Stress-strain Field Research Articles

Complex stress state analysis for aluminum alloy accounting for damage accumulation

In this study, the limiting state determination of the aluminum alloy 2024 under a complex stress state was carried out. The purpose of the study is to determine the effect of accumulated damage in a material under a complex stress state on the characteristics of the material's bearing capacity. Various types of combined loading by tension, compression, torsion and internal pressure are considered. The object of numerical and experimental studies is a hollow cylindrical specimen with notch. In the numerical part, the exponential and power approximating function was used as the law of isotropic hardening. The damage accumulation law Lemaitre was used to determine the damage parameter. The generalized law of damage accumulation Lemaitre and the law of isotropic hardening were integrated into the ANSYS finite element code in the form of a dynamically linked library of user material for three-dimensional problems. Stress-strain state fields, damage fields, as well as the values of limiting stresses under various types of loading are obtained. Comparison study of different limiting stress state theories were numerically performed with take into account the damage accumulation under complex stress state.

Fatigue crack initiation and growth in a tooth root of sintered gears

In this study, the computational model for determination the fatigue life of sintered gears is presented. The total fatigue life of sintered gear, N, is divided into the crack initiation (Ni) and crack propagation (Np) period. The number of stress cycles for crack initiation in a gear tooth root, Ni, is determined using the strain-life approach and with consideration of the low-cycle fatigue parameters obtained previously for the same material as already used for the analysed sintered gear. The number of stress cycles for crack propagation from initial to the critical crack length, Np, is obtained using the simple Paris law and with consideration of fatigue crack growth material parameters taken from the author’s previous work. The comprehensive computational analyses in the framework of Ansys-software are performed to obtain the strain-stress field in a gear tooth root and for determination of the stress intensity factor in the crack tip.

Damage Prediction of Ferritic Pipeline Using Artificial Neural Network

The GTN model for complex geometries such as pipelines handles the constraint effect. In the case of using traditional data in fracture mechanics, we will face the issue of transferability. In other words, the mechanical fracture properties, determined by measurements of specimens, are valid for certain stress-state conditions, mainly for plain strain states. However, in the case of real complex geometries, we have stress triaxiality, and we can be far from the stress-strain condition of the specimens. Hence, the applicability of the measured values is limited. For this reason and others, instead of using the J-R curve or JIc, we can use a geometry and stress-strain field independent local GTN model to predict the pipeline's failure. The main important point is that we need to find reliable GTN parameters, so to reduce the time consumed during the determination of reliable GTN parameters for the pipeline, the artificial neural network (ANN) was integrated in this study, and the results show that we can reduce the time of GTN parameter identification from thirty days to six hours.

On the cleavage stress promoting crack path deflection and anisotropic fracture in cold drawn pearlitic steel

Crack path deflection is a phenomenon appearing in cold-drawn pearlitic steel wires as a consequence of the pearlite microstructure orientation induced by the manufacturing procedure, the deflection angle being approximately 90º, thereby representing a crack propagation step (fracture wall), a signal of splitting, delamination or debonding in the form of axial cracking (or micro-cracking) by means of a microscopic fracture mode in the form of enlarged and oriented cleavage in the direction of the wire axis (cold drawing direction). The described phenomenon is a signal of anisotropic fracture behaviour (strength anisotropy) associated with mixed-mode propagation. This paper demonstrates that, in addition to the oriented microstructure of the cold drawn pearlitic steels (at the two microstructural levels of pearlite colonies and lamellae), a sufficient level of stress triaxiality (constraint) is required, as in the case of cracked specimens in which a cleavage stress appears as a consequence of the singular stress distribution in the close vicinity of the crack tip (crack tip stress-strain field).

Strain model and experimental study of elastic viscoplastic for crack-tip zone of X80 steel pipe

The mechanical state of the process zone at the crack-tip is one of the main factors that affect crack initiation and growth in the long-term safe operation of oil and gas pipelines. Many tests showed that the stress and strain fields in the fracture-tip process zone can be used to define the crack propagation behavior. The goal of this paper is to improve the Hutchinson, Rice, and Rosengren (HRR) model by using cubic asymptotic polynomials to describe the stress-strain field at the crack-tip, as well as to validate the model by a thorough comparison with full-scale burst test results that account for the fracture zone's mechanical properties. The asymptotic polynomial elastic viscoplastic distribution model of stress-strain displacement field at the crack-tip is developed, and the HRR method is modified reasonably. The crack propagation test of the X80 steel pipeline in the burst test site is carried out. Experimentally, the distribution of stress and strain field in the crack-tip process zone of the X80 testing pipeline is obtained, then compared with the theoretical solution. The final results showed consistency, and the elastic viscoplastic model matched well with the running fracture test data for the X80 gas pipeline. Besides, the stress and strain fields distribution in the crack-tip process zone is verified through the full-scale test of the X80 steel pipeline, which provides a theoretical basis for the integrity evaluation of the steel pipeline.

Crack growth in rotor P2M steel at elevated temperature

The paper presents a comprehensive computational and experimental study of the crack growth rate during the creep-fatigue interaction in compact specimens of P2M steel at a temperature of 550 °C. The theoretical part of the study consisted in the formulation of the fracture resistance parameters through the classical and new constitutive equations of the cracked body state taking into account the accumulation of damage. Numerical calculations included the determination of the stress-strain state fields for the conditions of elasticity, plasticity, and creep, as well as the distributions of nonlinear stress intensity factors and the C*-integral along the crack length and along the crack front for each tested compact specimen. The interpretation of the experimental results for specimens of the same shape in plan but different thicknesses is given in terms of elastic and nonlinear stress intensity factors, taking into account the accumulation of creep damage. It was found that the crack growth rate under the fatigue and creep interaction increases monotonically as the crack size increases in comparison with harmonic fatigue by an order of magnitude or more on specimens of the same geometry. Taking into account the damage through the creep stress intensity factors causes differences in the cyclic fracture diagrams. The superposition of fatigue and creep contributions in terms of load holding time shows an order of magnitude increase in the total crack growth rate compared to the interpretation of the experimental data in terms of pure creep.

Interpretation of the generalized parameter of the probability of failure through the plastic stress intensity factor

The main purpose of this work is to statistically analyze the fracture toughness of compact specimens made of S55C steel in terms of elastic and plastic stress intensity factors. The fracture toughness tests results at three-point bending were used for a comparative statistical analysis of the fracture parameters. Five type of specimen configuration with various thicknesses were tested at a constant ratio between crack length and specimen width. The critical loads were obtained as a tests result for various combinations of crack length and specimen thickness. In addition, uniaxial tensile tests were carried out to determine the main mechanical properties of the material. Obtained material properties were used in numerical calculations. Numerical calculations were carried out to determine the elastic and plastic stress intensity factors. Three-dimensional finite element analysis was performed on the basis of the experimental data on curvilinear crack front positions in tested specimens. The crack tip stress-strain fields were obtained for each of the tested samples as a result of numerical calculations. These fields were used to calculate the values of the plastic intensity factors along the curvilinear crack fronts. A statistical analysis of the fracture toughness of compact specimens made of S55C steel was carried out based on the obtained critical values of elastic and plastic stress intensity factors. The advantages of using the plastic stress intensity factor as a generalized parameter for the fracture probability are demonstrated. In addition, the sensitivity of the plastic stress intensity factor to constraint effects avoids the introduction of additional parameters into the statistical models.

MUYAKAN EARTHQUAKE SEQUENCE in 2015 (Northern Baikal Region)

We present the results of studies of the seismic regime, focal mechanisms, and macroseismic data in the area of the largest Muyakan activation in 2015 (northern Baikal region). Due to the deployment of a network of temporary seismic stations, the number of registered earthquakes (KR≥3) increased significantly in 2015 and reached  30 thousand. Spatio-temporal development of the considered activation is characterized by stable low values of earthquake hypocenters and dividing the epicentral field into two clusters – eastern and north-western ones. Both clusters are connected with local stress-strain field (rift type and strike-slip, respectively), while the general regime of seismotectonic deformations of the crust in the activation area, calculated from the statistical analysis of 77 focal mechanisms of Muyakan earthquakes (KR≥9.2), demonstrates the predominance of submeri-dional horizontal extension. Macroseismic effects from the largest earthquakes of the Muyakan sequence were felt, predominantly, in Severomuysk settlement (=10–15 km, I=5). New data on strong motions, obtained from the records of the seismic station with the same name, have significantly complemented the database for the territory of the north-eastern flank of the Baikal rift zone. In general, the obtained results could be used to clarify the seismic hazard of the considered area and to improve the instrumental part of seismic scales.

Исследование напряженно-деформированного и температурного состояния режущей части инструмента с использованием лазерной интерферометрии

Introduction. The efficiency of the metalworking processes highly depends on the performance of the implemented cutting tools that can be increased by studying its stress-strain state and temperature fields. Existing stress analysis methods either have a low accuracy or are inapplicable for research during the operation of the tools made of materials with high mechanical properties. In addition, the study of temperature fields using known methods is difficult due to the small size of the cutting zone, high temperatures, and a heavy temperature gradient appearing during metal cutting. The purpose of this study is to develop new experimental methods for measuring the stress-strain and temperature fields in the cutting tool during its operation using laser interferometry. The methods include: obtaining interference fringe patterns using an interferometer with the original design, obtaining the tool deformation field during the cutting process by recording the changes in interference fringe patterns using a high-speed camera, processing fringe patterns with the separation of deformations caused by heating and cutting forces, and calculating temperature fields and stress distributions using mechanical properties and the coefficient of thermal expansion of the tool material. The advantages of the developed methods include: applicability under real operating conditions of the cutting tool, ability to study the non-stationary stress-strain state and temperatures during an operation, and achievement of a high spatial resolution and a small field of view for the investigated surface. Results and Discussion. The experimental study confirmed the efficiency of the methods. The results of the study included the fields of stresses and temperatures obtained during the orthogonal cutting of heat-resistant steel with a tool made of cemented tungsten carbide WC-8Co. The developed methods can be used to study the cutting tool efficiency at close to real conditions and in obtaining boundary conditions for the study stress-strain state of a workpiece material near the cutting zone.

A novel fatigue-oxidation-creep life prediction method under non-proportional loading

In this paper, a new life assessment framework is proposed based on the elastic-viscoplastic modeling and the damage behavior for the structural component under multiaxial non-proportional loading at high temperature. The viscoplastic constitutive model with the ability to capture the non-proportional hardening effect is used to obtain the stress–strain fields, in which a new method based on the rotation of strain axis is proposed to evaluate the notch rotation factor. The damage model, which can comprehensively capture the multiaxial fatigue-oxidation-creep behaviors, is used to assess the failure life. In addition, the proposed framework is evaluated by the life results under proportional and non-proportional fatigue loadings at 650 °C, and the errors are found to be within a factor of 2.

Experimental and numerical investigations of aluminium–steel self-piercing riveted joints under quasi-static and dynamic loadings

The mechanical response of aluminium–steelself-piercing riveted (SPR) joints is investigated under quasi-static and dynamic loadings using experimental and numerical methods separately. First, a 2D axisymmetric numerical model is constructed based on r-adaptivity method to simulate the SPR process and is subsequently validated by tests. Second, a novel generation method of 3D finite element (FE) model of SPR joints, of which the stress–strain field is mapped from the 2D axisymmetric model, is proposed to simulate the mechanical response of aluminium–steel​ SPR joints. The mechanical response of SPR joints under quasistatic and dynamic loadings are compared in detail by experimental tests and numerical simulation. The results reveal that the established 3D FE model can accurately simulate the quasi-static and dynamic strength of SPR joints. It is observed that the peak force of the SPR joints is larger under dynamic loading than under quasi-static loading; while the energy absorption by peeling and cross-tension SPR joints is lower under dynamic loading than quasistatic loading. Finally, the relationships between process parameters, process quality indexes and mechanical response of SPR joints are parametrically investigated under quasi-static and dynamic loadings, in which (1) increasing the rivet length reduces the minimum thickness, increases undercut, and increases energy absorption; (2) increasing the rivet length increases the peak force within a limited range for shear joints and cross-tension joints under dynamic loading; (3) the total effect of process parameters on the mechanical response of SPR joints under dynamic loading are similar to the effect observed under quasi-static loading.

Research on chip formation mechanism and surface morphology of particle-reinforced metal matrix composites

In this paper, a finite element (FE) cutting model for particle-reinforced metal matrix composites (PRMMCs) considering material damage was developed to predict SiC particle failure, cutting forces, and machined surface topography in SiCp/Al composite machining, and to analyze the dynamic mechanisms of chip formation and particle failure evolution. The validity of the simulation model was verified by comparing the simulation results with the cutting forces and surface topography obtained from the milling machining experiments. It was found that complex stress-strain fields exist in SiCp/Al composites with mesoscopic non-homogeneous structures, and alternating reticulation of tensile and compressive stress between particles was observed; particle failure due to tool-workpiece interaction exists in both direct and indirect ways; particle failure and local chip deformation during machining affect surface topography and chip shaping, resulting in serrated chips, pitting on the machined surface, and residual particle fragments.

Evolution law of stress-deformation-permeability of coal pillar along gob and its effect on stability of coal pillar

The interaction between stress field and seepage field is mainly manifested in two aspects: on the one hand, the change of stress field causes the change of structural plane such as joints and fractures in rock mass, and then changes the permeability of rock mass; On the other hand, the seepage force of seepage field will change the original stress state in rock mass. The two aspects of stress field and permeation field influence and interact with each other all the time, reaching a dynamic stable state, and this dynamic relationship forms the fluid-solid coupling mathematical model. Permeability coefficient is a bridge of interaction and coupling between stress field and seepage field. Only by establishing the relationship between permeability coefficient and stress field or strain field, can the influence of stress field on seepage field be reflected and the real fluid-solid coupling analysis be realized. As a governing equation as important as the constitutive equation in the coupled numerical analysis of stress field and seepage field, permeability coefficient-volumetric strain can be used in numerical analysis to make the calculated results more consistent with engineering practice.

Similarity Criteria of Water Drive Physical Simulation of Pressure-Sensitive Fractured Reservoirs

A mathematical equation of water drive physical simulation of pressure-sensitive fractured reservoirs was established based on previous research results. In this study, the similarity criteria of water drive physical simulation of pressure-sensitive fractured reservoirs were derived according to the similarity theory. First of all, based on the three-dimensional differential equation of rock mechanics, a dimensionless analysis was conducted to determine the similarity relationship between the displacement of oil by water of pressure-sensitive fractured reservoirs, the similarity criterion was obtained, and the similarity criteria were formed. Secondly, according to the similarity criterion, the similar relationship between the stress-strain fields of the real object and the simulated object was worked out. Thirdly, the finite element software COMSOL Multiphysics was applied to model and calculate the multifield coupling process in the percolation of pressure-sensitive fractured reservoirs, verifying the correctness of the established similarity criteria and similarity relationship. The verifying results shows that the similarity between the physical model and the actual model can be realized by magnifying the geometric size N times in a certain direction and adjusting the load and boundary conditions according to the similarity principle, which can be used for the design of the pressure-sensitive fractured reservoir simulation model for a physical indoor test.

Influence of permanent deformation on the fitting quality and the simulation prediction of filled elastomers

This work deals with the consequence of fitting hyperelastic material models to quasi-static multi-hysteresis test data with and without the correction of permanent deformation. Multi-hysteresis experiments are performed in different deformation states with equivalent amplitudes and equivalent strain rates. The investigations are performed on a carbon black filled ethylene propylene diene terpolymer rubber (EPDM). A second order polynomial hyperelastic material model was used to investigate the effect of elimination of permanent deformation during the fitting process. We find that the elimination of permanent deformation leads to a prediction of a stiffer material behavior. The validation of the obtained fitting parameters in the double-sided shear and uniaxial tension–compression loadings clearly shows that the elimination of the permanent deformation has a huge influence on the predicted stress field and strain field.

Application and discussion of various crack closure models to predict fatigue crack growth in 6061-T651 aluminium alloy

Fatigue is one of the main causes of failures as well as mechanical fractures in structural details made of aluminium alloys under cyclic loading, where the materials (during the crack growth process) are subject to the stress R-ratio effects and crack closure phenomenon.In this research work, a comparison of the effect of various crack closure/opening models on the fatigue crack growth behaviour of 6061-T651 aluminium alloy is presented. The crack closure models under consideration are the following: Elber; Katcher and Kaplan; Clerivet and Bathias; Schijve; Zhang; Newman; Savaidis; Codrington-Kotousov; and, Correia. A comparison between these models and experimental data is also done. Deterministic quadratic relations based on experimental results between U vs R and Reff vs. R are suggested and compared with various crack closure models under consideration, where U is a quantitative parameter function of crack opening and closing concept. This investigation into the crack closure/opening effects is made using experimental results from the first cycle and stabilised measurements (U1 and Us). Correia’s and Newman’s models presented a better agreement with the experimental results (Ud,s or Reff,s). In this study, the crack closure quantitative parameters based on the first cycle and stabilised measurements reveal to be different, where Uand Reff vary with the crack growth process, which suggests the assumptions listed by Hudak and Davidson, Ellyin, and Correia seem to be correct. Therefore, it can be concluded that the simultaneous monitoring of CTOD-based experimental measurements of the crack closure effects and getting the crack tip stress–strain field based on digital image correlation (DIC) measurements, supported by analytical/numerical solutions, seems to be a good way to describe the fatigue crack growth.

Characterization of Sand Production for Clayey-Silt Sediments Conditioned to Openhole Gravel-Packing: Experimental Observations

SummaryAs one of the geotechnical risks, sanding has been one of the main constraints for safely and sustainably developing marine natural gas hydrate. In this study, a cylindrical vessel that is packed with the clayey-silt sediment collected from the Shenhu area of the northern South China Sea is used to microscopically observe sand detachment, migration within matrix, invasion to gravel packing, and production for openhole gravel packing. More specifically, by injecting water from the vessel boundary, the seepage and stress-strain field for sediment near the wellbore after hydrate dissociation is simulated, and the sand failure characteristics [i.e., the produced sand volume and particle size distributions (PSDs)] are quantified. The sand failure pattern is found to largely differ from that of a sandstone reservoir, whereas fractures, wormholes, and fluidized channels are successively developed along with a large scale of sand production and inlet pressure variation. Followed is a steady flow state with a stable inlet pressure without noticeable sand failure. Correspondingly, the fracture is induced and propagated by the combinational effort of shear and tensile failure, whereas wormholes and fluidized channels are associated with the liquid dragging force. At the end of each test, foraminifera are found to accumulate near the external side of the gravel-packing region, which is beneficial to sand control. In the meantime, a compact mudcake, as an infiltration medium, is observed outside the gravel-packing layer. The 30/50 mesh gravel packing is able to control grain size up to 30.0 µm in diameter with a median of 5.0 µm, whereas the produced grains account for less than 1.0 vol% of the total sediment. By performing sensitivity analysis on sand production, depressurization shall be conducted at a small rate to not only control sand production, but also to induce flow paths at the early stage. Moreover, the sand production rate associated with fracture development is larger than those of wormholes and fluidized channels. This study focuses on the experimental observations on sand failure patterns, and the theoretical formulations and modeling will be presented and explained in a future work.3

T-stresses solution and out-of-plane constraint for central cracked plate (CCP) with I-II mixed mode crack under uniaxial compression

The crack tip constraint effect should be considered in the fracture assessment of structures with cracks, and the in-plane constraint and out-of-plane constraint should be illustrated simultaneously for the three-dimensional cracks in practical engineering structures. The constraint effect of central cracked plate (CCP) specimens with I-II mixed mode crack under uniaxial compression has been investigated quantitatively in present work. The relationship between T-stress components (Tx, Ty, Txy) and in-plane constraint parameter T11 has been established. The effects of a wide range of in-plane and out-of-plane geometrical configurations (including relative crack length a/W and thickness to width ratio t/W), material parameters (including elastic modulus E and Poisson's ratio ν), crack inclination angle β and friction coefficient μ corresponding to stress intensity factors (K), in-plane constraint parameter T11 and out-of-plane constraint parameters T33 and Tz at the crack tip have been calculated and discussed theoretically and numerically. It demonstrates that the constraint parameters can effectively express the stress-strain field at the crack tip. The relative crack length a/W has an influence on the in-plane and out-of-plane constraint parameters, and the thickness to width ratio t/W mainly affects the out-of-plane constraint parameters T33 and Tz. The out-of-plane constraint parameters should be considered for long cracks. There is a loss of out-of-plane constraint under compression when t/W less than or equal to 0.9, which can be much more directly and evidently investigated through the analysis of Tz than T33. The empirical equations for KII, T11 and Tz have been obtained according to theoretical analysis and simulation results, which are convenient and effective for application.

Finite element simulation of plough cone cutter

In order to improve the ROP of the PDC bit, a plough cone cutter was designed and finite element simulation was performed. Compared with conventional cutter, plough cone cutter has smaller stress field and strain field in the rock breaking process. The largest tangential rock breaking force and maximum axial rock breaking force is higher, but the average tangential rock breaking force and the average axial rock breaking force are smaller, and the rock breaking effect is better; the back dip angle has a significant impact on the rock breaking effect. Under the same plough cone cutter, with the increase of the inclination angle, the stress field and strain field of the rock after rock breaking will become smaller, and the rock breaking effect will be better. Therefore, the plough cone cutter with a backward inclination angle of 22° has an advantage in the rock breaking process.

Effect of geometrical irregularities on fatigue of lead sheathing for submarine high voltage power cable applications

High voltage subsea power cables are typically composed of several layers, including: a conductive core, a dielectric layer, a ductile metallic watertight barrier and a series of radial and axial armours and polymer layers. The watertight barrier serves the purpose of preventing water permeating to the dielectric due to the outer layers' polymer hygroscopicity. Water impregnation may cause dielectric breakdown, with fatal consequences on the integrity of the power cable. The watertight barrier is made of extruded lead alloy and is subjected, during the installation and operational life of the component, to axial and radial displacement-controlled fatigue which might lead to cracking, thus to a loss of its isolating properties. Lead, due to the low melting temperature, is characterized by creep deformation and damage even at room temperature. A steel tape is winded around the polyethylene sheathing surrounding the lead barrier, which is deformed, and a helical ridge is generated. This irregularity causes a local concentration of strain which might potentially lead to early failure of the lead sheathing. In this work the results of displacement-controlled fatigue testing at different strain rates of sheathing material including the irregularity is presented and compared to the results in equivalent conditions, but in the absence of the irregularity. The strain concentration caused by the defect is analysed with the implementation of a creep material model calibrated on the cyclic properties of the alloy and the notch sensitivity of the material for the class of defects, temperature and frequency in exam is obtained. The results are applied to the modelling of the stress-strain field in the component with and without irregularity and conclusions are drawn on the danger that such irregularities pose on the structural integrity on the power cable.