FE analysis of residual stress relaxation in a girth-welded duplex stainless steel pipe under cyclic loading

This study intends to characterize the residual stress relaxation in a girth-welded duplex stainless steel pipe exposed to cyclic loading. FE thermal simulation of the girth welding process is first performed to identify the weld-induced residual stresses. 3-D elastic–plastic FE analyses incorporated with the cyclic plasticity constitutive model which can describe the cyclic stress relaxation are next carried out to evaluate reconstruction of the residual stresses under cyclic mechanical loading. The results unveils that considerable reduction of the residual stresses in and around the girth weld occur even after the initial few loading cycles and degree of the stress relaxation is dependent on the magnitude of applied cyclic loading.     

A model for the Mullins effect during multicyclic equibiaxial loading

In this paper, we derive a model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress–strain cycles with increasing values of the maximum strain, specializing to equibiaxial loading. Since the carbon-filled rubber vulcanizate is initially isotropic, we can show that following initial equibiaxial loading the material becomes transversely isotropic with preferred direction orthogonal to the plane defined by the equibiaxial loading. This is an example of strain-induced anisotropy. Accordingly, we derive nonlinear transversely isotropic models for the elastic response, stress relaxation, residual strain and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These ideas are then combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed includes the effects of hysteresis, stress relaxation, residual strain and creep of residual strain. The model is found to compare extremely well with experimental data.     

Rate-dependent mechanical behavior of VHB 4910 elastomer

This article experimentally studied the large nonlinear deformation of VHB 4910 elastomer by uniaxial tests. The study reveals that the monotonic tensile stress-strain, hysteresis, cyclic stress softening, and multistep stress relaxation of this elastomer exhibit rate-sensitivity. Toughness, failure stress, and failure strain are shown to vary with strain rate. Maximum cyclic stress, hysteresis loss, residual strains in cyclic loading-unloading, and stress relaxation in multistep relaxation tests are also shown to be rate-sensitive. The analytical models are also proposed to predict certain important parameters, such as dissipative work, cyclic stress softening, cyclic residual strain, and relaxation stress in different states of deformation.     

岩石可释放应变能及耗散能的实验研究

地下岩石结构的变形破坏是能量耗散与能量释放的综合结果.岩石结构内部储藏的可释放应变能和己耗散能的计算,涉及到在当时工况下岩石的卸荷弹性模量和泊松比,并与加载速度与载荷水平有关.该文在不同加载速度及不同载荷水平下,对岩石试件进行了单压加卸载实验,得到了卸荷弹性模量与泊松比、可释放应变能与耗散能的变化规律;进行了SHPB动...     

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.     

Stress softening of elastomers in hydrostatic tension

Summary. This study is concerned with inelastic effects of non-reinforcing carbon-black filled elastomers when subjected to periodic hydrostatic loading-unloading cycles in tension. During cyclic testing of sufficient magnitude, a critical state may be reached where microcavities suddenly grow inside the rubber, possibly initiated at sites of internal imperfections. As a result of cavitation damage the tensile bulk modulus in the natural configuration is reduced. A series of hydrostatic tension tests are performed at room temperature to provide new insight into the progressive deterioration of the bulk stiffness. We define dilatational stress softening as a phenomenon where the hydrostatic stress on unloading and subsequent submaximal reloading is significantly less than that on primary loading for the same volumetric strain. Dilatational stress softening during initial loading cycles and the permanent volumetric change upon unloading are not accounted for when the mechanical properties are represented in terms of a strain-energy function, i.e. if the material is modelled as hyperelastic. In this paper a constitutive model is derived to include the progressive reduction of the bulk stiffness and the permanent volumetric change of carbon-black filled elastomers subjected to quasi–static loading. The basis of the model is the theory of pseudo-elasticity, which including a softening variable modifies the dilatational strain energy function. An acceptable correspondence between the theory and the data is obtained.     

Low-cycle fatigue of 1Cr–18Ni–9Ti stainless steel and related weld metal under axial, torsional and 90° out-of-phase loading

The fatigue behaviour of base metal and weld joints of 1Cr–18Ni–9Ti stainless steel has been studied under uniaxial, torsional and 90° out‐of‐phase loading. A significant degree of additional hardening is found for both base metal and weld metal under 90° out‐of‐phase loading. Both base metal and weld metal have the same cyclic stable stress–strain relationship under torsional cyclic loading and 90° out‐of‐phase cyclic loading. Base metal exhibits higher cyclic stress than weld metal under uniaxial loading, and Young's modulus and yield stress of weld metal are smaller than those of base metal. Weld metal exhibited lower fatigue resistance than base metal under uniaxial and torsional loading, but no significant difference was found between the two materials under 90° out‐of‐phase loading. A large scatter of fatigue life is observed for weld metal, perhaps because of heterogeneity of the microstructure. The Wang–Brown (WB) damage parameter and the Fatemi–Socie (FS) damage parameter, both based on the shear critical plane approach, were evaluated relative to the fatigue data obtained.     

Mechanical properties of concrete to cyclic uniaxial tensile loading using variable waveforms

The mechanical properties of concrete under cyclic tensile loading using square waveform, sine waveform and ramp waveform are studied. The experiments are performed on a closed-loop electro-hydraulic servo-controlled material testing system (MTS). The axial strain, dissipated energy per loading cycle, the damage evolution law and deformation modulus are mainly studied. The results show that the three-stage evolution law of axial strain and damage variable of concrete under ramp waveform and sine waveform are more obvious than those under the square waveform. The dissipated energy changes at different stages of fatigue life. At the beginning and end of the fatigue life, the rate of dissipated energy is higher than that at the medium stage of the fatigue time, which is attributed to the formation of cracks. The evolution of deformation modulus of concrete subjected to cyclic tensile loading using three loading waveforms also shows three stages: fast increase in the damage—increase at a slow constant rate—and accelerated increase in damage until failure.     

Micromechanical interactions in a superduplex stainless steel subjected to low cycle fatigue loading

Micromechanical interactions in an austenitic‐ferritic SAF 2507 steel under lowcycle fatigue loading was studied by experiment and simulation. Neutron diffraction measurements of residual lattice strains were made on specimens unloaded from different cyclic deformation stages, namely cyclic hardening, softening and saturation. With self‐consistent modelling, the micromechanical behaviour of the constituent phases was studied for the first loading cycle. The evolution of the residual lattice strain distributions with cyclic loading and the development of phase stresses have been analysed with respect to the initial residual stress field and the different mechanical properties of the constituent phases.     

Characteristics of energy storage and dissipation in TiNi shape memory alloy

The characteristics of energy storage and dissipation in TiNi shape memory alloys were investigated experimentally based on the superelastic properties under various thermomechanical loading conditions. The influence of strain rate, cyclic loading and temperature-controlled condition on the characteristics of energy storage and dissipation of the material was investigated. Temperature on the surface of the material was observed and the influence of variation in temperature on the characteristics was clarified. The results obtained can be summarized as follows. (1) In the case of low strain rate, the stress plateaus appear on the stress-strain curves due to the martensitic transformation and the reverse transformation during loading and unloading. In the case of high strain rate, the slopes of the stress–strain curves are steep in the phase-transformation regions during loading and unloading. The recoverable strain energy per unit volume increases in proportion to temperature, but the dissipated work per unit volume depends slightly on temperature. In the case of low strain rate, the recoverable strain energy and dissipated work do not depend on both strain rate and the temperature-controlled condition. (2) In the case of high strain rate, while the recoverable strain energy density decreases and dissipated work density increases in proportion to strain rate under the temperature-controlled condition, the recoverable strain energy density increases and dissipated work density decreases under the temperature-uncontrolled condition. In the case of the temperature-uncontrolled condition, temperature varies significantly due to the martensitic transformation and therefore the characteristics of energy storage and dissipation differ from these under the temperature-controlled condition. (3) In the case of cyclic loading, both the recoverable strain energy and dissipated work decrease in the early 20 cycles, but change slightly thereafter. (4) The influence of strain rate, cyclic loading and the environment on the characteristics of energy storage and dissipation is important to be considered in the design of shape memory alloy elements.     

Modeling of Nonlinear Mechanical Behavior for 3D Needled C/C-SiC Composites Under Tensile Load

This paper established a macroscopic constitutive model to describe the nonlinear stress–strain behavior of 3D needled C/C-SiC composites under tensile load. Extensive on- and off-axis tensile tests were performed to investigate the macroscopic mechanical behavior and damage characteristics of the composites. The nonlinear mechanical behavior of the material was mainly induced by matrix tensile cracking and fiber/matrix debonding. Permanent deformations and secant modulus degradation were observed in cyclic loading-unloading tests. The nonlinear stress–strain relationship of the material could be described macroscopically by plasticity deformation and stiffness degradation. In the proposed model, we employed a plasticity theory with associated plastic flow rule to describe the evolution of plastic strains. A novel damage variable was also introduced to characterize the stiffness degradation of the material. The damage evolution law was derived from the statistical distribution of material strength. Parameters of the proposed model can be determined from off-axis tensile tests. Stress–strain curves predicted by this model showed reasonable agreement with experimental results.     

Lateral behavior of concrete under uniaxial compressive cyclic loading

In reinforced concrete structures under seismic loading, concrete is subjected to compressive cyclic stress. Although cyclic stress–strain response has been described before, the cyclic behavior of strains in the direction orthogonal to loading has not been characterized yet. Such behavior can be of great importance for evaluating the efficiency of the confinement under cyclic loading. For this purpose an experimental program on cylindrical specimens of concrete strength from 35 to 80 MPa subjected to uniaxial cyclic compression was carried out. Stress versus longitudinal and lateral strains curves have been obtained both for the hardening and softening branches under monotonic and cyclic loading. Governing parameters of the lateral behavior are identified and correlated to describe the response of the lateral strain. Additionally, an analytical model to obtain the lateral deformations of concrete under cyclic uniaxial compression has been formulated and verified experimentally. Finally, some examples are presented in order to illustrate the applicability of the proposed model and its possible incorporation into a 3D constitutive cyclic model.     

INTERACTIONS BETWEEN TIME AND CYCLIC DEFORMATION PROCESSES IN A NIMONIC ALLOY

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

Thermomechanics of nanocrystalline nickel under high pressure-temperature conditions

We present a comparative study of thermomechanical properties of nano-polycrystalline nickel (nano-Ni) and micrometer-polycrystalline nickel (micron-Ni) by in situ high pressure-temperature (P-T) diffraction experiments. The yield strength of 2.35 GPa for the nano-Ni measured under high-pressure triaxial compression is more than three times that of the micron-Ni value. Contrary to tensile experiments of uniaxial loading, we observe significant work-hardening for the nano-Ni in high-pressure plastic deformation stage, whereas the micron-Ni experiences minor high-pressure work-softening and considerable energy dissipation into heat. The significantly reduced energy dissipation for the nano-Ni during the loading-unloading cycle indicates that the nanostructured materials can endure much greater mechanical fatigue in cyclic loadings. The nano-Ni exhibits steady grain growth during bulk plastic deformation at high-pressure loading, and drastic stress reduction and grain growth occur during the high P-T cycle. Our experiments utilized novel approaches to comparatively study micro- and nanostructured materials revealing recoverability of elastic/plastic deformations, strain corrections by diffraction elasticity ratio, and identifying dominances of stress relaxation, grain growth, and intrinsic residual stresses. The results should be of considerable interest to the fields of materials science, condensed matter, and computational physics.     

Experimental and theoretical studies on thermo‐mechanical fatigue test for aluminium cast alloy

Evaluation of the thermo‐mechanical behaviour and prediction of the service life of cast aluminium alloys are important for the design of automobile engine cylinder heads. In this study, cast Al alloy specimens are extracted from cylinder heads and subjected to in‐phase thermo‐mechanical cyclic loading. The hysteresis curves related to stress and strain were recorded under the individual thermo‐mechanical loading conditions. The number cycles to failure corresponding to multiple mechanical strain and temperature ranges were obtained. It is found that the cyclic stress amplitude decreases and the cyclic softening rate increases with increasing maximum temperature rise. A modified fatigue‐creep model based on energy conservation has been developed for prediction of the fatigue life of cylinder heads. The proposed method shows good agreement with the well‐established Ostergren model and low standard deviations. In summary, the proposed method described in this study provides an option for prediction of the thermo‐mechanical behaviour of metals.     

Fatigue life evaluation of tension‐compression asymmetric material using local stress–strain method

In this paper, the low‐cycle fatigue characteristics of cold‐drawn steel were investigated under strain‐controlled uniaxial fatigue load. Cyclic softening was observed throughout fatigue life except for the initial relatively short period which exhibited cyclic hardening. Positive mean stress was found under fully reversed strain loading, indicating that there was a significant cyclic asymmetry. A modified local stress–strain method was proposed to estimate fatigue life of notched tension‐compression asymmetric material. In order to verify this method, fatigue experiments on two kinds of notched specimens with different notch radius were carried out under constant and block load spectrum. It was found that the modified local stress–strain method was more accurate than the traditional ones, the maximum relative error between predicted and experimental fatigue life was less than 6%.     

Creep–Fatigue Interaction of Inconel 718 Manufactured by Electron Beam Melting

Electron beam melting of Ni-base superalloy Inconel 718 allows producing a columnar-grained microstructure with a pronounced texture, which offers exceptional resistance against high-temperature loading with severe creep–fatigue interaction arising in components of aircraft jet engines. This study considers the deformation, damage, and lifetime behavior of electron-beam-melted Inconel 718 under in-phase thermomechanical fatigue loading with varying amounts of creep–fatigue interaction. Strain-controlled thermomechanical fatigue tests with equal-ramp cycles, slow–fast cycles, and dwell time cycles are conducted in the temperature range from 300 to 650 °C. Results show that both dwell time and slow–fast cycles promote intergranular cracking, gradual tensile stress relaxation, as well as precipitate dissolution and coarsening giving rise to cyclic softening. The interplay of these mechanisms leads to increased lifetimes in both dwell time and slow–fast tests compared to equal ramp tests at higher strain amplitudes. Conversely, at lower mechanical strain amplitudes, the opposite is observed. A comparison with results of conventional Inconel 718 indicates that the electron-beam-melted material exhibits superior resistance against strain-controlled loading at elevated temperatures such as thermomechanical fatigue.     

Fatigue crack growth model for constant amplitude loading

A fatigue crack growth model under constant amplitude loading has been developed considering energy balance during growth of the crack. The plastic energy dissipated during growth of a crack within cyclic plastic zone and area below cyclic stress–strain curve was used in the energy balance. The near crack tip elastic–plastic stress and strain were calculated on the basis of Hutchinson, Rice and Rosengren (HRR) formulations. Fatigue crack growth rate in linear and near threshold region of da/dN versus ΔK curve can be determined on the basis of the proposed model in terms of low cycle fatigue (LCF) properties determined on smooth specimen. The predictions of the model have been compared with the experimental and theoretical results available in the literature using mechanical and fatigue properties. The model compares well in the threshold and intermediate region of the da/dN versus ΔK curve for wide range of material tested.     

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.     

Effects of mechanical heterogeneity on the tensile and fatigue behaviours in a laser-arc hybrid welded aluminium alloy joint

The effects of mechanical heterogeneity on the tensile and high cycle fatigue (10⁴–10⁷ cycles) properties were investigated for laser-arc hybrid welded aluminium alloy joints. Tensile–tensile cyclic loading with a stress ratio of 0.1 was applied in a direction perpendicular to the weld direction for up to 10⁷ cycles. The local mechanical properties in the tensile test and the accumulated plastic strain in the fatigue test throughout the weld’s different regions were characterized using a digital image correlation technique. The tensile results indicated heterogeneous tensile properties throughout the different regions of the aluminium welded joint, and the heat affected zone was the weakest region in which the strain localized. In the fatigue test, the accumulated plastic strain evolutions in different subzones of the weld were analyzed, and slip bands could be clearly observed in the heat affected zone. A transition of fatigue failure locations from the heat affected zone caused by accumulated plastic strain to the fusion zone induced by fatigue crack at pores could be observed under different cyclic stress levels. The welding porosity in the fusion zone significantly influences the high cycle fatigue behaviour.