Effect of strain rate on the tension–compression asymmetric responses of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si

An experimental investigation is performed to explore the tension–compression asymmetry of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si alloy over a wide range of strain rates. A split Hopkinson bar technique is used to obtain the dynamic stress–strain responses under uniaxial tension and compression loading conditions. Experimental results indicate that the alloy is a rate sensitive material. Both tension yield strength and compression yield strength increase with increasing strain rate. The mechanical responses of the alloy have the tension–compression asymmetry. The values of yield strength and subsequent flow stress in compression are much higher than that in tension. The yield strength is more sensitive to change with strain rate in tension than compression. The difference of the yield strength between tension and compression increases with the increase of strain rate. The tensile specimen is broken in a manner of ductile fracture presenting characteristic dimples, while the compressive specimen fails in a manner of localized shearing failure.     

The plastic deformation of oriented polypropylene: tensile and compressive yield criteria

Polypropylene, oriented by hot-drawing, has been deformed in tension and compression, at various angles to the initial draw direction. The behaviour in tension is described well by a three-part criterion of the type applied in previous work to fibre-composites [8, 9]. The Hill-von Mises treatment of the plasticity of an anisotropic metal, which has been previously extended successfully to polymers [1], can be applied to describe the tensile yield stresses but is unsatisfactory in its prediction of the form of the strain in polypropylene. In compression, the variation of the yield stress with the angle of the stress axis is much less than in tension, and the modes of deformation are different from those operating in tension at the same angle. In particular, compressing at right angles to the molecules produces shear in a direction normal to the molecules (transverse shear). The critical stress for transverse shear in compression is approximately the same as the critical stress for shear parallel to the molecules in tension.     

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.     

MICROMECHANICAL STRESSES DURING LOW CYCLE FATIGUE OF AN OVERAGED Al-Mg-Si ALLOY

The evolution of micromechanical stresses; flow stress, kinematic back stress and isotropic drag stress during room temperature, uniaxial, low cycle fatigue of overaged Al-Mg-Si alloy is studied. Continuous real-time measurements of yield stresses are made in cyclic tension and compression, within the hysteresis loop, at different strain amplitudes, strain rates and number of cycles. An asymmetry is observed in flow stress and kinematic back stress in tension and compression half cycles during cyclic hardening and saturation. The phenomenological results have been analyzed in terms of kinematic and isotropic type microstructural mechanisms.     

A notch strain calculation of a notched specimen under axial-torsion loadings

In this paper, a notch analysis model is presented for the numerical prediction of multiaxial strains of a notched 1070 steel specimen under combined axial and torsion loadings. The proposed model is based on the notion of a structural yield surface and uses a small-strain cyclic plasticity model to describe stress–strain relations. A notch load–strain curve is calculated with Neuber’s rule and incremental nonlinear finite element analysis. The presented model is applied to simulate the notch root deformations of a circumferentially notched specimen under cyclic tension–compression–torsion loading histories. The model predictions are evaluated with strain measurements at the notch root of the specimen in a comprehensive set of cyclic tests. The computed strain loops were in accord with experimental data and matched qualitatively with measured shear–axial strain histories irrespective of loading path of the test. In proportional balanced torsion-axial loading, the nonlinear shear strain–axial strain loops were calculated properly. The modeling errors were determined to be a function of the loading path shape, and compared to shear strains, axial strain predictions were more accurate.     

Quasistatisches Verformungsverhalten reiner Sintereisen im Temperaturbereich von –184 bis 600°C

Quasistatic deformation behaviour of pure sintered iron in the temperature range between –184 and 600°C The deformation behaviour of pure sintered iron materials with densities between 6,88 und 7,57 g/cm³ was investigated in tension tests in the temperature range of –184 and 600°C. Supplementary compression tests were carried out at 20°C. Increasing density leads to increasing material resistances and ductility properties due to the increase of the bearing specimen cross sections as well as due to smaller numbers of pores, more spherical pores with smaller notch effects and smaller numbers of mircocracks, which are initiated at pores. After equal deformations, due to pore closing effects and the impediment of crack initation, the flow stresses of compressively deformed specimens are larger than those of tensily deformed. The deformation behaviour is dominated at low temperatures by thermal activated glide processes of dislocations and their interactions with short range obstacles, at middle temperatures by dynamic strain ageing due to elastic interactions of glide dislocations and diffusing carbon atoms and at high temperatures by recovery controlled dislocation creep processes.     

Mechanical characterization of Co/Cu multilayered nanowires

The mechanical deformation properties of (110) Co/Cu multilayered nanowires were studied by Molecular Dynamics under uniaxial tensile and compressive stresses. The potential of the immiscible CoCu system was modeled by a second-moment tight-binding approximation. Stress-strain curves at different conditions were obtained and the elastic modulus and yield stress were analyzed. Both magnitudes are approximately independent of the strain rate, except at high values. They decrease linearly with increasing temperature. Below a volume-to-surface-area ratio, their values drastically increase and diverge from the bulk values. If the thickness of the Cu sublayers increases, the Young's modulus and yield stress decrease, although in a different way. The elastic modulus decreases linearly and the yield stress falls steeply whenever Cu is present in the nanowire, since the lattice distortion takes place firstly and fundamentally in Cu sublayers. The change in the axial stress at the interface is little significant on average and rather localized. Unlike, the transverse stress has a non-uniform distribution along the Cu sublayer, especially at the yield point. The Young's modulus and yield stress are larger in tension than in compression. Under tensile stress, nanowires slip via partial dislocation nucleation and propagation. Unlike, compressive deformation of nanowires takes place via both partial and full dislocations.     

三向碳碳材料的非线性双模量力学模型和强度准则

为了在平面十字形试件上实现拉拉、拉压、压压和拉剪的两向应力状态试验,设计并制造了双向加力装置和大剪切变形的测量仪,在试验基础上建立了三向碳碳材料的应力应变关系和强度准则.用纤维所受应力的正负号来决定两个方向里正应力异号时的模量(E_拉≠E_压)应该用哪一个.假定应变势存在,以保证弹性系数矩阵的对称性.非线性来自剪切变形.强度准则用二次型函数拟合实验数据,理论预报与实验吻合.      

Fatigue crack growth for a surface crack in a round bar under multi-axial loading condition

In this paper, the fatigue life, surface crack extension direction and crack growth rate in an elastic bar with a circular cross section are determined through experiments under cyclic torsion with axial static and cyclic tension/compression loading. The effects of the loading type, loading value and stress ratio on the crack growth behaviour are discussed. The results show that, under pure fatigue torsion loading, the crack extension direction is almost the same whatever the value of torsion loading. Under fatigue torsion with cyclic tension loading, it is found that the crack extension direction is mainly determined by the alternating parts of the stresses and is almost independent of the average parts of the stresses, whereas the fatigue life is obviously dependent on the average stress.     

Shear band spacing in gradient-dependent thermoviscoplastic materials

We study thermomechanical deformations of a viscoplastic body deformed in simple shear. The strain gradients are taken as independent kinematic variables and the corresponding higher order stresses are included in the balance laws, and the equation for the yield surface. Three different functional relationships, the power law, and those proposed by Wright and Batra, and Johnson and Cook are used to relate the effective strain rate to the effective stress and temperature. Effects of strain hardening of the material and elastic deformations are neglected. The homogeneous solution of the problem is perturbed and the stability of the problem linear in the perturbation variables is studied. Following Wright and Ockendon's postulate that the wavelength whose initial growth rate is maximum determines the minimum spacing between adjacent shear bands, the shear band spacing is computed. It is found that the minimum shear band spacing is very sensitive to the thermal softening coefficient/exponent, the material characteristic length and the nominal strain-rate. Approximate analytical expressions for the critical wave length for heat conducting nonpolar materials and locally adiabatic deformations of gradient dependent materials are also derived.     

Thermo-mechanical FE model with memory effect for 304L austenitic stainless steel presenting microstructure gradient

The main purpose of this study is to determine, via a three dimensions Finite Element analysis (FE), the stress and strain fields at the inner surface of a tubular specimen submitted to thermo-mechanical fatigue. To investigate the surface finish effect on fatigue behavior at this inner surface, mechanical tests were carried out on real size tubular specimens under various thermal loadings. X-ray measurements, Transmission Electron Microscopy observations and micro-hardness tests performed at and under the inner surface of the specimen before testing, revealed residual internal stresses and a large dislocation microstructure gradient in correlation with hardening gradients due to machining. A memory effect, bound to the pre-hardening gradient, was introduced into an elasto–visco-plastic model in order to determine the stress and strain fields at the inner surface. The temperature evolution on the inner surface of the tubular specimen was first computed via a thermo-elastic model and then used for our thermo-mechanical simulations. Identification of the thermo-mechanical model parameters was based on the experimental stabilized cyclic tension–compression tests performed at 20 °C and 300 °C. A good agreement was obtained between numerical stabilized traction–compression cycle curves (with and without pre-straining) and experimental ones. This three dimensional simulation gave access to the evolution of the axial and tangential internal stresses and local strains during the tests. Numerical results showed: a decreasing of the tangential stress and stabilization after 40 cycles, whereas the axial stress showed weaker decreasing with the number of cycles. The results also pointed out a ratcheting and a slightly nonproportional loading at the inner surface. The computed mean stress and strain values of the stabilized cycle being far from the initial ones, they could be used to get the safety margins of standard design related to fatigue, as well as to get accurate loading conditions needed for the use of more advanced fatigue analysis and criteria.     

Fracture of plasma-sprayed thick thermal barrier coatings under multiaxial stress states

Failure behaviour of free‐standing plasma‐sprayed coatings was investigated under combined axial and shear loading. Thin‐walled tubular specimens were loaded with various combinations of tension/compression and torsion. This allows the failure surface to be established for loading situations where the two principal stresses are of opposite signs. Specimens failed in one of the two modes, a tensile failure perpendicular to the maximum principal stress or a compression shear failure through the thickness. Failure data were adequately described by the maximum principal stress theory. Stress–strain curves fall within a single scatter band depending on the failure mode. In situ deformation tests showed that the mechanism was microcrack closing and sliding in compression and microcrack opening, coalescence and the development of new microcracks in tension.     

Plastic deformation and creep damage evaluations of type 316 austenitic stainless steels by EBSD

The inspection method of plastic and/or creep deformations has been required as the quantitative damage estimation procedure for structural components especially used in electric power plants. In this study, the method using electron backscatter diffraction (EBSD) was applied to the deformation and damage evaluation of austenitic stainless steels strained by tension or compression at room temperature and also tested in creep at high temperature. It was found that the value of Grain Average Misorientation (GAM) which showed the average misorientation for the whole observed area including over several dozen grains, was a very useful parameter for quantifying the microstructural change as either the plastic or creep strain increased. The unique linear correlation was obtained between GAM and plastic strain in tension and compression. For creep damage evaluation, the difference of grain average misorientation from the value of the unstrained specimen (ΔGAM) showed an excellent correlation with the inelastic strain below strain at which the tertiary creep began.     

Evaluation of low cycle fatigue life in AZ31 magnesium alloy

Magnesium alloys are attracting engineers for their practical application to structural components. Here fatigue properties, which is essential for structural use, have been examined on extruded AZ31 bar under uniaxial cyclic loading by both strain and stress controlled conditions. Adding fatigue tests with mean stresses under stress controlling conditions, fatigue life evaluation method has been discussed along with the analysis of cyclic stress–strain behavior. The specimen is easy to yield in compression by twinning. This leads to the asymmetric hysteresis curves. It also tends to deform quasi-elastically during unloading from compression; this makes the plastic strain amplitude smaller to the maximum one in the hysteresis curve. These asymmetric features fairly disappear at half-life in the stress controlled tests. The fatigue lives and deformation characteristics can be expressed nicely by Manson–Coffin type equation. On the contrary, the strain controlled tests retain the asymmetry till the end and produce tensile mean stresses. The fatigue lives are unsuccessfully evaluated by the above equation. Various mean stress correction models for cubic metals are not operative in magnesium alloys. A new model has been devised adding a correction term of −σ_m/2E to the above mentioned Manson–Coffin type equation. Strain controlled test, as it retains pyriform shape till the end, could be evaluated more accurately with the maximum plastic strain amplitude in the hysteresis curve.     

RATCHETTING IN PRESSURISED PIPES

Abstract— The plastic deformation of thin-walled cylinders has been experimentally examined for the loading conditions of ±1% axial strain with hoop stresses of approximately 0, 1/4, 1/2 and 3/4 of the initial uniaxial yield stress.
Two materials similar to those used in the pipework of PWR nuclear plant in the U.K. have been tested, namely 304S11 stainless steel and En6 low-carbon steel. The results of the tests were to be compared with the allowable stresses and deformations specified in the ASME Boiler and Pressure Vessel Code, Section III. The code specifies that a prescribed combination of primary stresses must not exceed 1.5 S _m, where S _m is a stress value defined for each material.
The results indicate that the limit of 1.5 S _m is excessively low for both materials and that in particular, the stainless steel could tolerate 5 S _m. Although the En6 steel is more prone to ratchetting than the stainless steel, the results suggest that it too could tolerate a higher primary stress than the code allows. Both materials are shown to satisfy the proposed ASME ratchet strain limit of 5% hoop strain after 10 cycles of ±1% axial strain range, for any value of internal pressure.     

Monotonic and Cyclic Deformations of Case‐Hardened Steels Including Residual Stress Effects

Abstract: Monotonic and cyclic deformations of case‐hardened steel specimens under axial loading were investigated experimentally and analytically. A finite element (FE) model for the case‐hardened specimens was constructed to study multiaxial stresses due to different plastic flow behaviour between the case and the core, as well as to evaluate residual stress relaxation and redistribution subsequent to cyclic loading. The multiaxial stress is shown to increase the effective stress on the surface, and, therefore, unfavourable to yielding or fatigue crack nucleation. The residual stresses are shown to relax or redistribute, even in the elastic‐behaving region, when any part of a case‐hardened specimen or component undergoes plastic deformation. Multi‐layer models were used to analyse and predict monotonic and cyclic deformation behaviours of the case‐hardened specimen based on the core and case material properties, and the results are compared with the experimental as well as FE model results. The predicted monotonic stress–strain curves were close to the experimental curves, but the predicted cyclic stress–strain curves were higher than the experimental curves.     

The plastic yield behaviour of polymethylmethacrylate

The yield behaviour of an amorphous glassy polymer has been investigated under a system of combined stress in an attempt to define a criterion for yield. Sheets of polymethylmethacrylate were compressed in plane strain and the compressive yield stress was determined as a function of the tension applied in the plane of the sheet. The compressive yield stress was found to decrease with applied tension more rapidly than would be expected if the shear yield stress of the material were independent of pressure. The results have been analysed in terms of a Coulomb yield criterion where the shear yield stress is expressed as a constant plus a friction term proportional to the pressure on the shear plane. Birefringent shear zones were observed in the deformed region after the load was removed and these zones were inclined at 52.9° to the plane of the sheet. It was found that if the stresses at yield were expressed as nominal stresses then the inclination of the shear planes predicted by the yield stress data coincided with the observed inclination. It also appears that it may be possible to define a fracture criterion in terms of the applied stress system.     

Comparative assessment of stress transfer efficiency in tension and compression

Raman spectroscopy is used to get an insight into the microstructural aspects of the compressional behaviour of carbon fibre composites. This is done by a comparative assessment of the stress transfer efficiency in tension and compression in single-fibre discontinuous model geometries. It was found that the axial stress is transferred in the fibre through the generation of shear stresses at the interface. The mechanism of stress transfer is independent of the loading mode. Furthermore, the values of maximum interfacial shear stress are a function of the applied strain for both tension and compression loading. Significant differences were found, however, in the mode of failure of the two systems. In tension, interfacial failure initiates from the fibre ends at relatively high applied strains and the stress transfer efficiency is affected by the onset of matrix plasticity. On the other hand, in compression, deterioration of the stress transfer efficiency occurs prior to any noticeable interfacial failure at the fibre ends due to fibre collapse at low strains. Finally, it is worth noting that in compression, the fibre fragments remain in contact, and thus can still bear load.     

Einfluß von last- und verformungsgesteuerten mehrachsigen Beanspruchungen auf die Anrißlebensdauer

Influence of load- and deformation-controlled multiaxial tests on fatigue life to crack initiation Generally, areas of components with notches or geometrical transitions are critical because of the resulting stress/strain concentrations. In these areas due to the stress-gradients and constraint local deformations are displacement controlled even if the material's yield stress is exceeded, as long as the deformations are below the structural yield point. Therefore, load controlled tests in the elasto-plastic region with unnotched specimens from ductile materials under combined axial loading and torsion are not suitable for the interpretation of component's behaviour because of uncontrolled local deformations. Thus, the influence of multiaxial stress/strain states on the fatigue behaviour of a component under elasto-plastic deformations can be determined reliably with unnotched specimens only by deformation controlled tests, if cyclic creep is not expected in critical areas.