Constant substructure creep of aluminum following stress reductions

A series of stress reduction experiments was conducted on high purity polycrystalline aluminum. Initial stresses of 8.27, 10.3 and 12.4 MPa at 573 K and 3.44 MPa at 673 K were used, and stress reductions were made during steady state creep at approximately 22% true strain. For each initial stress, the constant substructure strain rates are characterized by an exponential dependence of rate on the reduced stress. These data are consistent with an exponential form of the kinetic law for flow within subgrain interiors, which is based on the theory of obstacle-controlled dislocation glide. In addition, the experimentally determined slopes for each set of constant substructure strain rate-vs-reduced stress data vary approximately as the inverse of the initial stress. This finding suggests that the strength of the microstructure scales with the initial applied stress. Finally, it is proposed that the activation energy for dislocation glide can be determined from a combination of constant structure and steady state creep data. The results of this analysis suggest that the thermal activation process may be controlled by lattice self-diffusion.     

A Revised Criterion for the Portevin–Le Chatelier Effect Based on the Strain-Rate Sensitivity of the Work-Hardening Rate

An improved analysis is presented of the stability of plastic deformation under conditions where dynamic strain aging (DSA) occurs, which leads to instabilities known as the Portevin–Le Chatelier (PLC) effect. It is shown that PLC instabilities can occur for conditions that are not covered by the currently prevailing criterion presented by Estrin and Kubin (1991), which focuses on a negative strain rate sensitivity of the flow stress, caused by interactions of solutes with thermally activated glide of mobile dislocations. The current analysis recognizes that the strain-rate sensitivity of the flow stress consists of two contributions, one associated with glide of mobile dislocations and the second with work hardening, related to storage of immobile dislocations. In this paper, an instability criterion is proposed that takes into account the possibility of a negative strain-rate sensitivity of the work-hardening rate, which is caused by diffusion of solutes to immobile dislocations. The latter contribution leads to an extended instability criterion. This criterion also provides an explanation for the existence of a critical strain above which instabilities occur. In this article, previously published tensile test data are used to show that a negative strain-rate sensitivity of the work-hardening rate, which influences significantly the occurrence of the PLC effect, can indeed occur under DSA conditions.     

Constant structure creep in metals after stress reduction in steady state stage

Constant structure creep in several metals and alloys was investigated in structures corresponding to the steady state creep conditions. Results were interpreted by means of the back stress concept. In accord with postulates of the strain transient dip test technique, the residual effective stress is considered the controlling stress for dislocation glide. The suggested interpretation of constant structure creep data allows to obtain some information about parameters of the dislocation kinetics in the steady state creep. From the interpretation, a pronounced applied stress dependence of the mobile dislocation density as well as a specific relation between the activation area and the effective stress in steady state creep under various creep conditions result.     

Theory of workhardening 1934-1984

The evolution of the theory of workhardening through the past fifty years has laid a secure basis, but much research still lies ahead. A guiding principle in the prevailing, so-called meshlength theory is that glide dislocations arrange into stress-screened, low-energy structures, the most common being the cell structure, and that the flow stress is the stress needed to generate new glide dislocations. Further, it makes extensive use of the “principle of similitude”. Remnant stresses due to dislocations with just one Burgers vector orientation are very often relieved by additional dislocations with other Burgers vectors which form not in response to the applied stress but to those remnant stresses. Such dislocations are commonly misnamed “forest” dislocations. The theory closely reproduces stages II and III of the typical workhardening curve. Stage I results in single glide from sources which initially are isolated from each other so that pile-ups form, which then may interact among neighboring pile-ups of opposite sign, so as to generate mats of dipoles parallel to the active glide plane. Stage II behavior is expected as long as similitude is obeyed so that the average free dislocation path shrinks inversely proportional with the root of the dislocation density. Stage III, finally, results when the free dislocation path is constant. At low temperatures, thermal activation can make the critical difference for the release of hair-trigger poised loops. This is the cause of creep effects whose magnitude is limited to less than the elastic strain. Computer calculations indicate the presence of longer-range (i.e., cell diameter scale) stresses whose sign changes with the cell’s sense of rotation. This suggests that rectangled dislocation cells with a common rotation axis, arranged into a three-dimensional checkerboard pattern in which the sense of rotation alternates from cell to cell, should minimize stored energy. Such cell patterns are increasingly reported in the literature. The fact that the average cell diameter tends to be inversely proportional to the applied stress is also readily explained through those stresses. In retrospect, Taylor’s theory of workhardening may be recognized as a variant of the meshlength theory of stage III, in that it is based on a stress-screened network obeying the principle of similitude while the free dislocation path, given by the spacing between the mosaic block walls, remains constant. This paper is based on a presentation made at the symposium “50th Anniversary of the Introduction of Dislocations” held at the fall meeting of the TMS-AIME in Detroit, Michigan in October 1984 under the TMS-AIME Mechanical Metallurgy and Physical Metallurgy Committees.     

A model for subgrain superplastic flow in aluminum alloys

Aluminum alloys that contain low angle boundaries exhibit different superplastic behavior than alloys consisting of high angle boundaries. On a relative basis, the low angle boundaries increase the flow stress, but impart a greater resistance to cavitation; the strain-rate sensitivity of this material is generally smaller and the change in the strain-rate sensitivity with strain rate shows a minimum instead of a maximum as observed in the large angle boundary materials. As a result, the subgrain material can be deformed to large tensile strains at fast strain rates. A kinetic model for subgrain superplasticity that invokes a balance between the arrival and emission rates of dislocations at low angle boundaries is presented. It explains several features of subgrain superplasticity. It also explains why ultrafine dispersoids of intermetallics appear to stabilize the subgrain structure in aluminum. Early work on the correlation between flow stress and the subgrain size in dynamic recrystallization of metals may also be consistent with the model.     

Control of superplastic deformation rate during uniaxial tensile tests

Precise determination of superplastic flow behavior involves imposing known and controlled strain rate during deformation of these alloys. Examination of tensile specimens after superplastic deformation has revealed variations in strain and strain rate occurring as a function of position and the difficulty of maintaining a constant strain rate during testing. To quantify these strain and strain-rate gradients within the specimens, interrupted tensile tests and tests on gridded tensile specimens were performed. It was observed that more uniform strain and strain rates could be achieved with longer gauge length specimens. While longer gauge lengths make it possible to have better control over the imposed strain rate by minimizing the effects of material flow from the specimen grip regions, it has been realized that for smaller specimen gauge lengths, typically used in most laboratories, a more complex control of crosshead speed (CHS) during a test is essential to characterize superplastic behavior. A mathematical model has been developed in order to gain better insight into this material flow and to provide an improved crosshead control schedule for constant strain-rate testing. The results of this analysis have been validated on a superplastic aluminum-magnesium alloy (5083 Al).     

Experimental assessment of structure and property predictions during hot working

Uniaxial compression experiments were conducted in the hot-working range for a commercial purity aluminum alloy using constant strain-rate tests and strain-rate drop tests producing strain hardening, strain softening, and steady-state deformation behaviors. The structure of the deformed material was characterized by microhardness and grain shape. A single internal state variable constitutive model for flow stress was developed using the microhardness data to quantify the state variable. The change in the grain aspect ratio was related to the imposed bulk strain in the samples. The constitutive model was incorporated into a finite element program. A critical experimental assessment of predictions of the spatial variation in structure and properties throughout a workpiece was then made using a tapered compression specimen. Comparisons with experimental results indicated that the load was underpredicted by 10 pct and the microhardness by 6 pct, while the severity of the strain gradients was overpredicted. This was concluded to be due to an underprediction of the work-hardening rate at low strains. Additional calculations made with alternative constitutive models showed that the internal state variable model predicted the applied force much more accurately than alternative models.     

The origin of strain-rate sensitivity in OFHC copper

This investigation was conducted to determine the nature of the strain-rate sensitivity of OFHC copper at room temperature. In particular, the relative magnitudes of the dynamic contribution (particle inertia, suppression of thermal assistance, and so forth) and the nondynamic contribution (namely, the accelerated rate of strain hardening observed at high strain rates) to the strain-rate sensitivity were determined. Specimens were dynamically compressed using the Hopkinson pressure bar technique, and then were reloaded quasistatically to determine their respective yield strengths. The dynamic contribution to strainrate sensitivity was taken as the difference between the peak dynamic flow stress and the flow stress of the same specimen when reloaded quasistatically. The nondynamic contribution to strain-rate sensitivity of the flow stress was taken as the difference between the quasistatic flow stress in reloading of a specimen prestrained ε₀ dynamically and the flow stress at ε₀ for a sample deformed in uniaxial quasistatic compression. The room temperature dynamic flow-stress of OFHC copper, deformed at 500s⁻¹, was found to be 25 pct higher than the conventional quasistatic flow stress for this metal over a strain range of 0.08 to 0.20. The nondynamic contribution to strain-rate sensitivity was found to be about 60 pct of the total flow stress increase and has been attributed to a difference in strainhardening at different strain rates. Thus, it appears that in OFHC copper at room temperature and at strain rates of about 500s⁻¹, the nondynamic contribution to strain-rate sensitivity is more significant than the dynamic contribution.     

Temperature-dependent void-sheet fracture in Al-Cu-Mg-Ag-Zr

Previous research showed that tensile fracture strain increases as temperature increases for AA2519 with Mg and Ag additions, because the void-sheet coalescence stage of microvoid fracture is retarded. The present work characterizes intravoid-strain localization (ISL) between primary voids at large constituents and secondary-void nucleation at small dispersoids, two mechanisms that may govern the temperature dependence of void sheeting. Most dispersoids nucleate secondary voids in an ISL band at 25 °C, promoting further localization, while dispersoid-void nucleation at 150 °C is greatly reduced. Increased strain-rate hardening with increasing temperature does not cause this behavior. Rather, a stress relaxation model predicts that flow stress and strain hardening decrease with increasing temperature or decreasing strain rate due to a transition from dislocation accumulation to diffusional relaxation around dispersoids. This transition to softening causes a sharp increase in the model-predicted applied plastic strain necessary for dispersoid/matrix interface decohesion. This reduced secondary-void nucleation and reduced ISL at elevated temperature explain retarded void sheeting and increased fracture strain.     

Experimental study of the origin of strain-rate sensitivity in a common Pb-Sn alloy

The origin of strain-rate sensitivity existing in the room-temperature plastic distortion of a 60 pet Pb-40 pet Sn alloy is examined experimentally using simple tension loadings. It is found that the response of this material to both constant stress and constant strain-rate loadings is accurately described by a single uniaxial constitutive relation which is independent of the instantaneous level of straining rate and dependent explicitly only on stress, strain and lapse-time variables. The rate sensitivity exhibited by this alloy during room-temperature quasistatic tensile deformations is thus concluded to be explainable directly in terms of a combination of the competing effects of strain hardening and time-dependent thermal softening without the necessity of introducing explicit strain-rate mechanisms of any kind.     

Effect of the Strain Rate on the TRIP–TWIP Transition in Austenitic Fe-12 pct Mn-0.6 pct C TWIP Steel

The strain-rate dependence of the plasticity-enhancing mechanisms in Fe-12 pct Mn-0.6 pct C-0.06 pct N steel was investigated. At low strain rates, deformation-induced ε-martensite was formed. At high strain rate, the strain-induced formation of ε-martensite was inhibited, and mechanical twinning was the dominant plasticity-enhancing deformation mechanism. This transition was associated with an increased work hardening rate and a higher total elongation. Dynamic strain aging (DSA) took place at all strain rates. While propagating type C Portevin-Le Chatelier (PLC) bands were observed at low strain rates, isolated propagating type A PLC bands were observed at high strain rates. The critical strain for the occurrence of DSA had an anomalous negative strain-rate dependence at low strain rates and a normal positive dependence at high strain rates. The transition from negative-to-positive strain-rate dependence was associated with a sharp change in the strain-rate sensitivity of the flow stress. Transmission electron microscopy was used to analyze the relationship between the stacking fault energy (SFE), the strain rate, and the plasticity-enhancing mechanisms. The SFE and critical resolved shear stress for the onset of the twinning and the ε-martensite transformation were calculated and compared with experimental results.     

The effect of grain size and temperature on the superplastic deformation behavior of a 7075 Al alloy

The high-temperature deformation behavior of a 7075 Al alloy has been investigated within the framework of a recently proposed internal-variable theory for structural superplasticity (SSP). The flow curves were obtained by performing a series of load relaxation tests for specimens with various grain sizes, at temperatures ranging from 445 °C to 515 °C. The overall flow curves were then separated into two parts, according to the respective physical mechanisms, viz., the grain-boundary sliding (GBS) and the accommodating dislocation glide processes, contrary to the conventional approach which uses a single power-law relation. These individual curves were then analyzed based on the internal-variable theory. Much valuable information has been obtained in this way, providing new physical insight as well as a more comprehensive understanding of SSP. The GBS curve could be described as a Newtonian viscous flow, signified by the power-index value of M _g =1.0 for this alloy. The unresolved issue of threshold stress is also clarified and identified as a critical stress required for the GBS. The role of grain refinement is found to shift the grain-matrix deformation (GMD) curve into a higher stress and strain-rate region, while the GBS curve into a lower stress and higher strain-rate region along the respective characteristic scaling line to bring both curves into a common flow-stress region, in which the GMD and GBS can operate simultaneously, resulting in the usual superplastic deformation behavior.     

Dynamic-coarsening behavior of an α/β titanium alloy

The dynamic-coarsening behavior of Ti-6Al-4V with an equiaxed α microstructure was established via isothermal hot-compression testing of cylindrical samples cut from an ultra-fine-grain-size (UFG) billet. Compression experiments were conducted at 900 and 955 °C, strain rates between 10⁻⁴ and 1 s⁻¹, and imposed true strains between 0 and 1.4. Following deformation, quantitative metallography revealed marked coarsening of the primary α particles at low strain rates (10⁻⁴ and 10⁻³ s⁻¹). The dynamic-coarsening rate followed rⁿ vs time kinetics, in which n was between 2 and 3, or behavior between those of bulk-diffusion and interface-reaction controlled. An examination of the temperature and strain-rate dependence of theoretical coarsening rates, however, strongly suggested that bulk diffusion (with n=3) was more important. The dynamic-coarsening behavior was also interpreted in the context of the observed plastic-flow behavior. At low strain rates, high values of the strain-rate sensitivity (m>0.5) and the overall shape of log stress-log strain rate plots indicated that the majority of the imposed strain was accommodated by grain-boundary sliding (gbs) and only a small amount via dislocation glide/climb processes. In addition, an analysis of the flow hardening that accompanied dynamic coarsening indicated that the flow stress varied approximately linearly with the α particle size, thus providing support for models based on gbs accommodation by dislocation activity in grain-mantle regions.     

Role of Self-Organization of Dislocations in the Onset and Kinetics of Macroscopic Plastic Instability

The present paper examines two aspects of the problem of critical conditions of jerky flow in alloys, or the Portevin–Le Chatelier (PLC) effect. Recent development of dynamic strain aging (DSA) models proved their capacity to qualitatively reproduce complex non-monotonic behavior of the critical strain, providing that the parameters of theory are allowed to depend on strain. Experimental measurements of such strain dependences have been realized for the first time and used to revise the predictions of the critical strain and stress relaxation kinetics upon abrupt strain-rate changes. On the other hand, it is usually omitted from consideration that the PLC stress serrations can last very short time in comparison with the characteristic time of stress transients. The development of stress drops was studied with the aid of the acoustic emission (AE) technique. It is shown that such macroscopic instabilities are caused by clustering of AE events which otherwise occur all the time, including the periods of smooth plastic flow. The role of synchronization of dislocation avalanches in the development of abrupt stress serrations and its relationship with the predictions of the local DSA models is discussed.     

Segregation and wetting transition at dislocations

We investigate solute segregation and wetting transition at dislocations and the corresponding drag effect on dislocation glide using a continuum model developed previously for grain boundary and based on gradient thermodynamics. The dislocation core structure and stress field are described by the newly developed phase field model. This study differs from much previous work because it takes into account not only the long-range elastic interactions but the short-range chemical interactions between solute atoms and dislocation core as well as among solute atoms themselves. The latter leads to the prediction of a wetting transition at the dislocation core with respect to varying temperature, solute concentration, or dislocation velocity. The transition temperatures obtained during heating and cooling are different from each other, leading to a hysteresis loop in the solute concentration-temperature plot and the solute concentration-velocity plot. These predictions could provide new insights into the phenomena of sharp yield point drop and strain aging observed in metal alloys. This article is based on a presentation made in the “Hillert Symposium on Thermodynamics & Kinetics of Migrating Interfaces in Steels and Other Complex Alloys,” December 2–3, 2004, organized by The Royal Institute of Technology in Stockholm, Sweden.     

Theoretical calculation of anisotropie creep and stress-strain behavior for a class of metal-matrix composites

A unified microcontinuum theory is developed to calculate the development of the anisotropic creep strain and the stress-strain relations under a constant strain rate for a class of metal-matrix composites from the constitutive equations of its constituent phases. Here, the ductile matrix is strengthened with aligned, identically shaped, spheroidal inclusions, which may be disc-like, spheres, or whiskers, so that at a given volume concentration, its anisotropic properties will further depend on the inclusion shape. The principle of stress transfer from the ductile matrix to the reinforcing inclusions is established for both creep and constant strain-rate processes. The theoretical analysis points to enhanced response with reinforcement along the axial direction with whiskers, but disc-reinforcement is far superior along the transverse direction. It is also found that the stress-strain curve of the dual-phase system can reach a saturation stress under a constant strain rate. The simple theory developed here is intended for the low volume concentration and small creep strain range, and it is demonstrated that, within this range, the theoretical predictions for the development of creep strain of a Borsic/aluminum system and for the stress-strain curves of a silicon carbide/aluminum system are in close accord with the experimental observations. Formerly Graduate Student     

Plastic relaxation of internal stresses in a dislocation microstructure

Internal stresses are present in plastically deformed metals because plastic strain gradients develop at obstacles to flow. The internal stress builds up until it causes local plastic flow. This is called plastic relaxation. Here dislocation-rich obstacles to flow in pure f.c.c. and b.c.c. metals are modelled as ellipsoidal inclusions. A method due to Eshelby is used to calculate the stress concentrations in the obstacles when the metal shears uniformly, on a single glide plane. It is found that planar obstacles which lie either close to the glide plane or roughly perpendicular to the glide direction concentrate the stress on secondary systems. It is suggested that such obstacles are reinforced and stabilised by plastic relaxation and that they are stable components of the microstructure.