Showing papers on "Necking published in 2004"

A comprehensive failure model for crashworthiness simulation of aluminium extrusions

Abstract: A correct representation of the plastic deformation and failure of individual component parts is essential to obtaining accurate crashworthiness simulation results The aim of this paper is to present a comprehensive approach for predicting failure in a component based on macroscopic strains and stresses This approach requires the use of a number of different failure mechanism representations, such as necking (due to local instabilities), as well as ductile and shear fracture All failure criteria have been developed in a way to include the influence of non-linear strain paths The effectiveness of this approach in predicting failure is then discussed by comparing numerical results with test data by three point bending and axial compression tests of double chamber extrusion components All studies presented in this paper were carried out on extrusions made from aluminium alloy EN AW-7108 T6

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.

Uniaxial True Stress-Strain after Necking

Abstract: A weighted-average method for determining uniaxial, true tensile stress vs. strain relation after necking is presented for strip shaped samples. The method requires identification of a lower and an upper bound for the true stress-strain function after necking and expresses the true stress-strain relation as the weighted average of these two bounds. The weight factor is determined iteratively by a finite element model until best agreement between calculated and experimental loadextension curves is achieved. The method was applied to various alloys.

Mode I fracture of sheet metal

Abstract: The perceived wisdom about thin sheet fracture is that (i) the crack propagates under mixed mode I & III giving rise to a slant through-thickness fracture profile and (ii) the fracture toughness remains constant at low thickness and eventually decreases with increasing thickness. In the present study, fracture tests performed on thin DENT plates of various thicknesses made of stainless steel, mild steel, 6082-O and NS4 aluminium alloys, brass, bronze, lead, and zinc systematically exhibit (i) mode I "bath-tub", i.e. "cup & cup", fracture profiles with limited shear lips and significant localized necking (more than 50% thickness reduction), (ii) a fracture toughness that linearly increases with increasing thickness (in the range of 0.5-5 mm). The different contributions to the work expended during fracture of these materials are separated based on dimensional considerations. The paper emphasises the two parts of the work spent in the fracture process zone: the necking work and the "fracture" work. Experiments show that, as expected, the work of necking per unit area linearly increases with thickness. For a typical thickness of I mm, both fracture and necking contributions have the same order of magnitude in most of the metals investigated. A model is developed in order to independently evaluate the work of necking, which successfully predicts the experimental values. further-more, it enables the fracture energy to be derived from tests performed with only one specimen thickness. In a second modelling step, the work of fracture is computed using an enhanced void growth model valid in the quasi plane stress regime. The fracture energy varies linearly with the yield stress and void spacing and is a strong function of the hardening exponent and initial void volume fraction. The coupling of the two models allows the relative contributions of necking versus fracture to be quantified with respect to (i) the two length scales involved in this problem, i.e. the void spacing and the plate thickness, and (ii) the flow properties of the material. Each term can dominate depending on the properties of the material which explains the different behaviours reported in the literature about thin plate fracture toughness and its dependence with thickness. (C) 2003 Elsevier Ltd. All rights reserved.

Transition of deformation and fracture behaviors in nanostructured face-centered-cubic metals

Abstract: Tensile stress–strain curves demonstrate that single-phase nanocrystalline face-centered-cubic (fcc) metals are intrinsically ductile and their failure begins with necking. However, the area reductions and the fracture behaviors were found to be dependent on the grain size. When plastic deformation is governed by dislocation activity, the nanocrystalline samples behave similar to the conventional coarse-grained materials. As the grain size is reduced to the regime where grain boundary sliding dominates, the material shows very high strain-hardening rate and the tensile samples fail by microcracking with no noticeable reduction in area.

Ductile rupture in thin sheets of two grades of 2024 aluminum alloy

Abstract: The damage and rupture mechanisms of thin sheets of 2024 aluminum alloy (Al containing Cu, Mn, and Mg elements) are investigated. Two grades are studied: a standard alloy and a high damage tolerance alloy. The microstructure of each material is characterized to obtain the second phase volume content, the dimensions of particles and the initial void volume fraction. The largest particles consist of intermetallics. Mechanical tests are carried out on flat specimens including U-notched (with various notch radii), sharply V-notched and smooth tensile samples. Stable crack growth was studied using “Kahn samples” and pre-cracked large center-cracked tension panels M(T). The macroscopic fracture surface of the different specimens is observed using scanning electron microscopy. Smooth and moderately notched samples exhibit a slant fracture surface, which has an angle of about 45° with respect to the loading direction. With increasing notch severity, the fracture mode changes significantly. Failure initiates at the notch root in a small triangular region perpendicular to the loading direction. Outside this zone, slant fracture is observed. Microscopic observations show two failure micromechanisms. Primary voids are first initiated at intermetallic particles in both cases. In flat regions, i.e. near the notch root of severely notched samples, void growth is promoted and final rupture is caused by “internal necking” between the large cavities. In slanted regions these voids tend to coalesce rapidly according to a “void sheet mechanism” which leads to the formation of smaller secondary voids in the ligaments between the primary voids. These observations can be interpreted using finite element simulations. In particular, it is shown that crack growth occurs under plane strain conditions along the propagation direction.

Effect of cube texture on sheet metal formability

Abstract: The effect of the cube texture on the initiation of localized necking is studied numerically. The forming limit diagram (FLD) is constructed based on crystal plasticity theory in conjunction with the well-known M–K approach. It is found that, while the ideal cube texture decreases formability, a spread about cube significantly delays the initiation of localized necking when a sheet undergoes biaxial tension. The effect of the cube texture on the predicted FLDs is discussed in terms of the sharpness of the yield locus near equi-biaxial tension.

Identification of Material Parameters for Constitutive Equations

Abstract: This contribution addresses various topics on parameter identification for constitutive equations on the basis of experimental data. Starting from basic characteristics of inverse problems illustrated by simple examples, four different identification methods are introduced. Then particular aspects of the least squares approach are outlined, such as optimization, local minima, sensitivity analysis, consequences of instabilities, and stochastic methods. Uniform small strain problems and nonuniform large strain problems are considered, where for the latter finite element results are incorporated into the optimization process. The examples are concerned with a perturbation technique in order to detect possible instabilities, a stochastic analysis in order to examine the uncertainty of parameter estimates, and a necking problem observed with an optical method in order to take into account nonuniform large strains during the experiment. Keywords: inverse problems; optimization; stochastic methods; plasticity; large strains

Plastic deformation behavior of aluminum casting alloys A356/357

Abstract: The plastic deformation behavior of aluminum casting alloys A356 and A357 has been investigated at various solidification rates with or without Sr modification using monotonic tensile and multi-loop tensile and compression testing. The results indicate that at low plastic strains, the eutectic particle aspect ratio and matrix strength dominate the work hardening, while at large plastic strains, the hardening rate depends on secondary dendrite arm spacing (SDAS). For the alloys studied, the average internal stresses increase very rapidly at small plastic strains and gradually saturate at large plastic strains. Elongated eutectic particles, small SDAS, or high matrix strength result in a high saturation value. The difference in the internal stresses, due to different microstructural features, determines the rate of eutectic particle cracking and, in turn, the tensile instability of the alloys. The higher the internal stresses, the higher the damage rate of particle cracking and then the lower the Young’s modulus. The fracture strain of alloys A356/357 corresponds to the critical amount of damage by particle cracking locally or globally, irrespective of the fineness of the microstructure. In the coarse structure (large SDAS), this critical amount of damage is easily reached, due to the clusters of large and elongated particles, leading to alloy fracture before global necking. However, in the alloy with the small SDAS, the critical amount of damage is postponed until global necking takes place due to the small and round particles. Current models for dispersion hardening can be used to calculate the stresses induced in the particles. The calculations agree well with the results inferred from the experimental results.

Procedure for the Determination of True Stress-Strain Curves From Tensile Tests With Rectangular Cross-Section Specimens

Abstract: The problem of determining true stress-strain curves from flat tensile specimens beyond the onset of necking has been investigated based on finite element analyses under consideration of experimental accessible data using digital image correlation (DIC). The displacement field on the specimen surface is determined by in-situ deformation field measurement. A three-dimensional finite element study with different stress-strain-curves has been carried out to develop a formula, with which it is possible to calculate the true stress subject to the strain in the necking region. The method has been used to evaluate the true stress-strain curve with a so-called micro flat tensile specimen, which is normally used to determine the material properties in the material gradient around thin weldments.

In-Plane Mechanical Properties of an All-Oxide Ceramic Composite

Abstract: The present article examines the in-plane tensile properties of a two-dimensional (2D) all-oxide ceramic composite. The distinguishing characteristics of the material include fine-scale porosity within the matrix and the absence of a fiber coating. The anisotropy in the elastic-plastic properties has been studied through tension tests in the axial (fiber) direction and at 45° to the fiber axes, both in the presence and the absence of holes or notches. The notch sensitivity in the axial direction is comparable to that of conventional dense-matrix, weak-interface composites, demonstrating the effectiveness of the porous matrix in enabling crack deflection and damage tolerance. Furthermore, the notch sensitivity is rationalized using models that account for the effects of inelastic straining on the local stress distributions around notches and holes, coupled with a scale-dependent failure criterion. In the off-axis orientation, the tensile strength is dictated by a plastic instability, analogous to necking in metals. Following instability, deformation continues within a diffuse localized band, with a length comparable to the specimen width. Similar deformation and fracture characteristics are obtained both with and without holes. The off-axis properties are discussed in terms of the comminution and rearrangement of matrix particles during straining.

Size-effects in plane strain sheet-necking

Abstract: A finite strain generalization of the strain gradient plasticity theory by Fleck and Hutchinson (J. Mech. Phys. Solids 49 (2001a) 2245) is proposed and used to study size effects in plane strain necking of thin sheets using the finite element method. Both sheets with rigid grips at the ends and specimens with shear free ends are analyzed. The strain gradient plasticity theory predicts delayed onset of localization when compared to conventional theory, and it depresses deformation localization in the neck. The sensitivity to imperfections is analyzed as well as differently hardening materials.

A mesoscopic approach for predicting sheet metal formability

Abstract: A mesoscopic approach for constructing a forming limit diagram (FLD) is developed. The approach is based on the concept of a unit cell. The unit cell is macroscopically infinitely small and thus represents a material point in the sheet, and is microscopically finitely large and thus contains a sufficiently large number of grains. The responses of the unit cell under biaxial tension are calculated using the finite element method. Each element of a mesh/unit cell represents an orientation and the constitutive response at an integration point is described by the single crystal plasticity theory. It is demonstrated that the limit strains are the natural outcomes of the mesoscopic approach, and the artificial initial imperfection necessitated by the macroscopic M–K approach is not relevant in the mesoscopic approach. The effects of strain-rate sensitivity, single slip hardening and latent hardening, texture evolution, crystal elasticity and spatial orientation distribution on necking are discussed. Numerical results based on the mesoscopic approach are compared with experimental data.

Creep mechanisms and physical modeling for Ti–6Al–4V

Abstract: The creep behavior of Ti–6Al–4V is investigated at 500 and 600 °C under constant load. The correlation between the values of activation energy and stress exponents indicates that the primary creep, as well as the steady-state creep, was controlled by dislocation climb in the hexagonal phase. The increase in tertiary creep rate was related to the necking development and to nucleation and coalescence of microvoids. The creep rupture data follows the Monkman–Grant relationship under the explored test conditions. Continuum damage mechanics has been applied to develop a constitutive equation, denominated ν concept, which express the strain–time relation. The physical modeling is based on the Ion et al. and Kachanov–Rabotnov formalism. The approach leads to the definition of an operational parameter set, which characterize the three stages of the normal creep curve. For a preliminary evaluation, the parameter set together with an experimental database allows the interpolation and the calculations of creep strain and lifetime. Good agreement has been shown between creep predictions and experimental data of creep curves to different stresses for short-term tests.

Comparison of the plastic deformation and failure of A359/SiC and 6061-T6/Al2O3 metal matrix composites under dynamic tension

Abstract: A comparison is presented of the dynamic plastic deformation and tensile failure of two metal-matrix composites (one with a cast alloy matrix and the other with a wrought alloy matrix). The two composites are ceramic particle reinforced aluminum alloys: F3S.20S (A359 aluminum alloy reinforced by 20% SiC particles) and W6A20A (6061-T6 aluminum alloy reinforced by 20% Al2O3 particles). The corresponding unreinforced matrix alloys were also examined. The effects of strain rate on the tensile responses of these composites were determined using the tension Kolsky bar. The microstructures and fracture surfaces of the specimens of each composite were examined using SEM and optical microscopy. The experimental results show that the flow stresses of both composites are higher than that of their matrix alloys, whereas the composite fracture strains are lower. The fracture strains of the W6A20A composite and the 6061-T6 monolithic matrix alloy were much higher than those of the F3S20S composite and the A359 monolithic matrix alloy. Both the W6A20A composite and 6061-T6 monolithic matrix alloy behaved in a ductile manner with necking prior to fracture, while both the F3S.20S composite and A359 monolithic matrix alloy behaved in a brittle manner with no necking prior to fracture. Microscopic examination revealed tensile failure of the A359 matrix alloy and its composite to be controlled by the microcracking of Si network, which formed in the interdendritic silicon rich region, whereas failure of the 6061-T6 based composite is controlled by cracking of reinforcement particles.

Influence of microstructure-driven strain localization on the ductile fracture of metallic alloys

Abstract: Most models in the literature that are used to understand and predict ductile failure, ductility or fracture toughness implicitly consider that the plastic response of the material is homogeneous at the level of the microstructure. However, in a number of situations, plasticity is intrinsically localized, because the microstructure is spatially heterogeneous, or because the loading leads to strain localization on the microscale, such as in fatigue loading, or because the dynamics of plastic flow are unstable, such as in Portevin-Le Chatelier instabilities. This paper presents, from analysing various examples, the influence of these strain localization phenomena on the ductile fracture behaviour of metallic alloys. Examples to illustrate these effects will be chosen from, firstly, internal necking between cavities growing to ductile fracture, secondly, damage mechanisms from fatigue persistent slip bands, thirdly, the effect of Portevin-Le Chatelier bands on toughness and, fourthly, damage mechanisms in alloys with precipitate-free zones at grain boundaries.

Deformation Behavior of NiTi/Polymer Shape Memory Alloy Composites – Experimental Verifications

Abstract: Composites containing NiTi shape memory alloy (SMA) long-fiber, short-fibers or Ti long-fiber in a Polycarbonate (PC) matrix have been fabricated by the injection molding technique. Also, prestrained SMA long-fiber/Epoxy matrix composites have been fabricated. The fracture behavior and thermo-mechanical deformation behavior are examined; (1) Fracture behavior – uniaxial tensile tests up to fracture for SMA long-fiber and short-fiber composite (SMAC). (2) Thermomechanical deformation behavior – tensile loading–unloading tests for Pseudoelastic (PE) long-fiber/PC matrix composites. Several thermo-mechanical loading tests for Shape Memory Effect (SME) long-fiber/PC matrix and SME long-fiber/Epoxy matrix composites were used.The obtained results are as follows: (1) The stress–strain relation up to the final fracture of the Shape Memory Alloy Composites (SMACs) showed the repeated up-and-down of the stress which corresponds to the necking of the specimen, fiber fracture, and matrix fracture. The strain for the...

Superplastic behavior and microstructure evolution in a commercial Al-Mg-Sc alloy subjected to intense plastic straining

Abstract: A commercial Al-6 pct Mg-0.3 pct Sc-0.3 pct Mn alloy subjected to equal-channel angular extrusion (ECAE) at 325 °C to a total strain of about 16 resulted in an average grain size of about 1 µm. Superplastic properties and microstructural evolution of the alloy were studied in tension at strain rates ranging from 1.4 × 10−5 to 1.4 s−1 in the temperature interval 250 °C to 500 °C. It was shown that this alloy exhibited superior superplastic properties in the wide temperature range 250 °C to 500 °C at strain rates higher than 10−2 s−1. The highest elongation to failure of 2000 pct was attained at a temperature of 450 °C and an initial strain rate of 5.6 × 10−2 s−1 with the corresponding strain rate sensitivity coefficient of 0.46. An increase in temperature from 250 °C to 500 °C resulted in a shift of the optimal strain rate for superplasticity, at which highest ductility appeared, to higher strain rates. Superior superplastic properties of the commercial Al-Mg-Sc alloy are attributed to high stability of ultrafine grain structure under static annealing and superplastic deformation at T ≤ 450 °C. Two different fracture mechanisms were revealed. At temperatures higher than 300 °C or strain rates less than 10−1 s−1, failure took place in a brittle manner almost without necking, and cavitation played a major role in the failure. In contrast, at low temperatures or high strain rates, fracture occurred in a ductile manner by localized necking. The results suggest that the development of ultrafine-grained structure in the commercial Al-Mg-Sc alloy enables superplastic deformation at high strain rates and low temperatures, making the process of superplastic forming commercially attractive for the fabrication of high-volume components.