Adiabatic Shear Band Localization Research Articles

An Investigation on unstable flow during hot deformation of Inconel X750 superalloy using 3D processing map and shear band formation criterion

In this study, deformation efficiency and instability criteria were employed to delineate the unstable flow regions for Inconel X750 superalloy through high temperature deformation. High temperature stress–strain data attained from isothermal hot compression experiments in the temperature range of 950–1150 °C and strain rates between 0.0001 and 1 s⁻¹ to identify safe and un-safe deformation domains in terms of an integrated 3D processing maps. These domains were validated through detailed microstructure observation and material tendency to shear band formation in terms of the competition between work hardening and strain rate sensitivity i.e. flow localization parameter. The superimposed effect of microstructure features like dynamic precipitation, dynamic recovery (DRV), and dynamic recrystallization (DRX) with destructive shear banding were responsible for controlling the material behaviour. Based on the TEM images, it was observed that material revealed stable flow at lower strain rates while adiabatic shear band and flow localization occurred at higher strain rates due to activation of slip systems and cell formation.

Interaction of microstructure evolution mechanism in Ti-0.3Mo-0.8Ni alloy with initial lamellar microstructure during isothermal compression below the β-transus

The flow behavior and interaction of microstructure evolution mechanisms for a near α Ti-0.3Mo-0.8Ni alloy with as-cast lamellar microstructure are investigated at temperatures of 800∼880 °C in the α+β region with wide strain rate range from 0.01s−1 to 30s−1 during isothermal compression. It is demonstrated that the main reasons of flow softening in the true stress-true strain curves are the kinking of lamellar α, dynamic α→β transformation (DT), dynamic spheroidization (DS), and dynamic recovery (DRV) of β grain. The instability phenomena such as adiabatic shear band (ASB) and flow localization (FL) are the main causes of the stress collapse in the curves at higher strain rate. The dislocation density at the kinking position of initial lamellar α is higher. With the increase of strain rate, the mechanism of the DS changes from flat separation to slat shear. The diffusion of the β-stabilizer results in starting the DT, promoted by the thermodynamic coupling. The interactions between different microstructure evolution mechanisms are extremely complex. In the early stage of hot deformation, the DT promotes the kinking of lamellar α. With the increase of deformation amount, the DT inhibits the DS at higher strain rates, and conversely, the DS promotes the DT. At lower strain rates, the DT and DS accelerate each other in the middle and late stages of hot deformation. The DT and DS are restricted by the process of lamellar α kinking in the middle and late stages of hot deformation.

Microstructure evolution and processing map of Al–Cu–Li–Mg–Ag alloy

Microstructural evolution of AA2195 aluminum alloy was recorded under different conditions (400–500 °C/0.01–10 s−1) during isothermal compression via metallurgical microscopy, electron backscattered diffraction and transmission electron microscopy/scanning transmission electron microscopy. By means of the dynamic material modeling, the processing map (PM) at the strain of 0.7 was also constructed using flow stress data. It was shown that the unstable criterion was adiabatic shear band (ASB) and flow localization (FL). ASB was easily formed at high strain rates (>1 s−1) due to non-uniform deformation heating. FL was attributed to local coarseness of T1 precipitates near grain boundaries or inhomogeneous distribution of T1 precipitates in the matrix. The stability domain showed that the absence of T1 precipitates contributed to the formation of fine homogeneously distributed continuous dynamic recrystallization (CDRX). In the light of PM and microscopic observation, the optimal processing conditions suitable for AA2195 aluminum alloy were proposed as 475–500 °C/0.01–0.1 s−1 with an exception of 490–500 °C/0.01 s−1.

Adiabatic shear band localization in an Al–Zn–Mg–Cu alloy under high strain rate compression

An investigation was conducted to study the effect of high strain rate compression on the microstructure and mechanical properties of a spray deposited and hot formed by forging and extrusion followed by T74 (393 K/8h + 433 K/24 h) heat treatment Al–Zn–Mg–Cu alloy. The results show that the strength of the Al alloy is increased with increasing strain rate from 1.0 × 10−3 s−1 to 5.0 × 103 s−1 assisted by the strain hardening rate effect. Typical adiabatic shear bands area is found in the Al–Zn–Mg–Cu alloy after compression at high strain rate. Grains are significantly refined within the shear bands areas to ∼180 nm assisted by the dislocation accumulation combined with the temperature rise during the high strain rate compression. Precipitates are observed within the shear bands mainly of fine η' precipitates. These precipitates are close to Mg (Zn, Cu, Al)2 assisted by diffusion provided by dislocations.

High strain rate compressive behaviors and adiabatic shear band localization of 3-D carbon/epoxy angle-interlock woven composites at different loading directions

When serving as a lightweight structural member in many areas, the dynamic mechanical behavior of fiber-reinforced polymeric matrix composites, especially under different strain rates, means a lot to the optimization of structure design as to high-speed impact. Under different loading rates and directions, we experimentally and numerically investigated the strain rate effect on the impact compressive behavior of 3-D angle-interlock woven composites (3-D AWCs) composed of carbon fiber and epoxy resin. Based on the factual geometrical architecture of 3-D AWC, the meso-scale model, which considers the interfacial damage between the reinforcements and matrix, was established to visually characterize the deformation history and damage morphologies of 3-D AWCs during impact compression process. Further, we performed high strain rate compressive tests on the split Hopkinson pressure bar (SHPB) apparatus integrated with a high-speed photography system for capturing images of progressive damage process to validate the proposed mesoscopic model. The stress-strain curves of various strain rates show strain rate effect varies depending on loading direction. The rate sensitivity on the compressive failure strength exists at weft direction and through-thickness direction except for warp direction. Moreover, both from images and finite element model results, the localized adiabatic shear band induced by intense plastic strain, initiates mainly from epoxy resin matrix and propagates along the interface at all three loading directions.

Hot Deformation Behavior and Intrinsic Workability of Carbon Nanotube-Aluminum Reinforced ZA27 Composites

Using a controlled thermal simulator system, hybrid carbon nanotube-aluminum reinforced ZA27 composites were subjected to hot compression testing in the temperature range of 473-523 K with strain rates of 0.01-10 s−1. Based on experimental results, a developed-flow stress model was established using a constitutive equation coupled with strain to describe strain softening arising from dynamic recrystallization. The intrinsic workability was further investigated by constructing three-dimensional (3D) processing maps aided by optical observations of microstructures. The 3D processing maps were constructed based on a dynamic model of materials to delineate variations in the efficiency of power dissipation and flow instability domains. The instability domains exhibited adiabatic shear band and flow localization, which need to be prevented during hot processing. The recommended domain is predicated to be within the temperature range 550-590 K and strain rate range 0.01-0.35 s−1. In this state, the main softening mechanism is dynamic recrystallization. The results from processing maps agree well with the microstructure observations.

The investigation on the unstable flow behavior of Ti17 alloy in α+β phase field using processing map

Abstract In this study, five existing instability criteria (Prasad's, Murty's, Sematin's, Gegel's and Malas's criterion) were employed to delineate the unstable flow regions for Ti17 alloy during hot deformation. Experimental stress–strain data obtained from isothermal hot compression tests in the temperature range of 780–860 °C and strain rate range of 0.001–10 s−1 were utilized to develop the instability maps. These domains were validated through detailed microstructure observation. The material exhibited stable flow at lower strain rates while adiabatic shear band and flow localization occurred at higher strain rates (≥1 s−1). It was observed that the maps at strain of 0.9 developed by Prasad's and Murty's criteria have a good ability for predicting unstable flow at high strain rates and entire temperatures. However, the Semiatin's criterion under-predicts the instability regions in the test temperatures and strain rates. On the contrary, the Gegel's and Malas's criteria over-predict the instability domains, especially for the low strain rate region.

Analysis of anisotropy and plastic spin effects on localization phenomena

The main objective of the paper is the investigation of the influence of the anisotrophy and plastic spin effects on criteria for adiabatic shear band localization of plastic deformation. A theory of thermoplasticity is formulated within a framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration such effects as plastic non-normality, plastic-induced anisotropy (kinematic hardening), micro-damage mechanism, thermomechanical coupling and plastic spin. The next objective of the paper is to focus attention on cooperative phenomena in presence of the plastic spin, and the discussion on the influence of synergetic effects on localization criteria. A particular constitutive law for the plastic spin is assumed. The necessary condition for a localized plastic deformation region to be formed is obtained. This condition is accomplished by the assumption that some eigenvalues of the instantaneous adiabatic acoustic tensor vanish. A procedure has been developed which allows us to discuss two separate groups of effects on the localization phenomenon along a shear band. Plastic spin, spatial covariance and kinematic hardening effects are investigated at an isothermal process in an undamaged solid. In the second case, an adiabatic process in a damaged solid is discussed when the spatial covariance terms and the plastic spin are neglected. Here the thermomechanical coupling, micro-damage mechanism and kinematic hardening effects are examined. For both cases, the criteria for adiabatic shear band localization are obtained in an exact analytical form. Particular attention is focused on the analysis of the following effects: (i) plastic non-normality; (ii) plastic spin; (iii) covariant terms; (iv) plastic strain-induced anisotropy; (v) micro-damage mechanism; (vi) thermomechanical couplings. Cooperative phenomena are considered, and synergetic effects are investigated. A discussion of the influence of the plastic spin, kinematic hardening and covariant terms on the shear band localization conditions is presented. A numerical estimation of the effects discussed is given.

Analysis of the influence of various effects on criteria for adiabatic shear band localization in single crystals

The paper aims at the investigation of the influence of various effects on criteria for shear band localization in inelastic single crystals. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. Particular attention is focussed on the analysis of the effects as follows: (i) spatial covariance and plastic spin; (ii) thermomechanical coupling; (iii) non-Schmid; (iv) evolution of substructure; (v) nondissipative thermal term; (vi) cooperative phenomena (synergetic). The theory of thermoviscoplasticity of inelastic single crystals is presented within a framework of the rate type covariance constitutive structure with a finite set of the internal state variables. By assuming that the mechanical relaxation time is equal to zero the thermo-elasto-plastic (rate independent) response of single crystals is accomplished. An adiabatic inelastic flow process of the single crystal is formulated and investigated. Symmetric double slip and single slip processes are considered. The formulation of macroscopic adiabatic shear bands is investigated. The criteria for adiabatic shear band localization for a single slip process are presented in exact analytical form. For a symmetric double slip process these criteria are estimated numerically. The discussion of the influence of various effects is presented, and the comparison of the results obtained with available experimental observations is given.

Numerical modelling of localized fracture of inelastic solids in dynamic loading processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by microdamage and thermal softening during dynamic plastic flow processes. By applying ideas of synergetics it can be shown that as a result of instability hierarchies a system is self-organized into a new shear band pattern system. This leads to the conclusion that inelastic solid body considered during the dynamics process becomes a two-phase material system. Particular attention is focussed on attempt to construct a physically and experimentally justified localized fracture theory that relates the kinetics of material failure on the microstructural level to continuum mechanics. The description of the microstructural damage process is based on dynamic experiments with carefully controlled load amplitudes and duration. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history-dependent, non-linear process. The theory of thermoviscoplasticity is developed within the framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of microdamage mechanism and thermomechanical coupling. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well-posed. The viscoplastic regularization procedure assures the unconditionally stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial–boundary value problem) as well as on its numerical solutions. Convergence, consistency and stability of the discretized problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elasto–viscoplastic model the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging over 103−104 s−1 is presented. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data. © 1997 John Wiley & Sons, Ltd.

Localized Fracture in Inelastic Polycrystalline Solids under Dynamic Loading Processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by micro-damage and thermal softening during dynamic plastic flow processes. The theory of thermoviscoplasticity is developed within a framework of the rate type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of micro-damage mechanism and thermomechanical coupling. The micro-damage mechanism has been treated as a sequence of nucleation, growth, and coalesence of microcracks. The micro-damage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature, and history dependent, nonlinear process. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent micro-damage mechanism is considered. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well posed. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem), as well as on its numerical solutions. Convergence, consistency, and stability of the discretised problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elastoviscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging from 10-1-104 s-1 is presented. Three particular examples have been considered; namely, a dynamic adiabatic process for a thin-walled steel tube and dynamic adiabatic and quasi-static processes for a thin steel plate. In each case, a thin shear band region of finite width which undergoes significant deformations and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data.

Analysis of the influence of the substructure of a crystal on shear band localization phenomena of plastic deformation

Abstract The main objective of the present paper is the discussion of the influence of the evolution of the substructure of single crystal on the shear band localization phenomena. A constitutive model of an inelastic crystal within the thermodynamic framework of the rate type covariance constitutive structure with internal state variables is developed. Thermomechanical couplings are considered and internal heating generated by the rate of internal dissipation is described. It has been proved that the description of a rate independent adiabatic single slip process in elasto-plastic single crystal is reduced to one fundamental evolution equation for the Kirchhoff stress tensor. Using the analysis of acceleration waves the necessary condition for a localized plastic deformation region to be formed is obtained. The criteria for adiabatic shear band localization are presented in an exact analytical form. Numerical estimations for the critical hardening modulus rate and the direction of the macroscopic shear band are given. The influence of various effects on shear band localization criteria is investigated. It has been found that the influence of the dislocation substructure is combined with the thermomechanical coupling and leads to distinct synergetic effect. The possibility of deviation from the Schmid rule of the critical resolved shear stress is also investigated. Comparison of the numerical results with available experimental data is presented.

Adiabatic shear band localization of inelastic single crystals in symmetric double-slip process

The main objective of the present paper is the development of a viscoplastic regularization procedure valid for an adiabatic dynamic process for multi-slips of single crystals. The next objective is to focus attention on the investigation of instability criteria, and particularly on shear band localization conditions.

Adiabatic shear band localization of inelastic single crystals in symmetric double-slip process

Adiabatic shear band localization of inelastic single crystals in symmetric double-slip process

Instability phenomena and adiabatic shear band localization in thermoplastic flow processes

The main objective of the paper is the development of the viscoplastic regularization procedure valid for a broad class of thermodynamic plastic flow processes in damaged solids. The additional aim is to investigate instability phenomena and adiabatic shear band localization criteria when spatial covariance, thermomechanical coupling, strain induced anisostropy and micro-damage softening effects are taken into consideration. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. In the first part of the paper the formulation of an inelastic flow process is given and particular attention is focussed on the thermomechanical coupling effects. The thermodynamic theory of elastic-viscoplastic damaged solids is presented within a framework of the rate type covariance material structure with a finite set of the internal state variables. A notion of covariance is understood in the sense of invariance under an arbitrary spatial diffeomorphism. Rate sensitivity effect is introduced by the assumption of the viscoplastic overstress conception. A notion of a relaxation time has been used to control the description of mechanical as well as thermal disturbances. By the assumption that the mechanical relaxation time is equal to zero the thermo-elastic-plastic (rate independent) response of the damaged material is accomplished. In the second part of the paper the existence of a solution to the initial-boundary value problem is examined and its stability property is investigated based on the application of nonlinear semi-group methods and an analysis of continuity of evolution operators. For an adiabatic process the investigation of acceleration waves is given. The determination of eigenvalues of the appropriate acoustic tensor is presented. This helps to assess the well-posedness of the initial-value problems which describe the thermodynamic plastic flow processes. Differences for two constitutive assumptions, namely for rate dependent and rate independent responses, are examined. In the case of an adiabatic process and elastic-viscoplastic response of a material the conditions for the existence, uniqueness and well-posedness of the initial value problem have been investigated. Criteria for adiabatic shear band localization of plastic deformation are obtained by assuming that some eigenvalue of the instantaneous adiabatic acoustic tensor for rate independent response is equal to zero. Several particular cases of the constitutive model have been considered.

Adiabatic shear band localization fracture of solids in dynamic loading processes

On presente l'application d'une recente theorie de rupture viscoplasique avec des micro-endommagements au probleme de localization des bandes de cisaillement dans les corps non-elastiques soumis a la charge dynamique aux grands taux de deformation d'ordre 10 3 -10 4 sec −1 . Dans la premiere partie de l'article un processus adiabatique d'ecoulement non-elastique est formule et etudie. On formule ensuite le probleme de Cauchy et on precise les conditions pour ce qu'il soit bien pose. Le temps de relaxation est utilise comme un parametre de regularisation. La regularisation viscoplastique assure la stabilite de l'algorithme d'integration a l'aide de la methode des elements finis

Adiabatic shear band localization in elastic-plastic single crystals

The main objective of the paper is the investigation of shear band localization criteria for finite elastic-plastic deformations of a single crystal subjected to an adiabatic process. The next objective is to focus attention on the temperature dependent plastic behaviour of the single crystal considered. A constitutive model is developed within the thermodynamic framework of the rate type covariance constitutive structure i.e. it is invariant with respect to diffeomorphism. To achieve this aim a multiplicative decomposition of the deformation gradient is adopted and the Lie derivative is used to define all objective rates for introduced vectors and tensors. Thermomechanical couplings are investigated and a method is developed which allows us to use the standard bifurcation procedure in the examination of the adiabatic shear band localization. The general evolution equation for the Kirchhoff stress tensor is obtained. The fundamental matrix in this evolution equation describes thermomechanical couplings as well as local lattice deformation and rotation. For the particular elastic properties of the single crystal and for some simplified case of the coupling effects the criteria for adiabatic shear band localization are obtained in their exact analytical form. The influence of two important thermal effects, namely thermal expansion and thermal plastic softening on the criteria of localization is investigated. The similar influence of spatial covariance effects (which arise from the difference between the Lie derivative and the material rate of the Kirchhoff stress tensor) is also examined.It has been shown that by incorporating the thermomechanical effects and the spatial covariance effects into a constitutive law of the elastic-plastic single crystal, the plastic hardening modulus hcrit at the inception of localization is in fact small but positive.It has also been proved that this thermomechanical theory of single crystals can describe the misalignment of the shear bands from the active slip systems in the crystal's matrix. The computed critical value of the strain-hardening rate hcrit, as well as the difference between the direction of the macroscopic shear band and the primary slip systems of the single crystal appeared to be in accord with recent experimental observations [cf. Chang and Asaro (1981, Acta Metall.29, 241–257) for Al-Cu single crystals and Spitzig (1981, Acta Metall.29, 1359–1377) for Fe-Ti-Mn single crystals].

Adiabatic shear band localization in elastic-plastic damaged solids

The main objective of the paper is the investigation of shear band localization conditions for finite elastic-plastic rate independent deformations of a damaged solid body subjected to an adiabatic process. For the kind of process considered, the thermal effects may play a dominating role. The next objective of the paper is to focus attention on temperature-dependent plastic behaviour of the body considered. Thermomechanical couplings are investigated, and a method is developed that allows application of the standard bifurcation procedure in examination of the shear band localization criteria when influence of thermomechanical couplings and thermal softening effects, together with hardening and micro-damage effects, are taken into consideration. Particular attention is focused on the coupling phenomena generated by the heat resulting from internal dissipation. A set of the coupled evolution equations for the Kirchhoff stress tensor and for temperature is considered. The assumption that the thermodynamic process is adiabatic permits elimination of the rate of temperature and permits us to obtain the general evolution equation for the Kirchhoff stress tensor. The fundamental matrix in this evolution equation describes thermomechanical couplings. For the particular elastic properties of the material and for some simplified cases of the coupling effects the criteria for shear band localization have been obtained in exact analytical form.

The localization of plastic deformation in thermoplastic solids

The main objective of this paper is the investigation of the influence of thermomechanical couplings and thermal softening effects on adiabatic shear band localization criteria for finite rate-independent deformation of an elastic-plastic body. The constitutive equations for thermoelastic-plastic J2-flow theory are formulated within a framework of the rate type covariance structure with internal state variables. Two alternative descriptions are presented. Both constitutive structures formulated are invariant with respect to diffeomorphisms and are materially isomorphic. Particular attention is focused on the coupling phenomena generated by the internal heat resulting from internal dissipation. An identification procedure has been developed which permits the determination of the exact form of the evolution equation for the internal state variable vector. A set of coupled evolution equations for the Kirchhoff stress tensor and for temperature is investigated. The assumption that the thermodynamic process considered is adiabatic permits the elimination of the rate of temperature and gives the fundamental cvolution equation for the Kirchhoff stress tensor. This important result allows the use of the standard bifurcation method in the examination of the adiabatic shear band localization criteria. For the particular clastic properties of the material and for some simplified case of the coupling effects the criteria for adiabatic shear band localization are obtained in exact analytical form. Discussions of the influence of thermomechanical couplings, thermal expansion, thermal plastic softening effects and the covariance terms on the localization criteria are presented.