Onset Of Plastic Instability Research Articles

An improved analysis of small punch deformation for evaluating tensile properties

Small punch (SP) method is a promising technique for evaluating tensile properties using small volumes of test material, yet its applicability is bound by large errors in estimation of tensile yield strength (YS) using the yield force (FY) determined by the existing two tangent, offset or bilinear function fitting methods. In this study, a yield force (FY) based on the occurrence of yielding across the specimen thickness is identified through finite element analysis and a methodology is formulated for determination of FY from experimental data, supported with acoustic emission (AE) technique. The YS-FY correlation for various structural steels, Inconel and Aluminium exhibit excellent linearity and standard errors within ±7 %. Based on the onset of plastic instability in SP deformation at an inflection point (Fs, us) of force-deflection curve, the specimen deflection us is shown to correlate with tensile uniform strain better than parameter um (deflection at peak load). The tensile properties of neutron irradiated SS 316 evaluated from SP tests using the methodologies and SP-tensile correlations formulated in this work, are found to be within 6–8 % of the uniaxial tensile test results.

Mesoscopic unit cell analysis of ductile failure under plane stress conditions

Ductile failure under plane stress conditions is analyzed at the meso-scale using periodic unit cell model simulations of void growth in a plastically deforming matrix. Equivalent strains to failure by the onset of plastic instability at the macro-scale are estimated using the loss of ellipticity criterion for the equilibrium equations. Failure loci obtained from the cell model simulations are compared with the predictions of an instability-based ductile failure model and the Hosford–Coulomb damage indicator model, under both proportional and non-proportional loading conditions. The instability-based model is shown to quantitatively predict the shape of the failure locus under proportional loading, including the presence of a cusp at uniaxial tension and a ductility minimum under plane strain tension, in the absence of heuristic adjustable parameters in the failure criterion. It is shown that the characteristic shape of the plane stress failure locus is primarily due to the Lode dependence of the failure criterion, and not the damage growth law as assumed in the damage indicator models. Under non-proportional loading involving a step change in loading direction at an intermediate strain, the instability-based model correctly predicts the non-linear variation of the failure strain as a function of the intermediate strain; unlike a linear variation predicted by the damage indicator models, which is not in agreement with the cell model simulations. Forming limit curves showing the strains to the onset of localized necking in thin sheets are also obtained from the cell model simulations using an appropriate modification of the macroscopic instability criterion.

Estimation of UTS from small punch test using an improved method

Small punch test is a promising method for evaluating the tensile and fracture properties from small volumes of material especially for assessing material degradation of structural components in service. In this paper, the existing methods to determine ultimate tensile strength (UTS) from small punch test are revisited and an improved method is proposed and validated through finite element analysis and experiments. In the new method, the force corresponding to the inflection point in the slope of force-deflection curve in the membrane stretching regime is identified for UTS correlation. The onset of plastic instability during small punch deformation is associated with this inflection point. The UTS correlation determined from the slope based method exhibited stronger linearity with lower relative error compared to the existing methods for a wide range of material strength and ductility.

Ductile failure under non-proportional loading

Ductile failure by void growth in an elasto-plastic material subjected to non-proportional loading, involving step changes in the stress triaxiality or the Lode parameter, is investigated using periodic unit cell model simulations. The equivalent strains to failure by the onset of void coalescence, defined as the localization of plasticity along a band of voids at the micro-scale, are determined as a function of the loading path parameters. The observed trends for the ductility under non-proportional loading are found to be inconsistent with the predictions of a continuum damage mechanics model based on the attainment of a constant critical damage variable, even if the model has been calibrated to predict accurate results for the ductility under proportional loading. It is shown that a recently developed failure criterion based on the onset of plastic instability in a porous material, coupled with a micromechanics-based void growth law, predicts the loading path dependence of failure under non-proportional loading, in better agreement with the cell model simulation results than the continuum damage model. In particular, the triaxiality dependence of the ductility is found to be primarily due to the hydrostatic stress dependence of void growth, while the Lode dependence is primarily due to the instability-based failure criterion with a relatively minor effect of the Lode parameter on void growth. Implications of these findings on the current modeling approaches to ductile failure under shear dominated loading are discussed.

Understanding imprint formation, plastic instabilities and hardness evolutions in FCC, BCC and HCP metal surfaces

Nanoindentation experiments in metal surfaces are characterized by the onset of plastic instabilities along with the development of permanent nanoimprints and dense defect networks. This investigation concerns massive molecular dynamics simulations of nanoindentation experiments in FCC, BCC and HCP metals using blunted (spherical) tips of realistic size, and the detailed comparison of the results with experimental measurements. Our findings shed light on the defect processes which dictate the contact resistance to plastic deformation, the development of a transitional stage with abrupt plastic instabilities, and the evolution towards a self-similar steady-state characterized by the plateauing hardness p p at constant dislocation density ρ p . The onset of permanent nanoimprints is governed by stacking fault and nanotwin interlocking, the buildup of nanostructured regions and crystallites throughout the imprint, the cross-slip and cross-kinking of surfaced screw dislocations, and the occurrence of defect remobilization events within the plastic zone. As a result of these mechanisms, the ratio between the hardness p p and the Young's modulus E becomes higher in BCC Ta and Fe, followed by FCC Al, HCP Mg and large stacking fault width FCC Ni and Cu. Finally, when nanoimprint formation is correlated with the uniaxial response of the indented minuscule material volume, the hardness to yield strength ratio, p p / σ ys , varies from ≈ 7 to ≈ 10, which largely exceeds the continuum plasticity bound of ≈ 2.8. Our results have general implications to the understanding of indentation size-effects, where the onset of extreme nanoscale hardness values is associated with the occurrence of unique imprint-forming processes under large strain gradients.

Enhancing Strength-Ductility Synergy of a Co-Free Complex-Concentrated Alloy Via Tailored Multi-Heterogeneous Microstructure

The development of high-performance alloys with excellent strength-ductility synergy is a long-lasting research theme for materials science community, which also holds for the newly emerged complex-concentrated alloys (CCAs). Here, a multi-heterogeneous microstructure: featuring a multiscale grain distribution involving recrystallized ultrafine and fine grains mixed with unrecrystallized coarse grains, and high-content L1 2 nanoprecipitates, was intentionally introduced into a Co-free CCA through appropriate thermomechanical processing strategy. As such, the hetero-deformation induced (HDI) hardening and precipitation strengthening were co-effectively used, resulting in a high yield strength of 1.2 GPa, and an ultimate tensile strength of 1.4 GPa with exceptional uniform elongation of ~17.6%. The strength-ductility synergy of the multi-hetero microstructure was much enhanced over its precipitate-strengthened counterparts without heterogenous grains. We demonstrated that the high yield strength is mainly due to both the precipitate strengthening from nanoprecipitates and HDI strengthening from heterogeneous grains distribution. Benefiting from the structurally incompatible deformation accompanying with copious geometrically necessary dislocations near the hetero-interfaces, such multi-hetero microstructure revealed a distinctive up-turn strain hardening behavior due to the HDI hardening upon straining, and thus delayed the onset of plastic instability. Particularly, the unique lamellar-like distribution between recrystallized fine and ultrafine grains with high density of interfaces could effectively induce massive HDI hardening during deformation. The processing strategy described here is relatively simple and desirable for large scale process in modern industry at an economic cost.

Prediction of necking in HCP sheet metals using a two-surface plasticity model

In the present contribution, a two-surface plasticity model is coupled with several diffuse and localized necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension–compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension–compression yield asymmetry. Diffuse necking is predicted by the general bifurcation criterion. As to localized necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the prediction of diffuse and localized necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated.

Effect of anisotropy on the mechanical properties of polyurethane foams: An experimental and numerical study

The mechanical behaviour of anisotropic, closed-cell PU foams has been studied from the experimental and simulation viewpoints. Anisotropic PU foams with different densities were tested in compression along the rising and the perpendicular directions to determine the mechanical properties (elastic modulus and plateau stress). In addition, the microstructure of the foams (cell size distribution and anisotropy, cell wall thickness, etc.) was carefully measured and the mechanical properties of the solid PU within the foam were determined by means of nanoindentation. This information was used to build realistic representative volume elements of the microstructure of the foams by means of Laguerre tessellations and the mechanical behaviour was obtained by means of the finite element simulation of these representative volume elements. The numerical simulations corroborated the large increase in the stiffness, in the stress at the onset of plastic instability and in the plateau stress of the foam along the rising direction, in agreement with the experimental results. In addition, the analysis of the elastic response in the representative volume elements showed that deformation along the rising direction (parallel to the longer axis of the cells) was dominated by the axial deformation of the struts while bending controlled the deformation perpendicular to the rising direction. The stress at the onset of plastic instability was controlled by the buckling of the struts, which was triggered at lower stresses in the direction perpendicular to the rising direction because of bending.

A coupled dislocation dynamics-continuum barrier field model with application to irradiated materials

A new computational methodology for 3-dimensional (3D) Discrete Dislocation Dynamics (DDD) in barrier-strengthened materials is developed. We couple the discrete 3D DDD framework with the Finite Element Method (FEM) solution of a continuum field equation for the evolution of dispersed barriers. Coupled model parameters are obtained from detailed statistical analysis of 3D DDD simulations of single dislocation-barrier interactions. We develop a crystal lattice based continuum material point arrangement method to precisely distribute localized plastic strain as a result of dislocation-barrier interactions, enabling the method to be crystal-structure sensitive. The model is demonstrated by an application to the study of the physics of dislocation channel formation and plastic instability phenomena in irradiated materials. The results are shown to be in agreement with experiments on the magnitude of radiation hardening and the onset of plastic instability. Plastic flow localization in irradiated materials was shown to be more prevalent at high irradiation dose. The method enables future studies of the plastic deformation in precipitation-strengthened alloys, hydrogen-embrittled materials, and the plasticity of irradiated materials.

On the estimation of ultimate tensile stress from small punch testing

Finite element simulations of the small punch test are performed in order to critically evaluate and improve empirical correlations for the estimation of the ultimate tensile stress from force-deflection and force-displacement curves. For this purpose, generic elastic-plastic material properties are used. A systematic variation of the ultimate tensile stress and total uniform elongation is performed to investigate the effects of these parameters of the uniaxial stress-strain curve on the characteristics of small punch test curves. It is shown, that the maximum force Fm of the small punch test curve is not the appropriate parameter for the estimation of the ultimate tensile stress. Instead, the force Fi at a punch displacement of 1.29 times the specimen thickness (or alternatively at bottom deflection of 1.1 times the specimen thickness) should be used. This force is associated with the onset of plastic instability. A correlation between the force Fi and the ultimate tensile strength is proposed and validated by more than 100 small punch tests of nine different steel heats.

Analysis of Plastic Flow Instability During Superplastic Deformation of the Zn-Al Eutectoid Alloy Modified with 2 wt.% Cu

The aim of this work is to analyze the plastic flow instability in Zn-21Al-2Cu alloy deformed under 10−3 s−1 and 513 K, which are optimum conditions for inducing superplastic behavior in this alloy. An evaluation using the Hart and Wilkinson–Caceres criteria showed that the limited stability of plastic flow observed in this alloy is related to low values of the strain-rate sensitivity index (m) and the strain-hardening coefficient (γ), combined with the tendency of these parameters to decrease depending on true strain (e). The reduction in m and γ values could be associated with the early onset of plastic instability and with microstructural changes observed as function of the strain. Grain growth induced by deformation seems to be important during the first stage of deformation of this alloy. However, when e > 0.4 this growth is accompanied by other microstructural rearrangements. These results suggest that in this alloy, a grain boundary sliding mechanism acts to allow a steady superplastic flow only for e 0.7 as another mechanism is thought to take over.

Stabilized plasticity in ultrahigh strength, submicron Al crystals

It is well known that micrometer-sized and/or submicrometer-sized metallic crystals exhibit “smaller is stronger” size effect: the yield strength σ varies with sample dimension D roughly as a power-law σ∼D−m. For some materials, near-theoretical strength values can be attained by reducing the dimensions of crystals to sub-micrometric or nanometric values. At these size scales, however, plastic instabilities, such as strain bursts, strain softening or low strain hardening rates, become operative due to the avalanche-like dislocation generation and escape; such instabilities contribute to disappointing flow intermittency. From a scientific standpoint, the onset of plastic instabilities has hindered fundamental study of the deformation behavior of materials near theoretical strength values. From a technological standpoint, these instabilities limit potential applications in microelectromechanical devices, for example. In this study we demonstrate that by concurrently introducing grain boundaries and secondary phase particles, plastic instabilities can be dramatically suppressed in submicron Al pillars at large strain and that this behavior is attributable to substantial dislocation storage and subsequent grain boundary (GB) mediated plasticity. Consequently the crystals possess superior strength with flow stress larger than 1.0GPa.

Onset of the Portevin-Le Chatelier Effect: Role of Synchronization of Dislocations

The problem of the onset of the Portevin-Le Chatelier (PLC) effect is revised by combining a study of the kinetics of the flow stress evolution upon abrupt changes in the applied strain rate and acoustic emission (AE) accompanying plastic deformation of an AlMg alloy. The kinetic measurements allow evaluating the strain-rate sensitivity of the flow stress and the time characteristics of transient processes as functions of plastic strain. Using known criteria of plastic instability, domains of instability are constructed in the (strain, strain rate) plane. A particular accent is put on the strain-rate range corresponding to the so-called “inverse” behavior. The comparison of such maps with experimental data on the critical strain testifies to the insufficiency of these criteria for explaining the onset of the PLC effect. Moreover, the slow transient kinetics contradicts observations of the fast development of stress drops. The AE measurements bear witness that the stress serrations are associated with bursts in duration of acoustic events generated by the collective motion of dislocations. The possible role of synchronization of dislocation dynamics on the onset of plastic instability is discussed.

Analytic study of the onset of plastic instabilities during plane tension and compression tests on metallic plates

Abstract In this article, we propose an approximate analytic formulation of the growth-rate of plastic instabilities (symmetric and antisymmetric modes with respect to the median plane of the plate) during plane tension or compression tests on metals supposed to satisfy the Von Mises plasticity criterion, valid for any elastoviscoplastic constitutive law, and long and medium wavelengths λ (in comparison with thickness e ) along the loading direction (typically e ≤ λ , and even e /3 ≤ λ in the absence of viscous effects). This work generalizes important published results. For static tests, or dynamic ones in the field of long wavelengths, this formulation retrieves the formulae proposed by Fressengeas and Molinari (Instability and bifurcation in the plane tension test, 1992, Archives of Mechanics 44 (1), 93; Fragmentation of rapidly stretching sheets, 1994, European Journal of Mechanics A/Solids , 13 (2), 251) for the development of plastic necking instabilities during plane tension tests on rigid viscoplastic materials obeying Norton's constitutive law. In the absence of viscosity, for static tests, it retrieves the bifurcation stress proposed by Hill, Hutchinson (Bifurcation phenomena in the plane tension test, 1975, Journal of the Mechanics and Physics of Solids 23 , 239) and Young (Bifurcation phenomena in the plane compression test, 1976, Journal of the Mechanics and Physics of Solids 24 , 77).

Enhanced Plasticity of Cu-Based Laminated Composites Produced by Cold Roll-Bonding

Two different laminated composites with submicron-scale grain size and strong interface bonding toughness, Cu/Al and Cu/Cu, were fabricated by cold-roll bonding at ambient temperature, and then annealing of the laminated composites was conducted to get different interface bonding toughness. It was found that a better strength-plasticity combination for the laminated composites could be obtained through stronger interface bonding toughness, which effectively delayed the onset of plastic instability and premature local necking of the material. Uniform elongation of both Cu/Al and Cu/Cu laminated composites was enhanced compared with that of the cold-rolled Cu. At the same strength level, plasticity of the Cu/Cu laminated composite is better than that of the Cu/Al one and that of the cold-rolled Cu. Mechanisms of plasticity instability and fracture of the laminated composites were evaluated.

Towards Predictive Control of Extrusion Weld Seams: An Integrated Approach

Longitudinal weld seams are an intrinsic feature in hollow extrusions produced with porthole dies. The formation of longitudinal weld seams is a solid bonding process, controlled by the local conditions in the extrusion die. Being the weakest areas within the extrusion cross section, it is desirable to achieve adequate properties of these weld seams. In our research, the concept of a weld seam integrity indicator as a means of quantifying bonding efficiency is introduced. The value of this indicator depends on a number of factors: the material flow within the die weld chambers, an adequate pressure level acting on the weld planes and finally the evolution of the metal microstructure. Optimisation of the welding conditions leads to a higher value of the weld seam integrity indicator and thus to improved weld seam properties. The objective of the research presented in this paper is to assess the feasibility of this concept. In lab-scale experiments, AA6060 and AA6082 aluminium alloy billets were formed into strips by means of the direct hot extrusion process. By utilising porthole dies a central longitudinal weld seam is formed. The effect of different geometries of the weld chamber and the processing conditions on the quality of the weld seam are investigated. Characterisation of these weld seams through mechanical testing, focusing on the ability of the weld seam area to accommodate plastic deformation following the onset of plastic instability, and microstructural analysis provides insight into bonding performance. The outcome of this characterisation provides a basis for an estimation of the weld seam indicator. Through computer modelling, the particular process conditions related to weld seam formation are calculated and correlated with the experimental results. The experimental results clearly demonstrate that weld seam formation is controlled by a combination of factors as described above. Inadequate fulfilment of these conditions, verified by the FE-simulations, is the cause of inferior weld seams, associated with low values of the weld seam integrity indicator. Through further elaboration of the concepts presented in this work, the weld seam integrity indicator is to be developed, with the future aim of predicting the weld seam performance through finite element simulations.

Forming limit diagrams of tubular materials by bulge tests

This study uses bulge tests to establish the forming limit diagram (FLD) of tubular material AA6011. A self-designed bulge forming apparatus of fixed bulge length and a hydraulic test machine with axial feeding are used to carry out the bulge tests. Loading paths corresponding to the strain paths with a constant strain ratio at the pole of the bulging tube are determined by FE simulations linked with a self-compiled subroutine and are used to control the internal pressure and axial feeding punch of the test machine. After bulge tests, the major and minor strains of the grids beside the bursting line on the tube surface are measured to construct the forming limit diagram of the tubes. Furthermore, Swift's diffused necking criterion and Hill's localized necking criterion associated with Hill's non-quadratic yield function are adopted to derive the critical principal strains at the onset of plastic instability. The critical major and minor strains are plotted to construct the forming limit curve (FLC). The effects of the exponent in the Hill's non-quadratic yield function and the normal anisotropy of the material on the yield locus and FLC are discussed. Tensile tests are used to determine the anisotropic values in different directions with respect to the tube axis and the K and n values of the flow stress of the tubular material. The analytical FLCs using the n values obtained by tensile tests and bulge tests are compared with the forming limits from the forming limit experiments.

Plastic instability in dual-pressure tube-hydroforming process

The tube-hydroforming process has become an indispensable manufacturing technique in recent years. Successful tube hydroforming requires bulging to take place without causing any type of instability such as bursting, wrinkling or buckling. The dual-pressure tube-hydroforming process was introduced to achieve a favorable tri-axial stress state in the deformation process. In this paper, the effect of applying counter pressure on plastic instability of thin-walled tubes is analyzed. It is concluded that in dual-pressure tube hydroforming, the onset of plastic instability is delayed and the ductility of the metal is increased.

Modeling tensile response and flow localization effects in 316SS after exposure to spallation and fission irradiation environments

The mechanical stability of structural materials under irradiation is a major concern for reactor component design and life cycle evaluation. The most important issue is the loss of ductility due to the development of radiation damage defect structures in the material. The acute loss of material tensile ductility is often characterized by a process where the material necks at very low uniform elongations in tensile loading, just following the yield point, a process commonly referred to as flow localization. The process where small tensile strains lead to plastic instability is examined through the analysis of tensile test data for 316SS irradiated either in a fission neutron spectrum or in a mixed proton and neutron spectrum characteristic of spallation sources. In both cases, it is found that uniform elongation levels are limited by a critical material strength. It is shown that there is a direct correlation between the material yield strength and the uniform elongation for the materials examined here. It is also shown that the large differences in He and H production between the two kinds of radiation environments have little or no effect on tensile properties. A further implication of the work is that the specifics of the post-yield flow and strain hardening processes are less important than the critical stress for determining the onset of plastic instability.

Effect of temperature on the fracture mechanisms of 8090 Al–Li alloy and 8090 Al–Li/SiC composite

Abstract The fracture mechanisms in tension were analyzed in a peak-aged 8090 Al–Li alloy and 8090 Al–Li/SiC as a function of temperature. Failure in the alloy changed from intergranular fracture at ambient temperature to ductile void growth above 150 °C, leading to a tenfold increase in the elongation to failure. Damage in the composite was always nucleated by particle fracture, and the ductility, which was controlled by the onset of plastic instability, increased moderately with temperature.