Macroscopic Shear Bands Research Articles

Deformation of single crystal Hadfield steel by twinning and slip

The stress–strain behavior of Hadfield steel (Fe, 12.34 Mn, 1.03 C, in wt%) single crystals was studied for selected crystallographic orientations ( [ 1 ̄ 11] , [001] and [ 1 ̄ 23] ) under tension and compression. The overall stress–strain response was strongly dependent on the crystallographic orientation and applied stress direction. Transmission electron microscopy and in situ optical microscopy demonstrated that twinning is the dominant deformation mechanism in [ 1 ̄ 11] crystals subjected to tension, and [001] crystals subjected to compression at the onset of inelastic deformation. In the orientations that experience twinning, the activation of multiple twinning systems produces a higher strain-hardening coefficient than observed in typical f.c.c. alloys. Based on these experimental observations, a model is presented that predicts the orientation and stress direction effects on the critical stress for initiating twinning. The model incorporates the role of local pile-up stresses, stacking fault energy, the influence of the applied stress on the separation of partial dislocations, and the increase in the friction stress due to a high solute concentration. On the other hand, multiple slip was determined to be the dominant deformation mechanism in [ 1 ̄ 11] crystals subjected to compression, and [001] crystals deformed under tension. Furthermore, the [ 1 ̄ 23] crystals experience single slip in both tension and compression with planar type dislocations. Using electron back-scattered diffraction patterns, macroscopic shear bands (MSBs) were identified with a misorientation of 9° in the compressed [ 1 ̄ 11] single crystals at strains as low as 1%.

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.

Slip pattern, microstructure and local crystallography in an aluminium single crystal of copper orientation {112}〈111〉

The evolution of microstructure and local crystallography has been examined in single crystals of {112}〈111〉 orientation of pure Al deformed at room temperature by channel die compression to strains of ϵ=0.5 and ϵ=1.5. Despite the channel die deformation mode used, a sample rotation towards the {4 4 11}〈11 11 8〉 orientation was observed. Macroscopic shear bands were not seen. Instead, bands of localised glide on crystallographic planes were observed, associated both with shearing of the microstructure and with +TD rotated orientations. Such strain localisation increased with increasing deformation. The complexity of slip within these regions was confirmed by calculation of dislocation boundary characteristics from local TEM orientation measurements. Dislocation densities calculated using Frank’s formula are consistent with the observed macroscopic slip pattern.

Mechanism for the formation of shear bands with (hhl) orientation of boundaries in single crystals with an FCC lattice

We propose a model for the formation of a macroscopic shear band with invariant planar boundaries of the (hhl) type, whereh/l is a rational number, associated with two slip systems along the (111) and (111) planes. We introduce the concepts of stress mesoconcentrator for the excess dislocation charge localized within the volume of a cylinder of diameterD≈0.1 μm and shear carriers along the (hhl) planes of the superdislocation type. We discuss a number of consequences of the proposed model.

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.

Localized deformation modes and non-Schmid effects in crystalline solids. Part II. deformation patterns

Abstract A rate-dependent multiple slip model incorporating non-Schmid effects and thermal deformation, developed by Dao and Asaro (1993), is implemented into finite element codes to study deformation patterns before and after the shear band initiation in single crystals. Simulations using different hardening rates and different non-Schmid effects show that non-Schmid effects provide a consistent explanation for the formation of coarse slip bands (CSB), and that high hardening rates, typical of single crystals, can cause localization to not persist. Serrated flow is found accompanying the development of CSB's even with significant strain hardening. Elastic anisotropy has important influences on the onset of shear bands that form in single slip. Whether macroscopic shear bands (MSB) form first on directions that are close to what would be the primary slip plane or conjugate slip plane in a single crystal test, depends on the slip system geometry with respect to the loading orientation and the hardening function (self hardening and latent hardening). The transition from coarse slip bands to macroscopic shear bands is simulated and analyzed in detail, showing the importance of non-Schmid effects and the hardening function. Geometric effects, especially non-uniform lattice rotations, play important roles in the formation of both coarse slip bands and macroscopic shear bands. Consistency between the calculations and the theory predictions of the critical conditions of localization in Part I of this series (Dao and Asaro, 1996) as well as the existing experimental evidences are found.

Localized deformation modes and non-Schmid effects in crystalline solids. Part I. Critical conditions of localization

Abstract A general strain rate independent crystallographic slip theory which incorporates non-Schmid effects, is presented. This constitutive law is a rate independent isothermal idealization of the theory developed by Dao and Asaro (1993). The non-Schmid factors are estimated for Ni3A1 as well as for some simple metals. A general method to study the bifurcation modes for the general three-dimensional multiple slip geometry is described. Three-dimensional bifurcation analyses for single slip mode as well as multiple slip mode are presented. With moderate non-Schmid effects, coarse slip bands (CSB) are found possible in single slip modes as well as multiple slip modes, where critical localization criteria may be satisfied with significant strain hardening. Non-symmetric multiple slip geometries are examined and the bifurcation results show that shear bands close to the conjugate slip system are often more favored. Non-Schmid effects, elastic anisotropy and stress state may have important influences on the critical localization conditions. A mechanism for the transition from coarse slip bands to macroscopic shear bands (MSB) is suggested. The predictions of the theory are compared with existing experimental observations and good agreement is obtained for both the coarse slip bands and macroscopic shear bands.

Formation, microstructure and development of the localized shear deformation in low-carbon steels

An investigation has been made into the effect of microstructural parameters on the propensity for forming shear localization produced during high speed torsional testing by split Hopkinson bar with different average rates of 610, 650 and 1500 s −1 in low carbon steels. These steels received the quenched, quenched and tempered as well as normalized treatments that provide wide microstructural parameters and mechanical properties. The results indicate that the occurrence of the shear localization is susceptible to the strength of the steels. In other words, the tendency of the quenched steel to form a shear band is higher than that of the other two steels. It is also found that there is a critical strain at which the shear localization occurs in the steels. The critical strain value is strongly dependent on the strength of the steels. Before arriving at this point, the material undergoes a slow work-hardening. After this point, the material suffers work-softening, corresponding to a process during which the deformation is gradually localized and eventually becomes spatially correlated to form a macroscopic shear band. Examinations by SEM reveal that the shear localization within the band involves a series of sequential crystallographic and non-crystallographic events including the change in crystal orientation, misorientation, generation and even perhaps damage in microstructures such as the initiation, growth and coalescence of the microcracks. It is expected that the sharp drop in the load-carrying capacity is associated with the growth and coalescence of the microcracks rather than the occurrence of the shear localization, but the shear localization is seen to accelerate the growth and coalescence of the microcracks. The thin foil observations by TEM reveal that the density of dislocations in the band is extremely high and the tangled arrangement and cell structure of dislocations tends to align along the shear direction. The multiplication and interaction of dislocations seems to be responsible for work-hardening of the steels. The avalanche of the dislocation cells corresponds to the sharp drop in shear stress at which the deformed specimen is broken. Double shear bands and kink bands are also observed in the present study. The principal band develops first and its width is narrower than that of the secondary band.

Damage and fracture of a cross woven C/SiC composite subject to compression loading

In order to understand the mechanical behaviours of ceramic matrix composites under various loading conditions, the compression stress-strain behaviour of a cross woven C/SiC ceramic matrix composite was characterized in terms of damage and fracture mechanisms, which were observed by scanning electron microscope (SEM) on a side-polished sample. The compression stress-strain curve was found to consist of two stages. The first stage, which extends to about 300 MPa, covers linear elastic deformation with a compression modulus of 140 GPa. The second stage starts with the occurrence of compression damage modes, which include ply delamination, bundle separation and transverse bundle cracking. Depending on the local structure of the sample, the second stage of the stress-strain curve can be either mostly linear or non-linear. The fracture of the composite under compression is by kinking, shearing and bending fracture of fibre bundles individually or in groups, forming a macroscopic shear band in the sample.

Analysis of Shear Band Development in a Viscoplastic Double Slip, Single Crystal in Tension

Using an idealized planar single crystal model undergoing symmetrical double slip in tension, the effect of rate sensitivity on shear band initiation and on shear band development is analysed. The behavior of the crystal is assumed to be rigid-viscoplastic. By analysing the kinematics and statics of shear banding, the deformation modes involving shear banding pattern are formulated. By a linearized stability analysis, the critical condition for shear band initiation is obtained. To study shear band development, the formulated constitutive equations are numerically solved, and the maximum value of the localized shear is predicted. The results show three different stages of shear band development. The first corresponds to a slow progression of shear localization in the band, the second to a rapid shear localization accompanied with an unloading of surrounding material, and the third to a resumption of deformation in the surrounding material and to a progressive saturation of the shear band. All three stages depend strongly on rate sensitivity, especially the first stage which does not exist in the rigid-plastic case. Even very small rate sensitivity can delay significantly or even preclude the shear band formation. Finally a discussion of the results illustrates how a macroscopic shear band forms and propagates.

Microstructure and Texture of Copper Single Crystal of (112)[ [formula omitted][formula omitted]1] Orientation Undergoing Channel-Die Compression at 77 K

The development of macroscopic shear bands (MSB) in copper single crystal of (112)[ 1 1 1] orientation subjected to channel-die compression in liquid nitrogen is analysed. The influence of twinning on the local orientation inside MSB, defined by the position 011〈110〉 is demonstrated. The crystalographic nature of MSBs whose material shear plane is parallel to the plane 111 has been documented.

Shear band post-bifurcation in oriented copper single crystals

By in situ SEM observation performed in oriented copper single crystals strained in tension, the formation and propagation processes of macroscopic shear bands (MSB) as well as the consequences of their interactions are analysed. We found that an MSB consisted of a collection of parallel shear bands on slip lines scale. The observed lengthening and thickening of MSB were related to saturation of the individual shear bands and to nucleation of new ones in the adjacent matrix. In order to understand this phenomenon, a post-bifurcation model is applied to an idealized planar double slip single crystal. We show that shear banding is effectively characterized by the three observed stages: bifurcation, large shear strain localization and saturation. The bifurcation is accompanied by unloading in the matrix. The saturation is due to the fact that the geometrical softening leading to the bifurcation decreases with localized shear.

Coarse slip bands and the transition to macroscopic shear bands

Coarse slip bands and the transition to macroscopic shear bands

Dynamic void collapse and material failure mechanisms in metallic crystals

The micromechanical failure mechanisms of compression-induced high strain-rate void collapse in monocrystalline copper are studied. A theoretical and a computational constitutive model are introduced to study the material failure mechanisms of shear-strain localization and cleavage fracture in monocrystalline fcc structures. An explicit dynamic finite-element algorithm is introduced for the integration of the numerically stiff micromechanical visco-plastic constitutive relations. The combined effects of strain hardening, strain-rate history, lattice rotation, and thermal softening on void collapse are investigated, and criteria for the formation of macroscopic shear-bands and tensile cracks formation are developed. The computed results are compared with experimental results and observations, and it is shown that the material failure mode is governed by the competition between the strengthening and the softening mechanisms of the crystalline structure. Shear bands may form, if the thermal and geometrical softening mechanisms of the crystal surmount the dynamic strain hardening and the strain-rate hardening of the crystal. An increase in the strain hardening and the strain-rate hardening of the crystal retards the formation of shear bands. Material failure, in this case, is due to the coupled effects of large stress concentrations and physically limiting values of plastic strain-rates, temperatures, resolved shear-stresses, and dislocation velocities near the tip of the collapsed void. These physically limiting values result in the homogeneous generation of dislocations and the local unloading of the stresses from compression to tension at the void tip. This opening mode of stress, at the void tip, in combination with the limiting values, can result in tensile cracks occurring normal to the compression stress axis.

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].

The use of digital processing in studying stretch-forming sheet metal

The objective of this study was to demonstrate the feasibility of upgrading old and tedious approaches of obtaining materials parameters to a computerized process in an affordable, fast and technically efficient manner. The formability and instability of plastic flow in cold-rolled 70/30 cartridge brass in the form of localized deformation is examined using a digital-image-processing technique, allowing for a detailed description of the evolution of the nonuniform deformation pattern in the post-localization regime and making it possible to characterize the localized macroscopic shear bands. Computer interfacing was carried out and a powerful and an efficient package of software was developed for monitoring and managing the DIP system and for analyzing material flow during a uniaxial tension stretching.

Evaluation of macroscopic shear banding using a digital image processing technique

Evaluation of macroscopic shear banding using a digital image processing technique

Macroscopic shear bands in cross-rolled α brass

Macroscopic shear bands in cross-rolled α brass

Substructure evolution and deformation modes in shock-loaded niobium

An electron microscopy study has been conducted of the substructure evolution of polycrystalline niobium shock loaded to 6 and 37 GPa. It was found that dense dislocation tangles and loops dominate the substructure of samples shocked at 6 GPa, whereas slip bands and microbands on {110} and twins on {112} in addition to tangles and loops are observed in samples shocked at 37 GPa. The twins observed possess the characteristic lenticular shape similar to those seen in shock-loaded molybdenum and are consistent with the shape predicted by existing twin models. The twin elements and characters do not appear to be different from those induced by conventional deformation at low strain rates. Slip bands on {110} are considered to result from an independent deformation mode which is not a consequence of the termination of twin growth inside the crystal. Microbands, which are the most predominant feature, were developed within 10° of {110} planes with a slight misorientation (1° or less) across the bands. Macroscopic shear bands were not found in either of the shock-loaded samples. Comparison between the microstructures in shock-loaded and slowly deformed samples shows no drastic difference. It is argued that the prevalent deformation modes in shock-loaded niobium are not extraordinarily distinct from conventional deformation.

Shear band formation in plane strain compression

Shear band formation during plane strain compression of single crystals and polycrystals of an Al-3 wt% Cu alloy was studied. X-ray and electron diffraction, optical microscopy, and electron (TEM/STEM) microscopy were used to document the structure and micromechanisms of the localization process. Complementary finite element studies were performed using the measured single crystals' single slip system strain hardening data. The experimental observations and the computed deformation response are in very close agreement, and indicate that localization, through macroscopic shear band formation, occurs in continuously strain hardening, damage-free material. Shear band formation was preceeded by the development of very coarse slip which, like the shear bands, propagated across entire grains and, in single crystals, across the entire crystal. The computations and experiments showed that geometrical softening, caused by nonuniform lattice reorientation, is an important micromechanical influence on the localization process in both single crystals and polycrystals. Also, the propagation of shear bands across grain boundaries in polycrystals was looked at experimentally and computationally. Particular attention was paid to the crystallography of shear band transmission through grain boundaries.