Lower Yield Point Research Articles

On the yield point of floating-zone silicon single crystals

Abstract In initially dislocation-free silicon single crystals deformed in compression (single slip) at low strain rates, the lower yield stress τ1y exhibits a three-stage temperature dependence with a plateau (1170K ≲ T ≲ 1320 K at [ydot]≅ 2 × 10−5 s−1) between the low- and high-temperature regimes, where τ1y decreases with increasing T. Pre-strained silicon crystals were deformed in the temperature range of dislocation velocity measurements (820 K ≲ T ≲ 1070 K). With the assumption that pre-straining, which minimizes yield-point phenomena, ensures dislocation structures (i.e. internal stresses) that are at worst only weakly dependent on the deformation conditions, the activation Gibbs free energies derived from activation volumes measured at the lower yield point are found to be in very good agreement with activation energies for dislocation velocity at the same stresses.

Mechanical properties of GaAs crystals

Mechanical properties of GaAs crystals grown by the liquid encapsulated Czochralski technique and the boat technique are investigated by means of compression tests. Stressstrain characteristics of a GaAs crystal in the temperature range 400°–500°C are very similar to those of a Si crystal in the temperature range 800°–900°C. This seems to reflect the fact that the dislocation mobility in a GaAs crystal in the former temperature range is comparable to that in a Si crystal in the latter temperature range. Dislocations in GaAs crystals are found to be easily immobilized at an intermediate temperature due to gettering of impurities and/or impurity-point defect complexes. In comparison to a Si crystal, the surface of a GaAs crystal seems to involve irregularities that act easily as effective generation centers for dislocations. Thus the magnitude of the yield stress of an aged GaAs crystal is controlled by the surface condition and is not influenced by the density of dislocations involved in the crystal. The socalled steady state of deformation is realized in a GaAs crystal in the deformation stage after the lower yield point as in Si and Ge crystals. Dislocation distributions in a deformed GaAs crystal observed by transmission electron microscopy is very similar to those in deformed Si and Ge crystals.

Elastic mimicry of elasto-plastic responses

Abstract A range of successively more elaborate elastic models is developed, with responses that in many ways mimic those of plastic specimens under load. The bilinear stiffness of a simple one degree-of-freedom elastic prop, which experiences a symmetric point of bifurcation, is first used to model the fundamental elasto-plastic response: the introduction of an imperfection corresponds to the Ramberg-Osgood approximation, rounding off the bilinearity. Upper and lower yield points are reproduced by a model termed the elastic hook, in which an elastic spring of the first model is itself replaced by an elastic prop with a bilinear stiffness. Finally, the normality relation of incremental plasticity theory is reproduced by two props at right-angles: responses are also traced for two hooking models in this configuration, for which no real comparison in plasticity theory seems to exist at present.

金属焼結体の高速圧縮変形挙動

A dynamic compression test was carried out on sintered Cu and Fe compacts to clarify their deformation behaviour using a drop-hammer testing machine. The results obtained were as follows:1) At the high strain rate of about 3×102/sec, the sintered Fe compacts showed sharp pseudo-yield points, but pre-strained specimens did not show such pseudo-yield behaviour.2) For the first impact of Cu compacts, the dynamic load increased gradually with increasing time, but in the subsequent dynamic tests, the load increased abruptly and then became constant.3) The dynamically-deformed sintered Fe showed upper and lower yield points. On the contrary, the specimens statically deformed showed only single yield point.

Finite amplitude plastic shock wave treated with summed infinitesimal amplitude elastic-plastic waves through dislocation dynamics

In the high strain rate region of a finite amplitude plastic shock wave constitutive equations need to be strongly history dependent and thus are difficult to use in the description of plastic deformation because the deformation is dominated by a dislocation dynamics which is far removed from quasi-equilibrium conditions. The Johnston-Cilman (1969) theory of the upper and lower yield point is the prototype of an analysis of a type of plastic flow that is more meaningfully described through dislocation dynamics than by setting up some sort of constitutive eqution which does not fully incorporate internal variables. In this paper it is shown that a finite amplitude elastic-plastic wave can be treated as a sum of infinitesimal amplitude elastic-plastic waves in which the plastic deformation rate is effectively linearized through a varying parameter η which is a measure of the relative strengths of the elastic and plastic strain rates. The waves treated are planar and the sum of their transverse elastic and plastic strains is always null. Dislocation dynamics determines the value of the η parameter. The plastic waves treated are of moderate amplitude (stress/bulk modulus small compared to 1).

Studies of epoxy resin systems: Part C: Effect of sub‐Tg aging on the physical properties of a fully cured epoxy resin

AbstractThe effect of sub‐Tg aging on the properties of an epoxy resin system, diglycidyl ether of butanediol, DGEB, cured with 4‐4′ diaminodiphenyl sulfone, DDS, has been studied. Aging was found to increase the DSC (differential scanning calorimetric) endothermic peak, the density, and the upper yield point. In contrast, the lower yield point was relatively unchanged. This result, together with the observation of the elimination of the DSC endothermic peak by deformation and the absence of a yield point after deformation, suggested that the aging effect was eliminated by deformation. The thrermally stimulated depolarization (TSD) α‐peak was found to decrease in strength with aging time. All of the observations were best rationalized on the basis of the free‐volume concept.

Studies of epoxy resin systems: Part B: Effect of crosslinking on the physical properties of an epoxy resin

AbstractAn epoxy system consisting of diglycidyl ether of butanediol, DGEB, cured with 4‐4′ diaminodiphenyl sulfone, DDS, has been used for a study of the effect of crosslinking density on the properties of the epoxy resin. Because of the low curing rate at room temperature and the low glass‐transition temperature, this system was amenable to a wide range of controlled cross‐linking density. The crosslinking density was monitored by FTIR (Fourier transform infrared spectroscopy), which followed the change in concentration of the epoxy groups during the curing reaction. The bulk density was found to increase linearly with the crosslinking density. The modulus, the upper yield point, the lower yield point, and the degree of retraction of a deformed sample all increased with the degree of crosslinking. The thermally stimulated depolarization (TSD) β‐peak was found to vary with crosslinking density, but the γ‐peak was not changed. The TSD a peak was found to decrease in strength, but increased in temperature as the crosslinking density increased. This observation suggests that TSD measurements arc a good monitor of crosslinking density of epoxy resins, particularly near the final stage of the crosslinking reaction.

Strength of the Surface Layer of Mild Steel

The load-strain curves of thin-walled hollow cylinders of mild steel under compression, bending or torsion and rectangular cross-sectional beams with small height under bending deviate from the elastic line before reaching the lower yield point. In this paper these experimental results are attributed to yielding of the surface layer of the material. It is concluded that the surface yeild stress is 3/4 of the inherent yield stress of bulk material under uniform stress such as simple tension or compression.

Properties of high-strength weldable steel 03G4AF

1. Steel 03G4AF after quenching and high tempering exhibits high strength and ductility. With increasing sheet thickness the strength properties of this steel decrease. However, a low-temperature temper may increase the yield point of sheet 10 and 20 mm thick to 650–700 MPa without reducing impact strength. Steel 03G4AF exhibits high impact strength down to −40°C (specimens with a sharp notch). 2. The wear resistance of steel 03G4AF is greater than that for steel 14Kh2GM with the same ultimate strength and lower yield point. 3. The fatigue strength of steel 03G4AF is somewhat greater than that for steel 14Kh2GM and it is 1.5 times greater than that for steels of the 09G2S type. 4. Steel 03G4AF may be recommended for making bodies of large-capacity dumper trucks (for welding conditions and choice of welding materials for this steel see article by E. D. Raimond et al. in this issue).

Study of fresh concrete flow curves

Two constants — plastic viscosity and upper yield point obtained by extrapolation from measurements at high speeds of shear in rotation viscometer — are often considered as sufficient to describe fresh concrete rheological behaviour. In the present work the investigation has been expanded to include tests at low shear velocities and at lower yield point because of a practical significance in concrete technology. Tests have shown that three shapes of fresh concrete flow curves appear, which display characteristic shear thinning along the transition from the area of low shear velocities to the area of high shear velocities. Shear thinning or thickening in the region of higher rotation speeds are characteristic for some mixes. The phenomena of shear thickening and thinning can partly be explained as being due to dilatancy and to the related changes in the fluid phase to pore air ratio in fresh concrete. Simple shear static tests have shown that fresh concrete dilatancy is proportional to the square of shear stress.

Vibration damping steel material and process for producing the same

A vibration damping steel containing C ≤ 0.10% and Mn ≤ 0.40% as the essential constituents and having a lower yield point or 0.2% proof stress of 7-28kg/mm2 with the degree of refinement of the steel being not less than 0.18 while still maintaining the specific gravity at 7.859g/cm3 or less, and a process for producing the same. This steel material is particularly suited for use in items which to produce and transmit vibration and noise.

Mechanism of deformation of low-alloy steels under dynamic loading

1. Within the investigated interval of plastic strain rates ɛpl = 10−4-3 · 103 sec−1 there is a change in the mechanism of plastic strain for normalized steel 16G2AF and quenched-and-tempered steels 10 KhSND and 10KhN1M. At ɛpl≥ 102 sec−1, the thermally activated mechanism of plastic strain is replaced by the ductile braking of dislocations (viscous drag). 2. The greater sensitivity of the upper yield point σyu to strain rate relative to the lower yield point σyl or tensile strength σu indicates that at the beginning of yielding (low density of mobile dislocationspm) ductile braking of dislocations plays a more important role in the strain process than it does at later stages of tension, where thermally activated dislocation slip is the dominant mechanism (larger value ofPm). 3. Investigated medium- and high-strength steels 16G2AF, 10KhSND, 10KhNlM, and 12KhGN2MFBAYu have a greater tendency than low-carbon steel St.3 toward substitution of the thermally activated mechanism of slip for the mechanism of ductile dislocation braking. 4. Dynamic tension of steels 10KhSND, 10KhN1M, and 16G2AF up to σpl = 3 · 103 sec−1 does not lead to twinning; plastic deformation occurs exclusively by dislocation movement. In the range σpl = 10−4-3 · 103 sec−1, the above steels fracture by the mechanism of void initiation, growth, and coalescence (tough cup fracture), with there being no signs of brittle fracture.

Micro behavior at the notch tip during load increasing in brittle fracture beyond general yield

The micro behavior near the notch tip during load increasing was studied by using both plastic replication and optical microscope on mild steel specimen until the final stage of general yielding fracture at low temperature. Results show that a microcrack has already initiated at lower yield point, and the overall path of crack propagation appears to smear out such microcracks by the main crack starting from the notch root. Further, the ferrite grain size dependence of the brittle fracture stress and the temperature characteristics of the number of grains containing microcracks initiated prior to fracture are similar to that in unnotched (uncracked) ones established in the literature. Further, the effects of ferrite grain size and temperature on the crack tip opening displacement (CTOD) have been studied experimentally. The usefulness of the comparative study on cracked and uncracked specimens is discussed.

A probabilistic approach to polycrystalline plasticity part II: applications

Using our constitutive theory for polycrystalline plasticity, we have calculated characteristic yield conditions for several sample materials in which the dependence of the dislocation velocity on stress is given by an empirical power function. The shape of the yield surfaces for these materials varies resembling that of von Mises when the stress exponent is small and that of Tresca when the exponent is large. Additional examples illustrate the ability of the proposed theory to model such phenomena as the development of anisotropy during plastic deformation, material hardening and softening, the occurrence of upper and lower yield points, and a Bauschinger effect.

Static strain-aging in commercial purity alpha titanium

Static strain-aging was investigated in commercial purity α-Ti, containing 0.41 at. pct of oxygen as the principal interstitial impurity. 17 μM grain size specimens, prestrained to 0.02 strain at a nominal strain-rate of 3.3×10−4S−1, were agedin situ between 555 and 630 K for lengths of time between 150 and 2.55×105 seconds. Both the upper and lower yield point increments were employed as measures of the aging progress. Under the stated conditions, the static strain-aging response of the titanium appeared to consist of four stages, of which only Stages 1 and 2 were considered in this work. Stage 1 corresponded to a Haasen and Kelly type of yield point, while Stage 2, after correcting for the time-independent yield point increment of Stage 1, conformed to Cotrell aging,i.e., the increase in flow stress after aging followed at2/3 behavior. The activation energy deduced for the process is in good agreement with that for the diffusion of oxygen in titanium.

Yield Point Standardization

Abstract The yield point, that is, the stress at which a steel starts to suffer a pronounced permanent set, is a very important property. There is in international standardization a dilemma about whether to use upper yield point (ReH) or lower yield point (ReL) as the characterizing yield point value in steel standards and in practical material testing. This dilemma may to a great extent be due to the people involved in standardization themselves exaggerating the difference between ReH and ReL. Both yield point values are dependent on the strain rate, which again may be greatly influenced by the compliance of the testing system. Some confusion may exist regarding the term “upper yield point” as compared with the term “yield point.”

Composition and mechanical properties of gutta-percha endodontic points.

Gutta-percha endodontic filling points were found to contain approximately 20% gutta-percha (matrix), 66% zinc oxide (filler), 11% heavy metal sulfates (radiopacifier), and 3% waxes and/or resins (plasticizer). The mechanical properties were indicative of a partially crystalline viscoelastic polymeric material. They were found to obey Hooke's law and displayed a prominent upper and lower yield point when stressed beyond the proportional limit. The essential differences in mechanical properties of individual brands were found to be a function of the gutta-percha and zinc oxide concentration.

等しい強さの不完全時効状態と過時効状態の延性の比較

In order to determine the optimum aging temperature to give superior toughness to an age-hardening alloy, a comparison of the experimental values of ductility in the under- and over-aged states having similar strength was made using various kinds of iron and aluminum alloys, for example, Fe-Cu, Fe-Cr, Fe-Ni-Cu, Fe-Ni-Mo-C, Fe-Co-Cr-W, Al-Si and Al-Ag alloys. The following conclusions have been drawn from the data by the authors and other investigators: (1) In general, the under-aged alloy has a higher ductility, a lower yield point and a larger strain hardening exponent than those in the over-aged alloy having similar tensile strength. (2) In the alloys strengthened by precipitation of G.P. zone or by decomposition into two phases, in other words, having a coherent second phase, premature fracture often takes place in the under-aged state. (3) In the heavily cold worked alloys and secondary-hardened high alloy steels, the superior toughness may be obtained after slight over-aging.

Deformation of annealed low carbon steel at high strain-rates

The strain-time history of annealed low carbon steel is measured under constant stress loading conditions as a function of grain size, duration of loading, and position along a cylindrical specimen. The transition from elastic to plastic deformation is examined in terms of the elastic wave front attenuation, the delayed yielding time, and the macroscopic plastic deformation of the specimen. The experimental results are then compared with theoretical predictions. The theoretical model assumes that the deformation process can be separated into pre-yield and post-yield regimes separated by the advent of the delayed yielding. The agreement between the experimental results and theoretical predictions appears to be quite good. The results show that the effects of grain size cannot be neglected in certain loading regimes, that the upper and lower yield points can exist even under constant stress loading, and that it is unrealistic to treat the pre-yield and post-yield phenomena as being identical processes for metals which exhibit the yield-point phenomenon.

A note on yield point phenomenon in wave propagation

The propagation of stress pulses in a plastic material which exhibits delayed yielding and upper and lower yield points is considered by the method of expansion behind the wave front. The material model includes an evolutionary equation the presence of which is responsible for the yield phenomena and it is shown that it also leads to a very pronounced negative stress gradient behind the wave front.