Hardening Softening Research Articles

Hardness and shear band evolution in bulk metallic glasses after plastic deformation and annealing

Strain-induced hardening and annealing-induced softening are typical in crystalline metals. Bulk metallic glasses (BMG) exhibit the opposite behavior, namely, strain-induced softening and annealing-induced hardening. In addition, reversible softening–hardening–softening occurs in a BMG subjected to a three-step deformation–annealing–deformation process. The hardness changes after deformation and annealing can be correlated with the shear band patterns around/underneath Vickers indents. Shear bands produced during indentation of as-cast BMG are semicircular and radial, consistent with the stress distribution beneath the indenter. In contrast, the shear bands in the pre-strained BMG are irregular and convoluted, and appear to be a mixture of the shear bands produced during the prior compression and those in the as-cast BMG. After annealing, the shear bands tend to recover their semicircular and radial shapes consistent with the annealing-induced hardening.

MODELING OF SERRATED CHIP FORMATION IN HIGH SPEED ORTHOGONAL MACHINING

Modeling of serrated chip formation is important to provide guidance for further development of this process and predict the quality of machined parts. The simulation of serrated chip formation is hard to achieve due to the lack of a proper material model which represents real phenomenon within a narrow adiabatic shear band. In the present study, a material constitutive law containing strain hardening and thermal softening was proposed to predict adiabatic shear localization within serrated chips. The outcomes of FEM simulation show the capability to predict serrated chip formation. The effective strain distributions and the forces are computed within this study.

New constitutive equation for plasticity in high speed torsion tests of metals

Present work investigates a phenomenological plasticity equation for the plastic behavior of metals deformed in high speed torsion tests. The tests were carried out at room temperature in a laboratory torsion test equipment and also in an universal tensile test machine on annealed commercial pure copper and aluminum specimens. The tensile tests were performed at room temperature by an universal testing machine at low strain rate of 0.017/s. The experimental torsion tests were carried out at constant angular speed that imposed a constant shear strain rate to the specimen. In the tests, the rotation speed were set to 61 rpm and 200 rpm which imposed high strain rates of about 2/s and 6.5/s respectively in tubular specimens. The torsion test lasted between 0.5 s and 1 s. The experimental hardening curves of equivalent stress versus strain in torsion were sigmoidal type and were fitted by different constitutive equations for plasticity that takes into account the strain hardening and thermal softening effects due to local temperature increase as the Johnson-Cook model, the modified Voce equation and others. The specimen local temperature increase was calculated assuming adiabatic deformation process. It is proposed a new constitutive equation or modified Voce equation for the equivalent flow stress which considers the effects of strain hardening, strain rate hardening and thermal softening for the best fit to the present experimental data of annealed aluminum and copper.

High Speed Machining of AISI 1050 Steel: Modelling and Experimental

An analytical approach is used to model orthogonal cutting process. The material characteristics such as strain rate sensitivity, strain hardening and thermal softening are considered. The chip formation is supposed to occur mainly by shearing within a thin band called primary shear zone. The analysis is limited to stationary flow and the material flow within the primary shear zone is modelled by using a onedimensional approach. Thermomechanical coupling and inertia effects are accounted for. At the tool-chip interface, a temperature dependent friction law is introduced to take account of the extreme conditions of pressure, velocities and temperature encountered during machining. Comparisons between model predictions and experimental results are performed for different cutting conditions.

Low Cycle Fatigue Behavior and Microcracks Nucleation on Duplex Stainless Steels

The cyclic hardening–softening response, the cyclic stress–strain curve and the substructure evolution of a high nitrogen duplex stainless steel S32750 have been evaluated and the results compared with reference to low and medium nitrogen duplex stainless steels, S32205 and S32900 grades, respectively. The beneficial effects of nitrogen on the cyclic properties of most modern alloys have been analyzed in terms of the flow stress components, i.e. the internal and the effective stress.

Quantitative Evaluation of Dislocation Structure Induced by Cyclic Plasticity

In the present study, a new approach is conducted to evaluate dislocation structure induced by cyclic plasticity. First, cyclic plastic loading tests are carried out up to 100 cycles with three different small strain amplitudes on SUS316L stainless steel at room temperature. The test result presents the dependence of the strain amplitude on cyclic hardening and softening behaviors. Specifically, it is found that the cyclic loading test with strain amplitude of 0.25% shows both cyclic hardening and cyclic softening, while the cyclic loading tests with strain amplitudes of 0.75% and 1.0% show no cyclic softening. Secondly, the dislocation structures of the specimens after cyclic loading are observed by using a transmission electron microscope (TEM), and this observation reveals that the dislocation structure after cyclic loading test depends on the strain amplitude. Finally, a quantitative evaluation method of the dislocation structure is also proposed. The TEM images are converted into binary images and the resolution dependence of the generated binary image is used to visualize the characteristics of the dislocation structure. The relationship between strain amplitudes of cyclic plasticity and dislocation structure organization is clarified by the evaluation method. Finally, the heterogeneity of the dislocation structure is discussed.

Effects of Annealing Temperature and Si Content on Mechanical Properties of Cold Drawn Pearlitic Steel Wires

The effects of annealing temperature and silicon content on mechanical properties on cold drawn pearlitic steel wires were investigated. Cold drawn steel wires, containing Si, 0.99 ~ 1.4%, were annealed at the temperature of 200 ~ 450°C with different annealing time. The variation of microstructural evolution with annealing temperature was not affected by silicon content. For steels containing high silicon content above 1.0%, the increase of silicon content did not cause the changes of peak temperature showing age hardening and age softening, except for the increase of tensile strength due to solid solution hardening.

A One-Dimensional Nonlocal Damage-Plasticity Model for Ductile Materials

This paper presents a new 1-D non-local damage-plasticity deformation model for ductile materials. It uses the thermodynamic framework described in Houlsby and Puzrin (2000) and holds, nevertheless, some similarities with Lemaitre’s (1971) approach. A 1D finite element (FE) model of a bar fixed at one end and loaded in tension at the other end is introduced. This simple model demonstrates how the approach can be implemented within the finite element framework, and that it is capable of capturing both the pre-peak hardening and post-peak softening (generally responsible for models instability) due to damage-induced stiffness and strength reduction characteristic of ductile materials. It is also shown that the approach has further advantages of achieving some degree of mesh independence, and of being able to capture deformation size effects. Finally, it is illustrated how the model permits the calculation of essential work of rupture (EWR), i.e. the specific energy per unit cross-sectional area that is needed to cause tensile failure of a specimen.

The analysis of deformation size effects using multiple gauge length extensometry and the essential work of rupture concept

Size dependence of the load–displacement and stress–strain curves is a phenomenon widely reported in the literature and readily observed in experiments. The present paper introduces two developments in the analysis of ductile rupture, one in the area of experimental technique and interpretation, and one in the area of numerical modelling. Firstly, the new experimental technique is described of multiple gauge length optical extensometry (laser scanning) that provides a uniquely powerful means of collecting the data needed for the study of size effects, from a single tensile test on a ductile specimen. The interpretation procedures are presented based on the considerations about the nature of deformation and energy expenditure within different material volumes in a tensile specimen. Consequently, the property of the specimen can be defined and identified that relates to the energy consumption per unit cross-sectional area required to rupture the specimen entirely (the essential work of rupture). Another energetic measure is also obtained from the test that relates to the plastic work dissipation per unit volume in pre-peak deformed material. Secondly, the observed size effects and specific energy determination procedures are discussed in the context of non-local coupled plasticity-damage modelling. Conventional local numerical models of inelastic deformation fail to predict the sequence of deformation responses observed in the tensile test, namely, uniform deformation followed by strain localisation, necking and rupture. It is shown here that coupled non-local damage-plasticity modelling is capable of capturing the hardening–softening and global–local plasticity transitions, and hence the trends observed in ductile fracture. The predictions of the coupled non-local damage-plasticity modelling for different deformation regimes are shown to agree qualitatively with the experimentally observed behaviour. The two aspects of the proposed approach, experimental and modelling, are presented here together since they are intimately linked at the fundamental level. The implications of the proposed approach are discussed for the deformation analysis of plastically deforming and damageable materials and structures at various scales, from macroscopic to miniature.

Load-displacement and bearing capacity of foundations on granular soils using a multi-surface kinematic constitutive soil model

A finite element approach based on an advanced multi-surface kinematic constitutive model is used to evaluate the bearing capacity of footings resting on granular soils. Unlike simple elastic-perfectly plastic models, often applied to granular foundation problems, the present model realistically accounts for stress dependency of the friction angle, strain softening–hardening and non-associativity. After the model and its implementation into a finite element code are briefly discussed, the numerical difficulty due to the singularity at the footing edge is addressed. The bearing capacity factor Nγ is then calculated for different granular materials. The effect of footing size, shape, relative density and roughness on the ultimate bearing capacity are studied and the computed results compare very favourably with the general experimental trends. In addition, it is shown that the finite element solution can clearly represent counteracting mechanisms of progressive failure which have an important effect on the bearing capacity of granular foundations. Copyright © 2006 John Wiley & Sons, Ltd.

Investigation on Fatigue Behavior of Zircaloy -4 Alloy in Room Temperature and 380°C Condition

Zr-4 alloy is the material of nuclear fuel shell in nuclear power plant’s PWR. This paper presents this material’s general mechanical property and fatigue behavior that are tested in accordance with ASTM in room temperature and 380°C condition. The test results show that there is no cyclic hardening or cyclic softening phenomena for Zr-4 alloy applied by cyclic loading in room temperature condition. The fatigue design curve is obtained by processing fatigue test results with adopting ASME Sec.Ⅲ based on the test results of strain fatigue property. The research result shows the fatigue design data at different temperature may be corrected by elastic modulus with room temperature curve. This paper’s result may be used in PWR component design.

Localized nonlinearity and size-dependent mechanics of in-plane RC element in shear

Structural nonlinearity and stress-carrying mechanics of reinforced concrete are greatly associated with local kinematics at crack planes and non-uniform stress fields in un-cracked concrete regions mobilized in the vicinity of cracks, especially when much less and/or highly anisotropic amounts of reinforcement are placed in space. An exact local stress field approach is implemented to in-plane reinforced concrete elements for deriving size-independent/dependent spatial averaged stress–strain relation, stress carrying mechanics and their interaction of high complexity. Much attention is directed to size sensitivity of overall responses involving transient tension softening–stiffening, interlock shear hardening–softening and average yield strength of reinforcing bars, which were previously formulated based on mere superimposition of these constituent mechanics under uniaxial stresses. Single crack localization and transitory phase of lightly reinforced concrete in-plane elements are chiefly investigated since those are out of scope of non-localized stress field approach with smeared crack concept.

The Microstructure and Mechanical Properties of Directionally Solidified NiAl-15Cr Alloy at Various Temperatures

The microstructure and tensile mechanical properties of directionally Solidified NiAl-15Cr alloy at various temperatures have been investigated in this paper. The results reveal that the microstructure consists of dendritic β-NiAl phase, interdendritic γ/γ’, γ’ phase transient layer and α-Cr precipitation in β-NiAl phase. With the increase of temperature obvious Brittle-Ductile-Transition (BDT) behavior is observed and the BDT temperature (BDTT) is sensitive to initial strain rate. When the initial strain rate increases by two-order magnitude, the BDTT has an approximate 150K increase. In the temperature range of 1123-1373K, the alloy exhibits good tensile plasticity and poor strength comparing with the NiAl/Cr(Mo,Hf) alloy. Superplastic-like deformation behavior with large elongation (exceed 200%) is achieved at 1323K. The balance between strain hardening (by dislocation glide) and strain softening (dynamic recover and recrystallization) is responsible for the large tensile elongation of this alloy.

Superplasticity in a directionally solidified multiphase Ni-25Al-25Cr alloy

Abstract A Ni-25Al-25Cr (at.%) alloy was directionally solidified under Ar atmosphere in an Al2O3–SiO2 ceramic mold by the standard Bridgman method. The microstructure of the as-fabricated alloy was studied using optical microscopy, X-ray diffraction and scanning electron microscopy. The alloy was composed of β-NiAl dendritic arms, α-Cr interdendritic regions, fine α-Cr particles in the dendritic arms, and β-NiAl + α-Cr eutectic in the interdendritic regions. The mechanical properties were studied by tensile tests in the temperature range 1123–1373 K. The results showed that the alloy exhibits superplastic behavior at appropriate testing conditions. The balance between work hardening (by dislocation glide) and work softening (by dynamic recovery and recrystallization) is responsible for the large tensile elongation of the alloy.

Impact shear-numerical analyses of ASB evolution and failure for Ti-6AI-4V alloy

In this contribution a study is reported on a shear zone evolution at high strain rates for Ti-6Al-4V-alloy. Such process of deformation, leading to development of Adiabatic Shear Band (ASB), is typical for fast and impact shearing. A very special experimental technique developed at LPMM-Metz has permitted for shear tests at a wide range of strain rates and also for development of an advanced constitutive relation valid for that range of strain rates and also for a range of temperatures (range of strain rates from 10 -4 l/s to about 10 5 l/s). This experimental technique called the Modified Double Shear has been applied to test Ti-6Al-4V alloy. In order to estimate the effect of stress concentration on the sensitivity to ASB triggering four different specimen geometries with different stress concentrators were tested and analyzed. After identification of all material constants for Ti-6Al-4V alloy in the advanced constitutive relation, this relation has been introduced into the finite element code ABAQUS Explicit. The constitutive relation accounts for the effects of strain hardening, rate sensitivity and thermal softening. In this way a complete dynamic approach with elastic-plastic wave propagation, adiabatic shear band development and failure could be studied numerically for all four geometries with different stress concentrators. In addition, the Critical Impact Velocity (CIV) in shear has been estimated analytically and numerically for Ti-6Al-4V. A very good agreement between experiments and numerical simulations are achieved.

A Gaussian sinc‐collocation approach for a whipping cantilever with a follower shear force at its tip

AbstractA spatial discretization scheme, based on a set of Gaussian sinc functions, is proposed for the temporal projection of a set of partial differential equations (PDEs), describing the non‐linear dynamics of an elastic–plastic hardening–softening (EPHS) cantilever, subjected to a follower shear force at its tip. The dynamics so described correspond to planar whipping of a pipe conveying fluid, ruptured near a right‐angled bend. The constitutive EPHS moment curvature relationship used here follows the earlier work of Reid et al. (Proceedings of the Royal Society of London, Series A 1998; 454: 997–1029). Compared to the more classical Lagrangian polynomial‐based collocation functions, the Gaussian sinc functions have better localization properties. Moreover, for a relatively large number of collocation points, use of such functions does not lead to numerical overflow or underflow problems, often associated with the use of higher order polynomial collocation functions. The spatial discretization leads to a set of non‐linear ordinary differential equations (ODEs) in time, which are in turn integrated via a fourth order adaptive Runge–Kutta scheme. Some numerical results for a cantilever whipping in a plane are presented to further illustrate the present approach. The method is a step forward towards the development of a mesh‐free non‐linear beam element, suitable for dynamic analyses of pipe networks and pipe‐on‐pipe impact problems. Copyright © 2003 John Wiley & Sons, Ltd.

Non-local coupling of viscoplasticity and anisotropic viscodamage for impact problems using the gradient theory

A general framework for the analysis of heterogeneous media that assesses a strong coupling between viscoplasticity and anisotropic viscodamage evolution is formulated for-impact related problems within the framework of thermodynamic laws and nonlinear continuum mechanics. The proposed formulations include thermo-elasto-viscoplastici- ty with anisotropic thermo-elasto-viscodamage, a dynamic yield criterion of a von Mises type and a dynamic viscodamage criterion, the associated flow rules, non-linear strain hardening, strain-rate hardening, and temperature softening. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. That is, the damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The evolution laws are impeded in a finite deformation framework based on the multiplicative decomposition of the deformation gradient into elastic, viscoplastic, and viscodamage parts. Since the material macroscopic thermomechanical response under high-impact loading is governed by different physical mechanisms on the macroscale level, the proposed three-dimensional kinematical model is introduced with manifold structure accounting for discontinuous fields of dislocation interactions (plastic hardening), and crack and void interactions (damage hardening). The non-local theory of viscoplasticity and viscodamage that incorporates macroscale interstate variables and their higher-order gradients is used here to describe the change in the internal structure and in order to investigate the size effect of statistical inhomogeneity of the evolution-related viscoplasticity and viscodamage hardening variables. The gradients are introduced here in the hardening internal state variables and are considered to be independent of their local counterparts. It also incorporates the thermomechanical coupling effects as well as the internal dissipative effects through the rate-type covariance constitutive structure with a finite set of internal state variables. The model presented in this paper can be considered as a framework, which enables one to derive various non-local and gradient viscoplasticity and viscodamage theories by introducing simplifying assumptions.

Modeling texture and microstructural evolution in the equal channel angular extrusion process

Abstract In this work, we develop a modeling framework for predicting the visco-plastic deformation, microstructural evolution (distributions of grain shape and size) and texture evolution in polycrystalline materials during the equal channel angular extrusion (ECAE) process, a discontinuous process of severe shear straining. The foundation of this framework is a visco-plastic self-consistent (VPSC) scheme. We consider a 90° die angle and simulate ECAE up to four passes for four processing routes, (A, C, B A and B C , as denoted in the literature) for an FCC polycrystalline material. We assume that the FCC single crystal has a constant critical resolved shear stress (CRSS), so that hardening by dislocation activity is suppressed, and the influence of grain shape distribution and texture as well as their interaction can be isolated. Many deformation microstructural features, such as grain size and shape distribution, texture, and geometric hardening–softening, were highly dependent on processing route. Using a grain subdivision criterion based on grain shape, route A was the most effective, then route B A and route B C and lastly route C, the least effective for grain size refinement, in agreement with redundant strain theory. For producing refined equiaxed grains, route B C was more effective than routes B A and A. We show that grain–grain interactions tend to weaken texture evolution and consequently geometric hardening and softening in all routes.

Drained cavity expansion in sands exhibiting particle crushing

AbstractThe expansion of cylindrical and spherical cavities in sands is modelled using similarity solutions. The conventional Mohr–Coulomb failure criterion and the state parameter sand behaviour model, which enables hardening–softening, are used in the analysis. The sand state is defined in terms of a new critical state line, designed to account for the three different modes of compressive deformation observed in sands across a wide range of stresses including particle rearrangement, particle crushing and pseudoelastic deformation. Solutions are generated for cavities expanded from zero and finite radii and are compared to those solutions where a conventional critical state line has been used. It is shown that for initial states typical of real quartz sand deposits, pseudoelastic deformation does not occur around an expanding cavity. Particle crushing does occur at these states and causes a reduction in the stress surrounding the cavity. This has major implications when using cavity expansion theory to interpret the cone penetration test and pressuremeter test. Copyright © 2002 John Wiley & Sons, Ltd.

Cyclic deformation behaviour of superduplex stainless steels

The cyclic hardening–softening response, the cyclic stress–strain curve (CSSC) and the substructure evolution within the constitutive phases of a high nitrogen superduplex stainless steel SAF 2507 have been studied and the results compared with reference to low and medium nitrogen duplex stainless steels (DSSs), particularly AISI 329 and SAF 2205 grades, respectively. All three materials were manufactured in the form of hot rolled and solution annealed cylindrical bars with the same diameter. It is shown that the previously reported description of the CSSC of a DSS in terms of three regimes, each associated to distinct controlling cyclic deformation mechanisms, applies well in the case of the superduplex steel too. The main differences between the cyclic deformation behaviour of the DSSs studied are: (i) the CSSC of the SAF 2507 steel is placed at higher stress levels, mainly as a consequence of nitrogen alloying; (ii) the initial hardening period is shorter whereas the softening stage is more prolonged; and (iii) increasing nitrogen content promotes a more planar glide deformation character in austenite.