Intermediate Strain Amplitudes Research Articles

On the determination of a set of material constants for a high‐cycle accumulation model for non‐cohesive soils

AbstractThe paper discusses the determination of a set of constants for the high‐cycle accumulation model (HCA) proposed by the authors. The HCA model predicts permanent strains or excess pore water pressures in non‐cohesive soils due to a cyclic loading with a large number of cycles and with small to intermediate strain amplitudes. The laboratory tests necessary for the determination of the material constants and their analysis are explained in detail in this paper. Copyright © 2009 John Wiley & Sons, Ltd.

Rheological Properties of Physical Gel Formed by Triblock Polyampholyte in Salt-Free Aqueous Solutions

Linear and nonlinear viscoelastic properties of an asymmetric triblock copolymer poly(acrylic acid)−poly(2-vinylpyridine)−poly(acrylic acid) (PAA−P2VP−PAA) in salt-free aqueous solutions have been investigated. At pH 3.4, long-range electrostatic interactions prevail, due to protonated P2VP units and negative PAA end groups. Above a critical Cg = 2.5% w/w, a transient network is formed through intermolecular electrostatic interactions between negatively charged groups located at the end PAA blocks and positively charged protonated pyridine groups located at the middle long P2VP block. The so-formed network exhibits some atypical rheological behavior characterized by a strain hardening of storage modulus in intermediate strain amplitudes and a pronounced shear thickening in moderated shear stresses. The shear-induced changes in the structure of the network have been attributed to enhancement of the number of elastically active bridges through association of free dangling ends and a transition from intra- t...

Fourier-transform rheology experiments and finite-element simulations on linear polystyrene solutions

Large amplitude oscillatory shear strain was applied to anionically synthesized linear polystyrene solutions in dioctylphthalate. The resulting torque was analyzed in Fourier space with respect to frequency, magnitude, and phase (Fourier-transform rheology). The concentration of the solutions was varied to achieve different degrees of entanglement. In addition, numerical simulations were performed using the Giesekus constitutive equation fitted on the basis of linear viscoelastic data. We found a good qualitative agreement between experiments and predictions; a quantitative agreement was reached for intermediate strain amplitudes. Some deviations were observed at very low strain amplitudes. We present a descriptive relation for the relative magnitude of the third harmonic as a function of strain amplitude using a modified damping function. From this relation we obtained a universal parameter that describes the scaling behavior law for the increasing non-linearity (e.g., measured by the relative intensity ...

Microstructural study of the parameters governing coarsening and cyclic softening in fatigued ultrafine-grained copper

Abstract The cyclic deformation behaviour of ultrafine-grained (UFG) copper produced by equal-channel angular pressing was investigated. Special attention was paid to the parameters governing cyclic softening and cyclic grain coarsening. UFG copper shows significant cyclic softening for the tests performed at intermediate plastic strain amplitudes Δep1/2, that is in the range 2 × 10−4 ≤ Δepl/2 ≤ 1.0 × 10−3. Within this range, the cyclic softening as well as the intensity of grain coarsening increase with decreasing plastic strain amplitude. By contrast, under stress control, corresponding to a plastic strain amplitude range 2.4 × 10−5 ≤ Δepl/2 ≤ 1.2 × 10−4, cyclic softening as well as the intensity of grain coarsening decrease with decreasing plastic strain amplitude. Furthermore, cyclic softening and grain coarsening were also found to be enhanced by decreasing the deformation rate (and thus increasing the test time) and/or by increasing the temperature. These findings indicate that the responsible micro...

Cyclic saturation and fatigue fracture of tungsten monofilament-reinforced multicrystalline copper composites

Studies on cyclic saturation and fatigue fracture behavior have been conducted on tungsten monofilament-reinforced multicrystalline copper composites. A model was proposed to link the cyclic stress–strain response of the multicrystalline composites to those of monolithic single crystals and fibers. The results calculated by the model show very good agreement with the experimental data at all applied strain amplitudes by which the composites were fatigued. The fatigue fracture mechanism of the composites highly depends on applied plastic strain amplitudes. Most cracks initiate at grain boundaries in the matrix, and propagate toward and break the fiber at low and intermediate plastic strain amplitudes. At a high plastic strain amplitude, fatigue cracks initiate at the fiber even before surface cracks become pronounced, and propagates from inside outwards at a high growth rate.

Fracture behavior of monofilament-reinforced multicrystalline copper composites

Studies on monotonic tensile fracture and fatigue fracture have been performed on tungsten monofilament-reinforced multicrystalline copper composites and the failure modes are reported. Monotonic tensile fracture is not very sensitive to the initial fiber breaks and grain boundaries in tungsten monofilament-reinforced multicrystalline copper composites. Multiple breaks of the fiber and multiple necking of the matrix near the fiber segment breaks, commonly observed in tensile tests of composites, are reported here. However, the fatigue fracture is very sensitive to a fiber break, and to microstructural features such as grain boundaries and dislocation structures. Once the fiber breaks into two segments, the composite will quickly fail. The fatigue fracture mechanism of the composites depends on applied plastic strain amplitudes. Most cracks initiate at grain boundaries in the matrix at low and intermediate plastic strain amplitudes and the fiber greatly improves the fatigue behavior. At a high plastic strain amplitude, fatigue cracks initiate at the fiber, and the fiber seems ineffective for improving the fatigue life.

The influence of temperature on low cycle fatigue behavior of nickel base superalloy GH4049

Low cycle fatigue tests on nickel base superalloy GH4049 were conducted at various temperatures from 500 to 850°C in laboratory air. The strain-life and cyclic stress-strain data were analyzed and the change in fatigue life behavior and fatigue parameters with increasing temperature was discussed. At low and intermediate total strain amplitudes, the fatigue life was found to decrease with increasing temperatures. The fracture surface of the fatigue specimens was studied using scanning electron microscopy. It was found that fatigue crack initiation is transgranular, however, fatigue crack growth exhibits a strong dependence on temperature. The cyclic deformation process, creep and oxidation are thought to be the main causes of fatigue life reduction and intergranular cracking.

Dislocation structures in fatigued polycrystalline copper

The dislocation structures in fatigued polycrystalline copper with small average grain size were investigated over a plastic strain range from 1.5 x 10 −5 to 10 −2. It was found that the dislocation structures are arranged into three types of configurations, which correspond to the three regions in the cyclic stress-strain curve. Cylidirical loop patch structure are present in region A for low strain amplitudes, similar to those observed previously in coarse grained polycrystals. Moreover, irregular loop patches are also formed in this region for small grains polycrystals rather thanin region B at intermediate strain amplitudes for coarse grained polycrystals. In region B, persistent slip band (PSB) structures are formed but with a low volume content compared with the coarse grained polycrystals. In region C, at high plastic strains, the dislocation structures are dominated by dipolar walls. In addition, labyrinth structures are developed in region C instead of region B for coarse grained polycrystals. All the dislocation structures observed are viewed as forms of dipolized structures. A dipolized dislocation arrangement model is proposed to describe the formation process of dislocation structures. It is shown that all the dislocation configurations formed in cycled polycrystalline copper are low energy structures.

Cyclic response and dislocation structures of AISI 316L stainless steel. Part 2: polycrystals fatigued at intermediate strain amplitude

Polycrystalline AISI 316L stainless steel has been cycled at intermediate strain amplitudes. Cyclic response was analyzed in terms of the cyclic stress-strain curve (CSSC), softening behavior, the friction stress and the back stress. Dislocation structures were determined by transmission electron microscopy (TEM). It was found that cyclic softening behavior occurred and this has a significant influence on the dislocation structures by stimulating the activity of cross slip. The cross slip system becomes the second most important slip system, and causes the development of dislocation wall structure. Compared with the cyclic response of 316L single crystals, which are planar in slip character, polycrystals show a tendency towards wavy slip, despite the low stacking fault energy and high friction stress. It is concluded that grain boundaries, together with dislocation “starvation”, have a major influence on the fatigue behavior of polycrystals by increasing the tendency to multi-slip, decreasing the capacity of strain transfer from grain to grain and from band to band, and changing the limit of stress or strain sustainable by a given dislocation structure in the sequence that occurs.

Cyclic response and dislocation structures of AISI 316L stainless steel. Part 1: single crystals fatigued at intermediate strain amplitude

Cyclic response of AISI 316L stainless steel has been studied at ambient temperature by using monocrystalline specimens. The cyclic stress-strain (CSS) curve, obtained by conducting step ascending tests, was observed to contain a plateau in the plastic strain range from ε pl = 5 × 10 −5 to ε PL = 2 × 10 −3, with the saturated plateau stress about 59 MPa. Cyclic softening was observed in both step ascending tests and constant plastic strain tests, and is attributed to the following three factors: dislocation starvation; interaction between dislocations and interstitial solute atoms; and transformation of dislocation structures. Dislocation structures in the steel, revealed by TEM, were found to consist mainly of planar edge dislocations arranged into tangles on the primary slip plane. It was found that both the distance between slip bands and the width of the dislocation tangles decrease with applied number of cycles. On prolonged cycling, the dislocation structure was found to transform from planar arrays into a structure similar to “loop patches” observed in pure copper. Despite the low stacking fault energy of the steel, cross slip was frequently observed and was considered to play an important role in the transformation of the dislocation structures.

Effect of ramp treatment on the cyclic response of coarse-grained copper

Recent studies on the effects of different variables, both intrinsic and extrinsic to the material itself, on the cyclic response of polycrystalline copper have been encouraging in the drive to understand the phenomenon of localized deformation during fatigue. In studying the effect of two intrinsic material parameters (grain size and annealing texture) on the cyclic response of f c c polycrystals, several sets of workers [1-3] have reported that the cyclic response of coarse-grained metal shows much more pronounced cyclic hardening and higher stresses, at low and intermediate strain amplitudes, than those for fine-grained metal. This behaviour is associated, in copper, with the strongly defined hard (1 1 1 ) ( 10 0) fibre texture, inherited in the coarsegrained material after annealing at relatively high temperatures [1]. Llanes et al. [1] also showed that in large-grained, strong-textured copper specimens, double and multiple slip related structures are already promoted in a relatively large number of grains (those oriented to favour multiple slip) at plastic strain amplitudes as low as 10 .4 . This early multiple slip activation homogenizes the deformation and seems to be the main factor contributing to the very strong cyclic hardening and the 10w levels of localization of deformation observed in the cyclic stress-strain curve (CSSC) of coarse-grained copper. In terms of the effect of extrinsic variables, Llanes and co-workers [4-6] observed enhancement of strain localization in small-grained copper in association with the use of ramp-loading both as loading mode and as mechanical pretreatment, in agreement with previous results [7-12]. From these studies it is now well established that ramp-loading promotes a gradual substructure evolution which leads to: a much more homogeneous substructure, from grain to grain; localization of slip in primary systems; and formation of persistent slip bands (PSBs). In the CSSC of small-grained copper, and in support of the results of Wang and Laird [7], Llanes and Laird [4] observed that ramp-treated copper polycrystals show, under subsequent conventional strain control testing, lower cyclic hardening rates, and therefore a greater tendency to localize deformation, than nontreated samples. However, the fact that Llanes and Laird [4] were unable to obtain the clear plateau behaviour observed by Wang and Laird [7] in the CSSC of ramp-treated small-grained copper suggests that the observation of a plateau in the CSSC of

Effect of grain size and annealing texture on the cyclic response and the substructure evolution of polycrystalline copper

In attempting to interpret the mechanical response of polycrystalline copper, for which the results in the literature show marked scatter, the effects of microstructure on the cyclic behavior and the substructure evolution of copper polycrystals have been investigated. The microstructure is described by a complex factor—grain size and texture combined. It is found that there is a very significant effect of microstructure in the cyclic response of copper at low and intermediate strain amplitudes, where dislocation structures which localize deformation are expected to be present. In general, the cyclic response of coarse-grained copper shows a much more pronounced cyclic hardening and higher saturation stresses than those for fine-grained copper. This behavior is associated with a well defined hard 〈111〉−〈100〉 fiber texture, inherited in the coarse-grained material after annealing at relatively high temperatures. The multiple slip associated with the 〈111〉−〈001〉 oriented grains homogenizes the deformation very early, resulting in strong cyclic hardening, and a faster substructure evolution into cell structure.

Effect of ramp-treatment on the cyclic stress-strain curve of “small grained” copper

Various cyclic mechanical tests have been used in order to elucidate the effects of ramp-loading, as mechanical pretreatment, on the cyclic response of “small-grained” copper. The grain size of this copper is not small in an absolute sense, but small in relation to that of other copper samples we have studied. This “small” grain size is associated with a particular texture which is significant here. Two parameters definitive of ramp-loading—peak stress and number of cycles during the ramp—have been used as the main experimental variables. The results have been analyzed in relation to transmission electron microscopy (TEM) reports of the structures published elsewhere. In studying the cyclic stress-strain curve (CSSC) of ramp-treated small-grained copper it is found that the well-defined matrix structure inherited from the efficient cyclic hardening characteristic of ramp-treatment promotes higher stress and lower cyclic hardening values in the CSSC of ramp-loaded specimens, at low strain amplitudes, than those obtained in the CSSC of conventionally tested samples. At intermediate strain amplitudes, pronounced strain localization is promoted in ramp-treated copper for a very uniform and homogeneous evolution, from grain to grain, of the developed matrix into primary slip dislocation structure, i.e. persistent slip band (PSB) and wall structure. However, plateau-like behavior was not observed. The observation of early PSB nucleation in some grains, in association with a weak but noticeable 〈111〉-〈100〉 hard texture in the ramp-treated specimens, showed that the variations in PSB nucleation stress from grain to grain were not totally suppressed, and therefore plateau-like behavior in the CSSC was inhibited. Comparison of the results presented here with those of Z. Wang and C. Laird, Mater. Sci. Eng., 100 (1988) 57, whod did report a plateau, suggests that the observation of a plateau in the CSSC of polycrystals may be very sensitive to small differences in material structure and experimental procedure.

The influence of strain amplitude on the transient current behaviour in corrosion fatigue of Fe‐26Cr‐1Mo

Corrosion fatigue damage and its electrochemical characteristics of high purity ferritic stainless steel (Fe‐26Cr‐1Mo) under symmetrical tension and compression strain control have been investigated in 1M H2SO4 and 3.5 % NaCl solution by using three‐electrode technique at imposed passive potential. The tests were carried out at the total strain amplitudes of 4 × 10−3, 8 × 10−3, 1.0 × 10−2 and 1.2 × 10−2. The effects of the strain amplitude on the electrochemical dissolution and plastic deformation on the surface were studied particularly. At low strain amplitude (Δεt = 4 × 10−3), the passivity‐maintaining current was small and stable because of the small slip activity. The maximum current at the tensile half cycle, ltp, was always bigger than lcp, or sometimes equal to lcp, the maximum current at the compressive half cycle in 3.5 % NaCl. At high strain amplitude (Δεt = 1.2 × 10−2), the enhanced deformation on the surface induced the increasing dissolution. The increasing anodic current reflects the breakdown of the surface film, and only one current peak occurs within one cycle. At intermediate strain amplitude (Δεt = 8 × 10−3), the current behaviour was very stable after cyclic hardening in 3.5%, NaCl, but periodical jumpings of current during cycling were observed in the saturation region in 1 M H2SO4.

Strength differential in AlLi alloy 8090

Cyclic strength differential (SD) data have been derived from the variation of the tensile and the compressive stress amplitude with elapsed cycles during low cycle fatigue (LCF) for the quaternary AlLi alloy 8090 in the T8E51 condition. LCF test specimens were machined out of the rolled plate such that the direction of stressing was along the longitudinal (L), L+45° and long transverse (LT) directions. The analysis of cyclic stress amplitude data corresponding to the half-life revealed an SD effect at all strain levels in the L+45° and LT directions. In the case of the L direction, at strain levels below 8.5 × 10 −3, the SD is more than compensated by the Bauschinger effect resulting from the prestretch. The alloy exhibits a similar SD behaviour under monotonic loading conditions. The magnitude of cyclic SD at intermediate strain amplitudes in all the three test directions decreases upon cycling, which behaviour can be attributed to the relaxation of prestretch-related residual stresses leading to a decrease in σ T only in the L direction and σ C only in the L+45° and LT directions. As microstructural features vary in the differently heat-treated conditions, a comparison has been made of the monotonic SD data in the stretched and aged (T8E51) condition with those in the solution-treated, in the peak-aged (T6) and in the overaged (T7) conditions.

Mechanical behavior of cast particulate SiC/AI (A356) metal matrix composites

Mechanical tests were carried out to study the deformation behavior of particulate SiC-reinforced Al (A356) matrix composites produced through direct casting using the molten metal mixing method. The matrix alloy-Al (A356) was also tested as a control material for comparison. The elastic constant and yield strength of the composite material were found higher than those of the control alloy, but the ultimate tensile strength (UTS) and the ductility were lower. The Tsai-Halpin equation was found applicable for calculating the elastic constant if an average particle aspect ratio could be determined. The strain-hardening behavior of the tested composite material appeared very different from that of the control alloy. The high strain-hardening rate in the early stage of plastic deformation of the composite was rationalized by the interaction between the hard particles and the ductile metal matrix; on the other hand, the low hardening rate recorded from intermediate strain amplitude to fracture was attributed to the early coalescence of voids and other microdamages. Particle-matrix interface debonding, particle cracking, and void for-mation in the metal matrix were considered to be responsible for the low ductility. Deformation asymmetry of the composites was noticed, not only through the Bauschinger effect, but also through the difference in virgin specimens’ yield stresses in tension and compression.

Fatigue damage and crack nucleation mechanisms at intermediate strain amplitudes

Polycrystalline copper was fatigued in rotary bending at constant intermediate surface strain amplitudes at 26 Hz under ambient conditions. The specimens were interrupted at various life fractions, their surfaces prepared metallographically and scrutinised to ascertain the types of fatigue damages, namely, short cracks which are confined to individual grains or isolated grain boundary facets, and their role in fatal crack formation. The results show that, at intermediate strain amplitudes, slip band and twin boundary crack damages predominate during early stages of cycling, while grain boundary crack damages remain relatively insignificant even at the stage when fatal cracks have developed. However, depending on the strain amplitude level, the transgranular crack damages may or may not be instrumental in fatal crack formation. At the lower amplitude end of the transition region, fatal cracks are formed by interlinkage of slip band and twin boundary damages. At the higher amplitude end, even though grain boundary damages are negligible initially, they degenerate rapidly on further cycling and eventually evolve into fatal cracks. The present findings show that some 0.05% plastic strain amplitude is required to propagate intergranular cracks. Once the above condition is met, cracks would propagate rapidly along the interface and the crack nucleation mode would change from transgranular to intergranular.

An intermediate plateau in the cyclic stress-strain curve of α brass

Cyclic stress-strain curves for the saturated or quasi-saturated state during tests on polycrystalline 70Cu30Zn α brass showed a grainsize-dependent plateau for intermediate plastic strain amplitudes. This plateau was associated with the spread of pronounced slip bands (in which relatively strong recovery had occurred) across grain boundaries.