observed in other micro-pillar studies, is found to be a function of both diameter and orientation. Although the precise mechanism for hardening is unknown, transmission electron microscopy reveals dislocations throughout the pillar and into the base material suggesting that dislocation interactions and deformation below the pillar play a role in the observed strain hardening. Furthermore, a slight crystallographic rotation of the pillar is observed likely contributing to the observed mechanical properties. By exploring the role of crystallography on the plastic deformation behavior, this study provides additional insight into the nature of the size effect.

High strain rate properties of metals and alloys

Abstract: The high strain rate dependence of the flow stress of metals and alloys is described from a dislocation mechanics viewpoint over a range beginning from conventional tension/compression testing through split Hopkinson pressure bar (SHPB) measurements to Charpy pendulum and Taylor solid cylinder impact tests and shock loading or isentropic compression experiment (ICE) results. Single crystal and polycrystal measurements are referenced in relation to influences of the crystal lattice structures and nanopolycrystal material behaviours. For body centred cubic (bcc) metals, the strain rate sensitivity (SRS) is in the yield stress dependence as compared with the face centred cubic (fcc) case of being in the strain hardening property. An important consequence is that an opposite ductility influence occurs for the tensile maximum load point strain that decreases with strain rate for the bcc case and increases with strain rate for the fcc case. Different hexagonal close packed (hcp) metals are shown to foll...

Effect of Retained Austenite Stabilized via Quench and Partitioning on the Strain Hardening of Martensitic Steels

Abstract: A novel heat-treating process, quench and partitioning (Q&P), has been proposed as a fundamentally new way to produce martensitic microstructures containing retained austenite. The two-step process hypothesizes carbon enrichment of the austenite by decarburization of the martensite. Significant amounts of retained austenite have been measured in the final microstructure, although evidence for transition carbide formation in the martensite also exists. The mechanical properties obtained via Q&P are reported for a CMnAlSiP steel after intercritical annealing for A50 specimens. Tensile strength/total elongation combinations, ranging from 800 MPa/>25 pct to 900 MPa/20 pct to 1000 MPa/10 pct, indicate that Q&P is a viable way to produce high strength steel grades with good ductility. The instantaneous strain hardening of Q&P steels shows a significant dependence on the partitioning conditions applied. Lower partitioning temperature (PT) leads to continuously decreasing instantaneous n-values with strain, similar to the strain hardening behavior observed for dual-phase (DP) steels, whereas higher PTs for the same partitioning time increase the strain hardening significantly. After an initial increase, the observed n-values remain high up to considerable amounts of strain, resulting in similar strain hardening behavior observed for austempered transformation-induced plasticity (TRIP) grades. Assessment of the mechanical stability of the retained austenite indicates that the TRIP effect is effectively contributing to the increased strain hardening as function of strain.

The continuous strength method

Abstract: Many of the principal concepts that underpin current metallic structural design codes were developed on the basis of bilinear (elastic, perfectly-plastic) material behaviour; such material behaviour lends itself to the concept of section classification. The continuous strength method represents an alternative treatment to cross-section classification, which is based on a continuous relationship between slenderness and (inelastic) local buckling and a rational exploitation of strain hardening. The development and application of the continuous strength method to structural steel design is described herein. Materials that exhibit a high degree of nonlinearity and strain hardening, such as aluminium, stainless steel and some high-strength steels, fit less appropriately into the framework of cross-section classification, and generally benefit to a greater extent from the continuous strength method. The method provides better agreement with test results in comparison to existing design codes, and offers increas...

Strain hardening behaviour and the Taylor factor of pure magnesium

Abstract: Taylor orientation factors for strain hardening in textured and random polycrystals of magnesium were derived from the ratio of the strain hardening rates of polycrystals to that of single crystals deforming by equivalent polyslip. For polycrystals with textures that inhibit basal and prismatic slip while favouring pyramidal polyslip, the Taylor factor is estimated to be between 2.1 and 2.5, increasing to about 4.5 for randomly textured polycrystals. The micromechanics of strain hardening in polycrystals are discussed.

Mechanical properties of Mg–Al–Zn alloy with a tilted basal texture obtained by differential speed rolling

Abstract: The mechanical properties of the differential-speed-rolled Mg–3Al–1Zn alloy sheet with a basal pole tilted at about 15° in the rolling direction were systematically investigated at room temperature. Compared with the normal symmetrically rolled sheet exhibiting approximately the same average grain size, the uniform elongation and the strain hardening exponent increased while the proof stress and the Lankford value decreased especially in the rolling direction. The c-axis tilted texture activated the { 1 0 1 ¯ 2 } extension twinning at the early stage of tensile deformation, and depressed the dynamic recovery and in turn enhanced the uniform elongation. The initial texture had a significant influence on the deformation at the initial stage while it showed a much weaker effect on the deformation after reaching the strain instability condition.

Microstrain and grain-size analysis from diffraction peak width and graphical derivation of high-pressure thermomechanics

Abstract: An analytical method is presented for deriving the thermomechanical properties of polycrystalline materials under high-pressure (P) and high-temperature (T) conditions. This method deals with non-uniform stress among heterogeneous crystal grains and surface strain in nanocrystalline materials by examining peak-width variation under different P–T conditions. Because the method deals directly with lattice d spacing and local deformation caused by stress, it can be applied to process any diffraction profile, independent of detection mode. In addition, a correction routine is developed using diffraction elastic ratios to deal with severe surface strain and/or strain anisotropy effects related to nano-scale grain sizes, so that significant data scatter can be reduced in a physically meaningful way. Graphical illustration of the resultant microstrain analysis can identify micro/local yields at the grain-to-grain interactions resulting from high stress concentration, and macro/bulk yield of the plastic deformation over the entire sample. This simple and straightforward approach is capable of revealing the corresponding micro and/or macro yield stresses, grain crushing or growth, work hardening or softening, and thermal relaxation under high-P–T conditions, as well as the intrinsic residual strain and/or surface strain in the polycrystalline bulk. In addition, this approach allows the instrumental contribution to be illustrated and subtracted in a straightforward manner, thus avoiding the potential complexities and errors resulting from instrument correction. Applications of the method are demonstrated by studies of α-SiC (6H, moissanite) and of micro- and nanocrystalline nickel by synchrotron X-ray and time-of-flight neutron diffraction.

On the modelling of non‐linear kinematic hardening at finite strains with application to springback—Comparison of time integration algorithms

Abstract: The paper discusses the derivation and the numerical implementation of a finite strain material model for non-linear kinematic and isotropic hardening. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening. In addition, a comparison between several numerical algorithms for the integration of the evolution equations is conducted. In particular, a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables, as well as two modifications of the backward Euler scheme are discussed. Finally, the applicability of the model for springback prediction is demonstrated by performing simulations of the draw-bending process and a comparison with experiments. The results show an excellent agreement between simulation and experiment. Copyright © 2007 John Wiley & Sons, Ltd.

Strain-Controlled Low-Cycle Fatigue Properties of a Newly Developed Extruded Magnesium Alloy

Abstract: To reduce fuel consumption and greenhouse gas emissions, magnesium alloys are being considered for automotive and aerospace applications due to their low density, high specific strength and stiffness, and other attractive traits. Structural applications of magnesium components require low-cycle fatigue (LCF) behavior, since cyclic loading or thermal stresses are often encountered. The aim of this article was to study the cyclic deformation characteristics and evaluate LCF behavior of a recently developed AM30 extruded magnesium alloy. This alloy exhibited a strong cyclic hardening characteristic, with a cyclic strain-hardening exponent of 0.33 compared to the monotonic strain-hardening exponent of 0.15. With increasing total strain amplitude, both plastic strain amplitude and mean stress increased and fatigue life decreased. A significant difference between the tensile and compressive yield stresses occurred, leading to asymmetric hysteresis loops at high strain amplitudes due to twinning in compression and subsequent detwinning in tension. A noticeable change in the modulus was observed due to the pseudoelastic behavior of this alloy. The Coffin–Manson law and Basquin equation could be used to describe the fatigue life. At low strain ratios the alloy showed strong cyclic hardening, which became less significant as the strain ratio increased. The lower the strain ratio, the lower the stress amplitude and mean stress but the higher the plastic strain amplitude, corresponding to a longer fatigue life. Fatigue life also increased with increasing strain rate. Fatigue crack initiation occurred from the specimen surface and crack propagation was mainly characterized by striation-like features. Multiple initiation sites at the specimen surface were observed at higher strain amplitudes.

Identification of Mechanical Material Behavior Through Inverse Modeling and DIC

Abstract: Inverse methods offer a powerful tool for the identification of the elasto-plastic material parameters. One of the advantages with respect to classical material testing is the fact that those inverse methods are able to deal with heterogeneous deformation fields. The basic principle of the inverse method that is presented in this paper, is the comparison between experimentally measured strain fields and those computed by the finite element (FE) method. The unknown material parameters in the FE model are iteratively tuned so as to match the experimentally measured and the numerically computed strain fields as closely as possible. This paper describes the application of an inverse method for the identification of the hardening behavior and the yield locus of DC06 steel, based on a biaxial tensile test on a perforated cruciform specimen. The hardening behavior is described by a Swift type hardening law and the yield locus is modeled with a Hill 1948 yield surface.

Grain structure and dislocation density measurements in a friction-stir welded aluminum alloy using X-ray peak profile analysis

Abstract: The dislocation density and grain structure of a friction-stir welded 6061-T6 aluminum alloy were determined as a function of distance from the weld centerline using high-resolution micro-beam X-ray diffraction. The results of the X-ray peak profile analysis show that the dislocation density is about 1.2 × 1014 m−2 inside and 4.8 × 1014 m−2 outside of the weld region. The average subgrain size is about 180 nm in both regions. Compared to the base material, the dislocation density was significantly decreased in the dynamic recrystallized zone of the friction-stir welds, which is in good correlation with the TEM observations. The influence of the dislocation density on the strain hardening behavior during tensile deformation is also discussed.

Analysis of the mechanical properties and deformation behavior of nanostructured commercially pure Al processed by equal channel angular pressing (ECAP)

Abstract: In the present paper commercially pure Al was processed by equal channel angular pressing (ECAP) up to 8 passes using route B C . For ECAP processing a proper die set was designed and constructed. Transmission electron microscope (TEM) and electron backscatter diffraction (EBSD) were used to evaluate the microstructure of the pressed materials. Mechanical properties and the deformation behavior of the ECAP processed material were investigated by the hardness and compression tests. The significant increase in hardness and yield stress after ECAP was discussed by two strengthening mechanisms. Based on these mechanisms, variations of the hardness and yield stress as a function of the pass numbers were related to the calculated dislocation densities and the average boundary spacing. Also it was suggested that the absorption of the dislocations into grain boundaries would be an effective recovery process for the absence of the strain hardening.

Evaluation of crack opening performance of a repair material with strain hardening behavior

Abstract: One of the novel mechanical properties of strain hardening cementitious composites (SHCC) is that they exhibit multiple fine cracks and strain hardening in tension. This promotes the use of SHCC as an effective repair material, because penetration of substances through the fine cracks is greatly reduced. Most research on SHCC has focused on its behavior and results obtained from uniaxial tensile tests. However, the crack distribution of the repair material (SHCC) layer is more concentrated adjacent to an existing crack in a substrate. So the design procedure considering the crack opening, which represents the potential for localized fracture, should be established for appropriate material selection. In this paper, the performance of SHCC as a repair material was assessed through three tests: uniaxial tensile tests; zero-span tensile tests; and flexural tests of RC beams repaired with SHCC. Comparisons between crack opening performances and the observed crack patterns of the three tests were conducted. The crack opening and crack pattern obtained from the zero-span tensile tests were similar to those of the repaired beam specimens. According to the zero-span tensile tests, the performance of cracking behavior of the repair material on an existing crack can be estimated. On the other hand, the deformation capacity of SHCC obtained from the uniaxial tensile tests cannot be directly applied to the design of surface repair application.

A study on the mechanical properties of cryorolled Al–Mg–Si alloy

Abstract: The mechanical properties of a precipitation hardenable Al–Mg–Si alloy subjected to cryorolling and ageing treatments are reported in this present work. The severe strain induced during cryorolling of Al–Mg–Si alloys in the solid solutionised state produces ultrafine microstructures with improved mechanical properties such as strength and hardness. The improved strength and hardness of cryorolled alloys are due to the grain size effect and higher dislocation density. The ageing treatment of cryorolled Al–Mg–Si alloys has improved its strength and ductility significantly due to the precipitation hardening and grain coarsening mechanisms, respectively. The reduction in dimple size of cryorolled Al–Mg–Si alloy upon failure confirms the grain refinement and strain hardening mechanism operating in the severely deformed samples.

Correlation of tensile and flexural responses of strain softening and strain hardening cement composites

Abstract: Closed form equations for generating moment–curvature response of a rectangular beam of fiber reinforced concrete are presented. These equations can be used in conjunction with crack localization rules to predict flexural response of a beam under four point bending test. Parametric studies simulated the behavior of two classes of fiber reinforced concrete: strain softening and strain hardening materials. The simulation revealed that the direct use of uniaxial tension and compression responses under-predicted the flexural response for strain softening material while a good prediction for strain hardening material was obtained. The importance of strain softening range on the flexural response is discussed using non-dimensional post-peak parameters. Results imply that the brittleness and size effect are more pronounced in the flexural response of brittle materials, while more accurate predictions are obtained with ductile materials. It is also demonstrated that correlations of tensile and flexural results can be established using normalized uniaxial tension and compression models with a single scaling factor.

Effect of ferrite volume fraction on work hardening behavior of high bainite dual phase (DP) steels

Abstract: AISI 4340 steel was heated to 910 °C for 1 h then directly transferred to 750 °C and intercritically annealed for different times to obtain different ferrite volume fractions and then isothermally held at 350 °C for 40 min followed by air cooling to room temperature. Samples of these steels with dual phase ferrite–bainite structure were tensile tested at room temperature. The tensile flow stress data for this steel with different ferrite volume fraction was analyzed in term of Hollomon equation. It is seen that the two Hollomon equations can describe the flow behavior adequately and found that the work hardening takes place in two stages which each equation belong to the one of work hardening stages. In this study the effects of constituent volume fraction on Hollomon equation parameters (work hardening exponent and strength coefficient), onset strain of stage II work hardening, yield strength, ultimate tensile strength and ductility were investigated. Results showed that the yield strength, ultimate tensile strength and work hardening decrease linearly with increasing ferrite volume fraction whilst ductility increases. Finally, variations of these mechanical properties with differing ferrite volume fraction are used to rationalize the deformation mechanisms activated at different stages.

Strain hardening of polymer glasses: entanglements, energetics, and plasticity.

Abstract: Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.

Effect of grain refinement on mechanical properties of ball-milled bulk aluminum

Abstract: In this study, high quality bulk ultra-fine grained and nanocrystalline pure aluminum samples were prepared through room temperature ball milling, cold and warm compaction, sintering, and annealing processes. The as-received (−325 mesh) powder was subjected to different milling times in order to achieve specimens with different average grain sizes (d). The prepared samples were then subjected to uniaxial compressive loading to large strains (∼45%) to investigate the effect of grain size on the stress–strain response of the material. The 10-h milled bulk nanocrystalline samples (d = 82 nm) were tested at a very wide range of strain rates from quasi-static to dynamic regimes. The strain rate sensitivity of the material increased as the grain size was reduced to nanometer realm; the flow stress, and work hardening behavior were dramatically influenced by change in the grain size (milling time).