* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 3.6 Yield Phenomena 3.6.1 Introduction
Survey
Document related concepts
Colloidal crystal wikipedia , lookup
Bose–Einstein condensate wikipedia , lookup
Cauchy stress tensor wikipedia , lookup
Creep (deformation) wikipedia , lookup
Radiation damage wikipedia , lookup
Fracture mechanics wikipedia , lookup
Stress (mechanics) wikipedia , lookup
Hooke's law wikipedia , lookup
Shape-memory alloy wikipedia , lookup
Fatigue (material) wikipedia , lookup
Viscoplasticity wikipedia , lookup
Paleostress inversion wikipedia , lookup
Deformation (mechanics) wikipedia , lookup
Viscoelasticity wikipedia , lookup
Dislocation wikipedia , lookup
Transcript
3.6 Yield Phenomena 163 in accordance with theoretical models. They explained their observations as being a consequence of the very low stacking-fault energy, because the annihilation of dislocations is hindered by their high degree of dissociation into partials. HCP and BCC metals are prone to show serrations during low-temperature deformation. Thus, the enhanced ductility of zirconium at 4.2 may be attributed to the ability of this metal to twin readily at low temperatures (Briottet et al.). All stress/strain curves for the 4.2 tests exhibited sudden, characteristic drops in the load. Transverse specimens showed a much higher incidence of twinning, greater strain hardening, more plastic deformation between serrations and fewer serrations than longitudinal specimens. However, these researchers concluded that twinning per se is probably not responsible for the discontinuous yielding. In BCC, serrations in the stress/strain curves occur at high strain rates, such as are obtained by impact and/or low temperatures. Twin bands obtained in BCC iron by high strain rates, such as impact, are known as ‘Neumann bands’. The morphological change of solids has been largely developed in the last years. The localization of plastic deformation in homogeneous materials may be associated with instabilities of stress/strain curves. This phenomenon can have very different aspects: the Portevin-Le Chatelier effect, Lüders bands, twinning, thermomechanical effects and avalanches of dislocations. During the past years, more and more researchers have doubted the ideas that twinning is the main contributor to the instability of the stress-strain curve at low temperatures and the contribution of dislocation is emphasized. The cooperative contribution of the various causes of instability must be appreciated. Nevertheless, this section focuses on twinning. Twinning is associated with the coordinated deformation of a large number of atoms, possibly leading to serrations in the deformation curves (giving a jagged appearance). Loud clicks are heard during the formation of twins, commonly known as ‘tin cry’. This occurs because twin formation can be extremely rapid. The serration of the stress-strain curve is a sign of twin formation. Many investigators reported twin formation and serrated stress–strain curves associated with twinning. For further details on twinning, see the literature on the crystallography of deformation. 3.6 Yield Phenomena 3.6.1 Introduction In Sect. 1.2.2, the elastic and proportional limits were discussed in regard to the transition from the elastic to the plastic deformation regions. In Fig. 1.7, these transition points were indicated together with a 0.2% offset yield point. In Fig. 1.4, the stress/strain relation under tension was shown by means of tests done to 1020 (low-carbon) steel, 1070 steel and a polymer (polyethylene), characterizing sharp yield points and otherwise ductile materials. Most structures are designed to act in 164 3 Plastic Deformation brittle B B ductile D C σ sharp yield drop-LiF BCC iron C A A ε Fig. 3.15 Yielding in ductile materials, brittle materials, BCC iron and LiF. The C-D zone is the “yield elongation” region the elastic region, since permanent change in a structural material must be avoided. Nonetheless, the plastic region is of great importance for the fabrication and shaping of structural materials requiring high ductility. Thus, the transition from the elastic to the plastic regions is of great importance. Consequently, extensive research was carried out and is available in the literature. A number of interesting phenomena were observed while characterizing yield and information was also provided on the behavior of materials during their transition into the plastic range. Some of the data on yield are considered below. 3.6.2 Sharp Yield In metals, where the elastic–plastic transition is gradual, for practical purposes, the deviation from linearity may be taken to be the yield point (the 0.002 offset point). The most commonly known sharp yield was first observed in low carbon content BCC iron, also known commercially as ‘mild steel’. In this case, sharp yield is followed by a sudden drop to a lower value, before further deformation takes place. In Fig. 3.15 such a yield drop in low-carbon steel can be seen. Deformation in the C-D region occurs without an increase in the stress level beyond a specific value, known as the ‘lower yield point’. The highest stress in the elastic region is known as the ‘upper yield point’. The C-D region is not smooth, but jagged. This kind of yield-point drop can be detected in what is known as a ‘hard tensile machine’, which is characterized by very small elastic distortion. Note that N can also produce a sharp yield point followed by a sudden drop. In the theory put forth by Cottrell and Bilby, the yield in BCC iron was explained by the involvement of interstitial solutes, such as C or N, in the sharp yield. The nonhomogeneous deformation in the ‘yield-elongation’ region (the C-D zone) begins at a point of stress concentration, often at the grips, and propagates through the specimen as bands. The grips used for holding the specimens during tensile stress are sites of stress concentration. Beyond point D, deformation proceeds as 3.6 Yield Phenomena 165 stress increases with further straining, as shown in Fig. 3.15. The sharp-yield drop occurs not only in low C (or N) ’Fe single crystals, but also in polycrystalline iron, where the yield-elongation region is well developed. Cottrell has indicated that interstitial solid solutions, such as Cd, etc., may show similar yield-point drops, as seen in ’Fe, but less pronounced. Wain and Cottrell observed sharp yield points also in crystals of zinc containing N. Their experiments showed not only that yield points could be produced in zinc crystals, but also that this effect is associated with impurities in the metal, as in the case of yield in ’Fe. Johnson and Gilman, who studied LiF, revealed that sharp yield points also occur in this crystal. They reported that, in order to obtain a sharp yield drop, the necessary criteria are: (a) an increase in the number of moving dislocations and (b) a direct relation between the stress and the velocity of the dislocations. By knowing the strain rate, given as: "P D nvb (3.5) and the velocity of dislocation motion: v D k£m (3.6) they were able to calculate stress-elongation curves for LiF showing sharp yield drops. By varying the exponent, m, in Eq. 3.6 and the density of the mobile dislocation ¡ of Eq. 3.7, the magnitude of the yield drop could be changed. In the early stages of deformation, the density of mobile dislocations is given as: ¡ D ¡0 C C©’ (3.7) The exponent, m, is in the range 1–100. For a certain value of ¡, increasing m decreases the yield drop. The value of m for LiF is 16.5 and for ’Fe, 35. Equation 3.6 is an empirical relation with k being a constant. In Eq. 3.5, n is the number of moving dislocations/cm2 . Calculations were performed for © < 0:1, namely in the early stages of the deformation. A dislocation-density evaluation is done either using the etch pits technique or by electron microscopy in the range of © < 0:1. Equation 3.7 gives ¡0 as the initial dislocation density, the constant C D 108 /cm2 and the constant ’ is 1 ˙ 0.5. 3.6.3 Lüders Bands When a yield drop is observed in mild steel, surface marks usually develop at the point of stress concentration. These band-like markings are called ‘Lüders bands’. Deformation in this range is non-uniform. Grips in the vicinity of specimen fillets are considered be locations of stress concentration. To best see these bands, the specimens should be reasonably well polished. Schematic Fig. 3.16 shows a specimen in which such bands may develop. Note that these bands should not be 166 3 Plastic Deformation Fig. 3.16 Lüders bands at 45ı from the tensile axis considered as slip lines or slip bands. The propagation of the Lüders bands continues while the deformation is going on, until the entire specimen is covered by such bands. In industry, especially in the automobile industry, these bands are liable to appear, particularly on fenders, as veins called ‘stretcher strains’, that ruin the surface finish. The appearance of Lüders bands happens when the sharp yield drop occurs, meaning that the propagation of such bands occurs without the further need of stress; as long as the yield-point elongation continues, these bands will spread. Only after the yield-point elongation stops will the stress rise again. The appearance of Lüders bands is a result of dislocations having been pinned by C (or N), and the higher stress is required to free pinned dislocations that have been anchored by interstitial atoms. As will be detailed below, the avoidance of the formation of stretcher strains can be achieved by applying a small prestrain shortly before the fabrication, but somewhat beyond the lower yield point (e.g., by skin rolling) and only then starting the actual fabrication of a mild steel part (e.g., to be used in the automobile industry). After reloading, no Lüders bands appear, since the sharpyield drop and the low yield-point elongation have been destroyed by the prestrain (or prefabrication straining). Adding Ti or similar elements, which react with either C or N or both, is another method for avoiding the appearance of stretcher strain marks. 3.6.4 Stain Aging Schematic Fig. 3.17 illustrates strain aging in mild steel. The yield phenomenon indicated by a sharp yield-point drop is shown in region I. Following inhomogeneous Tensile stress 3.6 Yield Phenomena 167 I II III Tensile strain Fig. 3.17 Strain aging. In region I, a sharp yield drop is seen with Lüders bands formation. In region II, no yield drop is seen. The reappearance of a sharp yield drop in region III is also shown deformation (represented by lower yield-point elongation) and after Lüders bands have formed and propagated, and passing it by some small deformation, if one interrupts the tensile test by unloading the specimen, one can observe an interesting behavior having practical applications in the automotive industry. If this specimen is reloaded immediately – or after the elapse of a short time – following unloading, the yield-point drop does not reappear and the Lüders bands do not form. A smooth transition from the elastic to the plastic regions is the result of the reloading, as shown in region II of Fig. 3.17. However, if a specimen has been unloaded and is left for a few days in the unloaded state, then the yield-point phenomenon reappears. This time, the upper yield point is higher than the one initially observed in that specimen, as shown in region III of Fig. 3.17. This is explained by the fact that the interstitial atoms C or N return to the dislocations and form what is called an ‘atmosphere’ around the dislocations re-pinning them. This re-pinning requires the time-dependent diffusion of C or N to the dislocations. This may take several days at room temperature, but, at higher temperatures, the increased diffusion rates of the interstitial C atoms shorten considerably the time for the yield point return. The involvement of the element of time in yield-point return also clarifies the use of the term ‘aging’ (strain aging), which is appropriate, since the process of straining also involves a temperature factor. That the new yield point is higher than the one initially observed is associated with the fact that some work hardening occurred in region I before unloading the specimen. The C or N atoms occupy the octahedral interstitial, distorting the unit cell tetragonally (i.e., into a body-centered tetragonal structure) and a large volume expansion occurs. 168 3 Plastic Deformation Fig. 3.18 The Portevin Le Chatelier effect. The influence of temperature on the appearance of a stress–strain curve under tension 273 K ~273 – 373 ~ 473 K σ ~ >600K ε 3.6.4.1 The Portevin Le Chatelier Effect (PLE) Another observed phenomenon, closely related to the yield-point phenomena associated with interstitial atoms, is that of temperature-dependent serrated curves. Serrated stress/strain curves are similar to those observed in twinned specimens, but their origin is different, as mentioned. In Fig. 3.18, a set of curves is shown along with the effect of temperature on their appearance. Such behavior, although observed initially in ’ Fe, is exhibited by several materials as they undergo plastic deformation, e.g., Al-Cu alloys (see, for example, Liang et al.), substitutional Al-2.5% Mg alloy (P. Barat et al.), etc. For the Portevin Le Chatelier effect [henceforth: PLE] to occur, solute atoms must segregate at the dislocation core. This requires sufficient mobility by diffusion of the segregated atoms. The local site of the dislocation core is energetically favorable, since it has space available to accommodate the solute atom which locks the dislocation, hindering its motion. A larger force (stress) is necessary to move the dislocation, as the cloud of solute atoms is dragged with it. At some stage, the dislocation eventually breaks away from the atmosphere of solute atoms, resulting in reduced drag stress for dislocation movement. Note that this process results in the formation of stretcher strains, mentioned above, which make the surface rough, prohibiting the use of that material in the automotive industry, unless remedied. Many interstitial and substitutional alloys exhibit repeated yield-stress drops under tension, as influenced by strain rate and temperature. At sufficiently high temperatures and at a specific strain rate, these serrations gradually disappear, due to the relatively higher diffusion of the solute atoms, preventing the recapture of their atmosphere. The effect of temperature is also shown in Fig. 3.18. Not only mild steels used in the automotive industry show Lüders bands as surface markings (see Fig. 3.19) or serrations resulting from the PLE effect, but other materials do as well. Al-Mg alloy sheets, potentially useful for automotive 3.6 Yield Phenomena 169 Fig. 3.19 Lüders markings on soft steel: (a) a tensile specimen; (b) a stamped sheet part (From Chadwick and Hooper 1953; B. B. Hundy 1953) applications, may also show yield-point related phenomena, as seen in Fig. 3.20. In (a) the surface markings are illustrated and in (b) serrated curves are illustrated. 3.6.5 The Cottrell-Bilby Theory Cottrell and Bilby did a theoretical study on yield-point phenomena (discussed in Sects. 3.6.2, 3.6.3, and 3.6.4). Their original concepts, regarding the dependence of the yield drop on impurities, discontinuous yielding and the strain aging associated with BCC iron, are based on dislocation locking by interstitial solutes (impurities). Various BCC metals and other structures may also show similar occurrences, but the first and most obvious encounter with yield phenomena occurred in ’ Fe. Cottrell and Bilby invented the concept of ‘atmosphere’, known ever since as ‘Cottrell atmosphere’, in order to explain how dislocations are anchored by interstitials, specifically C and N. These interstitial atoms settle down under the dislocation line to form an atmosphere. These atoms somewhat distort the lattice by forming a stress field around themselves and their own vicinity. This distortion may be reduced or relaxed once they settle down beneath the dislocation line. The preferential location of the C (N) atom below the dislocation is controlled by diffusion, which are timeand/or temperature dependent. Usually, after fabricating an iron billet (or some other shape), time goes by before it is used or tested. This elapsed time is sufficient for the C to diffuse into a dislocation and become mutually anchored there. Once an atom or atoms have diffused into a dislocation core, they will stay there. The dislocation has become pinned down and now, in order to tear such a dislocation away from its atmosphere, a somewhat higher force is required. This extra force is responsible for the upper yield point. After unpinning a dislocation, it is free to move at a lower 170 3 Plastic Deformation a x15 x7 b a)r=5-20% 1 b)r=30-70% a)r=5-10% 2 b)r=15-70% F a)r=5-20% 3 b)r=30-70% -3 -1 2 ε2=6.7-10 s -2 -1 3 ε3=6.7-10 s 1KN 1 ε1=6.7-10-4s-1 1mm Δl Fig. 3.20 Al-Mg alloy: (a) the surface appearance of a fender made of Al-Mg sheets; (b) load extension curves of AlMg6.5Mn sheets at different strain rates (Romahanji et al. 2004. Courtesy of Dr. Marija Korać, Technical Editor, metalurgija.Org., rs) stress, producing the lower yield point. Once a dislocation is free to move, the material can continue to deform plastically in the usual way, i.e., the stress increase will produce some strain in accordance with the work-hardening concept. Leaving a sample to age at room temperature for a few hours enables the carbon atoms to re-diffuse into the dislocation cores, resulting in the return of the upper yield point, as strain aging (region III in Fig. 3.17). Contrary to this, if a test specimen is pulled by tension immediately following unloading or within a short time afterwards, the yield point does not reoccur (region II, Fig. 3.17). The automotive industry is aware of this phenomenon and construction parts are shaped shortly after some prestrain is applied. Furthermore, as mentioned earlier, elements such as Ti, may be added to react with the interstitial atoms, such as N, in order to prevent the formation of Lüders bands. Cottrell atmospheres lead to the formation of Lüders bands, where the serration is believed to be the result of repeated yielding. Dislocations are repeatedly released from and recaptured by anchoring interstitial atoms.