Showing papers on "Necking published in 2008"

Uniaxial ratchetting and low-cycle fatigue failure of the steel with cyclic stabilizing or softening feature

Abstract: The ratchetting behaviour and low-cycle fatigue failure, as well as the interaction between them were investigated by uniaxial cyclic stressing tests for 42CrMo steel with annealing or tempering heat-treatment. The ratchetting strain and fatigue life of the material were measured in the uniaxial cyclic stressing with different loading levels. The effects of mean nominal stress, nominal stress amplitude and stress ratio on the ratchetting strain and final failure life were discussed. Simultaneously, the variations of responded strain amplitude with the number of cycles were illustrated to discuss the interaction between ratchetting and low-cycle fatigue failure behaviour. The experimental results show that the ratchetting and fatigue failure behaviours of the annealed 42CrMo steel are different from those of the tempered steel, since different cyclic softening/hardening features are caused by different heat treatments, i.e., the annealed 42CrMo steel presents cyclic stabilizing feature, but the tempered steel is cyclic softening. Two kinds of failure modes (i.e., ratchetting failure with obvious necking due to large ratchetting strain and fatigue failure due to low-cycle fatigue with nearly constant responded strain amplitude) take place, depending on mean nominal stress, nominal stress amplitude and stress ratio of uniaxial cyclic stressing, as well as the heat-treatment.

Material characterization at high strain rate by Hopkinson bar tests and finite element optimization

Abstract: In the present work, dynamic tests have been performed on AISI 1018 CR steel specimens by means of a split Hopkinson pressure bar (SHPB). The standard SHPB arrangement has been modified in order to allow running tensile tests avoiding spurious and misleading effects due to wave dispersion, specimen inertia and mechanical impedance mismatch in the clamping region. However, engineering stress–strain curves obtained from experimental tests are far from representing true material properties because of several phenomena that must be taken into account: the strain rate is not constant during the test, the specimen undergoes remarkable necking, so stress and strain distributions are largely non-uniform, and the temperature increases because of plastic work. Experimental data have been post-processed using a finite element-based optimization procedure where the specimen dynamic deformation is reproduced. Optimal sets of material constants for different constitutive models (Johnson–Cook, Zerilli–Armstrong and others) have been computed by fitting, in a least mean square sense, the numerical and experimental load–displacement curves.

Study on true stress correction from tensile tests

Abstract: Average true flow stress-logarithmic true strain curves can be usually obtained from a tensile test. After the onset of necking, the average true flow stress-logarithmic true strain data from a tensile specimen with round cross section should be modified by using the correction formula proposed by Bridgman. But there have been no firmly established correction formulae applicable to a specimen with rectangular cross section. In this paper, a new easy-to-use formula is presented based on parametric finite element simulations. The new formula requires only incremental plastic strain and hardening exponents of the material, which are simply presented from a tensile test. The newly proposed formula is verified with experimental data for high strength steel DH32 used in the shipbuilding and offshore industry and is proved to be effective during the diffuse necking regime.

Grain boundary effects on plastic deformation and fracture mechanisms in Cu nanowires: Molecular dynamics simulations

Abstract: Metallic nanowires have many attractive properties such as ultra-high yield strength and large tensile elongation. However, recent experiments show that metallic nanowires often contain grain boundaries, which are expected to significantly affect mechanical properties. By using molecular dynamics simulations, here, we demonstrate that polycrystalline Cu nanowires exhibit tensile deformation behavior distinctly different from their single-crystal counterparts. A significantly lowered yield strength was observed as a result of dislocation emission from grain boundaries rather than from free surfaces, despite of the very high surface to volume ratio. Necking starts from the grain boundary followed by fracture, resulting in reduced tensile ductility. The high stresses found in the grain boundary region clearly play a dominant role in controlling both inelastic deformation and fracture processes in nanoscale objects. These findings have implications for designing stronger and more ductile structures and devices on nanoscale.

Analysis of hardness–tensile strength relationships for electroformed nanocrystalline materials

Abstract: Tensile and hardness data from 198 electrodeposited nanocrystalline Ni- and Co-based specimens of varying shape, composition, microstructure and quality were analyzed in order to reveal whether the established hardness–strength relationships in frequent use for conventional coarse-grained metals and alloys can be applied to these ultrafine-grained materials. It was concluded that the H V = 3· σ UTS expression is a reliable predictor of the relationship between hardness and strength for nanocrystalline electrodeposits, provided the material is ductile enough to sustain tensile deformation up to a discernible peak load and does not instead fracture before the onset of necking instability. On the other hand, the widely used relationship H V = 3· σ Y was found to be inapplicable to this class of materials owing to the fact that they do not deform in an ideally plastic manner and instead exhibit plastic deformation that is characteristic of strain hardening behaviour.

Effect of ferrite grain size on tensile deformation behavior of a ferrite-cementite low carbon steel

Abstract: Stress–strain curves for ferrite-cementite (FC) steels with ferrite grain sizes between 0.47 and 13.6 μm were studied by tensile tests with strain rates of 103, 100, and 3.3 × 10−4 s−1 at 296 K. The stress–strain curves for the FC steels are categorized into two different types. In one type, the Luders deformation is interrupted due to the onset of necking, and in the other type, the Luders band propagates throughout the gage section of a tensile specimen followed by work-hardening. The lower yield and flow stresses increase while uniform and total elongations decrease with a decrease in ferrite grain size. The effect of ferrite grain size on flow stress is hardly dependent on strain rate. These experimental results reveal that the grain refinement strengthening contributes mainly to an increase in the athermal stress component.

Post-bifurcation analysis of a thin-walled hyperelastic tube under inflation

Abstract: We consider the problem of bulging, or necking, of an infinite thin-walled hyperelastic tube that is inflated by an internal pressure, with the axial stretch at infinity maintained at unity. We present a simple procedure that can be used to derive the bifurcation condition and to determine the near-critical behaviour analytically. It is shown that there is a bifurcation with zero mode number and that the associated axial variation of near-critical bifurcated configurations is governed by a first-order differential equation that admits a locally bulging or necking solution. This result suggests that the corresponding bifurcation pressure can be identified with the so-called initiation pressure which featured in recent experimental studies. This is supported by good agreement between our theoretical predictions and one set of experimental data. It is also shown that the Gent material model can support both bulging and necking solutions whereas the Varga and Ogden material models can only support bulging solutions. Relevance of the present method to the study of non-linear wave propagation in a fluid-filled distensible tube is also discussed.

On the dynamics of necking and fragmentation—II. Effect of material properties, geometrical constraints and absolute size

Abstract: In this series of papers, we investigate the mechanics of deformation localization and fragmentation in ductile materials. The behavior of ductile metals at strain rates between 4000 and 15,000 s−1 is considered. The expanding ring experiment is used as the primary tool for examining the material behavior in this range of strain rates. In Part I, the details of the experiment and the experimental observations on Al 6061-O were reported. Statistics of necking and fragmentation were evaluated and the process was modeled through the idea of the Mott release waves both from necking and fragmentation. Finally, it was shown that the strain in the ring in regions that strained uniformly never exceeded the necking strain. In the present paper, Part II, we address the issue of strain hardening and strain-rate sensitivity. Specifically, we examine different materials—Al 1100-H14, and Cu 101—in order to determine the role of material constitutive property on the dynamics of necking. These experiments reinforce the conclusion presented in Part I that the onset of necking essentially terminates the possibility of further straining in other parts of the ring and even more importantly that there is no influence of material inertia on the strain at the onset of necking in this wide range of materials. Furthermore, the effect of aspect ratio of the specimen is evaluated; this reveals that as the aspect ratio increases beyond about five, in addition to or instead of diffuse necking, localization into the sheet necking mode is observed; in this mode, the effect of ring expansion speeds is demonstrated to result in an increase of the strain at the onset of localization. In addition, an absolute size effect is observed: larger specimens exhibit localization at larger strain levels. These observations are explained in terms of plastic wave propagation and reproduced with finite element simulations. In future contributions as part of this sequel, we will explore the effect of other geometrical constraints and the effect of a compliant cladding or coating on the development of necking and fragmentation.

Identification of Heterogeneous Constitutive Parameters in a Welded Specimen: Uniform Stress and Virtual Fields Methods for Material Property Estimation

Abstract: Local strain data obtained throughout the entire weld region encompassing both the weld nugget and heat affected zones (HAZs) are processed using two methodologies, uniform stress and virtual fields, to estimate specific heterogeneous material properties throughout the weld zone. Results indicate that (a) the heterogeneous stress–strain behavior obtained by using a relatively simple virtual fields model offers a theoretically sound approach for modeling stress–strain behavior in heterogeneous materials, (b) the local stress–strain results obtained using both a uniform stress assumption and a simplified uniaxial virtual fields model are in good agreement for strains ɛ xx < 0.025, (c) the weld nugget region has a higher hardening coefficient, higher initial yield stress and a higher hardening exponent, consistent with the fact that the steel weld is overmatched and (d) for ɛ xx > 0.025, strain localization occurs in the HAZ region of the specimen, resulting in necking and structural effects that complicate the extraction of local stress strain behavior using either of the relatively simple models.

Observation of void nucleation, growth and coalescence in a model metal matrix composite using X-ray tomography

Abstract: A model material with a core/shell design has been fabricated. The core consists of 50 μ m diameter ZrO 2 /SiO 2 particles in a pure aluminum matrix (99.9%) while the shell consists of particle-free aluminum. Such a design allows the sample to deform in a controlled manner. Void nucleation, growth and coalescence were precisely captured via in situ tensile tests coupled with X-ray tomography. Samples with various volume fraction of particles in their core and various notch sizes have been tested. We show that the higher the volume fraction of particles and stress triaxiality, the lower the nucleation and coalescence strains. Depending on the interactions between voids and neck geometry, void growth occurs either mainly in the tensile direction or through the formation of a diamond-like shape. Finite element simulations and slip line fields demonstrate that the shape of the voids is a result of plasticity and neck geometry. Finally, a modified version of the Brown and Embury model for coalescence is developed to take into account the lower coalescence strains at high stress triaxialities.

Material aspects of dynamic neck retardation

Abstract: Neck retardation in stretching of ductile materials is promoted by strain hardening, strain-rate hardening and inertia. Retardation is usually beneficial because necking is often the precursor to ductile failure. The interaction of material behavior and inertia in necking retardation is complicated, in part, because necking is highly nonlinear but also because the mathematical character of the response changes in a fundamental way from rate-independent necking to rate-dependent necking, whether due to material constitutive behavior or to inertia. For rate-dependent behavior, neck development requires the introduction of an imperfection, and the rate of neck growth in the early stages is closely tied to the imperfection amplitude. When inertia is important, multiple necks form. In contrast, for rate-independent materials deformed quasi-statically, single necks are preferred and they can emerge in an imperfection-free specimen as a bifurcation at a critical strain. In this paper, the interaction of material properties and inertia in determining neck retardation is unraveled using a variety of analysis methods for thin sheets and plates undergoing plane strain extension. Dimensionless parameters are identified, as are the regimes in which they play an important role.

Dynamics of viscoelastic liquid filaments: low capillary number flows

Abstract: Many applications of viscoelastic free surface flows requiring formation of drops from small nozzles, e.g., ink-jet printing, micro-arraying, and atomization, involve predominantly extensional deformations of liquid filaments. The capillary number, which represents the ratio of viscous to surface tension forces, is small in such processes when drops of water-like liquids are formed. The dynamics of extensional deformations of viscoelastic liquids that are weakly strain hardening, i.e., liquids for which the growth in the extensional viscosity is small and bounded, are here modeled by the Giesekus, FENE-P, and FENE-CR constitutive relations and studied at low capillary numbers using full 2D numerical computations. A new computational algorithm using the general conformation tensor based constitutive equation [M. Pasquali, L.E. Scriven, Theoretical modeling of microstructured liquids: a simple thermodynamic approach, J. Non-Newtonian Fluid Mech. 120 (2004) 101–135] to compute the time dependent viscoelastic free surface flows is presented. DEVSS-TG/SUPG mixed finite element method [M. Pasquali, L.E. Scriven, Free surface flows of polymer solutions with models based on conformation tensor, J. Non-Newtonian Fluid Mech. 108 (2002) 363–409] is used for the spatial discretization and a fully implicit second-order predictor–corrector scheme is used for the time integration. Inertia, capillarity, and viscoelasticity are incorporated in the computations and the free surface shapes are computed along with all the other field variables in a fully coupled way. Among the three models, Giesekus filaments show the most drastic thinning in the low capillary number regime. The dependence of the transient Trouton ratio on the capillary number in the Giesekus model is demonstrated. The elastic unloading near the end plates is investigated using both kinematic [M. Yao, G.H. McKinley, B. Debbaut, Extensional deformation, stress relaxation and necking failure of viscoelastic filaments, J. Non-Newtonian Fluid Mech. 79 (1998) 469–501] and energy analyses. The magnitude of elastic unloading, which increases with growing elasticity, is shown to be the largest for Giesekus filaments, thereby suggesting that necking and elastic unloading are related.

Effect of loading history in necking and fracture

Abstract: The effect of Lode angle parameter, or the third deviatoric stress invariant, on plasticity and fracture is studied using flat-grooved transverse plane strain specimens. A generalized asymmetric plasticity model for isotropic materials with both pressure and Lode angle dependence is developed. Calibration method of the plasticity model is discussed in detail. Test results on 2024-T351 aluminum alloy confirmed the proposed plasticity model. Similarly, a generalized asymmetric 3D empirical fracture locus with six free parameters is proposed. The proposed fracture locus, which depends on both stress triaxiality (or pressure) and the Lode angle parameter, is calibrated using two types of methods: classical specimens under uniaxial testing, and the newly designed butterfly specimens under biaxial testing. Experimental results on 2024-T351 aluminum alloy, 1045 steel, and A710 steel validated the proposed 3D fracture locus. A concept of forming severity is introduced to study the loading history effect on metal forming limit diagram (FLD). Given the necking locus under proportional loading conditions, and using a non-linear accumulation rule of forming severity index, the proposed model well predicts the FLDs under different pre-loading conditions. As an extension of the ductile fracture locus defined and calibrated under proportional loading conditions, a new damage accumulation rule considering the loading history effect is proposed. The new model uses the accumulated difference between directions of the back stress tensor and the current stress tensor to describe the non-proportionality of a load path. Several types of tests with complex loading histories were designed and performed to study the loading history effect on ductile fracture. Extensive experimental studies on 1045 steel confirmed the proposed ductile fracture model. The proposed model is successfully applied to predict fracture of crushed prismatic tubes undergoing strain reversal. Thesis Supervisor: Tomasz Wierzbicki Title: Professor of Applied Mechanics