Tension-compression Loading Research Articles

Microscale based prediction of matrix crack initiation in UD composite plies subjected to multiaxial fatigue for all stress ratios and load levels

A criterion is developed which predicts matrix fatigue crack initiation for Uni-Directional (UD) composite plies subjected to multiaxial fatigue load at all stress-ratio's: Tension-Tension, Compression-Compression and Tension-Compression. This research is based on physical observations of matrix damage types and their respective driving forces. Existing fatigue prediction formulations, that partly succeed in predicting fatigue life to initiation, are investigated for their key attributes which are subsequently combined in a coherent way. The framework requires 7 material parameters: 4 for Tension-Tension load, 2 for Compression-Compression load and 1 to take into account the accelerated occurrence of damage under Tension-Compression load. The material parameters can be calibrated from only 7 crack initiation S-N curves. 5 experimental datasets, a variety of the two most common reinforcing fibres and matrix (Carbon and Glass fibres combined with an epoxy or PEEK resin), are selected for a thorough verification and validation of the criterion. The agreement of the prediction with experiment is, remarkably, excellent for Glass/Epoxy, good for Carbon/Epoxy and reasonable for Carbon/PEEK. This new framework establishes a solid base for further developments to predict matrix crack initiation and the inclusion of other failure types such as fibre kinking.

Investigation of different influences on the fatigue behaviour of industrial rubbers

Load conditions used typically for fatigue life investigations can differ strongly from the conditions for real rubber products. For example, the frequency of the laboratory measurements is increased and the product load curve is simplified to a sine. In this paper, industrial rubber blends (SBR/BR/NR blends) under tension–compression load are used. First, the influence of a higher frequency (5 Hz) compared to the product relevant frequency (1 Hz) is investigated. A higher frequency does not influence the fatigue life but certainly the sample temperature and material behaviour. This is further investigated by varying the ambient temperature for 1 Hz measurements and the strain rate. Second, a non-sinusoidal wave form depicting the product loading case is selected. The load oscillates between tension and compression with dwell periods in every cycle. The results are comparable to those of a sine wave with the same frequency.

Low-cycle fatigue strength of 10GN2MFA steel with a single-layer corrosion-resisting coating produced by electroslag strip cladding

The method of testing the uniform single-layer corrosion resisting coating, produced by electroslag strip cladding on 10GN2MFA steel, on the resistance to low-cycle fatigue strength using special specimens is described. Tests were carried out at a temperature of 20 °C with the symmetric axial tension–compression loading cycle (Re = –1) with the given amplitude of the parent and cladding metal. The tests were carried out in the strain amplitude range εa = 0.28–0.8%, the number of cycles to the initiation of a crack was Ni = 340–16,000 cycles, loading frequency f = (0.25–2.0). The area of formation of the cracks was recorded in the experiments. In most cases, the cracks formed in the heat-affected zone in the vicinity of the fusion line and propagated in both the parent and deposited metal. The results show that in the range of low-cycle fatigue for the investigated 10GN2MFA steel with a deposited layer, the calculation coefficient of the decrease of the cyclic strength of the metal with a deposited layer in relation to the fatigue curve for the carbon and alloyed steel with 0.8 ≤ σ0.2/σB ≤ 0.9, the value φS = 0.68 should be used in the calculations.

Stress corrosion cracking and corrosion fatigue characterisation of MgZn1Ca0.3 (ZX10) in a simulated physiological environment

Magnesium (Mg) alloys have attracted great attention as potential materials for biodegradable implants. It is essential that an implant material possesses adequate resistance to cracking/fracture under the simultaneous actions of corrosion and mechanical stresses, i.e., stress corrosion cracking (SCC) and/or corrosion fatigue (CF). This study investigates the deformation behaviour of a newly developed high-strength low-alloy Mg alloy, MgZn1Ca0.3 (ZX10), processed at two different extrusion temperatures of 325 and 400°C (named E325 and E400, respectively), under slow strain tensile and cyclic tension-compression loadings in air and modified simulated body fluid (m-SBF). Extrusion resulted in a bimodal grain size distribution with recrystallised grain sizes of 1.2 μm ± 0.8 μm and 7 ± 5 μm for E325 and E400, respectively. E325 possessed superior tensile and fatigue properties to E400 when tested in air. This is mainly attributed to a grain-boundary strengthening mechanism. However, both E325 and E400 were found to be susceptible to SCC at a strain rate of 3.1×10−7s−1 in m-SBF. Moreover, both E325 and E400 showed similar fatigue strength when tested in m-SBF. This is explained on the basis of crack initiation from localised corrosion following tests in m-SBF.

Microstructure damage evolution associated with cyclic deformation for extruded AZ31B magnesium alloy

Fatigue damage evolution of extruded AZ31B magnesium (Mg) alloy is investigated under strain-controlled tension-compression loading along the extrusion direction at various strain amplitudes, and the different cyclic deformation behaviors are observed. At the strain amplitude of 2%, the tensile peak stress displays significant cyclic softening, whereas the compressive peak stress shows consistent cyclic hardening. At 1%, moderate cyclic hardening is observed at both the tensile peak and compressive peak stresses. At 0.5%, the tensile peak stress presents stable cyclic hardening, whereas the compressive peak stress almost keeps constant. The microstructure morphologies associated with the cyclic deformation are analyzed by scanning electronic microscope (SEM). The degree of deformation twins is evaluated by analyzing X-ray diffraction (XRD) using a normalized parameter λ. The results show the fatigue crack initiation modes and its propagation modes are dependent on the strain amplitude. At 2%, grain boundary (GB) cracking and triple joint cracking are detected after 1st loading cycle. At 1%, fatigue crack initiates at grain boundary (GB cracking), twin boundary (TB cracking) and triple joint of three neighboring grains. Both grain boundary induced (GB-induced) intergranular and persistent slip band induced (PSB-induced) transgranular propagation modes play an important role in the early-stage crack growth. At 0.5%, crack initiation modes are similar to that at 1%, but GB-induced intergranular propagation mode dominates the early-stage crack growth. The effects of the microstructure (texture, grain size and uniformity) on the fatigue damage behavior are discussed.

Identification of Kinematic Hardening Material Parameters for Martensitic Steel Sheets

The identification of the material models which are used in the finite element analysis for the forming operation and springback are very important in terms of accurate predictions. The aim of this paper is to characterize both the anisotropy and the hardening of the ultra-high strength steel such as martensitic steel (MS steel) in order to identify material parameters of constitutive equation, which able to reproduce the mechanical behavior. Uniaxial tensile tests were carried out for characterizing the anisotropic plastic behavior of the MS steel. Cyclic tests under tension-compression load were also carried out for characterizing the Bauschinger effect during reverse deformation. Yoshida-Uemori hardening model associated with orthotropic yield criterion Hill’s 1948 is used to represent the in-plane mechanical behavior of the martensitic steel. The resented results show a very good agreement between model predictions and experiments: flow stresses during loading and reverse loading are well reproduced.

Biaxial tension–compression strength behaviour of UHPFRC in-plane elements

Ultra-high-performance fibre-reinforced concrete (UHPFRC) panel-shaped elements subjected to compression–tension loading are tested to investigate their in-plane structural behaviour under biaxial stress. Tension-stiffening and compression-softening ultra-high-performance concrete (UHPC) behaviours are analysed with and without fibre, based on the test results from 30 specimens subjected to various transverse tensile strains. The tension-stiffening bond factor of UHPC with fibre is found to be about twice that of UHPC without fibre. The compressive strength of a UHPC panel subjected to transverse tensile loading is decreased by 50 % without fibre and 30 % when the fibre is in the elastic range of the reinforcing bars. Sequential loading of biaxial stress onto UHPC is appropriate for determining the limited lower boundary for the reduction of compressive strength that characterises the transverse tensile effects of fibre reinforcement. In addition to the biaxial behaviour of the UHPC panel, the failure envelope of UHPC with and without fibre is suggested schematically by considering the existing references, and a failure envelope is proposed. The entire analytical investigation and proposed failure criteria will allow for the efficient optimisation of the geometries of UHPFRC structures.

On the feasibility of partial slip reversal and de-twinning during the cyclic loading of TWIP steel

A recently modified Elasto-Plastic Self-Consistent (EPSC) model which empirically accounts for both intergranular and intragranular back stresses has been successfully used to simulate the cyclic (tension-compression) loading behaviour of an Fe-24Mn-3Al-2Si-1Ni-0.06C TWinning Induced Plasticity (TWIP) steel between strain limits of ±1%. Lattice strain measurements acquired via in-situ neutron diffraction were used to further validate the modelling results. An improved prediction of the pronounced Bauschinger effect during unloading is achieved when the reversibility of partial slip in the 〈112〉 direction is accounted for. This result indicates a potential contribution of the stress-induced separation of partial dislocations to the observed early yielding at the low strain levels employed in this study. It also raises the possibility that de-twinning events could be operative during load reversal.

Gradient-type modeling of the effects of plastic recovery and surface passivation in thin films

The elasto-plastic responses of thin films subjected to cyclic tension-compression loading and bending are studied, with a focus on Bauschinger and size effects. For this purpose, a model is established by incorporating plastic recovery into the strain gradient plasticity theory we proposed recently. Elastic and plastic parts of strain and strain gradient, which are determined by the elasto-plastic decomposition according to the associative rule, are assumed to have a degree of material-dependent reversibility. Based on the above assumption, a dislocation reversibility-dependent rule is built to describe evolutions of different deformation components under cyclic loadings. Furthermore, a simple strategy is provided to implement the passivated boundary effects by introducing a gradual change to relevant material parameters in the yield function. Based on this theory, both bulge and bending tests under cyclic loading conditions are investigated. By comparing the present predictions with the existing experimental data, it is found that the yield function is able to exhibit the size effect, the Bauschinger effect, the influence of surface passivation and the hysteresis-loop phenomenon. Thus, the proposed model is deemed helpful in studying plastic deformations of micron-scale films.

High cycle torsional fatigue properties of 17-4PH stainless steel

Sensitivity to small defects under torsional fatigue loading condition is examined in the high cycle fatigue regime. Fatigue crack initiation and small crack growth behaviors were observed during fatigue testing and fractographic investigations were performed. The results are compared to the data obtained in the uniaxial fatigue tests, which allows the effect of biaxial stresses on the surface of material to be discussed. Finally, an approach for predicting the fatigue limit of 17-4PH stainless steel under torsional and tension-compression fatigue loadings is presented.

Using unit cell simulations to investigate fracture due to compression–tension loading

Experiments regarding impact against X65 steel pipes show that fracture typically arises in areas subjected to large compressive strains before tension. Fracture surfaces from these areas are brittle in character despite the material exhibiting ductile behaviour elsewhere. Smooth and notched tensile material tests always produced ductile fracture through nucleation, growth and coalescence of voids. The ductile-to-brittle transition seen in the component tests was however recreated in notched axisymmetric material tests, where the specimens were compressed to various levels of plastic strain before being stretched to failure. Increasing compression before tension showed a decrease in strain to fracture as hypothesised, and an increase in the cleavage surface fraction. In an attempt to gain a better understanding of this behaviour, unit cell simulations subjected to tension only and compression–tension loading were carried out. As well as exploring different chosen stress triaxialities, global analyses of the material tests were used to provide an average stress triaxiality for the axisymmetric unit cell simulations. These global simulations were able to represent the material tests with good accuracy. In tension tests where the stress triaxiality was fairly constant (notched tests), the unit cell analyses were able to predict a strain to coalescence within reasonable margin compared with the experimental values. Unit cell simulations including the compressive phase show that the higher the magnitude of the stress triaxiality is during compression, the higher the local stress in the cell, which in turn may trigger cleavage fracture.

Surface flaws behavior under tension, bending and biaxial cyclic loading

Fatigue surface crack growth and in-plane and out-of-plane constraint effects are studied through experiments and computations for the aluminum alloy D16T. A tension/bending central notched plate and cruciform specimens under different biaxial loadings with external semi-elliptical surface cracks are studied. The variation of the fatigue crack growth rate and surface crack paths is studied under cyclic tension, bending and biaxial tension–compression loading. For the experimental surface crack paths in the tested specimens, the T-stress, out-of-plane Tz factor, local triaxiality parameter h and the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of the In-integral are calculated as a function of the aspect ratio by finite element analysis to characterize the constraint effects along the semi-elliptical crack front. The plastic stress intensity factor approach is applied to the fatigue crack growth on the free surface, as well as at the deepest point of the semi-elliptical surface crack front, of the tested tension/bending plate and cruciform specimens. From the results, characteristics of the fatigue surface crack growth rate as a function of the loading conditions are established.

Experimental study of crack growth under non-proportional loading along with first modeling attempts

For various configurations examined in a series of fatigue experiments on thin-walled tubes under tension and torsion, the experimental results (crack path and crack growth life) are measured. Additionally, crack opening and closure was observed applying surface deformation field measurements using digital image correlation. Due to the high applied load amplitudes considerable cyclic plastic deformation occurred especially ahead of the crack front. The material’s cyclic plastic behavior was measured and a convenient plasticity model was used for its description. In the finite element analyses, actual geometries of cracked structures have been modeled. The non-linear nature of the cyclic deformation has been taken into account by applying the cyclic plasticity model. Plasticity-induced crack closure is captured by a contact formulation, actually however only for simple tension–compression loading. For the latter case, closure-free cyclic J-integrals were calculated. The crack growth rates measured in the experiments correlate well with the numerically determined cyclic J-integrals for the simple mode I case.

A continuum anisotropic damage model with unilateral effect

Abstract. A continuum damage mechanics model has been derived within the framework of irreversible thermodynamics with internal variables in order to describe the behaviour of quasi-brittle materials under various loading paths. The anisotropic character induced by the progressive material degradation is explicitly taken into account, and the Helmholtz free energy is a scalar function of the basic invariants of the second order strain and damage tensors. The elastic response varies depending on the closed or open configuration of defects. The constitutive laws derived within the framework of irreversible thermodynamics theory display a dissymmetry as well as unilateral effects under tensile and compressive loading conditions. This approach verifies continuity and uniqueness of the potential energy. An application to uniaxial tension-compression loading shows a good adequacy with experimental results when available, and realistic evolutions for computed stresses and strains otherwise.

Improved Nonlinear Cyclic Stress–Strain Model for Reinforcing Bars Including Buckling Effect and Experimental Verification

Buckling is an important nonlinear behavior of steel reinforcing bars subjected to repeated compression and tension strain reversals, which significantly affects the overall cyclic behavior of reinforced concrete (RC) elements and impairs their load-carrying and energy-dissipation capacities during strong earthquakes. The accuracy of numerical assessment of the seismic performance of RC elements can be much improved if the buckling effect is effectively included in the stress–strain model of reinforcing bars. In this paper, modified Gomes–Appleton cyclic steel stress–strain relationship intended for improved accuracy is presented, which is suitable for inclusion in programs based on Opensees platform for the nonlinear analysis of RC elements. The modification is developed to improve the simulation accuracy of the inelastic buckling stress–strain path by a simplified model based on the equilibrium of a plastic mechanism of buckled bar consisting of four plastic hinges. Then an adjustment coefficient is introduced to further modify the developed buckled bar stress–strain model. A comparison of the numerical simulated results with experimental results of 36 steel bars subjected to reversed tension-compression loading is performed to verify the accuracy and effectiveness of the proposed model.

Surface and through thickness crack growth in cruciform specimens subjected to biaxial loading

Fatigue surface crack growth are studied through experiments and computations for aluminum alloy D16T. Subjects for studies are cruciform specimens under different biaxial loading with external semi-elliptical surface crack. The variation of fatigue crack growth rate and surface crack paths behaviour was studied under cyclic uniaxial tension, equal biaxial tension and biaxial tension-compression loading. For the experimental surface crack paths in tested specimens the T-stress, the out-of-plane TZ factor, the local triaxiality parameter h and the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of In-integral were calculated as a function of aspect ratio by finite element analysis to characterization of the constraint effects along semi-elliptical crack front. Both elastic and plastic stress intensity factor approach was applied to the fatigue crack growth on the free surface of the cruciform specimens as well as in the deepest point of the semi-elliptical surface crack front. As result principal particularities of the fatigue surface crack growth rate as a function of loading conditions were established. The experimental and numerical results of the present study provide an opportunity to explore the suggestion that crack growth rate may be represented by the plastic stress intensity factor, rather than the magnitude of the elastic SIF alone.

Fatigue Performance of Laser Additive Manufactured Ti–6Al–4V in Very High Cycle Fatigue Regime up to 109 Cycles

Additive manufacturing technologies are in the process of establishing themselves as an alternative production technology to conventional manufacturing such as casting or milling. Especially laser additive manufacturing (LAM) enables the production of metallic parts with mechanical properties comparable to conventionally manufactured components. Due to the high geometrical freedom in LAM the technology enables the production of ultra-light weight designs and therefore gains increasing importance in aircraft and space industry. The high quality standards of these industries demand predictability of material properties for static and dynamic load cases. However, fatigue properties especially in the very high cycle fatigue regime until 109 cycles have not been sufficiently determined yet. Therefore this paper presents an analysis of fatigue properties of laser additive manufactured Ti-6Al-4V under cyclic tension-tension until 107 cycles and tension-compression load until 109 cycles. For the analysis of laser additive manufactured titanium alloy Ti-6Al-4V Woehler fatigue tests under tension-tension and tension-compression were carried out in the high cycle and very high cycle fatigue regime. Specimens in stress-relieved as well as hot-isostatic-pressed conditions were analyzed regarding crack initiation site, mean stress sensitivity and overall fatigue performance. The determined fatigue properties show values in the range of conventionally manufactured Ti-6Al-4V with particularly good performance for hot-isostatic-pressed additive-manufactured material. For all conditions the results show no conventional fatigue limit but a constant increase in fatigue life with decreasing loads. No effects of test frequency on life span could be determined. However, independently of testing principle, a shift of crack initiation from surface to internal initiation could be observed with increasing cycles to failure.

Different Applications of the Gleeble® Thermal–Mechanical Simulator in Material Testing, Technology Optimization, and Process Modeling

Abstract In this study, our aim is to present a compilation about different applications of the Gleeble® thermal–mechanical system concerning material testing, characterization of advanced thermomechanically controlled processes and modeling the multiaxial forging technique. The first topic aims to provide an accurate input dataset for developing an energy-based fatigue model for 15Ch2MFA reactor steel. The process characterization intends to quantify the effect of deformation-stored energy on the start temperature and kinetic of the austenite–ferrite transformation. The modeling topic purposes to predict the evolution of the flow stress and the hardening behavior during processing a mild steel by multiaxial forging. All of these experiments were carried out on a Gleeble® 3800 simulator using different mobile conversion units. The fatigue tests were conducted under uniaxial tension–compression loading with in-phase thermal cycles. To develop a new energy-based low-cycle fatigue (LCF) model, the energy balance of the plastic deformation was also investigated. Moreover, the evolution of the microstructure was observed by transmission electron microscopy (TEM) studies at the different stages of the nominal failure lifetime. The deformation-induced ferrite transformation (DIFT) effect was characterized by a high-resolution dilatometer under uniaxial hot compression tests. An advanced simulation program and experimental setup have been developed for the calculation of reliable flow curve from the data, sampled during the multiaxial forging simulation. Concerning the thermomechanical fatigue tests, the experimental results correspond to the Coffin–Manson curve. Furthermore, temperature evolution measurements were performed to provide input data to the calculation of the plastic strain energy partition converted to heat. Finally, the effect of the deformation stored energy on the start and finish temperature of austenite transformation was obtained and quantified.

Low cycle fatigue behavior of a 10Cr–2W–Mo–3Co–NbV steel

Low cycle fatigue (LCF) behavior of a 10% Cr–2% W–0.7% Mo–3% Co–NbV steel with 0.008wt.% B and 0.003wt.% N additions was studied under fully reversed tension–compression loading as a function of temperature from 20 to 650°С and constant strain amplitude from ±0.2% to ±1.0%. The effect of LCF on the steel’s microstructure was analyzed. It was demonstrated that the 10% Cr steel was susceptible to cyclic softening, even at room temperature, and could not withstand reversed plasticity. The fatigue lifetime curves at all temperatures could be described by the Basquin–Manson–Coffin relationship. The cyclic softening effect was attributed to the coarsening of the laths, primarily at 20 and 500°C, and the transformation of the tempered martensite lath structure (TMLS) to a subgrain structure at 600 and 650°C. In addition, a decrease in the dislocation density occurred under LCF. Increasing the reversed plasticity with the total strain amplitude accelerated the evolution of the TMLS and thus promoted cyclic softening. The propagation of fatigue cracks during Stage II was also facilitated by increasing the contribution of plastic deformation processes to the total strain amplitude, which led to a drop in the fatigue life with an increase in the constant strain amplitude.

Anisomorphic constant fatigue life diagrams of constant probability of failure and prediction of P–S–N curves for unidirectional carbon/epoxy laminates

The effect of stress ratio on statistical distribution of fatigue life of a unidirectional carbon/epoxy composite has been examined. Furthermore, a method for efficiently predicting a family of S–N curves with probability of failure as the parameter for any stress ratio of constant amplitude loading has been developed. For this purpose, fatigue life data are first collected at each of different stress levels for tension–tension (TT), tension–compression (TC) and compression–compression (CC) fatigue loadings, respectively. The experimental results show that the scatter in fatigue life tends to become larger in order of TT, TC and CC loading. Lognormal distribution is used to quantify the statistics of the static tensile and compressive strength data and the fatigue life data for each of different stress levels and stress ratios. It is found that lognormal distribution is applicable approximately not only to the static strength data in tension and compression, but also to the fatigue life data for each of different stress levels and stress ratios. The parameters of the distribution of fatigue life are shown to be dependent on the stress ratio of fatigue loading. The experimental P–S–N curves are established for each of different stress ratios using the distributions fitted to the static strength and fatigue life data. Then, a method for constructing the anisomorphic constant fatigue life (CFL) diagrams of constant probability of failure is developed. The proposed probabilistic anisomorphic CFL diagram approach allows not only accurately predicting the P–S–N curves for different stress ratios, but also adequately describing the stress-ratio dependent scatter in fatigue life of the unidirectional composite.