Deformation twinning

October 23, 2011

Sensitivity of deformation twinning to grain size in titanium and magnesium

A Ghaderi and M R Barnett

The impact of grain size on deformation twinning in commercial purity titanium and magnesium alloy Mg–3Al–1Zn (AZ31) is investigated. Tensile tests were carried out for the titanium samples; compression testing was employed for the magnesium specimens. Average values of the true twin length, true twin thickness and the number density of twins were determined using stereology. A key difference between these two materials is that twinning contributes little to the plastic strain in the titanium while it accounts for nearly all of the early plastic strain in the magnesium. In some respects (e.g. volume fraction and number density) the phenomenology of twinning differed between the two materials, while in others (e.g. twin shape and size) both materials showed a similar response. It is found that in both materials, twins span the entirety of their parent grains only for grain sizes less than ∼30 μm. Both the nucleation density per unit of nucleating interface (i.e. grain and twin boundaries) and the aspect ratio of twins scale with applied stress. The impact of grain size on twin volume fraction is modelled analytically.

[1] Elastic properties of surfaces on nanoparticles

W G Wolfer

Lattice parameter changes in nanoparticles can be used to determine the surface stress of solids. In the past a Laplace–Young relationship has been employed to interpret the lattice parameter changes as a function of the particle size. In the meantime, however, atomistic calculations revealed a purely mechanical origin of the surface stress that is consistent with elasticity theory for solid surfaces as developed by Gurtin and Murdoch. In this theory the equilibrium distance for surface atoms may differ from that in the bulk solid, and the elastic properties of the surface layer may also deviate from bulk values. We apply this Gurtin–Murdoch theory to spherical nanoparticles and reanalyze past data as well as results from recent theoretical calculations on lattice parameter changes, thereby enabling us to determine surface properties commensurate with the mechanical interpretation of surface stress.

[2] Orientation dependence of twinning and strain hardening behaviour of a high manganese twinning induced plasticity steel with polycrystalline structure

H Beladi et al

The twinning induced plasticity steel 0.6 C–18 Mn–1.5 Al (wt.%) employed in this study exhibited a strength of about 1 GPa, combined with a large uniform elongation of over 60% at moderate strain rates. This excellent combination of tensile mechanical properties was shown to be a result of complex dynamic strain-induced microstructural reactions, including dislocation glide, dislocation dissociation, stacking fault formation, dynamic recovery, mechanical twinning and dynamic strain ageing. The contribution of each of these processes was discussed with respect to the strain hardening behaviour. An important observation was that the propensity for mechanical twinning in a particular grain strongly depends on its crystallographic orientation and is clearly correlated with the magnitude of the corresponding Taylor factor. The current results reveal that the development of partial dislocations and stacking faults at an early stage of straining and the consequent interaction of gliding dislocations with stacking fault interfaces enhances the strain hardening rate. Subsequent or concurrent initiation of mechanical twins also contributes to strain hardening through a dynamic Hall–Petch effect limiting the dislocation mean free path and consequently enhancing dislocation storage. Dynamic strain ageing (DSA) took place at a late stage of deformation, adding to strain hardening. DSA is a factor reducing ductility by promoting strain localization.

[3] A phase field study of strain energy effects on solute–grain boundary interactions

T W Heo et al

We have studied strain-induced solute segregation at a grain boundary and the solute drag effect on boundary migration using a phase field model integrating grain boundary segregation and grain structure evolution. The elastic strain energy of a solid solution due to the atomic size mismatch and the coherency elastic strain energy caused by the inhomogeneity of the composition distribution are obtained using Khachaturyan’s microelasticity theory. Strain-induced grain boundary segregation at a static planar boundary is studied numerically and the equilibrium segregation composition profiles are validated using analytical solutions. We then systematically studied the effect of misfit strain on grain boundary migration with solute drag. Our theoretical analysis based on Cahn’s analytical theory shows that enhancement of the drag force with increasing atomic size mismatch stems from both an increase in grain boundary segregation due to the strain energy reduction and misfit strain relaxation near the grain boundary. The results were analyzed based on a theoretical analysis in terms of elastic and chemical drag forces. The optimum condition for solute diffusivity to maximize the drag force under a given driving force was identified.

[4] Severe deformation twinning in pure copper by cryogenic wire drawing

A Kauffmann et al

The effect of low-temperature on the active deformation mechanism is studied in pure copper. For this purpose, cryogenic wire drawing at liquid nitrogen temperature (77 K) was performed using molybdenum disulfide lubrication. Microstructural investigation and texture analysis revealed severe twin formation in the cryogenically drawn copper, with a broad twin size distribution. The spacing of the observed deformation twins ranges from below 100 nm, as reported in previous investigations, up to several micrometers. The extent of twin formation, which is significantly higher when compared to other cryo-deformation techniques, is discussed with respect to the state of stress and the texture evolution during wire drawing.

[1] Highly mobile twinned interface in 10 M modulated Ni–Mn–Ga martensite: Analysis beyond the tetragonal approximation of lattice

L Straka et al

The huge strains that Ni–Mn–Ga magnetic shape memory alloys can achieve are usually described in a tetragonal unit cell approximation of a five-layered modulated (10 M) crystal structure. Here we analyze the impact of a slight orthorhombic and monoclinic distortion of the 10 M structure in Ni50.2Mn28.3Ga21.5at.% single crystal. Combining dedicated experiments to probe the microstructure, structure and mechanical properties with calculation using elastic continuum theory, we prove the existence of fine a/b-laminates within modulation macrotwins of the order of 100 micrometers in size. This complex twin microstructure containing a Type II macrotwin interface is associated with an extraordinarily low twinning stress of between 0.05 and 0.3 MPa, while Type I twins exhibit twinning stress of about 1 MPa. The findings provide important guidelines for designing the martensitic microstructure for more efficient actuators.

[2] An analytical description of overall phase transformation kinetics applied to the recrystallization of pure iron

B B Rath and C S Pande

Experimental studies of recrystallization in deformed single crystals of pure iron are described. The results are used to analyze various parameters associated with the time evolution of the volume fraction of the growing phase during phase transformations in this system associated with the phenomena of nucleation and growth. In addition, using the experimental results, the phenomenon has been modeled by a new approach which may provide a different, and possibly more precise, description of the kinetics of the process. The proposed analytical approach uses easily measured metallographic parameters, obtained from a systematic two-dimensional surface examination, to provide a detailed description on the time dependence of nucleation, nucleation rate, growth rate and interfacial migration and compared with the classical approach based on Kolomogrov formalism.

[3] Plastic deformation mechanisms of fcc single crystals at small scales

C Zhou et al

Three-dimensional (3-D) dislocation dynamics simulations were employed to examine the fundamental mechanisms of plasticity in small-scale face-centered cubic single crystals. Guided by the simulation results, we examined two distinct modes of behavior that reflect the dominant physical mechanisms of plastic deformation at small scales. We found that the residence lifetimes of internal dislocation sources formed by cross-slip decrease as the system size decreases. Below a critical sample size (which depends on the initial density of dislocations) the dislocation loss rate exceeds the multiplication rate, leading to the loss of internal dislocation sources. In this case nucleation of surface dislocations is required to provide dislocations for deformation and the “starvation hardening” mechanism becomes the dominant deformation process. When the sample is larger than a critical size multiplication of internal dislocation sources provides the dominant mechanism for plastic flow. As the strain is increased the rising dislocation density leads to reactions that shut off these sources, creating “exhaustion hardening”.

[4] Dislocation density evolution and interactions in crystalline materials

P Shanthraj and M A Zikry

Dislocation density-based evolution formulations that are related to a heterogeneous microstructure and are physically representative of different crystalline interactions have been developed. The balance between the generation and annihilation of dislocations, through glissile and forest interactions at the slip system level, is taken as the basis for the evolution of mobile and immobile dislocation densities. The evolution equations are coupled to a multiple slip crystal plasticity formulation, and a framework is established that relates it to a general class of crystallographies and deformation modes. Specialized finite element (FE) methodologies have then been used to investigate how certain dislocation density activities, such as dislocation density interactions and immobilization, are directly related to strain hardening and microstructure evolution. The predictions are validated with channel die compressed (CDC) experiments, and are consistent with inelastic deformation modes of fcc metals.

[5] Growth of dislocation clusters during directional solidification of multicrystalline silicon ingots

B Ryningen et al

Highly detrimental dislocation clusters are frequently observed in lab-scale as well as industrially produced multicrystalline silicon ingots for solar cell applications. This paper presents an investigation of dislocation clusters and how they develop over the whole height of a pilot-scale ingot. A 12-kg ingot, cast in a pilot-scale directional solidification furnace using a standard slip cast silica crucible and standard coating containing silicon nitride powder, was studied with respect to dislocation clusters. Dislocation clusters originating from grain boundaries were identified and followed from an early stage to the top of the ingot. One possible model for growth and multiplication of the dislocations in the clusters during solidification where slip on the View the MathML source〈1 1 0〉 system must be allowed is described in detail. Another possible mechanism is also discussed.

[6] Appearance of dislocation-mediated and twinning-induced plasticity in an engineering-grade FeMnNiCr alloy

A Geissler et al

By comparing the microstructural and texture evolution with tensile stress–strain response of an Fe–24Mn–7Ni–8Cr (mass%) alloy, a slip-dominated deformation process and, at a later stage of deformation, twinning-induced plasticity are observed. The occurrence of deformation twinning is texture sensitive and occurs only in the 〈1 1 1〉 fibre texture component. Based on these experimental observations, a model is presented, which reflects an orientational and configurational peculiarity of face-centred cubic stacking faults bordered by two Shockley partials. With this model, the onset point of stacking fault growth, i.e. movement of the leading partial and stopping of the trailing partial, is evaluated. This point reflects the formation of twins in the sense that a twin is regarded as an arrangement of stacking faults on every consecutive slip plane. Furthermore, based on the tensile test results, a model-compatible description of the mechanical behaviour is shown and a reasonable stacking fault energy of about 8 mJ m−2 is calculated for the onset of partial dislocation breakaway, i.e. the onset of deformation twinning.

[1] A grain boundary phase transition in Si-Au

S Ma et al

A grain boundary transition from a bilayer to an intrinsic (nominally clean) boundary is observed in Si-Au. An atomically-abrupt transition between the two complexions (grain boundary stabilized phases) implies the occurrence of a first-order interfacial phase transition associated with a discontinuity in the interfacial excess. This observation supports a grain-boundary complexion theory with broad applications. This transition is atypical in that the monolayer complexion is absent. A model is proposed to explain the bilayer stabilization and the origin of this complexion transition.

[2] Universal Strain – Temperature Dependence of Dislocation Structures at the Nano-Scale

P Landau et al

The universal topology of experimental strain-temperature maps of dislocation structures of fcc metals allows the ordering of dislocation structure forming processes in these metals, which is not consistent with the stacking fault energy or the melting temperature. Using dimensional analysis, it is shown that the metals can be ordered by the activation energy for cross-slip. The experimental maps are scaled by the cross-slip activation energy to form a universal strain temperature map. The implications for dislocation rearrangement mechanisms are discussed.

[1] Significance of mechanical twinning in hexagonal metals at high pressure

W Kanitpanyacharoen et al

Diamond anvil cells (DAC) in radial synchrotron X-ray diffraction geometry were used to investigate texture development and identify deformation mechanisms in zinc and osmium at the Advanced Photon Source (APS) and the Advanced Light Source (ALS), respectively. Further experiments on cadmium and hafnium wires were carried out in the Deformation-DIA (D-DIA) multi-anvil press at APS to study the simultaneous effects of pressure, temperature and strain. At room temperature and increasing pressure the c-axis aligns near the compression direction in all hexagonal metals, but with considerable differences. Texture in zinc evolves gradually between 10 and 15 GPa and strengthens as pressure is increased to 25 GPa. In osmium, texture development starts very early (4 GPa). At ambient temperature cadmium and hafnium develop a similar textures as zinc and osmium, respectively. Texture in cadmium evolves gradually with axial shortening to 34%, whereas in hafnium texturing develops immediately after small strains. When hafnium is simultaneously heated to 700 K and deformed in compression, a texture develops with compression axes near View the MathML source. Simulations from a visco-plastic self-consistent (VPSC) polycrystal plasticity model suggest that the gradual texture evolution observed in zinc and cadmium is controlled primarily by View the MathML source basal slip and later accompanied by View the MathML source tensile twinning when the c/a ratio is below View the MathML source. Conversely, early texture development in osmium and hafnium at room temperature is contributed mainly by View the MathML source tensile twinning. However, the View the MathML source texture in hafnium at high temperature is attributed to basal and prismatic slip.

[2] Particle strengthening in fcc crystals with prolate- and oblate-shaped precipitates

B Sonderegger and E Kozeschnik

The prediction of precipitation hardening is a key factor for optimizing strength or creep performance of advanced structural materials. An essential part of this task is a reliable assessment of precipitate distances based on arbitrary discrete size distributions. Up to now, models are available for spherical precipitate shape. The present work advances these approaches to all kinds of spheroids. The results are expressed in compact form as a correction factor to the spherical case, only depending on the precipitate shape.

[3] Continuum modeling of dislocation starvation and subsequent nucleation in nano-pillar compression

A Jerusalem et al

The mechanical behavior of single crystalline aluminum nano-pillars under uniaxial compression differs from coarse-grained Al in that the former is characterized by a smoother transition from elasticity to plasticity. We propose an extension of the phenomenological model of dislocation starvation originally proposed in [Greer and Nix, Phys Rev B, 73:245410 (2006)] additionally accounting for dislocation nucleation. The calibrated and validated continuum model successfully captures the intrinsic mechanisms leading to the transition from dislocation starvation to dislocation nucleation in fcc nano-pillars.

[4] A Crystal-Plasticity Finite Element Method Study on Effect of Abnormally Large Grain on Mesoscopic Plasticity of Polycrystal

Y S Choi and T A Parthasarathy

In order to investigate the effect of an abnormally-large grain on plastic responses of polycrystal, elasto-viscoplastic crystal plasticity finite element simulations were performed using synthetic three dimensional microstructures with and without an abnormally-large grain. Results indicated that abnormally-large grain can be an important feature to cause the instability of mesoscopic plasticity by drawing hot spots of plastic shear. In particular, the maximum slip system shear hot spots are pronounced in the presence of the abnormally-large grain oriented in single slip.

[1] Migration of grain boundaries in free-standing nanocrystalline thin films

Dynkin and Gutkin

Theoretical models are suggested which describe stress-coupled migration of grain boundaries in free-standing nanocrystalline films under external loading. The critical stresses for the start of migration and the transition from stable to unstable migration are calculated and analyzed in dependence on the grain size, grain boundary misorientation angle, film thickness, distance from the closest free surface, and migration direction. It is shown that the least stable are low-angle grain boundaries of larger length which emerge on surfaces of thinnest films.

[2] Insight into the phase transformations between Ice Ih and Ice II from electron backscatter diffraction data

D J Prior et al

Electron backscatter diffraction data from polycrystalline water ice, cycled three times through the 1h to II phase transformation, show that an area equivalent to the original grain-size (∼450μm) now comprises equant 10μm grains with a non-random crystallographic preferred orientation (CPO). Pole figures show small-circle ring and fence patterns characteristic of CPO development controlled by an orientation relationship during phase transformation. Misorientation analysis shows that one of two orientation relationships can explain the data: 1h/II, {10-10}1h/{0001}II or 1h/II, {10-10}1h/{0001}II .

[3] Comment on ”Simulation of damage evolution in composites: A phase-field model”

Emmerich and Pilipenko

Here we reassess the results of [S.B. Biner, S.Y. Hu Acta Matt. 57(2009) 2088-2097] on phase-field simulations of damage evolution in composite materials. In particular we discuss the validity of the results presented therein in the framework of linear elasticity theory.

Update: Reply to “comment on simulation of damage evolution In composites: a phase-field model by H. Emmerich and D. Pilipenko ”

Biner and Yu