Evolution of dislocation structures and deformation behavior of iron at different temperatures: Part I. strain hardening curves and cellular structure

The deformation behavior of iron has been investigated at different temperatures by means of tension tests. There exist two temperature ranges for deformation. In the low-temperature range(T < 293 K), the flow stress σ, the work-hardening rate θ at ε = 0.06, and the yield stress σ_y decrease with increasing temperature, but in the higher temperature range(T ≥: 293 K), σ and θ at the same strain increase while σ_y decreases more slowly. The change of dislocation density, with temperature, atε = 0.06 exhibits the same tendency as that of the flow stress. The strainhardening rates decrease almost linearly with increasing stress up to necking in the low-temperature range, except the initial strain range. At the higher temperature range, the hardening rates decrease linearly with stress only at the early stage of deformation, but above certain strains, the decreases become more gradual; that is, the G-cr curves deviate from the linear region. The evolution of dislocation structure has also been observed by transmission electron microscopy (TEM). The results show that a substructural transition takes place in the nonlinear range of G-cr curves. In the linear decreasing region of strain-hardening curves, the deformation is controlled by the uniformly distributed dislocations or cell multiplication prevails. However, in the nonlinear region of G-cr curves, cell multiplication seems to be balanced by cell annihilation.     

The application of a dislocation model to the strain and temperature dependence of the strain hardening exponentn in the Ludwik-Hollomon relation between stress and strain in mild steels

With the aid of a dislocation model for the stress-strain relationship of α-Fe, analytical expressions for the strain and temperature dependence of the exponentn in the relation, σ= K · ε ⁿ, are derived. These account quite accurately for experimental results obtained with several low alloy steels. It is shown thatn varies continuously with strain but that the theoretical and experimental log σ-log ε curve in most cases can be approximated by two straight lines in accordance with the well-known “double-n” behavior. The strain, ε₁ at which the two lines intersect is equal to the strain at which the theoretical n(ε) curve has an inflection point. With the model presented it is also possible to account for the temperature dependence ofn(ε) and of ε₁ within the temperature range −78° to 500°C.     

Influence of grain size and stacking-fault energy on deformation twinning in fcc metals

This article investigates the microstructural variables influencing the stress required to produce deformation twins in polycrystalline fcc metals. Classical studies on fcc single crystals have concluded that the deformation-twinning stress has a parabolic dependence on the stacking-fault energy (SFE) of the metal. In this article, new data are presented, indicating that the SFE has only an indirect effect on the twinning stress. The results show that the dislocation density and the homogeneous slip length are the most relevant microstructural variables that directly influence the twinning stress in the polycrystal. A new criterion for the initiation of deformation twinning in polycrystalline fcc metals at low homologous temperatures has been proposed as (σ _tw −σ ₀)/G=C(d/b)^A, where σ _tw is the deformation twinning stress, σ ₀ is the initial yield strength, G is the shear modulus, d is the average homogeneous slip length, b is the magnitude of the Burger’s vector, and C and A are constants determined to have values of 0.0004 and −0.89, respectively. The role of the SFE was observed to be critical in building the necessary dislocation density while maintaining relatively large homogeneous slip lengths.     

Quantitative characterization of the substructure of AISI 316 stainless steel resulting from creep

The substructure of AISI 316 stainless steel resulting from creep deformation has been quantitatively characterized using transmission electron microscopy. The specimens were tested at temperatures and stresses ranging from 593° to 816°C and 8000 to 35,000 psi, respectively. Subgrains whose boundaries are predominantly (111) twist boundaries were formed in all tests at and above 704°C but were observed very infrequently at 650°C and were completely absent after creep at 593°C. The subgrain diameter,d, and the mobile dislocation density, ρ, were found to vary with the applied stress, σ_a, according to:d =kσ_a ^-1 and ρα σ_a ². Subgrain misorientation varys from less than 0.1 to 1 deg in each specimen seemingly independent of all parameters evaluated. A double triple node dislocation configuration was frequently observed in all specimens. Its relation to the deformation process is discussed in a mechanism involving the breaking of attractive dislocation nodes. Formerly Graduate Student, Materials, Science and Metallurgical Engineering Department, University of Cincinnati, Cincinnati, Ohio 45221     

Comparative study of the impact response and microstructure of 304L stainless steel with and without prestrain

This study compares the dynamic plastic deformation behavior and microstructural evolution of 304L stainless steel with and without metal-forming prestrain, using the compressive split Hopkinson pressure-bar technique and transmission electron microscopy (TEM) under strain rates ranging from 8 × 10² to 5 × 10³ s⁻¹ at room temperature, with true strains varying from yield to 0.3. Results show that the flow stress of unprestrained and prestrained 304L stainless steel is sensitive to applied strain rate, but the prestrained material exhibits greater strength. A higher work-hardening rate and higher strain-rate sensitivity are also found in the prestrained material, while an inverse tendency exists for the activation volume. A constitutive equation with our experimentally determined specific material parameters successfully describes both unprestrained and prestrained dynamic behavior. Microstructural observations reveal that the morphologies of dislocation substructure, mechanical twins, microshear bands, and α′ martensite formation are strongly influenced by prestrain, strain, and strain rate. The density of dislocations increases with increasing strain and strain rate for both materials. The dislocation cell size decreases with increasing strain, strain rate, and prestrain. An elongated cell structure appears in the prestrained material as heavy deformation is applied. Mechanical twins are found only in the prestrained material. Microshear bands and α′ martensite are more evident at large strains and strain rates, especially for the prestrained material. Quantitative analysis indicates that the amount of dislocations, mechanical twins, and α′ martensite varies as a function of work-hardening stress (σ−σ _y), reflecting different strengthening effects and degrees of microhardness.     

On the stress exponent and the rate-controlling mechanism of high-temperature creep in some solid solutions

The internal stress, σ_i, and the effective-stress exponent of the dislocation velocity,m*, have been determined during creep of Fe-3.5 at. pct Mo alloy at 1123 K under 10.8 to 39.2 MN/m² and of Ni-10.3 at. pct W alloy at 1173 K under 19.6 to 88.2 MN/m². Both alloys have been classified among class I alloys under a certain condition including the present one, because the applied-stress exponent of the steady-state creep rates,n, is almost 3. Values of σ_i obtained by stress-transient dip test were small and almost independent of the applied stress, σ_c, in Fe-3.5 Mo alloy. On the other hand, in Ni-10.3 W alloy σ_i increased with increasing σ_c as in the case of many pure metals. The value ofm* obtained by analyzing stress-relaxation curves immediately after creep deformation was unity in Fe-3.5 Mo alloy, whereas in Ni-10.3 W alloy it was about 2.5. These results indicate that the rate-controlling mechanisms in creep are different from each other in these two alloys and that the classification according ton-value does not always coincide with the classification according to the rate-controlling mechanisms. It is concluded that the fact thatn ≃ 3 is not a sufficient evidence supporting that creep is controlled by one of microcreep mechanisms.     

Stress-induced γ→ α martensitic transformation in two carbon stainless steels. Application to trip steels

The influence of the temperature θαof a prestraining of austenite above M_don the subsequent stress-induced γ→ α’ transformation in the(M _s, M_d) range is examined in two carbon stainless steels. It is shown that the yield stress, which is controlled by the transformation, increases with θαat given testing temperature and amount of prestraining. This behavior is related to the influence of θαon the nature and arrangement of the defects present in austenite after the prestraining: planar defects(i.e., stacking faults, twins, e platelets) predominate if θαis close to M_dwhereas undissociated dislocation cells are only to be observed if θif higher. This is consistent with the strong increase of the intrinsic stacking fault energy of the austenite, as inferred from measurements using the node method on a hot stage microscope. In addition, the ability of plane defects to propagate under stress is shown to be lower after a prestraining at higher θα, which is attributed to a segregation of impurity atoms on dislocations. It is concluded that the nucleation stress of the γ→ α’ transformation is the stress necessary to allow planar defects to propagate in the prestrained austenite. This work is part of a thesis prepared at the Centre des Matériaux de l’Ecole des Mines, Corbeil, France, and submitted at the University of Nancy, June 1972.     

High-temperature strength and ductility increases of Ti-Mo-Al alloys by step aging

Step-aging programs, based on principles of particle-dislocation interactions, were developed systematically to obtain increases in the high-temperature strength and ductility properties of Ti-7 at. pct Mo-Al alloys. A triple-step aging program applied to Ti-7 Mo-16 Al produced a yield stress σ_0.2 = 1,500 MN/m², elongation to fracture ε _F = 4 pct at room temperature, and σ_0.2 = 900 MN/m², ε _F = 12 pct at 600°C. A two-step aging program resulted in σ_0.2 = 1,350 MN/m², ε _F = 5 pct at room temperature; σ_0.2 = 800 MN/m², ε _F = 20 pct at 600°C. Formerly Assistant Research Professor, Materials Research Laboratory, Rutgers University     

Stress-strain behavior and the dislocation structure at small strains in iron deformed in tension, torsion and combined tension-torsion

Commercial iron specimens of 40 μm grain size were deformed to small strains in tension, torsion and combined tension-torsion at 300 K and the resulting dislocation structures, distributions and densities determined using transmission electron microscopy. Employing the von Mises yield criterion and the total plastic-work hypothesis, good agreement was obtained for the three testing conditions for: a) equivalent stress •σ vs equivalent strain •∈p curves, b) the dislocation structure, distribution and density ρ as a function of •∈p and c) •σ as a function of ρ^1/2. Furthermore, upon comparing the •σ vs ρ^1/2 curve for polycrystalline iron with the τ_RSSvs ρ^1/2 curve for single crystals of polyslip orientations, it appears that the theoretical value of 2.9 for the average Taylor factor —M (= •σ/τ_RSS) for bcc metals is appropriate. Almost equally good correlations were obtained on the basis of maximum shear strain and therefore a positive decision between the von Mises and τ_max-γTH _max yeild criteria could not be made. A single test in which the direction of straining in torsion was reversed yielded a density and distribution of dislocations (and a corresponding value of •σ) equivalent to that developed at a smaller strain in unidirectional straining. Formerly with the Department of Metallurgical Engineering and Materials Science, University of Kentucky, Lexington, Ky. Formerly with the Department of Metallurgical Engineering and Materials Science, University of Kentucky, Lexington, Ky.     

Obstacles for low-temperature dislocation motion in polycrystalline zinc

The thermally activated plastic flow of zinc has been investigated by means of differential-stress creep tests at 87°K and tensile tests in the temperature range 87° to 475°K. The thermal activation enthalpy as a function of stress and the total activation enthalpy (1.1 ev) have been obtained. The activation area is found to decrease with stress from about 800b² at zero effective stress to a constant value of 75b². The rate-controlling obstacle for low temperature deformation is identified to be the “forest” dislocation. The approximate stacking fault width and stacking fault energy in zinc are deduced to be “3.5b” and 75 erg per sq cm, respectively.     

Microstructural instability and superplasticity in a Zr-2.5 Wt Pct Nb pressure-tube alloy

The effect of microstructural evolution on superplastic deformation parameters, such as the nature of σ-ε plots, strain-rate sensitivity parameter, and activation energy, were studied for unstable and thermally stable microstructures of a Zr-2.5 wt pct Nb pressure-tube alloy. Two types of differential strain-rate tests (increasing temperature (IT) and decreasing temperature (DT), in the temperature range of 610 °C to 810 °C at 20 °C intervals) were conducted within a strain-rate range of 10⁻⁵ to 10⁻³ s⁻¹. Single specimens were used to obtain the σ-ε plots for all the test temperatures in the aforementioned temperature range. The effect of orientation (with respect to the axial direction of the tube) on the superplastic deformation parameters was also studied. The microstructural evolution was studied along the three orthogonal planes of the tube by water quenching underformed samples in the beginning of differential strain-rate tests at each test temperature. The observed apparent activation-energy values associated with deformation were in the two distinct ranges of 287 to 326 and 151 to 211 kJ/mole. In the temperature range of 730 °C to 810 °C, the apparent activation-energy value depended on the direction of approach of the test temperature. The mechanisms of superplastic deformation in this alloy were found to be dislocation climb—controlled creep in region III and grain-boundary sliding accommodated by grain-boundary diffusion or lattice diffusion in the α or β phases in region II. Based on the observed microstructural features, a model to explain the σ-ε plots and apparent activation energy has been proposed.     

The internal stress in titanium deformed at low temperatures (T<0.33TM)

The internal stressσ _i at 300 K produced by deforming commercial Ti-50A titanium (0.5 at. pct O _eq ) wire of 2 and 22μm grain size to 1 pet strain at temperatures of 78 to 650K was investigated employing the back-extrapolation and decrementai unloading techniques. Concurrent observations of the amount of twinning and the dislocation structure were made by transmission electron microscopy,σ _i by the decrementai unloading method was higher, and was inferred to have a stronger temperature dependence, than that by back-extrapola tion, the difference inσ _i being relatively independent of grain size.σ _i by both methods was found to be relatively independent of the deformation temperature and neither twinning nor dynamic strain aging was found to have a noticeable influence on its value. Since no pro nounced changes in dislocation structure or slip mode were observed for the present material as a function of deformation temperature, the difference inσ _i obtained here between the decremental unloading and the back-extrapolation methods could not be correlated with such changes as was possible by Williamset al. for titanium sheet material of higher in terstitial solute content. M. Doner was formerly affiliated.     

Studies on the Work-Hardening Behavior of AA2219 under Different Aging Treatments

Uniaxial tensile tests were performed to examine the influence of the precipitation state on the yield strength and work-hardening behavior of AA2219 for different aging treatments. The microstructural observations in four aging treatments (viz. natural aging, underaging, peak aging, and overaging) were made through transmission electron microscopy (TEM) to understand the type of phase or intermediate stages of the phase present (Guinier–Preston (GP) zones, θ″, θ′, and θ). To characterize the work-hardening behavior, the analysis of the experimental results has focused on two parameters, viz. the initial work-hardening rate Θ_max (≡dσ/dε) and the slope (dΘ/dσ) of the Θ-σ plot, which is related to the rate of dynamic recovery. The initial work-hardening rate (Θ_max) first drops as aging proceeds and then increases significantly upon overaging. The large increase in Θ_max is also associated with a concomitant increase in the slope (dΘ/dσ) of the Θ-σ curve. The material constants in the differential equation for the dislocation density are evaluated and flow stress vs plastic strain curves are generated using the flow stress contributions from the solid-solution, dislocation, and precipitation hardening. The model predictions are found to be in excellent agreement with the experimental data for a range of precipitation states from underaged (UA) to overaged (OA) conditions. Curves of flow stress due to dislocation hardening with the plastic strain were also generated in the presence of shearable and nonshearable precipitates.     

Stored energy,microstructure, and flow stress of deformed metals

The stored energy of plastic deformation has been estimated from transmission electron microscope measurements of dislocation boundary spacings and misorientation angles using Al (99.99 pct) cold rolled to reductions of 5 to 90 pct as an example system. In order to obtain the most accurate estimate of stored energy, it is necessary to take into account the presence of two classes of dislocation boundary, considering the boundary misorientation angle distribution and the stereology of each class independently. Stereological relationships are developed to predict the stored energy estimates that would result from electron backscatter pattern (EBSP) investigations on these microstructures. The calculations show that EBSP investigations can be used to estimate the stored energy, but that at low strains, the limited angular resolution will lead to a significant underestimation. A relationship between the flow stress (0.2 pct offset) and the stored energy is found, though the relationship differs significantly for the low and high strain regimes. At low strains, the flow stress is linearly related to the square root of the stored energy (E _s ) according to σ − σ ₀ = Mα[(G/K)E _s ]^0.5, where G is the bulk modulus, M is the Taylor factor, and K and α are constants.     

Depth of melt- pool and heat- affected zone in laser surface treatments

Predictions of penetration depthsd _α of a melt pool and/or transformation-hardening zone as influenced by laser power and scan speed are developed based on a simple conduction balance in the solid metal substrate. The prediction isd _α/d ∼p -^1/2—(θ_α — —)Q ^-1 whered is the laser beam width, θ_α is the ratio of “penetration temperature” to substrate far-field temperature, andP andQ are the dimensionless laser-scan speed and absorbed power, respectively. This scaling law, alternatively derived as an asymptotic limit of a classical closed-form solution, applies for moderate scan speeds and power. Evidence that it captures the dom-inant experimental behavior in cases of no meltingand melting is presented. The predicted depths also compare favorably to numerical simulations by finite elements (a three-dimensional (3D) workpiece of finite extent).     

Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫_o ^σ ε ⋅dσ from the constitutive equation relating the strain rate (ε) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J _max) whenm = 1. The efficiency of the power dissipation(J/J _max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT^•3 s^•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.     

Influence of strain rate and temperature on the deformation behavior of a metastable high carbon iron-nickel austenite

Austenitic specimens of Fe-15 wt pct Ni-0.8 wt pct C were tested in tension at strain rates of 10⁻⁴ s⁻¹ and 10⁻¹ s⁻¹ over the temperature range −20°C to 60 °C. The influence of strain rate and temperature on the deformation behavior depended on whether stress-assisted or strain-induced martensitic trans-formation occurred during testing. Under conditions of stress-assisted transformation, the ductility was low and independent of strain rate. However, when strain-induced transformation occurred, the duc-tility increased significantly and the higher strain rate resulted in greater ductility and more transfor-mation. Although the ductility increased continuously with temperature, the amount of strain-induced transformation decreased and no martensite was observed above 40 °C. Microstructural examination showed that the martensite was replaced by intense bands and that these bands contained very fine (111) fcc twins. The twinning resulted in enhanced plasticity by providing an additional mode of deformation as slip became more difficult due to dynamic strain aging at the higher temperature. This study confirms that the substructure following deformation will depend on the proximity of the deformation temperature to theM _s ^σ temperature. At temperatures much greater thanM _s ^σ , austenite twinning will occur, while at temperatures close toM _s ^σ , bcc martensite will form.     

Effect of hydrogen on the Young's modulus of iron

A Bordoni type apparatus was used to measure the change of the apparent Young's modulus ofα-Fe induced by hydrogen. The solution of the flexural vibration equation of a beam under stress indicatesE = C(σ)ω ². If the resonant frequencies of the first and the third tone are measured at about the same time,E andσ can be calculated. The change of the apparent Young's modulus after charging with hydrogen is defined as ΔE = ΔE ₁(H) + ΔE ₂, where ΔE ₁(H) relates to the change of the perfect crystal interatomic cohesive force and ΔE ₂ is induced by the change of stress. An artificially partial stress relaxation test was carried out to measure ΔE ₂. The results show that during aging, after both charging with hydrogen and artificial stress releasing, the change of the apparent modulus is the same,i.e., ΔE = ΔE ₂. Thus, the ΔE ₁(H) associated with the interatomic cohesive force does not evidently change during aging with escaped hydrogen of 7 to 8 wppm at room temperature,i.e., this amount of hydrogen does not decrease the interatomic cohesive force ofα-Fe.     

Transformation behavior of TRIP steels

True-stress (σ), true-strain (ε) and volume fraction martensite(f) were measured during both uniform and localized flow as a function of temperature on TRIP steels in both the solution-treated and warm-rolled conditions. The transformation curves(f vs ε) of materials in both conditions have a sigmoidal shape at temperatures above M_s ^σ (maximum temperature at which transformation is induced by elastic stress) but approach initially linear behavior at temperatures below M_s ^σ where the flow is controlled by transformation plasticity. The martensite which forms spontaneously on cooling or by stress-assisted transformation below M_s ^σ exhibits a plate morphology. Additional martensite units produced by strain-induced nucleation at shear-band intersections become important above M_s ^σ. Comparison of σ-ε andf-ε curves indicate that a “rule of mixtures” relation based on the “static” strengthening effect of the transformation product describes the plastic flow behavior reasonably well above M_s ^σ, but there is also a dynamic “transformation softening” contribution which becomes dominant below M_s ^σ due to the operation of transformation plasticity as a deformation mechanism. Temperature sensitivity of the transformation kinetics and associated flow behavior is greatest above M_s ^σ. Less temperature-sensitive TRIP steels could be obtained by designing alloys to operate with optimum mechanical properties below M_s ^σ.     

Effect of heat and thermomechanical treatments on the linear thermal expansion coefficient of an N30K10T3 invar

The N30K10T3 invar that has a temperature of the onset of martensite transformation of austenite M _s ≈ −80°C and a Curie point θ_C ≈ 200°C after water-quenching from 1150°C is studied. The decomposition of a supersaturated solid solution is shown to substantially influence the linear thermal expansion coefficient. The alloy is studied in the following three initial states: after quenching, after phase transformation-induced hardening (γ → α_m → γ_p.h), and after cold (20°C) plastic deformation by 30%.