Imposed Strain Amplitude Research Articles

Low-Cycle Fatigue Behavior of an As-Extruded AM50 Magnesium Alloy

The low-cycle fatigue behavior of an as-extruded AM50 magnesium alloy has been investigated. The cyclic stress response of the alloy strongly depends on the imposed strain amplitude. It is also noted that at the higher total strain amplitudes, the alloy exhibits a pronounced anisotropic deformation behavior in the direction of tension and compression, where the width of the σ-e hysteresis loop in the compressive direction is greater than that in the tensile direction. At the total strain amplitude of 1.5 pct, a serrated flow can be observed in both tensile and compressive directions of the σ-e hysteresis loop. This means that dynamic strain aging takes place during fatigue deformation. The relation between elastic and plastic strain amplitudes with reversals to failure shows a monotonic linear behavior and can be well described by the Basquin and Coffin–Manson equations, respectively. In addition, crack initiation and propagation modes are suggested, based on scanning electron microscopy observations on the fracture surfaces of fatigued specimens.

Pre- and post-transition behavior of shear-thickening fluids in oscillating shear

The dynamic shear-thickening behavior of concentrated colloidal suspensions of fumed silica in polypropylene glycol has been investigated. Dynamic frequency sweeps showed that, for any given solids concentration, the complex viscosity at different imposed strain amplitudes followed a unique power-law-type behavior up to the onset of strain thickening. Moreover, similar behavior was also observed in the post-transition state, i.e., the viscosities again superimposed at frequencies beyond the transition frequency. In an attempt to develop a parametric description of this behavior, both the Delaware–Rutgers rule and the concept of a critical shear stress for the onset of shear thickening in steady-state experiments were considered. However, neither approach could account for the observed trends over the entire range of strains and frequency investigated. Plots of the critical shear strains for the onset and the end-point of the transition as a function of frequency were, therefore, used to describe the state of the suspensions for an arbitrary combination of strain and frequency. Finally, Fourier transform (FT) rheology was used to evaluate the extent of non-linearity in the response of the suspensions to dynamic shear, and it was shown that the observed behavior was not significantly influenced by wall slip at the tool–specimen interface.

Low-Cycle Fatigue Behavior of Magnesium Alloy AZ91

Fully-reversed total-strain-amplitude-controlled fatigue tests were performed in laboratory air at room temperature for the magnesium alloy AZ91. Experimental results showed that during the experiment significant cyclic strain hardening occurred throughout the imposed strain amplitudes. It was found that the relationship between plastic strain amplitude, elastic strain amplitude and reversals to failure can be well described by Basquin and Coffin-Manson equations. In addition, the strain fatigue parameters of the AZ91 alloy were determined through analyzing the corresponding strain fatigue life data.

Multi-scale deformation behavior investigation of 18Cr–8Ni austenitic steel subjected to low-cycle fatigue loading

Fully reversed total-axial-strain-controlled low-cycle fatigue (LCF) tests have been conducted in air at room temperature on polycrystalline 18Cr–8Ni austenitic stainless steel samples. The cyclic deformation behavior was determined by analysis of the hysteresis loop associated with cyclic straining. Three types of hardness measurements, namely nano-indentation, micro-indentation and conventional Vickers hardness tests, with the indent size ranging from several tens of nm to several tens of μm, were performed on the cyclically deformed specimens to investigate the characteristics of the deformation resistance at various scales. A linear increasing dependence of the local deformation resistance on the applied strain amplitude was observed at both macro- and meso-scales. This local resistance corresponds with the dependence of the bulk deformation resistance on the imposed strain amplitude; however, no significant change in the deformation resistance at nano-scale was found among various strain amplitudes. Both the slip band and the dislocation structure in specimens cyclically deformed at various strain amplitudes were correlated with the multi-scale deformation resistance.

A Three Dimensional Discrete Dislocation Dynamics Analysis of Cyclic Straining in 316L Stainless Steel

The early stages of the formation of dislocation microstructures in low strain fatigue are analysed,using three-dimensional discrete dislocation dynamics modelling (DDD). A detailed analysis of the simulated microstructures provide a detailed scheme for the persistent slip band formation, emphasizing the crucial role of cross-slip for both the initial strain spreading inside of the grain and for the subsequent strain localization in the form of slip bands. A new ad-hoc posttreatment tool evaluates the surface roughness as the cycles proceed. Slip markings and their evolutions are analysed, in relation to the dislocation microstructure. This dislocation-based study emphasizes the separate contribution of plastic slip in damage nucleation. A simple 1D dislocation based model for work-hardening in crystal plasticity is proposed. In this model, the forest dislocations are responsible for friction stress (isotropic work-hardening), while dislocation pile-ups and dislocation trapped in Persistent Slip Bands (PSB) produce the back stress (kinematic workhardening). The model is consistent with the stress-strain curves obtained in DDD. It is also consistent with the stress-strain curves experimentally obtained for larger imposed strain amplitudes.

Deformation Conditions. Nonlinear Viscoelasticity Relationship for HDPE Solid-State Extrudate under Cyclic Fatigue.

Fatigue behavior of HDPE extrudates was investigated on the basis of nonlinear dynamic viscoelastic analyses. The HDPE extrudate was prepared by a solid-state extrusion at an extrusion temperature of 353 K with an extrusion ratio of 11.1. Fatigue tests were carried out under the conditions of strain-controlled frequency of 11 Hz and environmental temperature of 303 K. Three deformation conditions were applied to fatigue tests: tension-tension, tension-compression and compression-compression deformation. Relationship between stress and strain amplitudes during fatigue process indicated that in the cases of tension-compression and compression-compression deformations, fatigue lifetime remarkably decreased with increasing dynamic strain amplitude. Nonlinear viscoelasticity during fatigue process was evaluated quantitatively by nonlinear viscoelastic parameter NVP. With increasing imposed strain amplitude, nonlinear viscoelasticity under compression-compression deformation became more remarkable because kink-bands were formed and stress distribution became inhomogeneous. Analyses of hysteresis loss during fatigue process indicated that nonlinear viscoelasticity was closely related to hysteresis loss consumed for irreversible structural change. In particular, in the case of compression-compression deformation, nonlinearity of viscoelasticity increased remarkably with hysteresis loss consumed for structural change due to kink-band formation.

Strain localization in nickel single crystals cyclically deformed at 77 K

Nickel monocrystals oriented for single slip have been cyclically deformed at 77 K at plastic strain amplitude between 5 x 10-4 and 1 x 10-2 up to saturation of the stress amplitude. After unloading from maximum compression, the slip markings on the surface of the specimens were removed and the deformation continued for one half cycle in tension. As previously observed for room-temperature deformation, the plastic strain was found to be localized in narrow slip bands (SBs). Using atomic force microscopy at a given imposed strain amplitude, a wide spectrum of local plastic strains was found. The averaged resolved shear strain of the SBs was found to be independent of the imposed plastic strain amplitude and turned out to be a factor of three larger than the upper plateau strain limit of the cyclic stress-strain curve.

Low cycle constant amplitude fully reversed strain controlled testing of low carbon and stainless sheet steels for simulation of straightening operations

Ten sheet steel grades have been tested in fully reversed constant strain amplitude loading. Seven low carbon steels with proof stresses from 240 MPa to 1500 MPa were included together with one austenitic stainless steel and two duplex stainless steels. For each steel grade, tests at three different strain levels have been performed and hysteresis loops were recorded during twenty subsequent cycles. The development of cyclic hardening and softening was illustrated both as a function of strain amplitude and as a function of cycle number. Different constitutive models were evaluated to describe the cyclic flow data. It was found that the best fit was obtained with a constitutive model of the type σ a =σ 0−C· e −k·ε pl,a +σ x . σ a and ε pl,a are stress amplitude and plastic strain amplitude respectively in the hysteresis loops. σ 0, C and k are material constants. The variable σ x is a function of imposed strain amplitude and cycle number.

Rheological characterization of dry-formed networks of rayon fibres

The viscoelastic properties of low-density dry-formed fibre networks have been evaluated by dynamic mechanical measurements in shear. The fibres used were rayon fibres of different diameters (13, 30 and 60 μm) and lengths (2, 4 and 6 mm). The effects of network density and grammage on the viscoelastic properties of the network were demonstrated. An important objective of this study was to assess relations between mechanical properties and fibre or network characteristics. The primary mechanical parameters used to describe the networks were the storage modulus G0′ measured at very low imposed strain amplitudes (in the linear region) and the critical strain γC at which the network yields significantly. It was noted that if the network is to be able to withstand high deformations it should exhibit a high value Of γC, which in turn, is promoted by a short free segment length between fibre crossings and a large number of contact points per fibre in the network. Long and thin fibres provide an advantage in this context. The modulus G0′ appeared to be related to the ratio of the free segment length to the fibre diameter. A lower value of this ratio corresponds to a higher G0′ value and an improved load transfer through the network structure. The networks studied here should in general be regarded as weak compared with other types of networks, e.g. paper.

Effect of aggregation structure on non-linear dynamic viscoelastic characteristics of oriented high-density polyethylenes under cyclic fatigue

Non-linear viscoelastic properties under cyclic fatigue for oriented high-density polyethylenes (HDPEs) ith different molecular aggregation states were discussed in terms of the non-linear viscoelastic parameter (NVP). Non-linear viscoelasticity of the oriented HDPEs became dominant with an increase of imposed strain amplitude, and fatigue strength decreased with an increase in the magnitude of NVP. Also, in the case of the same magnitude of NVP, the fatigue strength of the oriented HDPE drawn at the crystalline relaxation temperature, T α c (drawing temperature, T d = 353 K) was greater than that of the oriented HDPEs drawn at the other temperatures, because PE drawn at T α c had the most stable aggregation structure. Higher-order structural change during the fatigue process by cyclic straining for the oriented HDPE at T d = 353 K was not so apparent compared with that for the oriented HDPEs prepared at the other temperatures. In the case of the oriented HDPE at T d = 300K, composed of crystallites with small dimensions, the larger the magnitude of imposed strain amplitude, the greater the increase in crystallite size and/or the orientation of molecular chains to the direction of cyclic deformation occurring with cyclic straining. Also, that became more dominant with an increase in the magnitude of imposed strain amplitude. In the case of the HDPE drawn at a higher temperature than T α c ( T d = 383 K), the HDPE was composed of crystallites with large dimensions, and the crystalline disordering accompanying the decomposition of lamellar crystals into the small fragments occurred at the initial stage of cyclic fatigue. The magnitude of NVP for the oriented HDPEs increased with an increase in the degree of strain concentration in the amorphous and/or crystallite boundary regions in the case of fatigue experiments at 300 K. Thus, it is reasonable to conclude that the non-linear viscoelasticity of the oriented HDPEs under cyclic fatigue at 300 K mainly originated from the deformation of the amorphous and/or crystallite boundary regions. Also, it was clarified that the appearance of non-linear viscoelasticity remarkably reduced the fatigue strength.

Cyclic stress-strain response and dislocation substructure evolution of a ferrite-austenite stainless steel

The hardening-softening response, the cyclic stress-strain behavior and the evolution of dislocation structures of an AISI-329 ferrite-austenite stainless steel have been studied. Fatigue testing has been conducted under fully reversed total strain control and constant total strain rate. Detailed transmission electron microscopy studies have been carried out in order to determine the individual substructure evolution, as a function of increasing imposed strain amplitude, in each constitutive phase. In general, the cyclic response of the studied material may be described in terms of three different regimes within the plastic strain amplitude ( ϵ pl) range investigated, i.e. from 2 × 10 −5 to 6 × 10 −3:at ϵ pl below 10 −4 the dominant cyclic deformation mechanisms are those correlated to planar glide of dislocations within the austenite which is the phase which carries a large part of the macroscopic strain in this first regime. On the other hand, at ϵ pl higher than 6 × 10 −4 the dominant substructure evolution is observed inside the ferritic matrix. In this case, strain localization is enhanced, within the ferritic grains, through the development of veins into the wall structure. Such evolution induces a pronounced decrease of the cyclic strain hardening rate in the cyclic stress-strain curve. At ϵ pl in-between these values, the cyclic behavior is characterized by a relatively high strain hardening rate and may be classified as a mixed “ferritic/austenitic-like” behavior. In this intermediate regime substructural changes are observed in both phases and the dislocation activity in each of them seems to be strongly influenced by their particular cyclic strain hardening behaviors. Finally, the results are analyzed and compared with data from the literature in terms of volume fraction and chemical composition of the constitutive phases.

A new testing methodology for the assessment of fatigue properties of structural adhesives

The monotonic and fatigue shear behaviour of an epoxy adhesive joint has been studied using a short overlap — thick adherend configuration. A specific in situ bonding procedure has been developed in order to accurately control the initial stress state of the joint before testing. The strength of the joint has been found to be strongly dependent on the strain rate and the joint thickness. This dependency was associated with a change in damage mechanisms from cohesive failure (for small joint thickness or elevated speed) to adhesive failure (for large joint thickness and low speed). This was attributed to changes in peel stresses and/or joint morphology with thickness. Fatigue tests were carried out at imposed strain amplitude. Fatigue logs giving the changes in the shape of the transverse loaddisplacement loops were at first considered. The latter have been found to be useful to differentiate between the different failure modes (i.e. cohesive and adhesive). In a second step, all the results were summarised in a fatigue map giving the endurance properties and the failure mode of the joint as a function of the joint thickness and the strain level. This method should be generally useful whenever an accurate determination of the contribution of adhesive and interface behaviour is required for the assessment of joint durability.

Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves

Hardening of polycrystalline copper subjected to tension-compression loading cycles in the plastic region is discussed with reference to changes in flow stress determined from equations describing dislocation glide. It is suggested that hardening is as a result of the accumulation of strain on a monotonic stress-strain curve. On initial loading, the behaviour is monotonic. On stress reversal, a characteristic cyclic stress-strain curve is followed until the stress reaches a value in reverse loading corresponding to the maximum attained during the preceding half cycle. Thereafter, the monotonic path is followed until strain reversal occurs at completion of the half cycle. Repetition of the process results in cyclic hardening. Steady state cyclic behaviour is reached when a stress associated with the monotonic stress-strain curve is reached which is equal to the stress associated with the cyclic stress-strain curve corresponding to the imposed strain amplitude.

Effect of glass fiber‐matrix polymer interaction on fatigue characteristics of short glass fiber‐reinforced poly(butylene terephthalate) based on dynamic viscoelastic measurement during the fatigue process

AbstractFatigue behaviors of glass fiber‐reinforced poly(butylene terephthalate) (PBT) were studied based on dynamic viscoelastic measurements during the fatigue process. The fatigue strength of glass fiber‐reinforced PBT was greatly improved by strengthening the interfacial adhesion between glass fiber and matrix PBT. The heat generation rate under cyclic fatigue for PBT reinforced with surface‐unmodified short glass fiber was always larger than that reinforced with surface‐modified short glass fiber because of the large net imposed strain amplitude of PBT matrix which occurred due to the interfacial debonding under cyclic fatigue. A fatigue fracture criterion based on the magnitude of hysteresis energy loss being consumed for a structural change was established for the PBT/short glass fiber composites in consideration of glass fiber‐matrix polymer interfacial interaction. © 1994 John Wiley & Sons, Inc.

Analysis of Fatigue Behavior of High-Density Polyethylene Based on Nonlinear Viscoelastic Measurement under Cyclic Fatigue

Fatigue behaviors of annealed and isothermally crystallized high-density polyethylenes (HDPEs) were investigated on the basis of nonlinear dynamic viscoelastic measurement during the fatigue process. Nonlinear viscoelasticity was evaluated in terms of nonlinear viscoelastic parameter (NVP) which was defined as the contribution of higher harmonics of Fourier expanded stress signal. In the cases of the annealed and isothermally crystallized HDPEs, the apparent dynamic storage modulus decreased, NVP and tan δ increased with an increase in the magnitude of imposed strain amplitude. Since the fatigue strength decreased when the contribution of NVP became dominant, the magnitude of NVP can be used as a measure of fatigue characteristics of polymeric solids. Also, the origin of NVP for the annealed and isothermally crystallized HDPEs was discussed on the basis of the spherulite structure.

Fatigue Behavior of Oriented Ultra-High Molecular Weight Polyethylene Prepared by Gel Drawing

High-modulus and high-strength PE specimens were prepared from the dry gel film of ultra-high molecular weight polyethylene (UHMWPE) and their fatigue behavior was investigated in terms of dynamic viscoelastic measurement during the fatigue process. In the case of oriented film with draw ratio less than 60, the maximum of E′ and the minimum of tanδ on approaching the point of failure were observed under small imposed strain amplitude suggesting that the proceeding of orientation of molecular chains under cyclic fatigue. However, this maximum of E′ and the minimum of tanδ were not observed for PE with draw ratio of 100. The temperature dependence of fatigue strength of drawn PE suggested the contribution of crystalline relaxation process to fatigue mechanism of oriented PE film.

Analysis of fatigue behavior of high‐density polyethylene based on dynamic viscoelastic measurements during the fatigue process

AbstractThe fatigue behavior of high‐density polyethylene was studied by measuring the variation in the dynamic viscoelasticity during the fatigue process. Brittle failure was observed under the conditions of small imposed strain amplitude, low ambient temperature, and large heat transfer coefficient to the surroundings. Ductile failure was observed under the conditions of large imposed strain amplitude, high ambient temperature, and small heat transfer coefficient to the surroundings. In the case of brittle failure, absolute value of dynamic complex modulus, ∣E*∣, showed maximum and phase difference, δ, did minimum on approaching the point of failure. In the case of ductile failure, ∣E*∣ decreased and δ increased monotonously from the start of the fatigue testing. The effect of environmental conditions on fatigue behavior was elucidated in terms of the heat transfer coefficient to the surroundings. As both forced convection of air and water enlarge the heat transfer coefficient, temperature rise of the specimen hardly occured and brittle failure took place preferentially. The coefficient, ϰ, was introduced to express the ratio of the actual generated heat to the hysteresis loss. With increase of the magnitude of the strain amplitude, the nonlinear viscoelastic behavior appeared and ϰ became smaller. A positive correlation between ϰ and lifetime was found. As the heat generation rate does not strongly affect lifetime, it was concluded that the hysteresis loss with low efficiency of heat generation would contribute to the fatigue failure. The relationship between average hysteresis loss and lifetime was proposed. The total hysteresis loss up to fatigue failure is constant, being independent of ambient temperature and imposed strain amplitude. The cumulative damage theory of fatigue failure was proposed based on hysteresis loss.

Evaluation of fatigue lifetime and elucidation of fatigue mechanism in plasticized poly(vinyl chloride) in terms of dynamic viscoelasticity

The fatigue behavior of plasticized poly(vinyl chloride) was investigated by means of a tension–compression-type fatigue apparatus. Complex elastic modulus and mechanical loss tangent were obtained continuously with time under the conditions of constant ambient temperature as a function of imposed strain amplitude. Brittle failure was observed under the conditions of low ambient temperatures and small strain amplitudes, or forced convection of air, whereas thermal failure was observed under the conditions of high ambient temperatures, or large strain amplitudes and natural convection of air. In the case of brittle failure, the dynamic storage modulus E′ exhibited a maximum and the loss tangent tanδ exhibited a minimum on approaching the point of failure. In the case of thermal failure, E′ decreased and tanδ increased monotonously until the onset of thermal failure. It was found that failure occurs when the effective energy loss reaches a certain magnitude depending on an ambient temperature. The fatigue criterion was represented schematically from a standpoint of self-heating. When the heat generation rate of the specimen under cyclic staining is larger than that of the heat transfer to the surroundings, thermal failure takes place. In this case, the specimen temperature increases up to a limiting constant temperature corresponding to the α-absorption temperature. When the heat generation rate is nearly equal to that of the heat transfer to the surroundings, the specimen temperature does not change appreciably and brittle failure takes place.

The cyclic deformation of magnesium single crystals

Magnesium single crystals of differing orientation were cyclically deformed at total strain amplitudes of ±0.0018 and ±0.009. Deformation occurred primarily by slip, although both twinning and kink band formation were observed. Observation of the substructure by electron microscopy indicated that duplex slip had occurred in all samples independent of orientation or imposed strain amplitude. The extent of secondary slip did, however, correlate with imposed strain amplitude. The secondary system was identified as a basal system, and it was shown that the operation of the secondary system, as inferred from hardening behavior, correlates well with the critical resolved shear stress necessary to activate the secondary basal system. A hardening mechanism is suggested for magnesium single crystals during cyclic deformation, including the occurrence of duplex slip. Although twinning was not the dominant deformation mode, one sample was tested in which extensive twinning occurred. It was shown that the twins formed are those that would be anticipated during unidirectional deformation. While the occurrence of some detwinning was noted, detwinning on a massive scale was not observed.