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 vs equivalent strain curves, b) the dislocation structure, distribution and densityρ as a function of and c) as a function ofρ ^1/2. Furthermore, upon comparing the vsρ ^1/2 curve for polycrystalline iron with theτ _RSS vsρ ^1/2 curve for single crystals of polyslip orientations, it appears that the theoretical value of 2.9 for the average Taylor factor 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 andτ _max-γ _ρ ^max yield 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 ) 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.     

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.     

Dislocation structure and work hardening in polycrystalline ofhc copper rods deformed by torsion and tension

The dislocation structure during work hardening in copper deformed by torsion and tension is investigated by X-ray line broadening and TEM. In the case of torsion the equivalent tensile flow stress and the rate of work hardening is lower than that obtained in tensile experiments. At the same time the dislocation density at the same equivalent strain is considerably larger in the torsionally deformed material and the TEM microstructure indicates a double-slip deformation mechanism. In the tensile deformed samples asymmetric X-ray line broadening indicates long-range internal stresses with relatively lower dislocation densities. In this mode of deformation multiple slip takes place. The lower equivalent flow stress and the smaller rate of work hardening in the torsionally deformed material is correlated with the restricted number of slip systems and the absence of strong long-range internal stresses, which leads to the relative ease of generating high dislocation densities.     

Correlations between stress,strain and dislocation arrangement in weakly deformed copper single crystals

The development of dislocation structure along the stress strain curve in stage I and the beginning of stage II of Cu single-crystals was followed up by means of etch pits. The following experimental results were found:

• 1.(i) The critical resolved shear stress is linearly (not proportional) dependent on the square root of the initial dislocation density.
• 2.(ii) The transition from stage I to II shows notably an unusual weak dependence of the etch pit density at the cross glide plane (primarydislocation density) on the shear strain.
• 3.(iii) A linear dependence arises between the flow stress in a certain slip plane and the square root of the etch pit density in this plane.
• 4.(iv) The latent hardening rises in stage I to a value of three and falls in stage II to a constant value of approx. 1.2.
• 5.(v) At unloading, the dislocations glide only slightly backwards.

They arrange themselves strongly in subboundaries.     

Structure evolution and stability of copper deformed at 80 K

It has been established that high-pressure torsion at 80 K does not lead to the formation of a homogeneous submicrocrystalline structure in copper. A significant volume of the structure is occupied by dislocation cells and deformation twins. Heating to the room temperature results in recrystallization. The volume fraction of a recrystallized structure increases with the low-temperature strain. Recrystallized structure with an average grain size larger than 1 ??m forms in copper deformed by rotation through 10 revolutions of an anvil and stored at a temperature of 273 K for a week. To create an equilibrium submicrocrystalline structure in copper turned out to be impossible.     

A comparison of the stresses developed in tension, shear peel, and torsion strength testing of direct bonded orthodontic brackets

Strength testing of direct bonded orthodontic bracket systems is commonly performed with tension, shear peel, or torsion loads. In general, the results of these tests are reported as an average stress that is computed by dividing the experimentally measured force at failure by the area of the bracket base. The average value, obtained in this manner, implies an evenly distributed stress field. In this project, finite element model (FEM) calculations were used to determine the more realistic stress distributions generated within the cement. The results indicate that the three loading modes produce very different non-uniform stress field patterns. Furthermore, the calculated stress peaks and the stress component proportions depend on the loading method. It was therefore concluded that the manner of loading affects the strength measurements and that the average stress does not adequately characterize bond strength.     

Room-temperature instability of the structure of copper deformed at a cryogenic temperature

The structural changes in cryodeformed copper are studied during long-term (1–2 year) storage at room temperature. The material is found to be unstable: grain growth is detected. The revealed structural instability casts doubt on the use of cryogenic deformation to form a nanocrystalline structure in copper.     

Orientation dependence of dislocation structures in cyclically deformed Cu-16 At. Pct Al alloy single crystals

The dislocation structures induced by the cyclic deformation of Cu-16 at. pct Al alloy single crystals oriented, typically, as for single slip and [023] and for double slip, were studied by transmission electron microscopy (TEM) and compared with the results of Cu single crystals. Completely unlike the dislocation structures of Cu single crystals of corresponding orientations, the dislocation structures of these oriented Cu-16 at. pct Al alloy single crystals show a typical planar morphology. As the applied-plastic-stain amplitude increases, the dislocation configuration changes, on the whole, from multipolar arrays to dislocation tangles in the primary slip plane and from low-density planar slip bands to well-developed persistent Lüder’s bands (PLBs) in the planes normal to the primary slip plane, respectively. Secondary slips can be clearly observed to activate from very low plastic-strain amplitudes in all three Cu-16 at. pct Al single crystals investigated. Interestingly, the crystallographic orientation has almost no effect on the dislocation structure of Cu-16 at. pct Al single crystals.     

Matrix behavior in copper-tungsten composites at small strains

Composites with up to 15 pct tungsten wires in a copper crystal matrix prepared by infiltration showed matrix microyield and flow stresses increasing with fiber fraction. Dislocation etch-pit observations showed that the walls of a cell structure in the matrix formed during fabrication were the operative dislocation obstacles and that this initial structure rather than fiber-matrix interaction during straining was responsible for the matrix strengthening.     

Surface tension and the sintering force in copper

The sintering force, defined as the uniaxial tensile force necessary to just stop the sintering contraction in the direction of the applied force, has been measured over the entire course of the sintering of an uncompacted copper powder. The force rises to a maximum at a den-sity of 95 pct, and then becomes immeasurable. The sintering force perpendicular to cross-section “a” of a sinter body can also be computed from the known surface tension γ of the metal, the average mean curvature ˉH of the surface of the porosity and the area fraction of porosityA _A , by use of the relationship:F = γˉHA _A a. The calculated sintering force is valid so long as the metal-void interface is composed of a multiply-connected minimal-area sur-face. This condition is met during late first stage and early second stage sintering. Under the same conditions, the surface tension of a sinterable solid can be determined through a measurement of the sintering force.     

Fatigue hardening in annealed and deformed aluminum and copper

Fatigue hardening in 2024 aluminum and in OFHC copper has been investigated by measuring the hysteresis-loop width at zero stress as a function of the number of tension-compression cycles with a constant stress amplitude. Prior to cycling, the specimens were either annealed, elongated, or twisted. For the annealed and the preelongated specimens, the loop width is shown to decay with the number of cycles as a second-order process, and for the pretwisted specimens, as a first-order process. This behavior can be accounted for by reasonable assumptions regarding the dislocation movements involved.     

Diffusive intergranular cavity growth in creep in tension and torsion

Creep experiments were performed at 500°C in tension and torsion on high conductivity copper tubes with a uniform initial coverage of implanted water vapor bubbles on all grain boundaries. No significant differences were found in the times to fracture over a wide stress range when the results were correlated according to the maximum principal tensile stress in the two fields. The results indicate that the cavities grow in a crack-like mode but at one tenth the rate predicted from the theoretical model of Pharr and Nix. This difference is attributed partly to load shedding from boundaries normal to the maximum principal tensile stress to slanted boundaries and partly to a lack of knowledge about the surface diffusion constant. The results indicate further, that the contribution to intergranular cavity growth by power-law creep in negligible in comparison to the contribution by diffusional flow. Complementary tension and torsion experiments performed in initially uncavitated samples result in shorter creep lives in torsion than in tension due to more effective cavity nucleation in the former. The times to fracture in both of these cases obey Monkman and Grant's law, indicating the presence of constraints on growth by the lagging deformations by power-law creep in the surroundings of the cavitating isolated grain facets.     

TEM investigations of the structural evolution in a pearlitic steel deformed by high-pressure torsion

A fully pearlitic steel was deformed by high-pressure torsion up to very high strains, and the changes in the microstructure were determined by analytic and conventional transmission electron microscopy. The imposed strain leads to a fragmentation and an alignment of the cementite lamellae parallel to the shear plane. The electron energy-loss near-edge-fine structures of the Fe-L_2,3-edge of the iron matrix and the cementite lamellae were measured with high spatial resolution. The results indicated that after high-pressure torsion, the iron matrix contains finely dispersed carbon-rich areas that do not show the electronic fingerprint of cementite. However, the refinement in microstructure leads to an enormous increase in mechanical strength.     

Dislocation substructure evolution in torsion of pure copper

The evolution of dislocation substructures in pure copper during torsion deformation at strains ranging from 0 to 440 pct has been investigated using transmission electron microscopy. The study reveals that checkerboard patterns have formed and shrunk in size at strains ranging from 10 to 60 pct. This was followed by the development of laminar dislocation structures consisting of paired sheets which evolved from short double walls delineating the checkerboard patterns. Linear strain hardening was found to be maintained in the paired sheets at strains from 120 to 330 pct. Dislocation wall annihilation and microbands located along the wall of paired sheets were observed in stage IV of the work-hardening curve. At higher strains, another set of wall formation intersects with the paired sheets. The strain hardening of copper under torsional loading from the checkerboard pattern to the laminar structure is described by the mesh length theory of dislocation structures.     

An electron-backscattered diffraction study of the texture evolution in a coarse-grained AZ31 magnesium alloy deformed in tension at elevated temperatures

Electron-backscattered diffraction (EBSD) has been used to investigate the texture evolution during tensile deformation at temperatures between 673 and 773 K of a coarse-grained commercial AZ31 magnesium alloy. A weak (0001) fiber texture was initially present in the hot-rolled magnesium alloy plate. The [0001] directions of the grains spread 0 to 45 deg around the normal direction (ND) of the magnesium alloy plate. This pre-existing weak texture evolved during tensile deformation into a strong texture close to the {0001} 〈1 00〉. The [0001] directions of the grains rotated toward the orientations perpendicular to the tension axis of the samples, indicating that the 〈11 0〉 slip system appeared to be the most active slip system, especially in the early stages of deformation. The EBSD Schmid-factor analysis revealed that, however, with an increase in strain and the rotation of the (0001) slip plane, the {11 2} 〈11 〉 slip system appeared to be more favorable. The {1 00} 〈11 0〉 and {1 01} 〈11 0〉 slip systems remained favored throughout the strains investigated, indicating that {1 00} and {1 01} are two important slip planes for cross slip using the 〈11 0〉 slip vector. It is found that the misorientation across one coarse grain (as high as 38.2 deg) is accommodated by low-angle grain boundaries (LAGBs). The formation of these LAGBs may be an intermediate stage of the coarse grain refinement that occurred during deformation. This article is based on a presentation made in the symposium entitled “Processing and Properties of Structural Materials,” which occurred during the Fall TMS meeting in Chicago, Illinois, November 9–12, 2003, under the auspices of the Structural Materials Committee.