Tension-compression Conditions Research Articles

Multi-Dimensional Iterative Constitutive Model of Concrete under Complex Stress Conditions in Composite Structures

In composite structures or complex concrete members, some concrete bears multiple forces, called core concrete. The properties of the core concrete are variable under complex stress conditions, which will influence the structure performance analysis. Therefore, it is necessary to establish an accurate and theoretical constitutive model of concrete under complex stress conditions. The elastic–plastic properties of concrete in complex stress conditions were analyzed first. Then, the failure criterion of concrete in complex stress conditions was discussed to identify the key parameters. And the relationship between the stress–strain curve and failure criterion was analyzed through mathematical derivation. Finally, the multi-dimensional iterative constitutive model of concrete under complex stress conditions was established and verified. Based on the analysis results, the concrete under multi-axial stress conditions shows a spindle-shape stress envelope diagram. The failure criterion should be established by the analysis of concrete under high multi-axial compression conditions, tension–compression conditions, and shear–compression conditions. The plastic modulus is the key to reflecting the plastic strain development trend and the stress–strain relationship.

Усталостная прочность сварных соединений сталей 30ХГСА–40ХМФА, полученных ротационной сваркой трением

Rotary friction welding (RFW) is used in the production of drill pipes for solid mineral prospecting. The need for the creation of the lightened drill strings for high-speed diamond drilling of ultradeep wells dictates the necessity of a greater focus on the study of a weld zone and setting the RFW technological parameters. This paper presents the results of experimental studies of a welded joint of a drill pipe of the H standard size according to ISO 10097, made of the 30ХГСА (pipe body) and 40ХМФА (tool joint) steels under the cyclic loads. The authors evaluated the influence of the force applied to the workpieces in the process of friction of the contacting surfaces (force during heating), and postweld tempering at a temperature of 550 °С on the cyclic life of welded joints, under the conditions of alternate tension-compression at the cycle amplitude stress of ±420 MPa. The study determined that with an increase in the force during heating, the microstructure changes occur in the zone of thermomechanical influence, contributing to an increase in the fatigue strength of welded joints. The authors identified the negative effect of postweld tempering on the fatigue strength of welded joints, which is expressed in the decrease in the number of cycles before failure by 15–40 %, depending on the magnitude of the force during heating. The optimal RFW mode of the specified combination of steels is determined, which provides the largest number of cycles before failure: the force during heating (at friction) Fh=120 kN, forging force Ffor=160 kN, rotational frequency during heating n=800 Rpm, and upset during heating l=8 mm. A series of fatigue tests have been carried out at various values of the cycle amplitude stress of the welded joint produced at the optimal mode and the 30ХГСА steel base metal; limited endurance curves have been plotted. It is shown that the differences in the limited endurance curves of the pipe body material (30ХГСА steel) and the welded joint are insignificant. The obtained results are supplemented by the microhardness measurement data and fractographs of fractured samples, revealing the mechanism of crack propagation under the cyclic loads.

Memory surfaces separating the processes of monotonous and cyclic loads

The processes of elastoplastic deformation of structural materials can consist of a sequence of monotonous and cyclic loading regimes, in which peculiar effects and features arise. Mathematical modeling of such processes, as well as resource assessment and forecasting, is a very difficult task. In addition, the analysis of transient processes from cyclic to monotonous and from monotonous to cyclic shows the need to separate these processes. Based on the analysis of the results of experimental studies of samples of stainless steel 12Х18Н10T under a rigid (controlled deformation) deformation process, which is a sequence of monotonic and cyclic loading modes, under conditions of uniaxial tension-compression at normal temperature, the features and differences in the processes of monotonic and cyclic loading are revealed. To describe these features and separate the processes of monotonic and cyclic loading modes in the theories of plastic flow with combined hardening, various variants of memory surfaces are introduced. An analysis of the results of experimental studies of stainless steel showed that in the space of the plastic strain tensor, the size of the memory surface is determined by the range of plastic strains, and the position of the center is determined by the values of average plastic strains under cyclic loading. Various variants of the memory surface are considered, their capabilities and disadvantages are identified, and the most adequate variant of the memory surface is determined. To confirm the operability of this version of the memory surface, together with the equations of the Bondar plasticity model, the calculated and experimental results were compared and a reliable agreement was obtained between these results both in terms of the kinetics of the stress-strain state and in terms of the number of cycles to failure.

Fatigue performance of laser powder bed fusion hydride-dehydride Ti-6Al-4V powder

Hydride-dehydride (HDH) Ti-6Al-4V alloy with particle size distribution of 50–120 µm is laser powder bed fusion ( L -PBF) processed using optimum processing parameters and a near-fully dense structure with a density of 99.9 % is achieved. Microstructural observations and phase analyses indicate formation of columnar β grains with acicular α/α′ phases in as-built condition. The roughness of the as-fabricated samples is significant with an average roughness of R a = 15.71 ± 3.96 µm and a root mean square roughness of R rms = 108.4 ± 24.9 µm, however, both values are reduced to R a = 0.19 ± 0.04 µm and R rms = 4.9 ± 0.6 µm after mechanical grinding. Mechanical tests are carried out on as-fabricated specimens followed by stress relief treatment. All samples are tested to failure in fatigue, under fully-reversed tension-compression conditions of R = −1. The as-built samples failed from the surface with crack initiation mainly at micro-notches, whereas after mechanically grinding, crack initiation changed to subsurface defects such as pores. Minimizing surface roughness by mechanically grinding eliminates surface micro-notches which improves fatigue strength in the high cycle fatigue region. Fatigue notch factor calculations showed that the effect of surface roughness was significantly lower when HDH powder is used compared to standard spherical powder. X-ray diffraction analysis revealed an in-plane compressive stress, micro-strain and grain refinement on the surface of the mechanically ground samples. Fractography observations (macroscale) revealed a fully brittle fracture in the first stage of crack growth with a transition to a dominantly ductile fracture in the third stage of crack growth. On the other hand, at the micro scale, even the brittle fracture regions showed evidence of ductile fracture within the α′ martensite laths.

Low cycle fatigue properties of refractory high-entropy HfNbTiZr alloy

Considerable effort has been applied toward developing refractory high-entropy alloys (RHEAs) with both high strength and good ductility. However, the deformation and fatigue failure mechanisms of these alloys under cyclic loading remain poorly understood. The present work addresses this issue by investigating the low-cycle deformation behavior and microstructural evolution of an HfNbTiZr RHEA with a nominal composition of 25 mol% each of Hf, Nb, and Ti, and Zr forming the balance under symmetric tension-compression conditions at room temperature. Analysis of the cyclic stress responses of the alloy reveals a variety of internal stress trends at different strain amplitudes (Δεa), which implies the operations of a variety of cyclic deformation mechanisms. Further analysis demonstrates that cyclic softening is mainly caused by a rapid decrease in frictional stress during the initial cycles representing roughly 10% of the total number of cycles to failure. In general, the microstructural characteristics of the alloy observed with an increasing number of cycles under various values of Δεa demonstrate that softening occurs due to the formation of slip bands (SBs) caused by high-density dislocations arising in conjunction with increasing plastic strain accumulation. Specifically, dislocation structures forming at a low value of Δεa = 0.8% mainly consist of planar SBs (PSBs), while low-density cross SBs (CSBs) form at Δεa = 1.1%, and the density of the CSBs increases with further increasing Δεa. In addition, a fatigue lifetime prediction model was presented that obtained good prediction accuracy for the HfNbTiZr RHEA investigated herein. Accordingly, the present study can be expected to provide a fundamental basis for understanding the deformation mechanisms of other RHEAs.

A 3D metamaterial with negative stiffness for six-directional energy absorption and cushioning

To attenuate the impact acceleration under multidirectional loads, a mechanical metamaterial with six-directional cushioning and energy-absorbing properties is urgently needed. The study proposes a 3D negative stiffness (NS) metamaterial (NS-MM), which exhibits a bidirectional NS effect and cushion capacity under compressive and tensile loading in three principal directions. The unit cell of NS-MMs contains three pairs of parallel cross-curved beams mounted in a cubical frame, and the NS effect is obtained by controlled elastic buckling of the cross-curved beams. The mechanical analysis of one unit cell is conducted toward predicting the static response. The static performance of the NS-MMs composed of 1×1×1 and 2×2×2 unit cells in three principal directions is investigated by numerical calculations and experiments with quasi-static tension–compression conditions. Comprehensive results indicate the proposed structure has the characteristics of shape recovery, bidirectional NS property, and good energy absorption under tension and compressive loads in one principal direction and has the same mechanical properties in three principal directions. Transient dynamic analysis is exploited to investigate the cushioning performance. The obtained response acceleration (RA) is effectively attenuated in both directions and limited to a certain threshold.

A PD-FEM approach for fast solving static failure problems and its engineering application

A method of coupling of peridynamics (PD) and finite element method (FEM) for fast solving static failure problems is proposed. It is based on the force coupling method and adopts interface elements to couple the PD and FE subregions. By assembling the global matrix of the coupling model and using the adaptive dynamic relaxation (ADR) method to solve it, the static solution of elasticity and crack growth problems can be obtained quickly. By introducing short-range repulsive force and re-defining the coupling force, it is not only suitable for simulating tensile failure problems, but also suitable for compression failure problems. Through comparative analysis, the accuracy and effectiveness of this approach are verified. And then the method is successfully applied to simulate the excavation process of an underground cavern group, and the simulation of damage and failure process of engineering rock mass under complex tension–compression conditions has been realized. The stability characteristics of the surrounding rock are revealed by analyzing the damage and deformation evolution laws. It provides an effective numerical simulation method for predicting the excavation damage zone (EDZ) distribution characteristics and deformation law of the surrounding rock during the excavation of an underground cavern group. At the same time, compared with pure PD, the calculation efficiency is greatly improved, which is of great significance for the realization of engineering-scale simulation.

ПОСТРОЕНИЕ ПОВЕРХНОСТИ ПАМЯТИ ДЛЯ РАЗДЕЛЕНИЯ ПРОЦЕССОВ МОНОТОННЫХ И ЦИКЛИЧЕСКИХ НАГРУЖЕНИЙ

Non-stationary and asymmetric processes of cyclic deformation are considered, which consist of a sequence of monotonic and cyclic loading modes, in which peculiar effects of landing and ratcheting of plastic hysteresis loops occur. Mathematical modeling of such processes of deformation and damage accumulation is based mainly on variants of plasticity theories belonging to the class of theories of plastic flow with combined (isotropic and anisotropic) hardening. In this paper, mathematical modeling of the processes of deformation and damage accumulation is based on a variant of the theory of plasticity – the Bondar model. Based on the analysis of the results of experimental studies of samples of stainless steel 12Х18Н10T under a rigid (controlled deformation) deformation process, which is a sequence of monotonic and cyclic loading modes, under conditions of uniaxial tension-compression at normal temperature, the features and differences in the processes of monotonic and cyclic loading are revealed. To describe these features and separate the processes of monotonic and cyclic loading modes in the theories of plastic flow with combined hardening, various variants of memory surfaces are introduced. An analysis of the results of experimental studies of stainless steel showed that in the space of the plastic strain tensor, the size of the memory surface is determined by the range of plastic strains, and the position of the center is determined by the values of average plastic strains under cyclic loading. Various variants of the memory surface are considered, their capabilities and disadvantages are identified, and proposed variant of the memory surface.To confirm the operability of proposed version of the memory surface, together with the equations of the Bondar plasticity model, the calculated and experimental results were compared and a reliable agreement was obtained between these results both in terms of the kinetics of the stress-strain state and in terms of the number of cycles to failure.

Geometrical modeling and mechanical behavior analysis of Nb3Sn Rutherford cable

The energy upgrade of the Large Hadron Collider and Future Circular Collider propose new requirement that the magnetic field of accelerate magnets is up to 16 T. Nb3Sn Rutherford cables are used in magnet design for such high level magnetic field. Rutherford cables must undergo complex stress conditions owing to the extreme magnetic environment and complicated cabling process which often leads to mechanical instability. In this study, a three-dimensional model is established and analyzed to better understand the mechanical behavior of Rutherford cables subjected to different loading conditions during the cabling process. A rapid approach to construct the geometry of a Rutherford cable is first presented, followed by an analysis of its mechanical behavior under axial tension, cyclic tension and transverse compression conditions. Instability behaviors, such as “pop-out” and “cross-over”, are investigated. The results show that the friction coefficient, laying angle and core play important roles in the cable mechanical performance. For better mechanical stability of the strands in Rutherford cables, it is recommended to select a higher friction value among the strands and a laying angle between 74° and 78° for non-cored cable, whereas a larger laying angle is suggested for copper-cored cable.

Application of variable equivalent amplitude for determination of fatigue life of elements subjected to block loading

This paper contains a proposition of a new method of determining the fatigue life of elements subjected to non-stationary loads. The model was based on the determination of the time-variable equivalent weighted amplitude. This amplitude is derived on a continuous basis as the arithmetic mean of nth root of the amplitudes that occur up to a given time. The analysis of the proposed model was carried out on the basis of selected literature insights based on specimens made of P91 and P92 steels. The experimental tests were performed under block loading with a zero mean value in the conditions of tension-compression with a small number of cycles.

Analysis of the fatigue life of metal composites with a layer of zirconium alloy

Methods of joining dissimilar materials gain interest and attention of highly demanding branches of modern engineering. Acquiring high-quality bond between steel and titanium or zirconium alloys is perceived as especially advantageous in terms of high strength and corrosion resistance. In the present paper results of fatigue tests performed on five different metal composites produced in the process of explosive welding has been gathered. All tested materials were manufactured by a collision of zirconium flyer plates with base plates made of steel or steel-titanium bimetal. Fatigue tests have been conducted under uniaxial force-controlled tension-compression conditions with a constant amplitude of load applied parallelly to bonding interface. The analysis includes the residual stresses measured by the hole-drilling strain gauge method in the flyer plates and the applied stresses calculated by three different models. A description of the initiation and propagation of cracks developing within the joint during cyclically changing loading is also included. Based on the collected data, application conclusions were formulated regarding the optimal use of the tested materials.

Nominal Stress-Based Estimation of Fatigue Life of Welded Joints

The paper presents methods for determining the fatigue life of welded joints with particular emphasis given to typical joints. In addition, the article presents various possible nominal stress-based ways enabling the calculation of stresses, including structural stresses and involving the most complex linear fracture mechanics. The paper also discusses recommendations by the International Institute of Welding related to the determination of the fatigue life of welded joints in flat elements exposed to tension-compression conditions. The work is focused on assessing the fatigue life of welded joints (selected types) in accordance with the guidelines specified in related recommendations issued by the International Institute of Welding and taking into consideration the analysis concerned with the safety of such structures.

Fracture of elastic-brittle and elastic-plastic material in cantilever cyclic bending

The paper analyses the fatigue tests of a specimen made of 16Mo3 steel and 6082-T6 aluminium alloy performed under bending and tensile conditions. It has been shown that in the case of bending of the 16Mo3 steel specimen, in low cycle fatigue (LCF) range, the fatigue life is increased with respect to the results obtained under tension-compression conditions. On the other hand, in the case of the aluminium specimen, the load condition practically does not affect the fatigue life. Microstructural analysis revealed almost homogeneous fatigue cracks in the 16Mo3 steel samples which are practically elastic-plastic. The analysed 6082-T6 aluminium alloy belongs to the group of materials characterized by elastic and brittle properties. In the case of pendulum bending in the obtained images, it is possible to notice the clear pits at an angle of about 45 degrees relative to the surface of the breakthrough. They penetrate the broken specimen to about 33%. In the middle of the material, the bending plane is clearly visible, where the stress is constant and equals 0 MPa.

CONSTRUCTION OF THE STRENGTH STATISTICAL CRITERIA WITH CONSIDERATION OF SOME BRITTLE MATERIALS FAILURE DETERMINISTIC ASPECTS FEATURES

The model of a stochastically defective plate from an isotropic material under conditions of comprehensive tension-compression is considered. Defect-cracks are characterized by two statistically independent geometric parameters, whose laws of probabilistic distribution are given. Based on the deterministic failure criteria, which takes into account the initial direction of the crack propagation, the statistical diagrams equations of the plate strength are written in the fracture loading mean values. Such diagrams are constructed for plates with different defect structure and different structure materials inhomogeneity. The effect of taking into account the initial direction of the crack propagation on the obtained limiting state curves is investigated.

Forming of hemispherical and hemi-ellipsoidal parts of low carbon steel sheet by mandrel free metal spinning process

Metal spinning (MS) is an efficient and economical alternative method for low-volume functional sheet metal products. It has higher potential to shape three dimensional parts without employing matching die. The focus in advancement of shape forming shall bring an effective approach to produce defect free shapes and economically viable products. This paper is going to discuss about the modification in the MS process, without using matching dies or mandrel to produce a hemispherical and hemi-ellipsoidal profile product. The forming occurs by the deformation of sheet metal when the roller feed is against the rotating metal blank. Low carbon extra deep drawing Al killed steel sheets of thickness 1.6 mm were exploited as forming material. Further the paper illustrates on thickness variation, hardness, micro-structure, surface roughness and forming limit diagram (FLD) of the various zone of the formed part. It is examined that as the depth varies, the changes in thickness of formed part also varies. Also, the surface roughness was proportionally increased with increasing in percentage of reduction in thickness. In all zone of the formed steel part are in tension- tension strain conditions, there is no tension compression and plane strain condition occurred in the forming process. Due to this reason wrinkles failure is eliminated in die less MS process.

Characterizing surface finish and fatigue behavior in binder-jet 3D-printed nickel-based superalloy 625

In this study, the fatigue properties of binder-jet 3D-printed nickel-base superalloy 625 were evaluated. Standard fatigue specimens were printed and sintered, then half of the samples were mechanically ground, while the other half were left in their as-sintered state. They were then characterized using micro-computed x-ray tomography, metallographic sample examination, and optical and stylus profilometry for surface topography. The micro-computed tomography observations showed that density of the as-printed sample was ∼50%, while the sintered sample neared full densification (98.9 ± 0.3%) upon sintering at 1285 °C for 4 h in a vacuum atmosphere. The metallographic examination showed equiaxed grains. The roughness of the as-sintered samples was significant with an RMS roughness of Rq = 1.39 ± 0.20 μm as measured over a line-scan of 5 mm, but this was reduced to Rq = 0.47 ± 0.02 μm after mechanical grinding. All samples were tested to failure in fatigue, under fully-reversed tension-compression conditions. While the as-sintered samples showed poor fatigue properties compared to prior reports on cast and milled parts, the ground samples showed superior performance. Scanning electron microscopy observation was conducted on the fractured surfaces and showed that the samples underwent transgranular crack initiation, followed by intergranular crack growth and final failure. In the mechanically ground sample, hardness increased nearly two-fold up to 75 μm beneath the sample’s surface, and X-ray diffraction indicated an in-plane compressive stress, grain refinement, and micro-strain on the mechanically ground sample. The reduced roughness, surface hardening, and compressive stress resulted in increased fatigue life of the binder-jetted alloy 625.

Damage Accumulation under Variable Loading of Cyclically Hardening Material at the Stages of Formation and Development of Cracks

The results of experimental studies of the kinetics of damage accumulation at the stages of formation and rates of development of cracks in cyclic loading of the cyclically hardening AD-33 aluminum alloy are presented, and an assessment is made of the levels accumulated in the process of loading of damage on the basis of the deformation and kinetic criteria. It is shown that the limiting state (final fracture) during cyclic loading of an aluminum alloy is described well when using deformation characteristics (cyclically reversible deformations and one-sided accumulated ones at the stage of formation, and reversible and one-sided accumulated displacement of crack edges at the stage of crack development) used in the deformation and kinetic criteria. It has been established that a cyclically hardening aluminum alloy at the stage of crack development under tension-compression conditions does not obey the first model of fracture mechanics.

The Effect of Loading Frequency on Fatigue Life of Green onyx under Fully Reversed Loading

Rock structures, in reality, may be subjected to reversed tension-compression loading conditions due to blasting, earthquake, and traffic or injection-recovery process. In this case, loading frequency may have a great influence on fatigue life and behavior of rocks. The effect of loading frequency on fatigue life of a crystalline rock sample under fully reversed loading condition was examined. A new apparatus, based on the R. R. Moore fatigue test machine, was used to assess the fully reversed loading condition. The experimental tests were conducted with five sets of loading frequency and five levels of stress based on the ultimate tensile strength of samples. The test results showed that the variation of ultimate fatigue stress versus loading cycle number (S-N curve) of crystalline rock samples were in accordance with the observed results in other materials such as metals and ceramics. The results showed that fatigue life of a component is positively correlated with the frequency level. The fatigue life improves with increasing the loading frequency, but the improvement was more tangible at lower stress levels than at higher stress levels. The effect of loading frequency in an ordinary S-N equation was also formulated. The results also showed that the loading frequency does not influence the fatigue limit.

Low cycle fatigue studies of WCLV steel (1.2344) used for forging tools to work at higher temperatures

The paper presents the results of low cycle fatigue studies of WCLV tool steel aimed at determining the diagrams of low cycle fatigue and verifying them based on the analysis of durability of the selected forging tool. Based on the macro- and microstructural tests as well as numerical modelling of industrial forging processes, the conditions for the implementation of laboratory fatigue tests were determined. The samples underwent periodical uniaxial loading (tension–compression conditions) at four levels of amplitude of total strain (0.5; 0.8; 1.0; 2.0%), at three temperatures (20, 300 and 600°C), based on the macro- and microstructural tests as well as numerical modelling of industrial forging processes. For the determination of the hysteresis loop based on the obtained fatigue results, the Ramberg–Osgood equation was applied. The fatigue diagrams in the bilogarithmic system were approximated by the Manson–Coffin–Basquin equation, and the diagrams of low cycle fatigue in the ɛa–Nf and σa–Nf system were obtained. The results of the laboratory tests concerning the fatigue strength of WCLV tool steel were preliminarily verified based on the analysis of the punch used to forge a lid forging, exhibiting a good agreement. The performed comparative analysis of the results of the fatigue tests and the numerical analysis combined with the studies of the microstructure revealed the possibility of their application in the aspect of forging tools’ durability as well thermo-mechanical fatigue strength.

Numerical investigation of the influence of rolling texture and microstructure on fatigue crack initiation in BCC polycrystals

The study aims to investigate the influence of the grain morphology and rolling texture on the fatigue crack initiation in BCC polycrystals. Several 2D polycrystalline aggregates having different grain size and shape distributions are generated based on an anisotropic tessellation and an ellipse packing algorithm. Uniform and typical BCC rolled textures containing both the α and γ fibers are considered for the crystallographic texture of the material. Finite element simulations using a crystal plasticity model are performed under cyclic uniaxial tension-compression condition. Twenty simulations are conducted for each type of microstructure in order to obtain significant statistical data. A critical plane fatigue indicator parameter (FIP) following the Tanaka-Mura model is applied to quantify the sensitivity of the microstructure against fatigue crack initiation. The distributions of relevant geometrical, crystallographic and mechanical quantities are analyzed. The effect of the grain size distribution, morphology and texture on the fatigue performance and scattering are discussed.