Cyclic stress-strain curves at finite strains under high pressures in crystalline polymers

The cyclic torsional stress-strain behaviour for crystalline polymers of polyethylene (PE), polypropylene (PP) and polyoxymethylene (POM) was investigated at finite strain amplitude under hydrostatic pressure up to 2000 kgf cm^–2. The following features for the cyclic stress-strain curves were indicated. (1) Two types of cyclic stress-strain curve were observed: one was a PE type where the present hysteresis loop was not so affected by the strain histories, and the other was a PP type where the hysteresis loop was greatly affected by the previous maximum strain. (2) In the pressure ranges tested, the shape of the cyclic stress-strain curves for the polymers used was not essentially altered by the hydrostatic pressure. (3) The stress-strain curves after the first strain reversal showed an unusual shape which has not been observed for metals. (4) The decrease in cyclic softening caused by the stress amplitude with increasing number of cycles at a constant strain amplitude test occurred irrespective of the hydrostatic pressure. (5) The stress-strain behaviour at a partly reversed cyclic loading was different from that expected at a fully reversed cyclic loading.     

EVALUATION OF LOW CYCLE FATIGUE UNDER NON-PROPORTIONAL LOADING

Abstract— A series of low cycle fatigue experiments have been conducted on a 42CrMo steel under tension-torsion loading. Thin-walled tube specimens were used. Low cycle fatigue under various loading paths, including circular and square paths, have been investigated.
The plastic work criterion for low cycle fatigue failure has previously been generally accepted, but it is difficult to calculate stress and strain for complex loading paths, especially for non-proportional loading. This present study suggests a simple method for the calculation of the stable cyclic stress and strain values based on a Modified Endochronic Constitutive Theory (MECT) that redefines an intrinsic time scale. The loading path effect under non-proportional loading is also considered when evaluating fatigue life.
The results show that the plastic work approach using the MECT method in multiaxial fatigue calculations correlates reasonably well the data and is a reflection of loading path dependence.     

Deformation und Versagen von StE460 und AlMg4,5Mn bei mehrachsig-proportionalen Beanspruchungen mit konstanten und variablen Amplituden

Deformation and failure behaviour of FeE460 and AlMg4.5Mn under multiaxial proportional loading with constant and variable amplitudes To calculate the fatigue life-to-crack initiation of engineering components under combined cyclic loading, experimentally secured knowledge on the cyclic deformation and failure behaviour of the materials used under the certain multiaxial cyclic stress and strain conditions are required. To obtain this, strain-controlled fully reversed experimental tests at tensional, torsional and combined loading with constant and variable amplitudes have been conducted using thin-walled tube specimens of FeE460 and AlMg4.5Mn. Experimental tests on standard uniaxially loaded hourglass specimens have also been conducted to study specimen form effects. Cyclic deformation behaviour can be uniformly described by the stabilised cyclic σ-ε-curve, if stresses and strains are expressed as equivalent values according to the von Mises criterion. Failure behaviour at constant and variable amplitude loading is characterized by the initiation and growth of short cracks at right angle to the direction of the greatest principal stress (mode I) in the case of tensional or combined loading and by short crack growing in both shear stress directions (mode II+III) in the case of torsional loading. At fully reversed constant amplitude loading, all three types of load can be described by one constant amplitude strain life-to-crack initiation curve. At variable amplitude loading (notch strain simulation with gaussian spectrum, H₀=10⁵), the experimental fatigue life-to-crack initiation values are lower than estimated values based on Miner-calculations using an equivalent stress-strain supported P_SWT-N-curve. The question of mean stresses and their evaluation is discussed.     

Biaxial cyclic deformation of an epoxy resin: Experiments and constitutive modeling

Biaxial (proportional and non-proportional) cyclic tests were conducted on thin-walled tubular specimens to investigate deformation behavior of an epoxy resin, Epon 826/Epi-Cure Curing Agent 9551. The focus was placed on the biaxial stress-strain response and their dependency on the load control mode, stress or strain range and loading path. Experimental results indicated that under strain-controlled equi-biaxial (proportional) cyclic loading, mean stress relaxation occurred in both axial and hoop directions, whereas under stress-controlled equi-biaxial cyclic loading, ratcheting strains accumulated in both principal directions. Under strain- or stress-controlled non-proportional cyclic loading, anisotropy in stress-strain responses was induced in both axial and hoop directions, and the axial and hoop hysteresis loops rotated in opposite directions. This was particularly evident at high stress or strain levels. The experimental results were further used to evaluate the predictive capabilities of a nonlinear viscoelastic constitutive model. Qualitative and quantitative comparison with the test data indicated a good agreement in predicting the complex stress-strain response under biaxial cyclic loading with various loading paths, applied stress or strain ranges and loading control modes.     

Very high cycle fatigue of VDSiCr spring steel under torsional and axial loading

Very high cycle fatigue (VHCF) properties of VDSiCr spring steel are investigated with ultrasonic equipment under fully reversed cyclic torsion loading and under cyclic axial loading at load ratios R = –1, R = 0.1 and R = 0.5. Shot‐peened specimens with surface finish similar to valve springs in combustion engines are tested until limiting lifetimes of 10¹⁰ cycles. Under cyclic torsion loading, specimens either fail below 10⁶ cycles with crack initiation at the surface or they do not fail. Under cyclic axial loading, failures above 10⁹ cycles were found for all load ratios with crack initiation at the surface or at internal inclusions. Ratio of mean endurance limit (50% failure probability at 10¹⁰ cycles) under fully reversed cyclic torsion and cyclic tension‐compression loading is 0.86. Cyclic torsion loading slightly below the endurance limit leads to cyclic softening first followed by cyclic hardening whereas cyclic stability is found for tension‐compression loading. Cyclic torsion reduces surface compression stresses whereas they are hardly affected by cyclic tension‐compression loading. Mean endurance limit at 10¹⁰ cycles for R = 0.1 is 61% of the endurance stress amplitude at load ratio R = –1, and for R = 0.5 it is 44% of the tension‐compression endurance limit. Endurance limits for cyclic torsion and cyclic tension‐compression loading are comparable, if effective stress amplitude is used that considers cyclic normal stresses and residual compression stresses at the surface.     

INTERACTIONS BETWEEN TIME AND CYCLIC DEFORMATION PROCESSES IN A NIMONIC ALLOY

Interactive creep–fatigue behaviour of a nickel-base superalloy (IN 597) has been examined at 850 °C under various strain-limited, cyclic torsional loading conditions. In one test, forward creep deformation was reversed by creep under equal magnitude stress levels and strain limits. In other tests, forward creep strain was reversed by fast monotonic plasticity with and without a subsequent period of relaxation. These cycles were repeated within each test until fracture. This paper examines empirically the influence of a number of test variables upon cyclic creep curves, and demonstrates the usefulness of predictions based upon continuous low cycle fatigue and simple creep data when used in conjunction with a mechanical equation of state. A cyclic equilibrium condition was not achieved from these tests. Instead, a progressive softening occurred giving reductions to the amount of creep strain, creep time interval and reversed peak stress with each new cycle. Such reductions are expressed from derived formulae that embrace the range of inelastic strain, cycle number, creep dwell stress, reversed peak stress, and times expended in creep and relaxation.
Observations made on accumulated creep strain reveal the contribution to a creep–fatigue fracture from cyclic creep. This has led to a modified form of the linear damage rule which can provide conservative life predictions for components operating in service under similar cyclic conditions.     

循环荷载水平与加载频率耦合作用下的软粘土特性研究

通过不排水循环三轴试验,并考虑不同循环应力水平及加载频率的影响,研究了软粘土在循环荷载作用下的孔隙水压力及变形特性,分别探讨了这些特性随循环加载时间和加载次数的不同变化规律。研究结果表明,对于相同循环应力水平,相同加载次数下不同加载频率的软粘土特性有所不同,而相同加载时间下不同加载频率的软粘土特性基本相同。此外,无论加载频率为何数值,一旦循环应力水平超过临界值,软粘土破坏必将发生。为了深入研究应力水平和加载频率的耦合作用,该文从应力控制循环加载试验中的应变速率着手,对软粘土的特性进行了分析。结果表明,在应力水平相同的情况下,软粘土在不同加载频率下的应变速率是基本相同的,由此可得对于软粘土在循环荷载作用下特性的影响,应力水平比加载频率更为重要。     

Multi-cycle viscoplastic deformation of polypropylene

Experimental data are reported on isotactic polypropylene in tensile cyclic tests with a strain-controlled program (150 cycles) and various maximum strains. A model is developed in cyclic viscoplasticity of semicrystalline polymers. The constitutive equations describe the mechanical response along each individual cycle of loading–unloading. Material constants in the stress–strain relations are found by fitting observations during several first cycles. For cyclic deformation with a large number of cycles, phenomenological equations are introduced to account for the effect of plastic flow and damage accumulation on adjustable parameters. It is demonstrated that the model qualitatively predicts changes in maximum stress and minimum strain per cycle with number of cycles. The stress–strain relations are applied to assess growth of residual strain under cyclic loading with large (tens of thousand) number of cycles.     

Key issues in cyclic plastic deformation: Experimentation

Cyclic plastic deformation phenomena include the Bauschinger effect, cyclic hardening/softening, strain range effect, loading history memory, ratcheting, mean stress dependent hardening, mean stress relaxation and non-proportional hardening. In this work, different cyclic plastic deformation responses of piping materials (SA333 C-Mn steel and 304LN stainless steel) are experimentally explored. Cyclic hardening/softening is depends upon loading types (i.e. stress/strain controlled), previous loading history and strain/stress range. Pre-straining followed by LCF and mean stress relaxation shows similar kind of material response. Substantial amount of non proportional hardening is observed in SA333 C-Mn steel during 90° out of phase tension-torsion loading. During ratcheting, large amount of permanent strain is accumulated with progression of cycles. Permanent strain accumulation in a particular direction causes cross-sectional area reduction and which results uncontrollable alteration of true stress in engineering stress controlled ratcheting test. In this work, true stress control ratcheting on piping materials has been carried out in laboratory environment. Effects of stress amplitude and mean stress on the ratcheting behaviors are analyzed. A comparison has also been drawn in between the true and engineering stress controlled tests, and massive difference in ratcheting life and strain accumulation is found.     

Cyclic loading and fatigue in ice

Isotropic polycrystalline ice was subjected to cyclic loading in uniaxial compression at ?5°C, with stress limits 0–2 and 0–3 MPa, and frequencies in the range 0.043 to 0.5 Hz. Stress-strain records showed hysteresis loops progressing along the strain axis at non-uniform rates. The effective secant modulus, which was about half the true Young's modulus, decreased during the course of a test. The elastic strain amplitude and the energy dissipated during a loading cycle both increased with increase of time and plastic strain. Strain-time records gave mean curves which were identical in form to classical constant-stress creep curves, with a small cyclic alternation of recoverable strain about the mean curve. The inflection point of the “creep curve”, marking the transition from strain hardening to strain softening, occurred at a plastic strain of 1% (±0.1%), which is about the same as the “ductile failure strain” found in constant stress creep tests and in constant strain-rate tests on ice of the same type at the same temperature. The dissipation of strain energy up to this “failure point” was much higher for the cyclic tests than for corresponding quasi-static tests ? 100 to 600 kPa (or kN-m/m³) in comparison to about 30 kPa. The number of cycles taken to reach the “failure point” was of no direct significance, varying greatly with stress amplitude and with frequency. The results of the tests suggest that maximum resistance under compressive cyclic loading occurs at an axial plastic strain of about 1%, which is essentially the same as the failure strain for ductile yielding under constant stress and under constant strain-rate.     

不同应力幅比加载下2A12铝合金的多轴疲劳性能

采用SDN100/1000电液伺服拉扭复合疲劳试验机对2A12铝合金进行不同应力幅比下的多轴疲劳实验,观察试样断口形貌并结合加载过程中的疲劳循环曲线进行失效机理分析。结果表明:单级加载条件下,随应力幅比的增加合金的疲劳寿命提高,纯扭转条件下断面存在平整的光滑区域,随应力幅比的增加断面划痕减少,并能观察到疲劳条带以及鱼骨状、鳞片状和蜂窝状特殊形貌;不同应力幅比累积路径下,多轴疲劳寿命随一级加载周次变化的规律不同;高-低应力幅比累积路径下,拉压方向一级高应力幅比加载阶段出现明显的循环硬化现象,材料产生"锻炼效应"。     

DISLOCATION STRUCTURE AND NON-PROPORTIONAL HARDENING OF TYPE 304 STAINLESS STEEL

Abstract— This paper describes the microstructure of Type 304 stainless steel after cyclic loading at room temperature under tension-torsion non-proportional strain paths. The degree of cyclic non-proportional hardening is correlated with changes in the dislocation substructure. Dislocation cells, dislocation bundles, twins and stacking faults are all observed. The type of microstructure formed and resultant stress response is dependent on the degree of non-proportional loading and strain range. Cyclic stress range was uniquely correlated with mean cell size.     

BIAXIAL CYCLIC DEFORMATION BEHAVIOUR OF STEELS

Abstract— The cyclic stress-strain curves for 1% Cr-Mo-V steel and AISI 316 stainless steel were determined under biaxial loading conditions at various temperatures and strain rates. It is shown that these curves may be correlated in terms of the maximum shear stress and strain amplitudes. It is argued that, even though metals obey the von Mises yield criterion for monotonie loading, the micromechanisms of slip which produce the stabilized cyclic stress-strain behaviour are governed by the Tresca criterion.     

Mechanical behaviour and formulation of stress-strain relation for non-linear viscoelastic cellulose nitrate under cyclic loadings

The cyclic deformations under various repeated stresses are quantitatively investigated using non-linear viscoelastic cellulose nitrate heated to 60° C. The non-elastic strain or creep-plastic strain is remarkably influenced by the repeated stress and the stress rate. The cyclic deformations corresponding to the repeated stress less than a certain stress level attain the saturated state called the shake down after some cycles. The stress-strain relations of the non-linear viscoelastic media in the loading and unloading processes are deduced from the invariant theory using an hypothesis of creep potential. The non-linear viscoelastic observations obtained on the cellulose nitrate at 60° C under cyclic loadings are found to fit the deduced relations for the loading and unloading processes independent of the repeated stress and the stress rate.     

Cyclic deformation behaviour of a nickel base alloy at elevated temperature

Low cycle fatigue tests for a hot extruded Nickel base alloy tube material have been performed at room temperature and at 204°C. The alloy shows a normal hardening and softening cyclic stress-strain response at room temperature. At 204°C, however, the cyclic stress-strain response shows a strain hardening first, followed by a relatively stable stress and finally a secondary cyclic strain hardening. This stable stress disappears with increasing strain amplitude. The mechanisms of the secondary cyclic strain hardening have also been investigated by transmission electron microscopy (TEM). Besides dislocation multiplication, interactions between stacking faults and moving dislocations and between interstitial atoms and moving dislocations could also contributed to this secondary cyclic strain hardening. The formation of micro-twins during cyclic loading at 204°C and its influence on the cyclic stress-strain response were also discussed.     

Effect of Particulate Silicon Carbide on Cyclic Plastic Strain Response and Fracture Behavior of 6061 Aluminum Alloy Metal Matrix Composites

In this paper, the cyclic stress response and cyclic stress–strain response characteristics, cyclic strain resistance and low-cycle fatigue life, and mechanisms governing the deformation and fracture behavior of aluminum alloy 6061 discontinuously reinforced with silicon carbide (SiC) particulates are presented and discussed. Two different volume fractions of the carbide particulate reinforcement phase in the aluminum alloy metal matrix are considered. The composite specimens were cyclically deformed using fully reversed tension–compression loading under total strain-amplitude-control. The stress response characteristic was observed to vary with strain amplitude. The plastic strain-fatigue life response was found to degrade with an increase in carbide particulate content in the metal matrix. The fracture behavior of the composite is discussed in light of the interactive influences of composite microstructural effects, cyclic strain amplitude and concomitant response stress, deformation characteristics of the composite constituents and cyclic ductility.     

MICROSTRUCTURAL STUDY OF CYCLIC STRAIN HARDENING BEHAVIOUR IN BIAXIAL STRESS STATES AT ELEVATED TEMPERATURE

This paper describes the cyclic strain hardening behaviour and dislocation structures of material in biaxial low cycle fatigue at elevated temperatures. In this study, push-pull, reversed torsion and combined push-pull/reversed torsion tests were carried out using a type 304 stainless steel in air. While there was no significant difference between the cyclic stress amplitudes in the push-pull and reversed torsion tests on a von Mises' base, combination tests exhibited a 40% increase in stress amplitude. Most of the dislocations in the first two types of test adopted ladder or maze structures, while in the later case cells were found. Changing the loading mode at a certain cycle, for example, from push-pull to reversed torsion, revealed that stress amplitude depended mainly on the concurrent applied strain mode and furthermore, that the strain mode before the interchange had little or no effect on the stress amplitude after the interchange. Tests were also performed in order to examine how prestrained material hardened in the three different loading modes, with the following results: prestrained material in push-pull or in reversed torsion exhibited an anisotropic stress response, while the material in the combined tests exhibited an isotropic response. These cyclic responses are discussed in connection with the dislocation structure.     

Uniaxial and non-proportionally multiaxial ratcheting of U71Mn rail steel: experiments and simulations

The ratcheting and strain cyclic characteristics of U71Mn rail steel were experimentally researched under uniaxial and non-proportionally multiaxial cyclic loading at room temperature. The effects of cyclic strain, stress and their histories on strain cyclic characteristics and ratcheting were studied, respectively. It is shown that: U71Mn rail steel exhibits a cyclic stabilization and non-memorization for previous loading history under strain cycling; however, the ratcheting of the material depends greatly not only on the current values of mean stress and stress amplitude, but also on their histories; the non-proportionality of multiaxial loading path only causes a negligible additional hardening for the material. Based on the Ohno–Wang non-linear kinematic hardening model [Int. J. Plast. 9 (1993) 375, 391], the uniaxial and multiaxial ratcheting behaviours of the material were simulated by a visco-plastic constitutive model. The simulated results are in good consistence with the experimental ones.     

Ratcheting‐fatigue behaviour of bainite 2.25Cr1MoV steel with tensile and compressed hold loading at 455°C

The ratcheting behaviour of a bainite 2.25Cr1MoV steel was studied with various hold periods at 455°C. Particular attention was paid to the effect of stress hold on whole‐life ratcheting deformation, fatigue life, and failure mechanism. Results indicate that longer peak hold periods stimulate a faster accumulation of ratcheting strain by contribution of creep strain, while double hold at peak and valley stress has an even stronger influence. Creep strains produced in peak and valley hold periods are noticeable and result in higher cyclic strain amplitudes. Dimples and acquired defects are found in failed specimen by microstructure observation, and their number and size increase under creep‐fatigue loading. Enlarged cyclic strain amplitude and material deterioration caused by creep lead to fatigue life reduction under creep‐fatigue loading. A life prediction model suitable for asymmetric cycling is proposed based on the linear damage summation rule.     

Fatigue behavior and dislocation substructures for 6063 aluminum alloy under nonproportional loadings

In this paper, the fatigue behavior and dislocation substructures of 6063 aluminum alloy were studied under several nonproportional path loadings, which were circle, ellipse, rectangle and square paths. After fatigue test the micro-structure especially the dislocation substructures of the failure materials was carefully observed with the transmission electron microscope (TEM) method. Under the same 93 MPa equivalent stress amplitude loading, the alloy has the shortest life and the most severe cyclic additional hardening with circle path loading among all the loading paths. This attributes to the complicated dislocation substructures and severe stress concentration of the alloy during the cycling process. While under the ellipse path loading, the alloy has a comparably long life and light cyclic additional hardening. The deformation of the alloy and the morphology of the dislocation substructures determine the fatigue behavior of 6063 alloy under the same equivalent stress amplitude loading. Under the circle path loading, the fatigue life decreases while the cyclic strain increases as the loading stress amplitude increases from 47 MPa to 163 MPa. The dislocation evolution of 6063 alloy during the cycling process under circle path loading was examined with TEM. It was found that the dislocation merges with each other and changes from single lines to crossed bands. The movability of dislocation reduces and the stress concentration degree rises during the cycling process.