Combined Tension-torsion Loading Research Articles

A probabilistic model for the high cycle fatigue behaviour of cast aluminium alloys subject to complex loads

This article is dedicated to the high cycle fatigue behaviour of cast hypo-eutectic Al–Si alloys and in particular the AlSi7Cu05Mg03 alloy. In a vast experimental campaign undertaken to investigate the fatigue damage mechanisms operating in this alloy, subject to complex loading conditions, it was shown that two different coexisting fatigue damage mechanisms occur in this materials, depending on the presence of different microstructural heterogeneities (i.e. micro-shrinkage pores, Si particles, Fe-rich intermetallic phases, DAS of the Al-matrix, etc.). In order to take into account both of these damage mechanisms, a probabilistic approach using the weakest link concept is introduced to model the competition between the two mechanisms. This approach leads naturally to a probabilistic Kitagawa type diagram, which explains the relationship between the fatigue behaviour of the material and the different casting processes or post-treatments (e.g. gravity casting and HIP).It is shown that the sensitivity to the different loading modes (i.e. uniaxial with and without mean stress, torsion and equibiaxial tension) depends on the microstructural heterogeneities responsible for crack initiation. For a porosity-free alloy, the predictions are very good for combined tension–torsion loading modes. When pores are present and control the fatigue strength, the predictions are very satisfactory for the uniaxial loads with different R-ratios and slightly conservative for multiaxial loads (i.e. torsion and equibiaxial tension). Never-the-less, they are much better than the predictions of the Dang Van criterion [1].

Fatigue life prediction of rubber-like materials under multiaxial loading using a continuum damage mechanics approach: Effects of two-blocks loading and R ratio

This contribution presents a continuum damage mechanics model for the high-cycle fatigue life prediction of rubber-like materials. The proposed model is an extension of that proposed by Wang et al. (2002) for multiaxial loadings. The damage strain energy release rate is first derived from a generalized Ogden strain energy density and then from the cracking energy density. A new multiaxial fatigue predictor is proposed and presented in its most general form with the aim of being applicable to all hyperelastic materials. The effects of variable amplitude and mean stretch are explicitly accounted for in the damage evolution law. The fatigue damage behavior of a carbon-filled styrene–butadiene rubber is experimentally investigated under tension, torsion and combined tension–torsion loadings both in constant and variable amplitudes, including the effects of different R ratios (i.e. different minimum and maximum stretches). The proposed model, which requires few damage parameters to be identified, is used to predict the number of cycles to failure and, a satisfactory agreement between predicted values and experimental data is clearly highlighted for the different loading paths.

Damage Mechanics in G/E Tubes under Tension-Torsion Cyclic Loading

In this work, multiaxial fatigue tests results on [0F/90U,3/0F] glass/epoxy tubes are discussed. Specimens are subjected to combined tension-torsion loadings, resulting in the stress components σ2 andτ12 in the 90° layers of the tubes. The effect of shear stress on damage mechanics has been investigated and a strong influence on both damage onset and propagation has been observed. SEM investigation of fracture surfaces shows the dependence of damage modes, at the microscopic scale, on the multiaxiality condition. Comparison with previous results on tubes with different lay-ups ([904], [0F/90U,3]) shows the strong influence of the constraining 0° fabric layers on the damage onset and propagation.

Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part II: A very high work hardening aluminum alloy (annealed 1100 Al)

Results are presented on the evolution of subsequent yield surfaces with finite deformation in a very high work hardening annealed 1100 aluminum alloy. In Part I [Khan, A.S., Kazmi, R., Stoughton, T., Pandey, A., 2009a. Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part 1: a very low work hardening aluminum alloy (Al-6061–T6511) 25, 1611–1625.] of this paper, similar results are presented for a very low work hardening aluminum alloy. Those results were very different from the present ones, and all the results were for proportional loading paths. The subsequent yield surfaces are determined in tension, free end torsion and combined tension–torsion proportional and non-proportional loading paths, using 10 με deviation from linearity definition of yield. Yield surfaces are also determined after linear, bi-linear, and non-linear unloading paths after finite deformation under tension, free end torsion, and combined tension–torsion loading. The initial yield surface is closer to the von-Mises surface and the subsequent yield surfaces show distortion, expansion, positive cross-effect, and “nose” in the loading direction. Additionally, the subsequent yield surfaces after non-proportional loading paths show shrinkage and compounded distortion. The yield surfaces after unloading depict strong anisotropy, positive cross-effect and exhibits different proportion of distortion in each loading conditions. The Young’s and shear modulus decrease with plastic deformation and this decrease is much less than those reported in the published literature.

Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part-I: A very low work hardening aluminum alloy (Al6061-T6511)

In the present study, the initial and subsequent yield surfaces in Al 6061-T6511, based on 10 με deviation from linearity definition of yield, are presented. The subsequent yield surfaces are determined during tension, free end torsion, and combined tension–torsion proportional loading paths after reaching different levels of strains. The yield surfaces are also obtained after linear, bi-linear and non-linear unloading paths after finite plastic deformation. The initial yield surface is very close to the von-Mises yield surface and the subsequent yield surfaces undergo translation and distortion. In the case of this low work hardening material, the size of the yield surfaces is smaller and negative cross-effect is observed with finite plastic deformation. The subsequent yield have a usual “nose” in the loading direction and flattened shape in the reverse loading direction; the observed nose is more dominant in the case of tension and combined tension–torsion loading than in torsional loading. The size of the yield surfaces after unloading is smaller than the initial yield surface but larger than subsequent yield surfaces obtained during prior loading, show much smaller cross-effect, and the shape of these yield surfaces depends strongly on the loading and unloading paths. Elastic constants (Young’s and shear moduli) are also measured within each subsequent yield surfaces. Evolution of these constants with finite deformation is also presented. The decrease of the two moduli is found to be much smaller than reported earlier in tension by Cleveland and Ghosh [Cleveland, R.M., Ghosh, A.K., 2002. Inelastic effects on springback in metals. Int. J. Plast. 18, 769–785]. Part-II and III [ Khan, A.S., Pandey, A., Stoughton, T., 2009a. Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation, Part-II: a very high work hardening aluminum alloy (annealed 1100 Al). Int. J. Plast., accepted for publication; Khan, A.S., Pandey, A., Stoughton, T., 2009b. Evolution of subsequent yield surfaces and elastic moduli under tension–tension stress space with finite plastic deformation in aluminum alloys, Part-III. Int. J. Plast., accepted for Publication] of the papers will include experimental results on annealed 1100 Al (a very high work hardening material) and on both Al alloys (Al6061-T6511 and annealed 1100 Al) in tension- tension stress space, respectively. The results for both cases are quite different than the ones that are presented in this paper.

Experimental and numerical study of the superelastic behaviour on NiTi thin-walled tube under biaxial loading

A 3D thermo-mechanical constitutive model for the polycrystalline shape memory alloy (SMA) has been used to predict the superelastic response of the textured thin-walled NiTi tubes under combined tension–torsion loading. This model is based on the work of Lim et al. and Wang. Considering the difference of Young’s modulus between austenite and martensite phase, some formulas have been modified. The new developed model has been implemented into ABAQUS as UMAT. In order to validate the model, thin-walled tube has been tested under biaxial loading. From the comparison between the simulated and experimental results, it is found that the model is quite good in predicting the overall loading–unloading process of the SMA. Both the experimental and simulated results demonstrate the significant differences in the superelastic responses under different biaxial loading paths. For both biaxial loading paths, at relatively low level of tensile strain, the overall behaviour of the tubes is smooth. But with the increase of the tensile strain level, the equivalent stress–strain curves fluctuate. For torsion–tension loading program, corresponding to about 4% strain, stress decrease upon tensile loading and stress increase upon tensile unloading are observed due to the change of shear stresses. For Type II loading program (tension followed by torsion, unload in reverse order), a stress decrease upon loading and a stress increase upon unloading are observed but the corresponding strains become big with the increase of the tensile strain level. In addition, according to the simulated results, the rate of martensite formation under tensile loading is higher than that under shearing loading.

Mild steel (En8) rod tests under combined tension–torsion loading

This paper examines the results obtained from combined tension–torsion loading tests carried out on Mild steel (En8) specimen. The loading of the specimen was carried out in different modes: (i) maintaining tensile force or axial displacement constant and increasing torque or angle of twist; (ii) maintaining torque or angle of twist constant and increasing load or axial displacement. A finite element solution of the problem was obtained to gain further insight into the effects of the loading modes. The results from the finite element analysis (FEA) were validated against experimental results.

Fissuration en fatigue de plaques composites sollicitées en traction–torsion

This study deals with the fatigue cracking of an unidirectional glass-epoxy composite material under combined tension–torsion loadings. Notched samples with a rectangular cross section have been used. They contained an initial crack which simulates a defect of fabrication of the material. In order to obtain the crack propagation rate, fatigue tests with a constant tension load and a cyclic twist angle were performed. Numerical calculations by the finite element method were performed. A three-dimensional finite-element modell was used in order to evaluate the strain energy release rate and the crack mode repartition, i.e. the parts of mode I, mode II and mode III. Micrographic observations with the electron microscope have shown the mechanisms of the crack propagation. Only the mode I acts, the effects of mode II and III have been found negligible. The rate of the crack propagation has been expressed as a function of the variation of the mode I stress intensity factor and has been found to obey the Paris law. The results have been corroborated with results of mode I test using DCB specimens.

Mikrorissentstehung und Mikrorisswachstum in Aluminiumlegierungen bei zyklischer Beanspruchung– Werkstoffliche Untersuchung und Simulation

Gezeigt wird die Modellierung und die Simulation des Mikrorisswachstums unter schwingender Beanspruchung. Mikrostrukturelle Barrieren sowie der Spannungszustand spielen dabei eine essentielle Rolle. Der metallische Werkstoff setzt sich in der Simulation aus hexagonalen Körnern zusammen, wobei die kristallographische Orientierung in jedem Korn anders ist. Das Risswachstum erfolgt zunächst bestimmt durch die Schubspannung in stage I (microstructurally short cracks). Mit Annäherung der Rissspitze an eine Korngrenze verlangsamt sich das Risswachstum. Nach Erreichen einer spezifischen Risslänge erfolgt das Risswachstum im stage II, d. h. unter Normalspannungseinfluss (physically small crack). Das Modell wird auf den Werkstoff AlMgSi1 angewendet. Hohlzylinder dieses Werkstoffs werden durch Zug-Druck, Torsion und mehrachsig beansprucht. Das simulierte Risswachstum zeigt im Hinblick auf die Rissorientierung und die Häufigkeitsverteilung eine gute Übereinstimmung mit den im Experiment erzielten Ergebnissen. Microcrack Initiation and Microcrack Growth in Aluminium Alloys Subjected to Cyclic Loading – Material Analysis and Simulation In this paper a model designed to simulate the growth of microcracks under the influence of cyclic loading is presented. Considering fatigue crack growth microstructural barriers as well as the state of stress play an essential role. The polycristalline metal was modelled as an aggregate of hexagonal grains with each of the grains showing a different crystallographic orientation. The crack growth is initially dominated by shear stresses leading to microstructurally short cracks (stage I). As the tip of the microcrack approaches a grain boundary the crack growth rate decreases. The transition from stage I to stage II crack growth is also considered in the model as the crack reaches a specific length and continues to grow under the influence of normal stresses (physically short cracks). The model is applied to tubular specimens of the aluminum alloy AlMgSi1 which are subjected to tension and torsion as well as to combined tension-torsion loading cycles. In terms of the microcrack distribution as a function of their orientation the simulated crack growth behaviour reveals a close match with the experimental results.

404 SiCウィスカ強化Al合金の引張・ねじり位相差負荷条件下の腐食疲労破壊特性(GS-11 複合材料(2))

We describe an investigation into the fatigue fracture behaviour under combined tension-torsion loading of a SiC whisker-reinforced A6061 aluminium alloy fabricated by a squeeze casting process. Special attention was paid to the environmental effects on fatigue fracture behaviour. Tests were conducted on both the composite and its unreinforced matrix material, A6061-T6, under out-of-phase load-controlled conditions with a constant value of the combined stress ratio, α=τ_<max>/σ_<max> in a 3.5% NaCl solution at free corrosion potential. The fatigue strength in air of the unreinforced matrix material under out-of-phase combined loading was smaller than that under in-phase loading. For the composite, however, the fatigue strength under out-of-phase combined loading was higher than that under in-phase combined loading. As contrast with these, the corrosion fatigue strength of both the matrix and composite under out-of-phase combined loading was higher than that under in-phase combined loading.

CORROSION FATIGUE FRACTURE BEHAVIOUR OF A SiC WHISKER–ALUMINIUM MATRIX COMPOSITE UNDER COMBINED TENSION–TORSION LOADING

We describe an investigation into the fatigue fracture behaviour under combined tension–torsion loading of a SiC whisker‐reinforced A6061 aluminium alloy fabricated by a squeeze casting process. Special attention was paid to the environmental effects on fatigue fracture behaviour. Tests were conducted on both the composite and its unreinforced matrix material, A6061‐T6, under load‐controlled conditions with a constant value of the combined stress ratio, α = τmax /σmax in laboratory air or in a 3.5% NaCl solution at the free corrosion potential. The corrosion fatigue strength of both the matrix and composite was less in the solution than in air. The dominating mechanical factor that determined the fatigue strength in air was either the maximum principal stress or the von Mises‐type equivalent stress, depending on the combined stress ratio. However, in the 3.5% NaCl solution, the corrosion fatigue strength of both materials was determined by the maximum principal stress, irrespective of the combined stress ratio. In the case of the matrix material, crack initiation occurred by a brittle facet normal to the principal stress due to hydrogen embrittlement. However, in the composite material, the crack was initiated not at the brittle facet, but at a corrosion pit formed on the specimen surface. At the bottom of the pit, a crack normal to the principal stress was nucleated and propagated, resulting in final failure. Pitting corrosion was nucleated at an early stage of fatigue life, i.e. about 1% of total fatigue life. However, crack initiation at the bottom of a pit was close to the terminal stage, i.e. about 70% or more of total fatigue life. The dominating factor which determined crack initiation at a pit was the Mode I stress intensity factor obtained by assuming the pit to be a sharp crack. Initiation and propagation due to pitting corrosion and crack growth were closely examined, and the fatigue fracture mechanisms and influence of the 3.5% NaCl solution on fatigue strength of the composite and matrix under combined tension–torsion loading were examined in detail.

A study of nonlinear viscoelasticity of an unsaturated polyester resin. Part 2. 3D model

In the first part of this paper, a uniaxial nonlinear viscoelastic model has been established to describe the long-term creep behaviour of an unsaturated polyester resin. The model was based on Schapery's thermodynamics-based theory, and included effects of physical ageing. In the present (second) part, this model is extended into a general three-dimensional form. In the 3D-model a creep contraction ratio and an instantaneous elastic Poisson's ratio are introduced. By assuming both ratios constant, albeit different from each other for all load levels, a model is obtained which is able to describe the experimentally obtained creep-recovery curves very well. A numerical scheme for the developed constitutive equations is then established and the 3D theory is implemented into a finite element method (FEW package. In addition tests have been carried out in order to verify the theory. Tensile creep tests performed on plate-shaped specimen with a central circular hole were used to check the model calculations. In such a test plate a two-dimensional stress state exists close to the hole. Also creep and relaxation processes occur simultaneously during the test. A further validation of the model was carried out by loading unsaturated polyester thin-walled tubes under a combined tension-torsion loading. The comparison between the experimental data and the FEM calculations shows a good agreement. The good agreement obtained under biaxial stress fields leads to the conclusion that the uniaxial creep-recovery tests characterized model can be used to describe three-dimensional loading situations satisfactorily.

Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces

Combined tension and torsion experiments with thin wall specimens of Cu-Al-Zn-Mn polycrystalline shape memory alloy (SMA) were performed at temperatureT =A f + 25 K. The general stress-strain behaviors due to the thermoelastic martensitic transformation, induced by a combination of external forces of axial load and torque, were studied. It is shown that the progress of martensitic transformation (MT) at general stress conditions can be well considered as triggered and controlled by the supplied mechanical work (a kind of equivalent stress) in the first approximation. Pseudoelastic strains in proportional as well as nonproportional combined tension-torsion loadings were found fully reversible, provided that uniaxial strains were reversible. The axial strain can be controlled by the change of torque andvice versa due to the coupling among tension and torsion under stress, not only in forward transformation, but also in reverse transformation on unloading. The pseudoelastic strains of SMA polycrystal are path dependent but well reproducible along the same stress path. The evolution of macroscopic strain response of SMA polycrystal, subjected to the nonproportional pseudoelastic loading cycles with imposed stress path, was systematically investigated. The results bring qualitatively new information about the progress of the MT in SMA polycrystal, subjected to the general variations of external stress.

An experimental study on subsequent yield surface after finite shear prestraining

An equimodulus surface is introduced and the subsequent yield surface after large finite shear prestraining is experimentally investogated. Fully annealed, thin-walled copper tubular specimens were subjected to large torsional loading and partial unloading; strain gages were carefully mounted on the specimen after the application of pure shear loading. Specimens were then subjected to various combined tension-torsion loadings. Influences of he von Mises and Tresca equivalent offset strains on the subsequent yield surfaces are studied. On examining the experimental results reported in this article, it was found that the smaller the offset strains, the more distorted are the subsequent yield surfaces. At the torsional preloading point, a rounded corner was developed, whereas in the region opposite to the preloading point, the subsequent yield surface was flattened. When large von Mises offset strains were used, the corresponding subsequent yield surfaces passed through the von Mises loading surface. But this was not the case when Tresca offset strains were used. The subsequent yield surface determined by the back extrapolation method was almost completely outside the von Mises loading surface. On the other hand, the subsequent yield surface determined by the back extrapolation method was close to the Tresca loading surface. It is also found that the equimodulus surface is distorted and cannot simply be described by the combined kinematic and isotropic hardening rule.

On non-proportional infinitesimal plastic deformation after finite plastic prestraining and partial unloading

E xperimental data from combined tension-torsion loading of thin-walled tubes of annealed polycrystalline copper subjected to loading, partial unloading, and then loading in a different direction are presented. Special attention is focused on the direction of the plastic strain increment, experimental values of which are compared with predicted values from the Ziegler and Mroz kinematic hardening models, and endochronic theory. The back stress terms in the above mentioned three constitutive models are calculated using the entire deformation history of more than 10% strain in extension (or 15% in shear), followed by partial unloading, and then loading in torsion (or tension). Thus, the main objective of the study is to investigate the effect of finite deformation on subsequent infinitesimal deformation due to 180° and 90° changes in loading paths in the tension-torsion loading space. Among the three constitutive equations used for comparison, the Mroz model is shown to predict the direction of the plastic strain increment closest to the experimental results.

ニッケルクロムモリブデン鋼（ＳＮＣＭ４３９）のせん断強度のひずみ速度および温度依存性

The influence of strain rate and temperature on the flow stress of nickel chromium molybdenum steel (SNCM 439) was studied through experiments. In the experiments, thin walled tubular specimens of short gage length were loaded at strain rates of 70-103sec-1 in shear by using a torsional split Hopkinson bar apparatus, and loaded at strain rates of 10-4-10-1sec-1 by using a combined tension-torsion loading apparatus and an Instron testing machine. The experiments were performed in shear over the temperature range -185°C to 120°C.It is shown that the strain rate sensitivity of the yield point and of the flow stress in the region of small strain at -185°C and -60°C is remarkable, and that, below about -50°C, the influence of temperature on the flow stress reveal itself remarkably. It is confirmed that the experimental results obtained on the strain rate dependency and the temperature effect on the flow stress can be described fairly well with the practical constitutive equation for an elastic/viscoplastic body proposed by one of the authors. The values of the parameters contained in the constitutive equation are also presented.

FATIGUE DAMAGE IN 1045 STEEL UNDER CONSTANT AMPLITUDE BIAXIAL LOADING

The progressive nature of fatigue damage under multiaxial stress states has been investigated. Experiments were performed on thin‐wall tubular specimens of 1045 steel in tension, torsion and combined tension‐torsion loading. Two equivalent strain amplitudes, one in the high cycle fatigue (HCF) region and one in low cycle fatigue (LCF) region were employed in this study. Four recently proposed damage theories were evaluated. Crack depth was used as a damage parameter in comparing damage curves under different loading modes.Different types of crack systems were observed in the HCF and LCF regions. The damage curve obtained in tension loading can be used to evaluate the damage behavior under combined tension—torsion loading. The results of torsion loading show that torsional damage behavior is different from the above two loading modes.

Large deformation behavior of some thermoplastics

AbstractIn this experimental study the deformation behavior of two thermoplastics under uniaxial and biaxial loadings has been investigated. The experiments were conducted on thin walled tubular specimens of nylon‐6, a semicrystalline polymer, and polymethyimethacrylate (PMMA),:an amorphous polymer. These specimens were subjected to tension, torsion and combined tension‐torsion loadings until very large deformations were produced or specimen failure took place. The results are presented in the form of generalized stress‐generalized strain curves which are applicable to all types of loadings, provided the generalized stress is monotonically increasing. In addition, the results show that the generalized stress‐generalized strain relationship for nylon‐6 is parabolic in nature, whereas that for PMM A can be represented by a bilinear curve. This characterization of the response of the thermoplastics under a biaxial stress field can be used to obtain a more realistic stress interaction between fiber and matrix in composite materials, since until now all theoretical studies on this aspect have assumed an elastic or elastic‐perfectly plastic behavior of the matrix.

Craze initiation of glassy polymers under the action of crazing agent

AbstractThis paper deals with the formation of crazes that may be caused by an external load on glassy polymers wetted with kerosene. First, the orientation of crazes has been determined when applying a uniaxial tension to a specimen of cold‐rolled polyvinyl chloride sheet at various angles to the rolling direction. The critical stress for craze initiation in poly(methyl methacrylate) and polyvinyl chloride rods has been investigated under combined tension–torsion loading. It is shown that: (1) in an anisotropic, as well as an isotropic polymer, the direction of crazes is perpendicular to that of the maximum strain calculated by taking into account the internal stress due to rolling; and (2) under the action of a crazing agent, crazing may occur even under the pure torsional load, i.e., in the absence of dilatational stress.

An experimental study of incremental response functions in the totally plastic region

Experimental data are obtained from thin-walled tubes of annealed polycrystalline aluminum subjected to combined tension-torsion loadings. These data reveal that the plastic deformation in the totally plastic region can be described in terms of a path independent loading function and incremental response functions according to which the component of the plastic strain increment vector is decomposed into two parts: one is due to the expansion of the loading surface and the other is due to the change of the corresponding component of the stress vector and vanishes when the directions of stress and strain vectors coincide.