The role of twinning in the cyclic stress-strain behavior of directionally solidified γ/γ′-δ

Under cyclic straining of the γ/γ’-δ directionally solidified alloy a special type of hysteresis loop with an inflection in the compressive loading region was obtained. Observations gave direct evidence that the inflection was due to a process in which the 5 twins formed during tension untwinned under the subsequent compression. Thin foil electron microscopy established the 5 twins to be two specific variants of the four {211} variants, the selectivity being imposed by the crystallographic relation of the 5 phase with the γ/γ’ matrix. Characteristic distribution of (010) 5 faults was also noted in the foils and they were found associated with the {211} untwinning events. The compressive {011} 5 twinning mode reported in literature was not observed; the forward plastic strain in tension was reversed by {211} untwinning mode at a compressive stress level much lower than that required for the onset of the {011} twins.     

The anisotropy of deformation and fracture in a directionally solidified Ni/Ni3Al-Ni3Cb lamellar eutectic alloy

The orientation dependence of deformation and fracture modes was investigated for a directionally-solidified Ni−Ni₃Al−Ni₃Cb lamellar eutectic alloy (Ni-20 wt pct Cb-2.5 wt pct al-6.0 wt pct Cr) using optical and transmission microscopy to examine tensile and compression specimens tested at temperatures below the softening point of the δ (Ni₃Cb) reinforcing phase (∼1050 K). In this temperature range there is a large difference between longitudinal and transverse tensile ductibility (>5 pct longitudinalvs<1 pct transverse). No single preferred fracture path (such as interfacial delamination) could be found to account for the low transverse tensile ductility. Analysis of the δ twinning geometry, however, indicated that the twinning strains for twins of the type {211}, which operate copiously in longitudinal tension, are negative in most transverse orientations, with Schmid factors being very low (<0.013) in the limited range of transverse orientations where {211} twin strains are positive. Examination of transverse tension test specimens broken at 1033 K confirm the absence of {211} twins, with only limited {011} twinning being found in selected grains, leading to the conclusion that the relatively low transverse tensile ductility of the eutectic results from the very limited number of deformation systems which operate in the δ reinforcing phase below the softening temperature.     

The influence of deformation path on the slow strain-rate stress corrosion cracking of admiralty brass sheet

The slow strain-rate stress corrosion cracking (SCC) of Admiralty brass sheet in an aqueous 0.1M CuSO₄ solution has been studied over a range of strain paths from uniaxial to equibiaxial tension. At a constant bulk solution pH and open circuit potential, the brass undergoes transgranular SCC characterized by cleavage-like cracks propagating on a macroscopic plane normal to the maximum principal strain axis for all strain paths. The average crack growth velocity is also independent of deformation path. It is thus concluded that the mechanism of transgranular SCC in this system does not depend on multiaxial strain path for the range of stress states examined. However, the fracture strain data show that the slow strain-rate SCC of the brass sheet results in ductility losses which are much larger in equibiaxial tension than in either uniaxial or plane strain tension. This behavior is attributed to stress corrosion cracks acting as linear imperfections whose presence causes failure of the uncracked ligament by a form of localized necking and whose influence is dependent not only on time but also on strain path.     

Strain Hardening of Hadfield Manganese Steel

The plastic flow behavior of Hadfield manganese steel in uniaxial tension and compression is shown to be greatly influenced by transformation plasticity phenomena. Changes in the stress-strain (σ−ε) curves with temperature correlate with the observed extent of deformation twinning, consistent with a softening effect of twinning as a deformation mechanism and a hardening effect of the twinned microstructure. The combined effects give upward curvature to the σ−ε curve over extensive ranges of plastic strain. A higher strain hardening in compression compared with tension appears to be consistent with the observed texture development. The composition dependence of stacking fault energy computed using a thermodynamic model suggests that the Hadfield composition is optimum for a maximum rate of deformation twinning. Comparisons of the Hadfield steel with a Co-33Ni alloy exhibiting similar twinning kinetics, and an Fe-21Ni-lC alloy deforming by slip indicate no unusual strain hardening at low strains where deformation is controlled by slip, but an unusual amount of structural hardening associated with the twin formation in the Hadfield steel. A possible mechanism of anomalous twin hardening is discussed in terms of modified twinning behavior (pseudotwinning) in nonrandom solid solutions. Formerly Graduate Student at Massachusetts Institute of Technology     

Effects of hydrogen on micro-twinning in a FeTiC alloy

In this study, it was observed that concurrent straining in the presence of a hydrogen concentration above a threshold value, or by high fugacity cathodic charging in the absence of external stress enhances twinning in the FeTiC alloy system. The twins observed have lamellar or prismatic shapes, with a crystallography consistent with that expected in b.c.c. crystals. The prismatic twins are bounded by {112} coherent interfaces with a co-zonal axis along a 〈111〉 twinning direction and incoherent boundaries at the ends. This study further supports the occurrence of hydrogen-induced plastic instability in metals. Micro auto-radiography technique has shown that the twin/matrix interfaces and TiC particles are strong traps for hydrogen.     

Basal slip and twinning in α-titanium single crystals

Single crystals of α-titanium, with small Schmid factors for prismatic slip, have been deformed in tension between 78 and 1120 K. At low temperatures, {1012} twinning has been observed in specimens having the angle between the basal plane and the tensile axis,x _B , close to 90 deg, whereas at intermediate orientations withx _B = 60 deg and 47 deg twinning occurs on the {1121} planes. A critical resolved shear stress law is not obeyed for either twinning mode. First order prismatic slip in the microstrain region appears to be responsible for the nucleation of {1121 twins. Slip is unlikely a pre-requisite for {1012} twinning. Basal slip without interference from twinning is observed in a variety of orientations at temperatures above 500 K. Plastic flow above 900 K may be described by an equation of the form:γ=Aτ ⁿ e^-Q/kT The relative ease of basal and prismatic slip in Ti and Zr is discussed in terms of the hcp ⇆ bcc allotropic transformation.     

plane-strain work hardening and transient behavior of interstitial-free steel

Stress transients resulting from abrupt changes in strain path have been shown to be important to subsequent formability. In order to investigate whether these transients result from strain aging or related interstitial effects, two-stage experiments were performed on Armco interstitial-free steel After a prestrain in plane-strain tension, the material was strained in uniaxial tension in the direction of zero initial extension. The stress-strain curve in plane strain was found to deviate markedly from that predicted by usual plasticity theory (Hill’s theory withM = 2.0). Comparison of monotonie curves from uniaxial and plane-strain tension using a newly-developed, self-consistent calculation suggested that IF steel follows Hill’s new theory with constantM ≈ 2.9. After the change from plane strain to uniaxial tension, positive stress transients (flow stress exceeds the monotonie flow stress) were measured. This form of transient agrees with ones measured for other steels. It therefore appears that the origin of the transient phenomenon is independent of interstitial content, and that static strain aging is not the mechanism by which these stress transients occur. Formerly A. E. Browning, Graduate Research Associate, Department of Metallurgical Engineering, The Ohio State University     

Deformation in wrought Mg−9Wt Pct Y

Considerable tensile-compressive yield strength anisotropy is normally associated with textured wrought magnesium alloys.¹ The ease of {1012} twinning is responsible for the lower compressive yield strengths of these materials. In Mg-9 wt pct Y, however, approximately equal tensile and compressive yield strengths of about 50 ksi have been previously reported.² This investigation was performed to study the deformation of wrought Mg-9 wt pct Y with the purpose of understanding its unusual isotropic behavior. It was found that almost no {1012} twinning occurs in this alloy, thus accounting for the absence of anisotropy. Initial plastic deformation both in tension and compression occurs almost entirely by slip, primarily on the basal plane. Subsequent deformation occurs by a combination of slip and {1121} twinning with short {1012} twins appearing only occasionally.     

Hydrogen embrittlement of titanium sheet under multiaxial states of stress

The influence of hydrogen on the ductility of commercially pure titanium sheet has been investigated over a range of stress states from uniaxial to equibiaxial tension. The data show that hydrogen embrittlement of plastically anisotropic Ti sheet depends on stress state, being the most severe in equibiaxial tension. Quantitative metallography indicates that the effect of stress state is primarily a result of two factors: (1) plane strain and equibiaxial tensile deformation are especially effective in causing the strain-induced fracture of hydrides and consequently void formation, and (2) the void link-up process in plane strain and equibiaxial tension initiates at a comparatively low bulk void density. The results are analyzed in terms of the influence of stress state on both hydride fracture and the occurrence of shear instabilities triggered by hydride fracture/void nucleation.     

Elastic strain energy of deformation twinning in tetragonal crystals

The aspect of elastic strain for a deformation twin with a pure shear strain is studied through Eshelby’s inclusion theory. Beta-Sn, TiO₂, and TiAl of tetragonal structures are considered. As the aspect ratio of a twin approaches zero, its elastic strain energy vanishes since the stress components coupled with the twin shear strain vanish, suggesting that the twin habit plane cannot be determined solely from the shear strain energy viewpoint, for any twin mode would provide a vanishingly small strain energy for a thin twin. The application of Johnson and Cahn’s shape bifurcation theory predicts that the transition from a circular to an elliptic shape would occur when the linear dimension of a lenticular twin is only in the order of 10 nm, indicating that most twins with a substantial aspect ratio should be influenced by growth kinetics. Under an applied stress, the free energy change is found to depend strongly on the orientation and the sense of the applied stress. The extreme condition of the free energy change usually occurs when the resolved shear stress becomes extreme in the direction of the twin shear strain, thus following the relationship of Schmid’s law. The analysis of the matrix stress field immediately outside a twin plate shows a bimodal stress distribution around the lateral tip of the lenticular plate. The locations of stress concentrations depend on both the twin aspect ratio and the elastic anisotropy. As the twin aspect ratio approaches zero, however, the two exterior stress concentrations merge together at the lateral tip of the lenticular plate, yielding a maximum stress value in the order of μg, where μ andg are shear modulus and twin shear strain, respectively.     

Influence of hydrostatic pressure and multiaxial straining on cavitating superplastic materials

A plasticity theory describing isotropic cavitating material has been developed to relate the flow characteristics of the matrix material to the cavitated one. Expressions have been derived to describe the behavior of the cavitating superplastic material during uniaxial tension, equibiaxial stress, and plane strain deformation with superimposed pressure. It is shown that the presence of pressure reduces the strain softening due to cavitation, in addition to decreasing the cavity volume fraction. The reduction in the strain softening at a higher cavitation level is more pronounced for uniaxial tension than for the other modes of deformation. For equibiaxial stress and plane strain, the strain-rate-sensitivity parameter is shown to be drastically affected by applying gas pressure without cavity elimination. This reduction in the strain softening becomes higher when a matrix material has a lower strain-rate-sensitivity parameter, as well as when a material is tested at a lower strain rate.     

Stress-State dependence of strain-hardening behavior in 2014 Al/15 vol Pct Al2O3 composite

The purpose of this investigation was to examine if the effective stress-strain function for discontinuously reinforced aluminum (DRA) matrix composites is independent of stress state, as they are for aluminum alloys. The rationale for such work is provided by the need to develop constitutive equations for applications in metal forming and forging problems. Experimental effectiveas curves at room temperature were determined for a particulate-reinforced composite, 2014 Al/15 vol pct A1₂O₃, and the matrix material, 2014 Al, under a variety of stress states. The tests consisted of uniaxial tension, equibiaxial tension (bulge test), and compression tests. To eliminate the effects of prior precipitation, all samples were given a solution-heat-treatment prior to tests. It was found that for the composite the effective yield stress in uniaxial tension was higher than that in equibiaxial tension but slightly lower than that in compression. However, the effective yield stresses for the matrix material in uniaxial tension and equibiaxial tension were nearly the same. The strain-hardening rate of the composite under equibiaxial tension was higher than that under either uniaxial tension or compression. It is suggested that nondeformable dead zones can develop around the particles during deformation whose shape changes with the applied stress state, and this is partly responsible for the observed differences in behavior. Formerly Graduate Student, the University of MichiganSenior Engineer     

高应变速率下钛-钢复合板界面组织特征及变形机制

在高应变速率下,钛-钢复合板不同材料以不同的变形机制协调变形,结合界面起到至关重要的作用.本文分析研究了高应变速率下钛-钢复合板的界面组织特征和变形机制.结果表明:在钢侧,随着应变速率的提高,小角度(3°~10°)晶界含量增多,织构组分{1相似文献   

Analysis of lattice parameter changes following deformation of a 0.19C-1.63Si-1.59Mn transformation-induced plasticity sheet steel

Austenite and ferrite lattice parameters were monitored using X-ray diffraction subsequent to deformation in uniaxial and biaxial tension and plane straining of a 0.19C-1.63Si-1.59Mn transformation-induced plasticity (TRIP) sheet steel. Details from peak position results suggest the presence of stacking faults in the austenite phase, especially after deformation in uniaxial tension. The results also indicate residual stress or composition effects (through changes in the average carbon concentration due to selective transformation of lower carbon regions of austenite). Compressive residual stresses in the ferrite matrix were measured, and found to increase with increasing effective strain in specimens tested in biaxial tension and plane strain. Strain partitioning between softer ferrite and harder austenite (and possibly bainite or martensite) may be responsible for these residual compressive stresses in the ferrite, although volume expansion from the γ → α′ transformation and texture gradients through the sheet thickness are also possible contributors.     

Twin Nucleation by Slip Transfer across Grain Boundaries in Commercial Purity Titanium

The role of strain transfer in the activation of deformation twinning at grain boundaries has been characterized in commercially pure titanium deformed in bending. Two different orientations of a textured polycrystal were deformed in bending and were analyzed using electron backscattered diffraction (EBSD) to determine the active slip and twinning systems in the surface tensile region. Prismatic slip and { 10[`1]2 } á [`1]011 ñ \left\{ {10\bar{1}2} \right\}\left\langle {\bar{1}011} \right\rangle twinning were the most widely observed deformation modes in both orientations. Nonprismatic slip systems were also activated, most likely to accommodate local strain heterogeneities. A slip-stimulated twin nucleation mechanism was identified for soft/hard grain pairs: dislocation slip in a soft-oriented grain can stimulate twin nucleation in the neighboring hard grain when the slip system is well aligned with the twinning system. This alignment was described by a slip-transfer parameter m′.[24] Twins activated by this mechanism always had the highest m′ value among the six available { 10[`1]2 } á [`1]011 ñ \left\{ {10\bar{1}2} \right\}\left\langle {\bar{1}011} \right\rangle twinning systems, while the Schmid factor, based on the global (uniaxial tensile) stress state, was a less significant indicator of twin activity. Through slip transfer, deformation twins sometimes formed despite having a very low global Schmid factor. The frequency of slip-stimulated twin nucleation depends strongly on the texture and loading direction in the material. For grain pairs having one grain with a large Schmid factor for twinning, nonparametric statistical analysis confirms that those with a larger m′ are more likely to display slip-stimulated twinning.     

Large Strain Deformation in Uranium 6 Wt Pct Niobium

The large strain deformation of polycrystalline uranium 6 wt pct niobium (U6Nb) was studied in situ during uniaxial tensile and compressive loading by time-of-flight neutron diffraction. Diffraction patterns were recorded at incremental strains to a maximum of approximately 0.13 tensile and 0.15 compressive true strain. A discrete reorientation of the crystallographic texture under tensile straining between 0.04 and 0.08 true strain is consistent with a previously unobserved mechanical deformation twinning mechanism, identified as either a (100) or (010) mechanical twin system. Beyond this, a continuous texture reorientation towards an (010) crystal orientations indicates that a slip mechanism is likely predominant. An analogous mechanical twin system was not observed in compression at large strain.     

Effect of Strain and Strain Path on Texture and Twin Development in Austenitic Steel with Twinning-Induced Plasticity

High-manganese (15 to 30 wt pct) austenitic steels exhibit extreme strain hardening because of twinning with increased strain. Twinning in these low stacking fault materials promotes retention of the austenitic microstructure and impedes dislocation motion. A dearth of information is available concerning the extent to which strain path influences twinning in so-called twinning-induced plasticity (TWIP) steels. The present study focuses on the influence of strain level and strain path on texture and twinning in a high-Mn content TWIP steel (Fe17.2Mn0.6C). Electron back-scatter diffraction was employed to measure the twin fraction, twin deviation, twin boundary length, grain misorientation, and volume fraction of different texture components as a function of both uniaxial and biaxial deformation. This information, which is part of the necessary first step toward linking crystallographic texture and twinning to mechanical properties, was used to quantitatively assess the extent to which these critical metallurgical features depend on the amount of straining and the strain path.     

Twinning Behavior of a Basal Textured Commercially Pure Titanium Alloy TA2 at Ambient and Cryogenic Temperatures

Twinning greatly affects the microstructure and mechanical performance of titanium alloys.The twinning behavior of a basal textured commercially pure titanium TA2 plates rolled to 4% reduction at the ambient and cryo-genic temperatures has been investigated.Microstructures of the rolled samples were investigated by optical micro-scope (OM)and the twinning analysis was carried out based on orientation data collected by electron back-scatter diffraction (EBSD).{1 122}contraction twins,{1 124}contraction twins and {1012}extension twins have been ob-served.Twinning mode activity varied with rolling temperature.Twinning is considered as the dominant deformation mechanism during rolling at both temperatures for the strain condition.Larger proportion of grains activates twin-ning during cryorolling,and greater number and more diverse types of twins are observed;manifestly related to the suppression of dislocation slips at the cryogenic temperature.{1 122 }contraction twins are the dominate twin type within samples rolled at both temperatures.Several {1 124}contraction twins are observed in the cryorolled sample while there are only a few in the sample rolled at room temperature.A few tiny {1012}twins have been identified in both samples.{1 124}contraction twins are preferentially activated at cryogenic deformation temperature and the{1012}extension twins may result in local strain accommodation.     

Plastic deformation of hafnium under uniaxial compression

The plastic behavior of polycrystalline hafnium (Hf) was investigated over a range of strain rates under uniaxial compression. Hafnium exhibited considerable ductility and a moderately rate-sensitive plastic behavior. The stress-strain response consisted of initial yielding followed by parabolic hardening. Microstructural observations on quasistatically deformed specimens revealed that yielding occurred by dislocation activity and that hardening was dominated by twinning on {1012} planes and by slip/twin interactions. A considerable reduction in dislocation and twinning activity was observed in specimens deformed at high strain rates. Failure occurred by shear localization and void growth and coalescence within the shear bands. Measurement of the temperature rise during high strain rate deformation was also made. From these measurements, the fraction of work converted to heat as a function of strain was determined and found to decrease with increasing strain.     

Constitutive Modeling of the Tensile Behavior of Al-TWIP Steel

High Mn steels demonstrate an exceptional combination of high strength and large ductility as a result of their high strain-hardening rate during deformation. The microstructure evolution and strain-hardening behavior of Fe18Mn0.6C1.5Al TWIP steel in uniaxial tension were examined. The purpose of this study was to determine the contribution of all the relevant deformation mechanisms—slip, twinning, and dynamic strain aging. Constitutive modeling was carried out based on the Kubin–Estrin model, in which the densities of mobile and forest dislocations are coupled to account for the interaction between the two dislocation populations during straining. These coupled dislocation densities were used to simulate the contribution of dynamic strain aging to the flow stress. The model was modified to include the effect of twinning. To ascertain the validity of the model, the microstructural evolution was characterized in detail by means of transmission electron microscopy and electron back-scatter diffraction.