Tensile Flow Stress Research Articles

Heterogeneous Deformation and Internal Stresses Developed in BCC Wires by Axisymmetric Elongation

BCC wires macroscopically deformed by axisymmetric elongation (wire drawing) develop an intense <011> fibre texture and exhibit a characteristic non-uniform deformation of the grains evident in transverse sections (grain curling or “Van Gogh sky structure”). The extraordinary grain morphology induced by the <011> fibre texture is also accompanied by a peculiar constant strain hardening rate in single-phase BCC wires (exponentially increasing in case of BCC containing composite wires) that allows to reach very high strengths. Here we present a calculation of the elastoplastic axial elongation of such an aggregate of BCC grains with the ideal <011> fibre texture, using a slip-gradient dependent large-strain crystal plasticity constitutive equation incorporated into a finite element method (FEM) code, i.e., with proper account of the influence of the evolving shape and size of individual grains and of the local grain interactions. The results reproduce well the observed macroscopic behaviour (linear flow stress-strain curve at large strains) and the peculiar mesoscopic structural changes (grain curling in transverse sections). The simulation is focused on the analysis of strain and dislocation density heterogeneities and on the building up of mesoscopic (inter- and intra-granular) internal stresses during deformation. The computed average transverse tensile stresses acting normal to the axially oriented {100} planes approximately parallel to the boundaries of the flattened grains is close to 0.3 times the tensile flow stress of the aggregate, in good agreement with previous calculations based on the Taylor-Bishop-Hill model or on elasticplastic self-consistent calculations and with available neutron diffraction measurements. Such a high level of internal tensile stresses explains the well-known tendency of high strength BCC wires to fail by longitudinal splitting.

Effect of ferrite volume fraction on work hardening behavior of high bainite dual phase (DP) steels

AISI 4340 steel was heated to 910 °C for 1 h then directly transferred to 750 °C and intercritically annealed for different times to obtain different ferrite volume fractions and then isothermally held at 350 °C for 40 min followed by air cooling to room temperature. Samples of these steels with dual phase ferrite–bainite structure were tensile tested at room temperature. The tensile flow stress data for this steel with different ferrite volume fraction was analyzed in term of Hollomon equation. It is seen that the two Hollomon equations can describe the flow behavior adequately and found that the work hardening takes place in two stages which each equation belong to the one of work hardening stages. In this study the effects of constituent volume fraction on Hollomon equation parameters (work hardening exponent and strength coefficient), onset strain of stage II work hardening, yield strength, ultimate tensile strength and ductility were investigated. Results showed that the yield strength, ultimate tensile strength and work hardening decrease linearly with increasing ferrite volume fraction whilst ductility increases. Finally, variations of these mechanical properties with differing ferrite volume fraction are used to rationalize the deformation mechanisms activated at different stages.

Superplastic Behavior of Copper-Modified 5083 Aluminum Alloy

An AA5083 aluminum alloy was modified with two different levels of Cu additions, cast by direct-chill method, and thermo-mechanically processed to sheet gauge. Copper additions reduced sheet grain size, decreased tensile flow stress and significantly increased tensile elongation under most elevated temperature test conditions. The high-Cu (0.8 wt.%) alloy had the finest grain size 5.3 μm, a peak strain-rate sensitivity of 0.6 at a strain-rate of 1 × 10−2 s−1, and tensile elongation values between 259 and 584% over the temperature range, 400-525 °C, and the strain rate range, 5 × 10−4 to 1 × 10−2 s−1, investigated. In biaxial pan forming tests, only the Cu-containing alloys successfully formed pans at the higher strain rate 10−2 s−1. The high-Cu alloy showed the least die-entry thinning. Comparison of ambient temperature mechanical properties in O-temper state showed the high-Cu alloy to have significantly higher yield strength, ultimate strength, and ductility compared to the base 5083 alloy.

Deformation induced ferrite and its influence on the elevated temperature tensile flow stress–elongation curves of plain C–Mn and Nb containing steels

The flow stress–elongation curves for a strain rate of 3 × 10−3 s−1 have been obtained for plain C–Mn and Nb containing steels over the temperature range 600–1000°C after solution treating at 1330°C and cooling at 60 K min−1 to the test temperature. The type of curve depended on whether the part of the trough at the low temperature end of the hot ductility curve was wide or narrow. Of the two phases, austenite and ferrite, ferrite independent of whether it is deformation induced or not, has been shown to have very much the better ductility. For plain C–Mn steels giving narrow trough behaviour, deformation induced ferrite (DIF) forms in equilibrium or near equilibrium amounts from the austenite, so that large amounts of DIF can form just below the Ae3. Ductility at the low temperature end of the trough is then dependent almost entirely on the amount of ferrite present. The improvement in ductility that occurs as the temperature is decreased, can therefore be related to the Ae3 temperature, because a large reduction in flow stress occurs close to the Ae3 in the curve of peak stress against temperature. This DIF is believed to form almost immediately on yielding in both steels with narrow and wide trough behaviour. However, in steels showing wide trough behaviour, although DIF forms readily at close to the Ae3, it only forms as a thin film surrounding the austenite grains. This film grows very slowly in thickness as the temperature is reduced. In this case, it is necessary for the test temperature to be below the Ar3, so there is sufficient ferrite present prior to deformation for ductility to improve and this temperature can be recognised by a discontinuity in the curve of strain to the peak stress against temperature as well as in the curve of peak stress against the temperature. It is therefore possible from analysis of the flow curves, by plotting the peak stress against temperature and the strain to the peak stress against temperature to obtain the Ae3 for narrow troughs and the Ar3 for wide troughs. In contrast, to the very low strain required to produce DIF, the strain for the onset of dynamic recrystallisation (DRX) in these coarse grained steels is in excess of 20%. The temperature at which the strain to reach the peak stress for ferrite changed to that needed for DRX could also be used to determine the temperature for the onset of DRX.

Tensile properties and microstructural aspects of 304L stainless steel weldments as a function of strain rate and temperature

This paper presents an investigation into the effects of loading rate and temperature on the tensile properties and microstructural evolution of 304L stainless steel weldments. The stress-strain behaviour during tension was determined by loading specimens in a material testing system at strain rates ranging from 10−3 to 10−1 s−1 and temperatures between −100 and 500°. Extensive quantitative microstructural examinations were performed to identify the correlation between the tensile response and the substructure of dislocations and α’ martensite. It was found that the tensile flow stress increased with increasing strain rate, but decreased with increasing temperature. For a test conducted below room temperature, a negative strain rate sensitivity was apparent at strains exceeding 0.3. Fracture feature examination revealed that an enhanced fracture resistance was evident in the base metal at low temperatures, whereas it is evident in the weld metal at high temperatures owing to their different hardening rates and microstructural states. Microstructural analysis revealed that both the dislocation density and the α’ martensite volume fraction increased with increasing strain rate, but decreased as the temperature was increased. In the range of -100-25°, both dislocations and α' martensite enhanced the strength of the tested weldment. However, between 300 and 500°, the strengthening effect was dominated only by dislocation mechanisms. For a given strain rate and temperature, a higher dislocation density existed in the weld metal, whereas a larger volume fraction of α' martensite was present in the base metal. Both increased dislocations and volume fractions of α' martensite yielded a greater work-hardening stress.

Effect of temperature and strain rate on tensile flow and work hardening behaviour of a Ti modified austenitic stainless steel

The tensile flow stress data for a 15Cr - 15Ni - 2.2Mo - Ti modified austenitic stainless steel in the temperature range 300 - 1023 K and in the strain rate range 6.3 × 10-5- 1.3 × 10-2 s-1 was analysed in terms of the Ludwigson and Voce equations. It was found that the Ludwigson equation described the flow behaviour adequately up to the test temperature of 923 K, whereas the Voce equation could be employed over the full temperature range. The peaks/ plateaus observed in the variation of these parameters as a function of temperature and strain rate in the intermediate temperature range have been identified as one of the manifestations of dynamic strain aging (DSA). Also the variation of these parameters with temperature and strain rate could clearly bring out the different domains of DSA observed in this alloy. The work hardening analysis of the flow stress data revealed that, in the DSA regime, the onset of stage III hardening is athermal.

Strengthening of Al/Ni-based composites by in situ growth of intermetallic particles

Squeeze cast Al matrix composites reinforced with continuous fibers of Inconel 601 were submitted to different annealing treatments aiming at tuning the amount of reaction at the fiber/matrix interface. The reaction develops in the form of intermetallic nodules growing onto the fibers. The tensile flow stress of the composites increases with increasing nodule volume fraction at the expense of a progressive loss of ductility. This loss of ductility is due both to the low cohesion of the oxide layer separating the matrix from the nodules and to brittle cracking at the root of attachment of the nodules onto the fibers. Damage development is evaluated from the evolution of strain hardening. The nodules grow underneath the oxide barrier layer that protects the fibers from reacting with Al during squeeze casting. Their mechanism of growth involves the partial reduction of the oxide layer by Al, followed by diffusion of Al and Ni through the Cr-rich oxide layer.

Hardness and flow strength in particulate metal matrix composites

Strain hardening and damage by particle cracking effects on the correlation between hardness and tensile/compressive flow stress have been assessed for several metal matrix composites. The Vickers hardness value (in kg mm −2) is equivalent to 0.3 times the compressive flow stress (in MPa) at an applied strain which is small (1–2%) for composites with high strength matrices or large (4–7%) for composites with low strength matrices. The strain at which the parameters correlate increases with the material's strain hardening exponent. A similar correlation is observed in tension only when damage has little effect on the strain hardening rate of the material. Damage introduced during fabrication may have a deleterious effect on the hardness/tensile flow stress correlation while the effect of damage developed during the tensile deformation is more limited. For most cases the use of hardness to predict the tensile flow stress is likely to lead to significant over-estimates.

Effects of Temperature, Strain Rate and Ferrite Grain Size on Tensile Flow Stress for Ferrite-Pearlite Steels.

Tensile tests below room temperature were conducted to investigate effects of temperature, strain rate and ferrite grain size on tensile flow stress for ferrite-pearlite (FP) steels with ferrite grain sizes between 3.6 and 46.2 μm. The temperature and strain rate sensitivity of flow stress for the FP steels is almost independent of ferrite grain size. The flow stress for the FP steels is expressed by Hall-Petch equation; σ=σ0+KD-1/2, where D refers to ferrite grain size and σ0 and κ constants. The slope κ of the equation is almost identical being independent of strain, temperature and strain rate. By summarizing the experimental results, it is possible to describe the flow stress of the FP steels by the following equation, σ=σt+182+5.8D-1/2+900ε where σt and ε mean thermal component of stress and true strain, respectively; σt is influenced by ε, temperature and strain rate.

Effect of lead content on vibration fracture behavior of Pb–Sn eutectic solder

According to resonant vibration fatigue tests, near-eutectic and Pb-rich hypoeutectic Pb–Sn specimens have higher crack-propagation resistance. The tensile flow stress of Pb–Sn solders that are near eutectic composition increases with decreasing Pb content. The solders were tested after either stabilizing at 373 K or natural aging for 20 days, which gave similar results. The naturally aged specimens show that the crack-propagation resistance increases with increasing aging time. A striated deformation was found to occur in Sn grain of the lower Pb specimen. This phenomenon is correlated with a deterioration of crack-propagation resistance.

Constitutive behavior and fracture toughness properties of the F82H ferritic/martensitic steel

A detailed investigation of the constitutive behavior of the International Energy Agency (IEA) program heat of 8 Cr unirradiated F82H ferritic–martensitic steel has been undertaken in the temperature range of 80–723 K. The overall tensile flow stress is decomposed into temperature-dependent and athermal yield stress contributions plus a mildly temperature-dependent strain-hardening component. The fitting forms are based on a phenomenological dislocation mechanics model. This formulation provides a more accurate and physically based representation of the flow stress as a function of the key variables of test temperature, strain and stain rate compared to simple power law treatments. Fracture toughness measurements from small compact tension specimens are also reported and analyzed in terms of a critical stress–critical area local fracture model.

Blade Fabrication Process for Titanium Matrix Composites

Continuous fiber reinforced titanium matrix composites (TMC) are attractive as one of the potential structural materials for aerospace applications, because of their high specific strength and stiffness. However, TMC parts are not yet put into practical use due to their limited damage tolerance and an enormous production cost resulting from process limitation requiring preliminary forming and elaborate tooling for consolidation. In order to reduce the production cost, superplastic TMC sheets (SiC/Ti-4.5Al-3V-2Mo-2Fe) were developed, and deformation properties, and cavitation behavior were investigated. The blade-shaped model was formed successfully out of the newly developed TMC sheet by means of Argon-gas-pressure forming technique. However, in order to reduce the defects that were observed in fiber/matrix interface of the deformed TMC, the tensile flow stresses in TMC sheet during deformation should be minimized. In this study a diaphragm forming method, whereby a TMC sheet is forced against the form tool surface by pressure acting on a driving sheet, was adopted to reduce the tensile stress generated in TMC sheet during superplastic forming of blade-shaped models. As a result, no defects were observed by an optical microscope in the TMC deformed by diaphragm forming method. Diffusion bonding techniques to attach the root blocks to the deformed TMC sheet and the reduction of the blade-fabrication cost are also discussed.

A correlation between tensile flow stress and Zener-Hollomon factor in TiAl alloys at high temperatures

A correlation between tensile flow stress and Zener-Hollomon factor in TiAl alloys at high temperatures

308 5083 アルミニウム合金の高温粘塑性構成式

Uniaxial tension tests were performed on fine-grain Al-Mg alloy (5083-O) sheets at various forming speeds (5.6×(10)^<-5>S^<-1> to 5.3×(10)^<-1>S^<-1>) at elevated temperatures (473 &acd; 623K). From the tests, it was found that the tensile flow stress is strongly influenced by forming speed and temperature. In order to describe such rate-and temperature-dependent stress-strain responses, a viscoplastic constitutive model is presented. In the mode, we assume that the viscoplastic strain rate consists of two components due to the grain-boundary sliding superplasticity and the ordinary viscoplasticity. The predicted stress-strain responses by this constitutive model are in good agreement with the corresponding experimental results.

Ti基複合材料ブレードの開発

The high specific strength and stiffness of titanium alloy matrix composites (TMCs) with continuous fiber reinforcement are attractive for aerospace structural applications. However, the enormous production cost of TMCs is a serious impediment to their practical applications. One promising approach to reduce the production cost is the application of a superplastic forming technique to TMC parts manufacturing. A series of superplastic-formable TMC sheets, SiC/Ti-4.5Al-3V-2Mo-2Fe (SCS-6/SP-700) composites, were developed, and both their superplastic deformation and the defects generated during this deformation were investigated. The diaphragm-forming method (DFM) was adopted of a superplastic forming technique to reduce the tensile flow stress generated in the TMC sheet during deformation, and using this technique blade-shaped models were successfully fabricated without any observable defects in the fiber/matrix interface. In this study, TMC blades for an aerospace engine have been developed using DFM, and their burst strength was evaluated by a spin test. TMC sheets with 39-ply SCS-6 were formed by DFM and isothermal forging. Two SP-700 root blocks were attached to the deformed TMC by means of vacuum hot pressing. This near-net-shaped composite was machined to the final configuration. While no defects were observed by optical microscopy in the TMC blades, several un-bonded areas were found in the diffusion-bonded interfaces. The configuration of these interfaces was complex, and the plastic deformation of the matrices did not confer sufficient contact between the mating surfaces due to one-directional loading of the pressing. As the result of the spin test, the TMC blades burst at a tip speed of 782 m/s, which was 11% lower than the expected speed based on the material data. The break originated in an un-bonded area.

Strength differential effect in four commercial steels

The difference between compressive and tensile flow stress of a material at a given strain termed as strength differential (S-D) effect, has been evaluated in case of four commercial steels via a series of heat treated conditions. The results have unequivocally established that the magnitude of S-D was maximum in the as quenched condition and tempering of the quenched structure led to a decrease in S-D. Spheroidised and/or annealed structures exhibited the lowest value of S-D. A linear relationship of S-D value with hardness and mean stress for each case has been established. Attempts have been made to explain the observed S-D effect in terms of models based on atomic mechanism and of continuum mechanics.

On the origin of the tensile flow stress in the stainless steel AISI 316L at 300 K: back stress and effective stress

The tensile behaviour of a polycrystal austenitic stainless steel at 0.2 T m is discussed in terms of back and effective stresses with the help of qualitative and quantitative TEM observations. Particular attention is given to the transition between stages I and II which occurs at a plastic strain equal to 1.5%. The effective stress evolution can be interpreted as a competition process between the increase of mobile dislocation density and dislocation interactions and an annihilation process. The main purpose of this work is to provide a basis for separating the two different contributions of the back stress, namely the intragranular back stress X intra arising from the heterogeneous dislocation distribution inside the grains and the intergranular back stress component X inter resulting from plastic strain incompatibilities between grains. Moreover, it is shown that the latter contribution is dominant at small strains (stage I), whereas the former one is more important subsequently (stages II and III), when cross-slip and multiple slip occur.

Texture and large–strain deformation microstructure

Large–strain plastic deformation at low homologous temperature implies, among other things, severe work hardening, strong crystallographic texturing, microstructural refining, and some degree of macroscopic redundant strain. In most cases, the development of texture does not seem to particularly increase grain interactions above their initial level which is at the origin of the Hall–Petch effect. Continued strain then leads asymptotically towards an absolute maximum of the tensile flow stress below G /50, where G represents the elastic shear modulus. However, it is well known that some simple deformation textures promote an extraordinary enhancement of the plastic grain interactions that need to be accommodated by monotonically increasing mesoscopic (grain–size range) strain gradients. Such behaviour is accompanied by a concomitant high work–hardening rate and by a remarkable extension of the strengthening limit. The [110] body–centred–cubic or [0001] hexagonal close–packed wire drawing textures constitute the paradigmatic case, for which the flow stress limit reaches up to G /20. A quantitative explanation of the phenomenon is given here with the help of a geometrical model of microstructural development.

Cavity Damage Accumulation in Alumina Doped with Zirconia or Magnesia

For an initial grain size of 1.0 μm, the accumulation of damage volume in a ZrO 2 -dispersed alumina is shown to proceed more slowly than that in a MgO-doped alumina under a given loading condition, irrespective of higher tensile flow stress in the former than in the latter. The slower damage accumulation in the ZrO 2 -dispersed alumina is caused from the slower formation and growth of cavities larger than the initial grain size. Such slower cavitation is also shown to delay the onset of microcracking. The delayed microcracking leads to higher tensile ductility in the ZrO 2 -doped material than in the MgO-doped one.

On the nucleation and growth of voids at high strain-rates

The nucleation and growth of voids at high strain-rate is studied in copper as a model face centered cubic (fcc) material using large scale molecular dynamics (MD) methods. After a brief introduction to dynamic fracture, results are presented for the homogeneous nucleation of voids in single crystal copper and the heterogeneous nucleation in nanoscale polycrystalline copper. The simulations suggest void growth occurs through anisotropic dislocation nucleation and emission in agreement with experiment and the observed anisotropy of the tensile flow stress in fcc crystals. A phenomenological model for the transition from intergranular to transgranular fracture at high strain-rate is presented.