Showing papers on "Necking published in 2009"

Influence of specimen dimensions and strain measurement methods on tensile stress–strain curves

Abstract: Miniature tensile specimens, having various sizes and geometries, are often used to measure the mechanical properties of bulk nanostructured materials. However, these samples are generally too small for use with conventional extensometers so that the strains are usually calculated from the crosshead displacements. This study uses experimental results and finite element modeling (FEM) to critically evaluate the influence of the specimen dimensions and strain measurement methods on the tensile curves obtained from miniature specimens. Using coarse-grained Cu as a model material, the results demonstrate that the values of strain obtained from the crosshead displacement are critically influenced by the specimen dimensions such that the uniform elongation and the post-necking elongation both increase with decreasing gauge length and increasing specimen thickness. The results provide guidance on the optimum procedures for the tensile testing of miniature specimens of both coarse-grained and nanostructured materials.

On the Application of Stress Triaxiality Formula for Plane Strain Fracture Testing

Abstract: Theoretical and experimental studies have shown that stress triaxiality is the key parameter controlling the magnitude of the fracture strain. Smooth and notched round bar specimens are mostly often used to quantify the effect of stress triaxiality on ductile fracture strain. There is a mounting evidence (Bai and Wierzbicki, 2008, "A New Model of Metal Plasticity and Fracture With Pressure and Lode Dependence," Int. J. Plast., 24(6), pp. 1071-1096) that, in addition to the stress triaxiality, the normalized third deviatoric stress invariant (equivalent to the Lode angle parameter) should also be included in characterization of ductile fracture. The calibration using round notched bars covers only a small range of possible stress states. Plane strain fracture tests provide additional important data. Following Bridgman's stress analysis inside the necking of a plane strain specimen, a closed-form solution is derived for the stress triaxiality inside the notch of a flat-grooved plane strain specimen. The newly derived formula is verified by finite element simulations. The range of stress triaxiality in round notched bars and flat-grooved specimens is similar, but the values of the Lode angle parameter are different. These two groups of tests are therefore very useful in constructing a general 3D fracture locus. The results of experiments and numerical simulations on 1045 and DH36 steels have proved the applicability of the closed-form solution and have demonstrated the effect of the Lode angle parameter on the fracture locus.

Malleable hypoeutectic Zr–Ni–Cu–Al bulk glassy alloys with tensile plastic elongation at room temperature

Abstract: A new bulk glassy alloy (BGA) showing macroscopic tensile plastic elongation at room temperature has been developed in the hypoeutectic Zr–Ni–Cu–Al alloy system. The hypoeutectic Zr–Ni–Cu–Al BGA shows a high Poisson's ratio, a low Young's modulus, and is highly malleable in compression. It exhibits a Poisson's ratio of 0.39, a Young's modulus of 73 GPa, and a distinct tensile plastic elongation of about 1.7% at room temperature with necking due to the operation of many shear bands. The tensile plastic deformability seems to originate from modifications of the glass structure with increasing the number of Zr–Zr atomic pairs in the hypoeutectic composition.

Large plasticity and tensile necking of Zr-based bulk-metallic-glass-matrix composites synthesized by the Bridgman solidification

Abstract: The microstructures of the in situ bulk-metallic-glass-matrix composites are usually controlled by changing the alloy compositions. In this paper, Zr-based bulk-metallic-glass-matrix composites containing dendrites with a fixed composition of Zr37.5Ti32.2Nb7.2Cu6.1Be17.0 are synthesized by the Bridgman solidification. The sizes and volume fractions of dendrites in the composites are controlled by adjusting the withdrawal velocities. A linear relationship between the spanning lengths of individual dendrites and the withdrawal velocities is established. Large plasticity and tensile necking can be obtained by only controlling the cooling condition.

Full Field Strain Measurement in Compression and Tensile Split Hopkinson Bar Experiments

Abstract: The 3D image correlation technique is used for full field measurement of strain (and strain rate) in compression and tensile split Hopkinson bar experiments using commercial image correlation software and two digital high-speed cameras that provide a synchronized stereo view of the specimen. Using an array of 128 × 80 (compression tests) and 258 × 48 (tensile tests) pixels, the cameras record about 110,000 frames per second. A random dot pattern is applied to the surface of the specimens. The image correlation algorithm uses the dot pattern to define a field of overlapping virtual gage boxes, and the 3-D coordinates of the center of each gage box are determined at each frame. The coordinates are then used for calculating the strains throughout the surface of the specimen. The strains determined with the image correlation method are compared with those determined from analyzing the elastic waves in the bars, and with strains measured with strain gages placed on the specimens. The system is used to study the response of OFE C10100 copper. In compression tests, the image correlation shows a nearly uniform deformation which agrees with the average strain that is determined from the waves in the bars and the strains measured with strain gages that are placed directly on the specimen. In tensile tests, the specimen geometry and properties affect the outcome from the experiment. The full field strain measurement provides means for examining the validity and accuracy of the tests. In tests where the deforming section of the specimen is well defined and the deformation is uniform, the strains measured with the image correlation technique agree with the average strain that is determined from the split Hopkinson bar wave records. If significant deformation is taking place outside the gage section, and when necking develops, the strains determined from the waves are not valid, but the image correlation method provides the accurate full field strain history.

Failure by simultaneous grain growth, strain localization, and interface debonding in metal films on polymer substrates

Abstract: In a previous paper, we have demonstrated that a microcrystalline copper film well bonded to a polymer substrate can be stretched beyond 50% without cracking. The film eventually fails through the coevolution of necking and debonding from the substrate. Here we report much lower strains to failure (approximately 10%) for polymer-supported nanocrystalline metal films, the microstructure of which is revealed to be unstable under mechanical loading. We find that strain localization and deformation-associated grain growth facilitate each other, resulting in an unstable deformation process. Film/substrate delamination can be found wherever strain localization occurs. Therefore, we propose that three concomitant mechanisms are responsible for the failure of a plastically deformable but microstructurally unstable thin metal film: strain localization at large grains, deformation-induced grain growth, and film debonding from the substrate.

Electromechanical instability in semicrystalline polymers

Abstract: When a layer of a semicrystalline polymer is subject to a tensile force in its plane and a voltage through its thickness, the deformation of the layer is initially homogeneous, but it then localizes. The electromechanical instability sets in when the force and the voltage reach critical conditions. The critical conditions are determined in this paper and are related to the following two special cases: the Considere condition for the necking instability and the Stark–Garton condition for the pull-in instability. The general critical conditions show that a tensile force can markedly reduce the critical voltage.

Fields of stored energy associated with localized necking of steel

Abstract: This paper describes an experimental procedure for the simultaneous determination of heat sources and mechanical energy involved locally during a heterogeneous tensile test. This procedure involves two complementary imaging techniques: digital image correlation (DIC) and infrared thermography (IRT). The first technique gives displacement fields from which strains are derived while the second provides temperature fields with which the heat sources are estimated using a local form of the heat equation. Moreover, a method based on integration of equilibrium equations under the plane stress assumption is used to determine the stress distribution during the test. The distribution of the local deformation energy developed by the material is then assessed using stress and strain-rate fields. Tensile tests were performed on thin flat steel samples. The results revealed early and gradual development of strain localization within the gauge part of the specimen. Energy balances were performed inside and outside the necking zone based on the assumption that the thermoelastic part of the behaviour remains linear and isotropic. Finally, indirect estimate of the stored energy led us to compute the time course of the local Taylor-Quinney coefficient. mechanical energy involved locally during a heterogeneous tensile test. This procedure involves two complementary imaging techniques: digital image correlation (DIC) and infrared thermography (IRT). The first technique gives displacement fields from which strains are derived while the second provides temperature fields with which the heat sources are estimated using a local form of the heat equation. Moreover, a method based on integration of equilibrium equations under the plane stress assumption is used to determine the stress distribution during the test. The distribution of the local deformation energy developed by the material is then assessed using stress and strain-rate fields. Tensile tests were performed on thin flat steel samples. The results revealed early and gradual development of strain localization within the gauge part of the specimen. Energy balances were performed inside and outside the necking zone based on the assumption that the thermoelastic part of the behaviour remains linear and isotropic. Finally, indirect estimate of the stored energy led us to compute the time course of the local Taylor-Quinney coefficient.

Strain and stress relation for non-linear finite element simulations

Abstract: This paper presents a procedure to determine an element-length dependent strain and stress relation until fracture that is suitable for implementation in finite element models. This material relation is obtained experimentally with an optical measuring system. The strain until fracture is calculated from the measured surface displacements. The stress is derived from the measured force and the cross-sectional area in the necking region. Furthermore, because of the digital nature of the optical measurements, the strain reference length, being a function of the pixel size, is clearly defined. For the numerical simulation the finite element length is equal to this strain reference length. The overall procedure allows a precise numerical simulation of the tensile experiment until the point of fracture without curve fitting or an iterative procedure to adjust the material relation for the chosen mesh size. This precise material relation can improve non-linear numerical simulations.

Atomistic study of the mechanical response of copper nanowires under torsion

Abstract: The length, loading rate and thermal effects on the torsional response of hollow copper nanowires are investigated with molecular dynamics simulation. Evolution of atomic configuration is studied, which shows that partial dislocations nucleated from the surfaces accommodate the plastic deformation of the nanowires under torsion. With the increase in torsional angle, necking appears and the corresponding cross-section transforms from a hollow square to a solid circle. Meanwhile, atomic rearrangement from being amorphous to fcc occurs, which becomes more obvious at higher loading rates. To understand the relation between material and geometrical instabilities, the torsional buckling mode is also investigated and found to strongly depend on both wire length and temperature.

Elongational and shear rheology of carbon nanotube suspensions

Abstract: Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids—castor oil or its blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated. The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear and elongational measurements is addressed and interpreted. The results conform to the Herschel–Bulkley rheological constitutive equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple shear flow, which suggests that the original Herschel–Bulkley model need modification with the yield stress being a function of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning of Herschel–Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes.

Formability of Advanced High Strength Steels

Abstract: Novel draw-bend tests of 3 dual-phase (DP) steels utilizing velocity control of both actuators revealed three patterns of failure depending on draw speed, draw speed ratio, and R/t ratio. Shear failure occurs preferentially for smaller R/t and higher deformation rates. During draw bend tests, the temperature rises are significant, up 100°C before necking, with consequent loss of strength in affected regions. A novel 1-D constitutive equation relating flow stress to strain, strain rate, and temperature was developed based on tensile tests. FE simulations using the measured constitutive response predicted the types of failures accurately, without introducing damage mechanics. The deformation-induced heating is a critical part of the failure process.