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.     

Cyclic viscoelastoplasticity of polypropylene: effects of crystalline structure

Observations are reported on two grades of polypropylene in tensile tests with various strain rates, relaxation tests with various strains, and cyclic tests with a stress-controlled program (ratcheting). Experiments are performed on isotactic polypropylene (iPP) manufactured by the Ziegler?CNatta catalysis and metallocene-catalyzed polypropylene (mPP). The time- and rate-dependent behaviors of iPP and mPP in tensile tests and relaxation tests are quite similar, whereas their responses in cyclic tests differ pronouncedly: The number of cycles necessary for mPP to reach a required ratcheting strain exceeds that for iPP by an order of magnitude. To rationalize these observations, a constitutive model is developed in cyclic viscoelastoplasticity of semicrystalline polymers, and its adjustable parameters are found by fitting the experimental data. Slowing down of growth of ratcheting strain in mPP is attributed to the presence of small crystalline domains in amorphous regions that act as physical cross-links. The effect of the strain rate on the number of cycles to failure is studied numerically.     

Zum Wechselverformungsverhalten der Magnesiumbasislegierung AZ31

The cyclic deformation behaviour of Mg – base alloy AZ31 The cyclic deformation behaviour of Mg – base alloy AZ31 was investigated in stress controlled tension-, compression-tests. Experiments with zero mean stress (R = -1) as well as with tensile or compression mean stress (R = 0, R = - ∞ resp.) were carried out. Cyclic strain hardening and a pronounced anisotropy of strength during the first loading cycles was observed with higher yield strength in tension compared with compression. Consequently, in tests with zero mean stress cyclic creep and compressive mean strains occured.     

Ratcheting progress at notch root of 1045 steel samples over asymmetric loading cycles: Experiments and analyses

The present study examines ratcheting response of steel samples with various notch diameters through conducting several cyclic tests. Ratcheting strain values were measured through strain gauges mounted at different distances from the notch root. Local ratcheting at the notch region was highly influenced by notch diameter, notch shape, distance from the notch root, and magnitude of the nominal mean/amplitude of loading cycles. Nominal force‐controlled cycles were kept below the yield point and the Neuber's rule accommodated for the maximum/minimum local stress components along those local strains measured through the strain gauges at the notch region. Plastic strains at the vicinity of notch root over loading cycles were further accumulated by means of the Chaboche hardening model. The local ratcheting strain while progressed at the notch root plastic zone over loading cycles resulted in mean stress relaxation controlled by the model.     

Dilational damage accumulation during fatigue of polypropylene

Plastic deformation in spherulitic polypropylene includes a component of dilatational strain. Residual volume changes have been measured as a function of uniaxial strain for tension, compression and cyclic tests. In compression, the volume changes were measured during the test while the specimen was under had and the stress maximum was found to be related to the onset of rapid dilation. The dilation for all modes of mechanical testing was found to be linearly dependent on the tensile component of the strain. Microstructural changes responsible for these observations were examined using transmission electron microscopy of permanganic etched interior surfaces of the deformed specimens. Microcrazes along interlamellar planes were found in all deformed specimens. Fatigue failure in symmetric tension/compression tests occurred by accumulation of crazes, predominantly on the tensile half cycles.     

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。     

Viscoelasticity, viscoplasticity, and creep failure of polypropylene/clay nanocomposites

Observations are reported on polypropylene/clay nanocomposites in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. New constitutive equations are derived in viscoelasticity and viscoplasticity of nanocomposites. Adjustable parameters are found by fitting the experimental data. The stress–strain relations are applied to the analysis of creep rupture. It is demonstrated that reinforcement of polypropylene with 1 wt.% of nanoclay induces an increase in time to failure by an order of magnitude.     

Closure-free biaxial fatigue crack growth rate and life prediction under various biaxiality ratios in SAE 1045 steel

Biaxial fatigue tests were performed on thin-walled tubular 1045 steel specimens in a test fixture that applied internal and external pressure and axial load. There were two test series, one in which constant amplitude fully reversed strains (CAS) were applied and another in which large periodic compressive overstrain (PCO) cycles causing strains normal to the crack plane were inserted in a constant amplitude history of smaller strain cycles. Ratios of hoop strain to axial strain of λ = ?1, ?0.625, ?ν and +1 were used in each test series. Fatigue crack growth behaviours under CAS and PCO histories were compared, and revealed that the morphology of the fracture surface near the crack tip and the crack growth rate changed dramatically with the application of the compressive overstrains. When the magnitude of the compressive overstrains was increased, the height of the fracture surface irregularities was reduced as the increasing overstrain progressively flattened the fracture surface asperities near the crack tip. The reduced asperity height was accompanied by drastic increases in crack growth rate and decreases in fatigue life. Using a pressurizing device attached to the confocal scanning laser microscope (CSLM), crack opening measurements were obtained. Crack opening measurements showed that the biaxial cracks were fully open at zero internal pressure for block strain histories containing in-phase PCO cycles of yield stress magnitude. Therefore, for the shear-strained samples, there was no crack face interference and the strain intensity range was fully effective. For PCO tests (with biaxial strain ratios of ?0.625 and +1), effective strain intensity data were obtained from tests with positive stress ratios for which cracks did not close. A number of strain intensity parameters derived from well-known fatigue life parameters were used to correlate fatigue crack growth rates for the various strain ratios investigated. Predicted fatigue lifetimes based on a fatigue crack growth rate prediction program using critical shear plane parameters showed good agreement with the experimental fatigue life data.     

STRESS RESPONSE UNDER THERMAL-MECHANICAL STRAIN CYCLING FOR A 1 CrMoV FERRITIC STEEL AND TWO 316 STAINLESS STEELS

Abstract— Isothermal and thermal-mechanical strain fatigue tests were conducted in air on representative service alloys; a 1 CrMoV steel, and two batches of 316 stainless steel. Data was obtained for thermal-mechanical in-phase and out-of-phase cycles, and also for isothermal tests at the maximum, minimum, and mid-temperature of the thermal-mechanical cycle. Dwell periods were also incorporated in the cycle to assess their effects.
A comparative evaluation has been made on the basis of the materials' cyclic stress response. In general, the results have shown that the thermal-mechanical strain cycling tests cause a large increase in stress range over those tested under isothermal conditions at maximum temperature. In addition, mean stress and strain offsets were developed in continuous cycle thermal-mechanical tests, whereas negligible offsets occurred in isothermal tests.
It appears that the response of the materials could not always simply be explained by reference to the temperature change itself.     

Low-cycle fatigue life of SiC-particulate-reinforced Al-Si cast alloy composites with tensile mean strain effects

The low-cycle fatigue behaviour of a SiC-particulate-reinforced Al-Si cast alloy with two different volume fractions has been investigated under strain-controlled conditions with and without tensile mean strains. The composites and the unreinforced matrix alloy showed cyclic hardening behaviour. The composite having a higher volume fraction of the SiC particles exhibited a more pronounced strain-hardening rate. For the tensile mean strain tests, the initial high tensile mean stress relaxed to zero for the ductile Al-Si alloy, resulting in no influence of the tensile mean strain on the fatigue life of the matrix alloy. However, tensile mean strain for the composite caused tensile mean stresses and reduced the fatigue life. The pronounced effects of mean strain on the low-cycle fatigue life of the composite compared to the unreinforced matrix alloy were attributed to the initial large prestrain causing non-relaxing high tensile mean stress in the composite with limited ductility and cyclic plasticity. Fatigue damage parameter using strain energy density accounted for the mean stress effects quite satisfactorily. Predicted fatigue life using this damage parameter correlated fairly well with the experimental life within a factor of 3. Moreover, the fatigue damage parameter indicated the inferior life in the low-cycle regime and superior life in the high-cycle regime for the composite, compared to the unreinforced matrix alloy.     

Low‐cycle fatigue life behaviour of BS 460B and BS B500B steel reinforcing bars

This paper investigates the low‐cycle fatigue resistance of BS 460B and BS B500B steel reinforcing bars and proposes models for predicting their fatigue life based on plastic‐strain (?_ap) and total‐strain (?_a) amplitudes. Constant‐amplitude, strain‐controlled low‐cycle fatigue tests were carried out on these bars under cyclic load with a frequency of 0.05 Hz. The maximum applied axial strain amplitude (?_s,max) ranges from 3 to 10% with zero and non‐zero mean strains. The strain ratios (R = ?_s,min/?_s,max) used are R =?1, ?0.5 and 0. Hysteresis loops were recorded and plastic and total strain amplitudes were related to the number of reversals (2N_f) to fatigue failure and models for predicting the number of reversals to fatigue failure were proposed. It is concluded that the predicted fatigue life of these bars is very accurate when compared with the measured experimental fatigue life results for wide range of values of strain ratios. It is also observed that based on plastic‐strain amplitude, BS B500B consistently has a longer life (higher number of cycles to failure) than those of BS 460B for all R values; however, at low plastic‐strain amplitudes they tend to behave similarly, irrespective of R value. Other observations and conclusions were also drawn.     

New model for the indirect determination of the tensile stress–strain curve of concrete by means of the Brazilian test

On the basis of the results from an experimental campaign and using simple expressions, a model for the indirect determination of the tensile stress?Cstrain curve of concrete by means of a splitting tensile test (Brazilian test) is proposed. By testing complete specimens as well as specimens cut along the loading plane it was possible to determine the equivalent tensile strength component produced in the cylinder subjected to diametral compression. The model made it possible to reproduce adequately the behavior observed in tests carried out with both cylindrical and cubic specimens of materials such as concrete, mortar and rock. This model, if complemented with a more extensive experimental campaign, would provide an expression for the determination of the tensile stress?Cstrain curve of several concretes or quasi-fragile materials.     

High-temperature behaviour of IN 738 LC under isothermal and thermo-mechanical cyclic loading

The temperature dependence of the cyclic behavior of IN 738 LC was studied. Cyclic iso- and non-isothermal tests were performed with proportional and non-proportional tension/torsion strain paths. It was shown that maximum and minimum stress values measured in isothermal strain controlled tests correspond quite well with results of non-isothermal tests. Thermal-mechanical constitutive equations based on the viscoplastic Chaboche model were used to describe the non-isothermal stress-strain behavior.     

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.     

Shrinkage stress in concrete under dry–wet cycles: an example with concrete column

This paper focuses on the simulation of shrinkage stress in concrete structures under dry–wet environments. In the modeling, an integrative model for autogenous and drying shrinkage predictions of concrete under dry–wet cycles is introduced first. Second, a model taking both cement hydration and moisture diffusion into account synchronously is used to calculate the distribution of interior humidity in concrete. Using the above two models, the distributions of shrinkage strain and stress in concrete columns made by normal and high strength concrete respectively under dry–wet cycles are calculated. The model results show that shrinkage gradient along the radial direction of the column from the center to outer surface increases with age as the outer circumference suffers to dry. The maximum and minimum shrinkage occur at the outer surface and the center of the column, respectively, under drying condition. As wetting starts, the shrinkage strain decreases with increase of interior humidity. The closer to the wetting face, the higher the humidity and the lower the shrinkage strain, as well as the lower the shrinkage stress. As results of the dry–wet cycles acting on the outer circumference of the column, cyclic stress status is developed within the area close to the outer surface of the column. The depth of the influencing zone of dry–wet cyclic action is influenced by concrete strength and dry–wet regime. For low strength concrete, relatively deeper influencing zone is expected compared with that of high strength concrete. The models are verified by concrete-steel composite ring tests and a good agreement between model and test results is found.     

Towards improved ODS steels: A comparative high‐temperature low‐cycle fatigue study

Within the frame of this work, the mechanical behaviour of a bimodal ferritic 12Cr‐ODS steel as well as of a ferritic‐martensitic 9Cr‐ODS steel under alternating load conditions was investigated. In general, strain‐controlled low‐cycle fatigue tests at 550°C and 650°C revealed similar cyclic stress response. At elevated temperatures, the two steels manifest transitional stages, ie, cyclic softening and/or hardening corresponding to the small fraction of the cyclic life, which is followed by a linear cyclic softening stage that occupies the major fraction of the cyclic life until failure. However, it is clearly seen that the presence of the nano‐sized oxide particles is certainly beneficial, as the degree of cyclic softening is significantly reduced compared with non‐ODS steels. Besides, it is found that both applied strain amplitude and testing temperature show a strong influence on the cyclic stress response. It is observed that the degree of linear cyclic softening in both steels increases with increasing strain amplitude and decreasing test temperature. The effect of temperature on inelastic strain and hence lifetime becomes more pronounced with decreasing applied strain amplitude. When analysing the lifetime behaviour of both ODS steels in terms of inelastic strain energy calculations, it is found that comparable inelastic strain energies lead to similar lifetimes at 550°C. At 650°C, however, the higher inelastic strain energies of 12Cr‐ODS steel result in significant lower lifetimes compared with those of the 9Cr‐ODS steel. The strong degradation of the cyclic properties of the 12Cr‐ODS steel is obviously linked to the fact that the initial hardening response appears significantly more pronounced at 650°C than at 550°C. Finally, the obtained results depict that the 9Cr‐ODS steel offers higher number of cycles to failure at 650°C, compared with other novel ODS steels described in literature.     

Ermüdungsverhalten von normalisiertem 42CrMo4 unter Torsionsbeanspruchung bei Raumtemperatur

Room Temperature Fatigue Behaviour of a Normalized Steel SAE 4140 in Torsion Cyclic deformation behaviour of a normalized steel SAE 4140 in shear strain-controlled torsion is characterized by cyclic softening and cyclic hardening. If mean shear stresses are superimposed to an alternating shear stress, cycle-dependent creep occurs, and the number of cycles to failure decreases. In shear strain-controlled torsional loading, mean stresses are observed to relax nearly to zero within a few cycles. Fatigue life is not influenced by mean shear strains.     

Modelling Residual Strains During Cycling of Ti–Ni and Ti–Ni–Cu Shape Memory Alloys in a Pseudoelastic Range of Behaviour Conditions

Abstract: Pseudoelastic behaviour of three types of Ti–Ni shape memory alloys in a pseudoelastic state has been studied under conditions of maximum strain‐ and maximum stress‐controlled cycling. Experimental results proved that residual deformation after unloading increases with the number of cycles; however, critical stress for the induction of martensite and the energy dissipated in one cycle decline during cycling. A higher critical stress for slip, and more intense cyclic dislocation hardening promoted by greater maximum deformation and greater maximum applied stresses, generally reduce the rate at which residual elongation grows with the number of cycles, and tend to stabilise the cyclic stress‐elongation diagrams. The small magnitude of critical stress for slip in low‐nickel alloys, and also cyclic strain hardening, induce greater internal stresses and a more marked decrease in critical stress for the induction of martensite as cycling progresses. Detailed analysis of plastic deformation propagation in cyclically loaded specimen helped develop a model of dependence of residual elongation on the number of cycles. This model enables identification of three main factors that govern the magnitude of residual elongation: one residual plastic elongation caused by dislocation hardening after the alloy is heat treated, and two cyclic strain hardening parameters describing how residual elongation grows with number of cycles, and how this residual elongation is reduced, as cycles increase, by the rising critical stress level for slip. The model has proved to yield very close agreement with experimental findings.     

Ratcheting assessment of steel alloys under uniaxial loading: a parametric model versus hardening rule of Bower

This study intends to compare ratcheting response of 42CrMo, 1020, SA333 and SS304 steel alloys over uniaxial stress cycles evaluated by a parametric ratcheting model and Bower's hardening rule. The parametric ratcheting equation was formulated to describe triphasic stages of ratcheting deformation over stress cycles. Mechanistic parameters of mean stress, stress amplitude, material properties and cyclic softening/hardening response of materials were employed to calibrate parametric equation. Based on the framework of cyclic plasticity theory, the modified Armstrong–Frederick nonlinear hardening rule of Bower was employed to assess ratcheting response of steel alloys under uniaxial stress cycles. Bower's model was chosen mainly due to simplicity of the model and its lower number of constants required to predict ratcheting strain over stress cycles as compared with other hardening rules. Ratcheting strain values predicted by Bower's model showed good agreements over stage I of stress cycles as compared with experimental values of ratcheting strain. Beyond of stage I stress cycles, Bower ratcheting strain rate stayed constant resulting in an arrest in ratcheting process. The predicted ratcheting strains based on the parametric equation were found in good agreements over three stages of ratcheting as compared with those of experimentally obtained.     

Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity

The fatigue-life of a polycrystalline superalloy under symmetrical cyclic strain controlled loading at a temperature of 650 °C is investigated by numerical simulations on the micro-level, focusing on the inhomogeneous evolution of plastic deformation in a polycrystalline aggregate. A methodology (Zhang et al., 2011, 2013) to predict the low-cycle fatigue life by micro-level simulations along with statistical analysis is applied following the steps: (1) A statistically representative volume element (RVE) consisting of a number of crystal grains is constructed by Voronoi tessellation. Stresses and plastic strains are calculated by a crystal plasticity model including nonlinear kinematic hardening. (2) The RVE is subjected to repeated symmetric tensile-compressive loading. (3) The inhomogeneous stress and strain fields are statistically analyzed during the load cycles. (4) Failure by LCF is strain controlled and occurs if either of the quantities, standard deviation of longitudinal strain in tensile direction, maximum or statistical average of first principal strains in the RVE at the tension peak of cyclic loading reaches a respective critical value. (5) Using the present methodology, a family of failure curves for fatigue lives under different strain amplitudes can be predicted by varying the critical values. Finally, appropriate critical values can be identified by a respective cyclic experiment with only one strain amplitude.