Plane Stress Conditions Research Articles

Random field modeling of local strength of a randomly arranged unidirectional fiber-reinforced composite material under transverse tensile loading

This study examines the random field modeling of local strength, which is the apparent strength of each window extracted from an SEM image of a cross-section of a randomly arranged unidirectional fiber-reinforced composite material specimen. In particular, computation of the spatially varying random apparent fracture strength based on the microstructure simulation is performed. To analyze the apparent fracture strength, single-scale analyses assuming plane-stress and plane-strain conditions, as well as multiscale stress analysis based on the homogenization theory, are attempted. In addition, the moving window method is employed to compute the respective random fields and their autocorrelation functions. First, the influence of the analysis method on the identified random field is investigated. Furthermore, the influence of the window and image size is discussed. The numerical results revealed that a smaller window leads to a more accurate evaluation of the apparent strength, and thus, is preferable for the identification of the respective random field.

Advancing contact of a 2D elastic curved beam indented by a rigid pin with clearance

A two-dimensional analytical solution is presented for stresses and displacements in an elastic curved beam forming an incomplete ring in frictionless and unbonded contact with a rigid pin loaded by a point force and in the presence of clearance. The circular beam is modeled as an incomplete elastic thick ring, constrained at both ends and in a plane stress state. The stress and displacement fields within the beam are derived from a biharmonic Airy stress function, according to the Michell solution in polar coordinates. The mixed boundary value problem is reduced to a set of dual series equations and then to a non-homogeneous linear system of infinite equations, which is then solved by truncation. The non-linear relations between the applied load and the contact angle or the pressure distribution are obtained by using an inverse method. The analytical results are compared with finite element predictions for a pin-lug connection and a reasonable agreement is observed for several typical geometries. The peaks of contact pressure and von Mises equivalent stress and their location within the curved beam are evidenced.

Determining damage initiation of carbon fiber reinforced polymer composites using machine learning

AbstractComputational progressive failure analysis (PFA) is vital for the analysis of carbon fiber reinforced polymer (CFRP) composites. The damage initiation criterion is one of the essential components of a PFA code to determine the transition of a material's state from pristine or microscopically damaged to macroscopically damaged. In this paper, data‐driven models are developed to determine the matrix damage initiation with the objective to save computation time. For 2D plane stress states, the computational cost for determining damage initiation can be dramatically reduced by implementing a binary search (BS) algorithm and predictive machine learning models. Machine learning models are evaluated against a regression problem of predicting damage crack angle as well as against a classification problem for predicting damage initiation outright. It is found that regression models perform much better for plane stress and 3D stress states when generating failure envelopes. In both cases, a neural network is able to produce a failure envelope that is over 99% accurate while reducing computational cost by over 90%.

Effects of specimen geometry and surface defect on high and very high cycle fatigue of TC17 alloy

The column specimen fails from the specimen interior, but the plate specimen fails from the specimen surface for TC17 alloy in very high cycle fatigue. The fatigue strength is lower for plate specimens than that of column specimens for the same surface defect. A model is developed for the fatigue strength σw,column of the column specimen and the fatigue strength σw,plate of the plate specimen with approximate plane stress state, i.e., σw,column=σw,plate/(1-v2), where ν is the Poisson ratio. The proposed model for the influence of specimen geometry and surface defect on the fatigue strength accords well with the experimental data.

Stress state mechanism of thickness debit effect in creep performances of a Ni-based single crystal superalloy

Weight reduction and advanced cooling schemes to improve aircraft engine efficiency drive the design of turbine blades toward thin-walled structures. The decrease of wall thickness leads to a decrease of creep rupture life and/or the increase of creep rate, which is termed as the thickness debit effect. To capture the nature of this effect and improve the reliability of turbine blades, creep tests at 1100 °C/130 MPa are carried out on sheet samples of a Ni-based single crystal superalloy with thicknesses from 0.60 to 2.17 mm. The creep rupture life is found to decrease with the decrease of sample thickness linearly, exhibiting an obvious thickness debit effect. The analysis of the microstructure evolution demonstrates that the rafting mechanism of the γ' phase of all samples remains the same (i.e. stress-induced, diffusion-controlled process) and is independent of the sample thickness. The fracture morphology reveals that the fracture mechanism of thin sample is a mixed fracture including micro voids and cleavage-like planes, while that of thick sample is micro voids-dominated. Environmental degradation suggests that surface damage due to oxidation and nitridation is not the primary causes for thickness debit effect, yet promotes the effect integrally. Finite element analyses and the observed dislocation configurations reveal that the thin sample is in a plane stress state, that activates six slip systems of the type {111}<110> and one slip system of the type {111}<112> during creep, while the thick sample is close to the ideal uniaxial stress state which activates all possible eight slip systems of the type {111}<110> and two slip systems of the type {111}<112>. Less slip systems activated in thin sample induce less work hardening, which results in heterogeneous deformation and shorter rupture life.

Вязко-пластическое растяжение отверстия при отбортовке нагретого листа

Correlations for stress-strain analysis for the cases of the hole extension in flanging when heated are recommended. The state of visco-plasticity of an anisotropic material, is approved in principle. Trim equations and yield conditions are used in the plane stress state sketch. Correlations for the work material continuity are obtained. The results of calculations are given.

On the inverse identification of wood elastic properties using a DIC-based FEMU approach

PurposeThis work aims to identify the linear elastic orthotropic material paramters of Pinus pinaster Ait. wood, using full-field measurements and an inverse identification strategy based on the finite element (FE) method updating technique.Design/methodology/approachCompression tests are carried out under uniaxial and quasi-static loading conditions on wood specimens oriented on the radial-tangential (RT) plane, with different grain orientations. Full-field displacements and strains are measured using digital image correlation (DIC), which are then used as a reference in the identification procedure. A FE model is implemented assuming plane stress conditions, where wood is modelled as an orthotropic homogeneous material. Based on the numerical results, a synthetic image reconstruction scheme is implemented to synthetically deform the reference experimental image, which is then processed by DIC and further compared to the experimental results.FindingsThe results for both approaches were similar when both specimen configurations were used in a single run. However, when using the DIC-based FEMU approach with the on-axis configuration, the identified modulus of elasticity in the tangential direction and shear modulus are closer to the reference values.Originality/valueThis approach ensures a fair comparison between both sets of data since the full-field strain maps are obtained through the same filter and therefore have the same strain formulation, spatial resolution and data filtering. Firstly, the identification is performed using a single configuration, either the on-axis or the off-axis specimen. Secondly, the identification is carried out by merging data from both on-axis and off-axis configurations.

Fast tooth deflection calculation method and its validation

For the development of high power density gearboxes the knowledge of the gear mesh behavior is important. Especially, the tooth deflection influences flank load distribution and is the basis for the design of flank modifications. Analytical and numerical approaches are suitable to evaluate the behavior. Since numerical methods are complex, elaborate and time-consuming, fast and accurate analytical methods are still important and are worth to be further developed and assessed.An analytical method for calculating tooth deformation for gears goes back to Weber and Banaschek from 1953. In the initial work the final equations are given without many intermediate steps in the plane strain assumption for materials with Poisson’s ratio ν = 0.3. This paper derives the tooth deflection equations in a more detailed and general manner for any linear material. The final equations are valid for the plane stress and plane strain state in one new closed representation and are therefore suitable for an efficient implementation. While the plane strain state is typical for gears, the plane stress state is significant for a thin slice model or special gearings. The presented method captures the shear influence with a more detailed calculation of the shear correction factor.A calculation study validates the results from the derived analytical tooth deflection calculation method with a plane Finite Element Model. In the study the point of application of force and the gear body are varied to cover the influence of different variants (size and mesh position). Finally limits of the analytical modeling and the validation are discussed.

A Finite Element Formulation for Highly Deformable Elastoplastic Beams Accounting for Ductile Damage and Plane Stress State

A Finite Element Formulation for Highly Deformable Elastoplastic Beams Accounting for Ductile Damage and Plane Stress State

Integrated shape and size optimization of curved tetra-chiral and anti-tetra-chiral auxetics using isogeometric analysis

Taking advantage of the powerful design potentials of isogeometric analysis, an integrated shape and size optimization framework for designing tetra chiral and anti-chiral auxetics is proposed to be capable of obtaining excellent designs without complicated implementation efforts. The framework utilizes a non-uniform rational basis spline (NURBS) based parametrization method that describes the chiral and anti-chiral structures with a small number of size and shape parameters. With this effective framework, systematic design studies considering both plane strain and stress conditions are performed to provide bounding graphs for the best achievable auxeticities under different stiffness requirements. Designs with tunable effective properties are also provided to demonstrate the capabilities of the proposed framework. The potential for electronic-skin applications is illustrated.

In-plane instability of shallow layered arches with interlayer slip

In this paper, a beam theory for predicting limit point buckling and bifurcation buckling of shallow arches composed of two layers flexibly bonded is presented. The flexibility of layer bond results in interlayer slip, which significantly affects the critical transverse loads. The presented theory is based on a layerwise assumption of the Euler–Bernoulli theory and a linear behavior of the interlayer. After establishing the equilibrium equations and boundary conditions, a numerical method for efficient solution of these equations is provided. In a first example, the presented theory is validated by comparative computations with a much more elaborate finite element analysis assuming a plane stress state. In several other examples, the effect of interlayer stiffness, load distribution and boundary conditions on the stable and unstable equilibrium paths of shallow arches with interlayer slip is investigated.

Moderately large vibrations of flexibly bonded layered beams with initial imperfections

In this paper, a beam theory is presented that allows to compute the moderately large dynamic response of slightly curved linear elastic layered beams with interlayer slip. The considered structural members are immovably supported, which leads to non-negligible membrane stresses at moderately large bending vibrations, and consequently to a geometrically nonlinear response. Based on a layerwise application of the Euler–Bernoulli theory, the boundary value problem is formulated for an arbitrary number of layers. A specification is then made for two- and three-layer beams. Several examples show the effect of an imperfect beam axis on the nonlinear dynamic response. A comparison of selected results with those of a much more expensive finite element analysis based on a plane stress state demonstrates the accuracy of the beam theory proposed.

Design and Performance Analysis of Super Highspeed Flywheel Rotor for Electric Vehicle

The optimal design of a super highspeed flywheel rotor could improve flywheel battery energy density. The improvement of flywheel battery energy density could enhance the performance of the flywheel lithium battery composite energy storage system. However, there are still many problems in the structure, material and flywheel winding of super highspeed flywheels. Therefore, in this paper, electric flywheel energy and power density parameters are designed based on CPE (Continuous Power Energy) function and vehicle dynamics. Then, according to the design index requirements, the structure, size and material of the electric flywheel rotor are designed. Furthermore, the numerical analysis model of stress and displacement of multi-ring interference fit flywheel rotor under plane stress state is established. On this basis, the influence laws of flywheel rotor wheel flange numbers and interlaminar interference on stress distribution of flywheel rotor are analyzed, and the assembly form of wheel flange is determined. Finally, the stress check of the flywheel rotor is completed. The results show that the super highspeed flywheel rotor designed in this paper meets vehicle dynamics requirements in terms of energy storage and power. In terms of strength, it meets the design requirements of static assembly stress and dynamic stress at maximum speed.

Experimental facility for studying the physical properties of materials in a plane stress state

An original experimental facility for studying the physical properties of materials during elastic-plastic deformation along two axes has been created. The facility has no ferromagnetic parts in the working area, thus enabling us to make more accurate magnetic measurements. Biaxial deformation is simulated by the finite element method in order to optimize the geometry of the specimen and to determine the stress state in the central zone of the specimen. Test experiments on the effect of biaxial tension on the coercive force of the 12G2S are performed.

Comment on “Erratum: ‘Two-dimensional porous graphitic carbon nitride C6N7 monolayer: First-principles calculations’ [Appl. Phys. Lett. 119, 142102 (2021)]” [Appl. Phys. Lett. 120, 189901 (2022)

Recently, Bafekry et al. [Appl. Phys. Lett. 120, 189901 (2022)] reported their density functional theory (DFT) results on the elastic constants of C6N7 monolayer. They predicted non-zero elastic constants along the out-of-plane direction for a single-layered material, which contradicts with basic physics of the stiffness tensor for plane stress condition. Moreover, in their work Young's modulus is erroneously calculated. On the basis of DFT calculations, herein we predicted the C11, C12 and C66 of the C6N7 monolayer to be 286, 73 and 107 GPa, respectively, equivalent with an in-plane Youngs modulus of 267 GPa. Using DFT calculations and a machine learning interatomic potential, we also show that C6N7 monolayer shows isotropic elasticity.

Methods and Case Studies of Ultra‐deep Fault Seal Evaluation

AbstractFault seals are significant for petroleum exploration and production. This study summarizes the fault sealing impacting factors, including lithological juxtaposition, mud smearing, fault rocks and the fault plane stress states, as well as evaluation methods like Allan maps and Shale Gouge Ratio (SGR). The seal evaluation for a wrench fault focuses on its particular structural features. The evaluation methods were applied to the Jinma–Yazihe structure and the Shunbei oilfield. The source rock is the Xujiahe Formation of the Upper Triassic, the reservoirs and caprocks being of the Shaximiao Formation of the Lower Jurassic. The fault sealing evaluations in major faults proved the reservoir formation processes in the wells Jinfo 1 (JF1) and Chuanya 609 (CY–609), based on the editions of the Allan map showing lithological juxtaposition, the calculation of SGR showing mud smear and analyses of fault stress states. The analyses of stress states were also applied to Shunbei 5 strike‐slip fault in the Shunbei area in Tarim Basin. The various sections along the fault were of different mechanical properties, such as compression and extension. Petroleum exploration has demonstrated that the extensional sections are more favorable for oil accumulation than the compressional sections. These evolutionary methods and other understandings will help in analyses of deep fault sealing.

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

Emerging manufacturing technologies, including 3D printing and additive layer manufacturing, offer scope for making slender heterogeneous structures with complex geometry. Modern applications include tapered sandwich beams employed in the aeronautical industry, wind turbine blades and concrete beams used in construction. It is noteworthy that state-of-the-art closed form solutions for stresses are often excessively simple to be representative of real laminated tapered beams. For example, centroidal variation with respect to the neutral axis is neglected, and the transverse direct stress component is disregarded. Also, non-classical terms arise due to interactions between stiffness and external load distributions. Another drawback is that the external load is assumed to react uniformly through the cross-section in classical beam formulations, which is an inaccurate assumption for slender structures loaded on only a sub-section of the entire cross-section. To address these limitations, a simple and efficient yet accurate analytical stress recovery method is presented for laminated non-prismatic beams with arbitrary cross-sectional shapes under layerwise body forces and traction loads. Moreover, closed-form solutions are deduced for rectangular cross-sections. The proposed method invokes Cauchy stress equilibrium followed by implementing appropriate interfacial boundary conditions. The main novelties comprise the 2D transverse stress field recovery considering centroidal variation with respect to the neutral axis, application of layerwise external loads, and consideration of effects where stiffness and external load distributions differ. A state of plane stress under small linear-elastic strains is assumed, for cases where beam thickness taper is restricted to 15^{circ }. The model is validated by comparison with finite element analysis and relevant analytical formulations.

Effect of Yield Strength on the Static and Dynamic Behaviours of Cylindrical Contact

The present paper considers the influence of yield strength on static and dynamic behaviour of cylindrical contact interface. The semi-cylinder is assumed to be in plane stress condition. A quasi-static analysis is executed by means of finite element (FE) software package ANSYS 18.2 to obtain several contact parameters. A key parameter, quantifying nonlinearity for the single-asperity cylindrical contact system is educed from the interference-contact force plot. The dynamic characteristics of the cylindrical contact interface is investigated by utilizing this parameter. In order to investigate the same, the contact interface is represented by a single degree of freedom spring-mass-damper system and the analysis is carried out for free-undamped as well as forced-damped vibration. It is found that, with higher Young’s modulus, the dynamic contact system becomes more nonlinear in nature. It is found that, with lower value of yield strength, the dynamic contact system becomes more nonlinear in nature. Moreover, the contact system is found to possess hardening type of nonlinearity.

Optimized reinforcement distribution in reinforced concrete structures under plane stress state

Optimized reinforcement distribution in reinforced concrete structures under plane stress state

Двухпараметрический критерий разрушения для трещины нормального отрыва

The study introduces a two-parametric criterion for maximum tangential stresses adapted to the Mode I crack, which includes T-stresses. The difference of this criterion is that the size of the fracture process zone is written with account for the T-stresses, while the tangential stresses in the fracture process zone are equated to the local strength of the material rather than to the ultimate strength, as it is usually done. The paper gives two-parametric fracture criteria for the case of plane stress and strain states, allowing the strain constraint along the crack front. Within the study, we obtained expressions for the effective stress intensity factor which include the T-stresses — ultimate strength ratio, in addition to the stress intensity factor. This expression allows us to determine the most dangerous point of the crack front and, provided we know the fracture toughness of the material, to estimate the crack resistance of the part with the crack. As an example of using the fracture criterion, we considered a semi-elliptical edge crack in a plate stretched in two directions.