In-plane Compressive Stress Research Articles

Comparative studies of the long-term corrosion behavior of Zr-Sn-Fe-Cr-Ni alloys in pure water at 360°C/18.6 MPa with high and low dissolved oxygen content

This study compared the uniform corrosion behavior of Zr-Sn-Fe-Cr-Ni alloys in deionized water at 360°C/18.6 MPa with high and low concentration of dissolved oxygen (DO). It was found that high concentration of DO accelerated the corrosion rate of the Zr-Sn-Fe-Cr-Ni alloys and led to an earlier corrosion transition. Increased DO concentration resulted in a higher content of t-ZrO2 near the metal-oxide interface, which induced greater in-plane compressive stress in the oxide film and a high-level phase transformation from t-ZrO2 to m-ZrO2. This, in turn, led to an earlier occurrence of corrosion transition.

Boosting the efficiency of InGaN-based green LEDs grown on Si through buffer strain engineering

InGaN-based micro-light-emitting diodes (LEDs) grown on Si have gained tremendous interest for full-color displays. Strain management is a key challenge for the epitaxial growth of InGaN-based long-wavelength LEDs on Si because the accumulated compressive strain can severely limit In incorporation and degrade the quality of InGaN multi-quantum wells (MQWs) when the conventional Al-composition step-graded AlN/AlGaN buffer is used for strain control. In this work, we demonstrate a promising approach to effectively reduce the in-plane residual compressive stress of GaN by using an AlN single-layer buffer. The in-plane lattice parameter of the GaN underlayer was increased from 3.183 to 3.189 Å with the residual compressive stress at room temperature reduced from 0.37 to ∼0 GPa, which significantly improved the In incorporation of InGaN MQWs and extended the photoluminescence wavelength from 510 to 550 nm. A remarkably high internal quantum efficiency of 78% was thus achieved for the as-grown InGaN-based green LEDs on Si. This work paves the way for the growth of high-efficiency InGaN-based long-wavelength micro-LEDs.

Peculiarity of hydrogen absorption in duplex steels: Phase-selective lattice swelling and stress evolution

Electrochemical hydrogen absorption in duplex steels is not fully understood. In this work, an in-situ synchrotron cross-sectional X-ray micro-diffraction analysis is performed on steel with comparable phase fractions of ferrite and austenite, coupled with electrolytic hydrogen charging. The results reveal that charging with a constant current density of 10 mA/cm² for 5 h leads to expanding the austenitic lattice to a depth of approximately 250 µm, up to ≥0.15 %. In contrast, the lattice parameter of the ferrite phase remains unchanged during this process. As the austenite expansion progresses, it generates different amounts of equivalent in-plane compressive stresses, which amount to approximately -150 and -450MPa in the austenite and ferrite phases at the sample surface, respectively. Using a finite element model of grain interaction, this difference is qualitatively interpreted by mutual mechanical constraints between ferrite and austenite, as well as between the hydrogen-charged surface layer and the underlying material.

Impact of temperature on residual stress and bonding in diamond-like carbon film: A molecular dynamics study under various deposition conditions

Diamond-like carbon (DLC) films exhibit excellent frictional properties; however, the high residual stress within the film, which causes detachment issues, limits their application in mechanical sliding surfaces. We have previously clarified via molecular dynamics (MD) simulations that the growth of sp3 clusters after the transition from sp2 to sp3 bonds during film formation causes the in-plane compressive stress in DLC films. In this study, we investigated whether this stress generation mechanism holds under various deposition conditions in the MD simulations, wherein incident energy, atomic flux, and substrate temperature were systematically changed. The results of the MD simulations consistently revealed that the compressive stress generation mechanism remains unchanged across different deposition conditions. With increasing incident energy and atomic flux and decreasing substrate temperature, in-plane compressive stress in the film increased owing to increased sp3 content. Conversely, when the incident energy was further increased, both stress and sp3 content decreased. Based on a molecular statistical calculation, it was shown that the stable bonding state changed from sp3 to sp2 at high temperatures. Because the temperature monotonically increased with increasing incident energy, it was concluded that the change in the stable bonding state caused the non-monotonic change in the stress and sp3 content at high temperatures.

Demonstration of 651 nm InGaN-based red light-emitting diode with an external quantum efficiency over 6% by InGaN/AlN strain release interlayer.

This work reports a high-performance InGaN-based red-emitting LED with a strain-release interlayer (SRI) consisting of an InGaN stress-release layer (SRL) and an AlN dislocation confinement layer (DCL) in unintentionally doped GaN (u-GaN). The SRL introduces a tensile strain which could decrease the in-plane compressive stress of the u-GaN layer, while the DCL could reduce the dislocation density and thus improve the crystal quality of the u-GaN layer. Consequently, a high-efficiency InGaN-based red-emitting LED with a peak wavelength of 651 nm and an external quantum efficiency of 6.04% is realized. In addition, the room-temperature photoluminescence (PL) mapping emission wavelength is uniform across a 4-inch wafer with a standard deviation of 3.3 nm. Therefore, the proposed SRI offers good potential for mass-producing high-performance and long-wavelength InGaN-based red-emitting LEDs.

Elastic properties and mechanical stability of bilayer graphene: molecular dynamics simulations

Graphene has become in last decades a paradigmatic example of two-dimensional and so-called van-der-Waals layered materials, showing large anisotropy in their physical properties. Here, we study the elastic properties and mechanical stability of graphene bilayers in a wide temperature range by molecular dynamics simulations. We concentrate on in-plane elastic constants and compression modulus, as well as on the atomic motion in the out-of-plane direction. Special emphasis is placed upon the influence of anharmonicity of the vibrational modes on the physical properties of bilayer graphene. We consider the excess area appearing in the presence of ripples in graphene sheets at finite temperatures. The in-plane compression modulus of bilayer graphene is found to decrease for rising temperature, and results to be higher than for monolayer graphene. We analyze the mechanical instability of the bilayer caused by an in-plane compressive stress. This defines a spinodal pressure for the metastability limit of the material, which depends on the system size. Finite-size effects are described by power laws for the out-of-plane mean-square fluctuation, compression modulus, and spinodal pressure. Further insight into the significance of our results for bilayer graphene is gained from a comparison with data for monolayer graphene and graphite.Graphic abstract

Phase composition of polycrystalline HfNx (0.45 ≤ x ≤ 1.60) and effects of low-energy ion irradiation on microstructure, texture, and physical properties

We have investigated the phase composition of HfNx as a function of x and the effects of low-energy ion irradiation on the microstructure and physical properties of polycrystalline layers grown on SiO2 at 350 °C by ultrahigh vacuum reactive dc magnetron sputtering of Hf in mixed N2/Ar discharges. X-ray diffraction and Rutherford backscattering spectrometry results show that the phases obtained in polycrystalline HfNx layers with increasing x are hcp-structure α-Hf:N (x ≲ 0.6); multiphase mixtures consisting of α-Hf, NaCl-structure δ-HfN, rhombohedral ɛ-Hf3N2, and/or ζ-Hf4N3 (0.6 ≲ x ≲ 0.9); δ-HfN single phase (0.9 ≲ x ≲ 1.3); and mixtures of δ-HfN and higher nitrides (x ≳ 1.3). HfNx layers with 0.9 ≲ x ≲ 1.2 grown under mild ion irradiation (incident ion energy Ei ≃ 7 eV and ion-to-Hf flux ratios Ji/JHf = 1−3) are underdense with mixed orientation, low in-plane stress, and rough surface morphology due to limited adatom mobilities resulting in kinetic roughening and atomic shadowing during film growth. However, the use of intense ion irradiation (Ei = 25 eV and Ji/JHf = 4−20) results in HfNx layers, which are fully dense with strongly 111-oriented texture, compressive in-plane stress, and smooth surfaces due to ion irradiation enhanced adatom surface mobilities. In addition, the latter films have lower resistivity and higher hardness. For stoichiometric δ-HfN layers, ρ decreases from 69.7 to 35.2 μΩ cm and H increases from 22.1 to 27.4 GPa, with increasing ion-irradiation intensity. However, for HfNx layers with 1.2 ≲ x ≲ 1.6, the correspondingly higher steady state atomic N surface coverages during deposition alter growth kinetics in favor of 001 texture with a fully dense structure and compressive in-plane stress.

Stress effect on the leakage current distribution of ferroelectric Al0.7Sc0.3N across the wafer

This study presents an investigation into the stress effect on the leakage current in ferroelectric Al0.7Sc0.3N films by experiments and density functional theory (DFT) computations. The experiments are based on 8-in. 100 nm Al0.7Sc0.3N films obtained from pulsed DC co-sputter deposition technology, which exhibit non-uniform compressive in-plane stress across the wafers and similar distributions of leakage current, suggesting close dependence between each other. DFT computations revealed that stress affects leakage current in two ways: the level of traps introduced by nitrogen vacancy and the formation energy of nitrogen vacancy in Al0.7Sc0.3N. By considering both factors, the leakage current of Al0.7Sc0.3N films increases with larger compressive in-plane stress, as observed in the experimental results. Additionally, the DFT calculation results indicated that the leakage current is more sensitive to compressive stress compared to the tensile, and the minimum leakage current can be obtained with neutral in-plane stress. These findings provide a guideline for stress engineering to optimize the AlScN-based ferroelectric devices.

Strain engineering of the electro-optic effect in polycrystalline BiFeO3 films [Invited

Electro-optic thin film materials, which change their refractive index upon the application of an electric field, are crucial for the fabrication of optical modulators in integrated photonic circuits. Therefore, it is key to develop strategies to tune the linear electro-optic effect. Strain engineering has arisen as a powerful tool to optimize the electro-optic coefficients in ferroelectric thin films. In this report, the electro-optical properties of polycrystalline bismuth ferrite (BiFeO3) thin films are studied. The electro-optic coefficients (reff) of low-cost solution-processed BiFeO3 films under different substrate-induced thermal stress are characterized using a modified Teng-Man technique in transmission geometry. The influence of poling state and substrate stress on the electro-optical properties are discussed. The films show a notable piezo-electro-optic effect: the effective electro-optic coefficient increases both under compressive and tensile in-plane stress, with compressive stress having a much more profound impact. Electro-optic coefficients of 2.2 pm/V are obtained in films under a biaxial compressive stress of 0.54 GPa.

Ultimate Shear Strength of Pitted Plates with Crack Using Finite Element Method

_ Ultimate strength of thin steel plates was studied under shear loading when pitting corrosion and cracking occur simultaneously. Nonlinear finite element method was used and the effects of different geometrical parameters, such as crack position, crack length, pit depth, pit diameter, number of the pits, and the inclination angle of the crack, were investigated. It was found that the degree of the pitting (DOP) significantly reduces the ultimate shear strength of the pitted plates when the corrosion is low. For high amount of corrosion, the reduction of the ultimate shear strength remains the same regardless of the amount of the DOP. In plates with short cracks, the crack length has no influence on the reduction of the ultimate shear strength. Also, it was found that the position of the crack is more effective than the length of the crack on the reduction of the ultimate shear strength of the cracked plates. In the cracked-pitted plates, there was no interaction between crack and pit for extremes value of DOP. For low value of DOP, the ultimate shear strength of the cracked-pitted plate was the same as the cracked plate, and for large value of DOP, it is the same as pitted plate. Introduction According to a study performed between 2002 and 2008 by American Bureau of Shipping (ABS) (“Review of Current Practices of Fracture” 2012), majority of reported fractures of the ships were structural failures, such as weld defect, buckling, fracture, and cracking. Cracks and corrosion are two more common defects, which are the main reasons of the failure of the aged steel structures. Plates and stiffened plates are the main structural elements in many structures, including airplanes, bridges, offshore structures, and ships. Ultimate strength evaluation of these structural elements is crucial for rational design of structures, such as Load Resistance Factor Design (LRFD) methods in civil engineering and Ultimate Strength (UTS) evaluation in ship structure. Many studies are carried out to evaluate ultimate strength of intact and damaged plates/ stiffened plates under in-plane compressive stress. Ranji (2012) studied ultimate strength of plate with general corrosion under in-plane compression. He proposed a spectrum for random generation of corroded surface and ultimate strength of corroded plate was evaluated using computer code ANSYS. Ranji and Zarookian (2015) analyzed ultimate strength of cracked stiffened plates with cracks having different stiffeners numerically.

Fatigue behavior of vacuum-sintered binder jetted fine 316L stainless steel powder

The study examined the impact of surface roughness on the high-cycle fatigue (HCF) properties of vacuum-sintered binder jetted gas atomized fine 316L stainless steel (SS) powder. The microstructure and density of the as-sintered specimens were analyzed using micro-computed tomography, indicating a relative density of ∼99.8 ± 0.1% with equiaxed grains surrounded by delta-ferrite phase at the grain boundaries (volume fraction of ∼2%). The as-sintered specimens had a rough surface with an arithmetical mean roughness of Ra = 6.56 ± 0.58 μm and root-mean-square roughness of Rq = 8.29 ± 0.68 μm. After mechanical grinding, the surface roughness was reduced to Ra = 0.21 ± 0.03 μm and Rq = 0.25 ± 0.04 μm. Microhardness analysis revealed an increase of nearly 70% up to 125 μm beneath the surface of mechanically ground specimens. The enhanced surface hardness was found to be related to an in-plane compressive residual stress on the mechanically ground sample. The fatigue endurance limit was evaluated using the staircase test methodology, with an average value of ∼170 and 225 MPa for the as-sintered and mechanically ground parts, respectively. High-cycle fatigue experiments were conducted at a stress ratio of Rσ = −1, and the results showed that surface grinding improved fatigue life at higher stress levels due to in-plane compressive stress and the reduction in surface roughness. Fractography revealed that the fracture mechanisms in the crack propagation and final fracture zones were striation marks and dimple features. Finally, the electron backscatter diffraction technique was used to study the deformation history at different sites close to the fracture surface.

Dielectric and Antiferroelectric Properties of AgNbO3 Films Deposited on Different Electrodes

AgNbO3 antiferroelectric materials have become a hot topic due to their typical double polarization–electric field loops. AgNbO3 films usually exhibit superior properties to bulks. In this work, AgNbO3 films were fabricated via the pulsed laser deposition on (001) SrTiO3 substrate with (La0.5Sr0.5)CoO3, LaNiO3 and SrRuO3 bottom electrodes, in which the (La0.5Sr0.5)CoO3, LaNiO3 and SrRuO3 bottom electrodes were used to regulate the in-plane compressive stress of AgNbO3 films. It is found that AgNbO3 films deposited on (La0.5Sr0.5)CoO3, LaNiO3 and SrRuO3 bottom electrodes are epitaxial with dense microstructure. In changing the bottom electrodes from (La0.5Sr0.5)CoO3, LaNiO3 to SrRuO3, the in-plane compressive stress of AgNbO3 thin films becomes weaker, which leads to increased relative dielectric permittivity and reduced antiferroelectric–ferroelectric phase transition electric field EF from 272 kV/cm to 190 kV/cm. The reduced EF implies weakened antiferroelectric stability in AgNbO3 films. It can be seen that the antiferroelectric stability of AgNbO3 films could be regulated by changing the bottom electrodes.

Atomic Layer Deposition of Sb2 Te3 /GeTe Superlattice Film and Its Melt-Quenching-Free Phase-Transition Mechanism for Phase-Change Memory.

Atomic layer deposition (ALD) of Sb2 Te3 /GeTe superlattice (SL) film on planar and vertical sidewall areas containing TiN metal and SiO2 insulator is demonstrated. The peculiar chemical affinity of the ALD precursor to the substrate surface and the 2D nature of the Sb2 Te3 enable the growth of an in situ crystallized SL film with a preferred orientation. The SL film shows a reduced reset current of ≈1/7 of the randomly oriented Ge2 Sb2 Te5 alloy. The reset switching is induced by the transition from the SL to the (111)-oriented face-centered-cubic (FCC) Ge2 Sb2 Te5 alloy and subsequent melt-quenching-free amorphization. The in-plane compressive stress, induced by the SL-to-FCC structural transition, enhances the electromigration of Ge along the [111] direction of FCC structure, which enables such a significant improvement. Set operation switches the amorphous to the (111)-oriented FCC structure.

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.

Tunable band gap of diamond twin boundaries by strain engineering

Diamond thin films are promising wide band gap semiconductor materials for applications in electronic and microwave devices. Revealing the mechanism of how twin boundaries impact the band gap of diamond is of critical importance since they are the most common defects in polycrystalline diamond films. Here, nanocrystalline diamond films are synthesized by microwave plasma-enhanced chemical vapor deposition. The atomic and electronic structures of diamond lamellar and fivefold twins, and their evolution behaviors with the increase of axial tensile strain, are investigated by combining aberration-corrected transmission electron microscopy with first-principles calculations. There is no intrinsic stress concentration at the lamellar twin boundary, and its band gap equals to that of the bulk diamond ( i.e. , 5.3 eV). An intrinsic in-plane compressive stress field is formed and the band gap is increased evidently ( i.e. , 0.6 eV) in the center of fivefold twins. When applying an axial tensile strain up to 15%, the band gaps of the bulk diamond, lamellar and fivefold twins reduce significantly to 2.2 eV, 2.1 eV and 2.4 eV, respectively, which are mainly due to the decrease of p z orbital energy caused by the increase of axial bond length during the tensile process. Under the same axial tensile strain, the band gap of the fivefold twin is always larger than those of the lamellar twin and the bulk diamond due to the formation of in-plane five-membered carbon rings in the center. The findings of the tunable band gap by strain engineering will benefit for the innovation and design of advanced diamond functional devices. • Atomic and electronic structures of diamond lamellar and fivefold twins under tensile strains have been investigated. • The band gap of fivefold twins is evidently larger than that of the bulk diamond. • Under axial tensile strains, the band gap of bulk diamond, lamellar and fivefold twins reduces significantly. • The reduction of band gap is due to the decrease of p z orbital energy caused by the increase of axial bond length.

Machining-induced residual stress analysis and multi-objective optimization for milling process of Mg–Li alloy

Machining-induced residual stress in an Mg–Li alloy can lead to a significant deformation of its machined thin-walled parts. To solve this issue, an integrated method that combined the grey relational analysis (GRA), back propagation (BP) neural network, and non-dominated sorting genetic algorithm-III (NSGA-III) was proposed in this study aimed to analyze the dominant mechanism of residual stress and achieve a super-objective cooperative optimization of residual stress in the LA103Z Mg–Li alloy milling process. A typical spoon-shaped distribution of surface tensile stress and subsurface compressive stress was presented in the Mg–Li alloy owing to the coupling interaction between the cutting force and temperature. The increase in the cutting temperature owing to an increase in the cutting speed was proven to be the overarching factor that induced residual stress by the correlation analysis of cutting parameters, force–heat of cut and residual stress. The BP prediction models of the residual stress were established, and the predicted values were in good agreement with the test values, with a maximum error of 5.07 %. The NSGA-III optimization algorithm was used to search for the lowest values of in-plane tensile and compressive stresses (σtx, σty, σcx and σcy). The optimized cutting speed, feed, and cutting depth were determined to be 61 m/min, 0.068 mm/z, and 0.58 mm, respectively. The maximum predictive error of four residual stresses was experimentally verified to be 15.94 %, which proved the feasibility of the multi-objective optimization approach. The residual stress level of the optimized scheme evidently decreased compared with that of the current milling scheme, with the maximum reduction of 28.37 %. Therefore, the propsoed approach can effectively reduce the risk of warping and distortion of machined Mg–Li alloy parts.

High Rate Deposition of Piezoelectric AlScN Films by Reactive Magnetron Sputtering from AlSc Alloy Targets on Large Area.

This paper reports on the deposition and characterization of piezoelectric AlXSc1-XN (further: AlScN) films on Si substrates using AlSc alloy targets with 30 at.% Sc. Films were deposited on a Ø200 mm area with deposition rates of 200 nm/min using a reactive magnetron sputtering process with a unipolar–bipolar hybrid pulse mode of FEP. The homogeneity of film composition, structural properties and piezoelectric properties were investigated depending on process parameters, especially the pulse mode of powering in unipolar–bipolar hybrid pulse mode operation. Characterization methods include energy-dispersive spectrometry of X-ray (EDS), X-ray diffraction (XRD), piezoresponse force microscopy (PFM) and double-beam laser interferometry (DBLI). The film composition was Al0.695Sc0.295N. The films showed good homogeneity of film structure with full width at half maximum (FWHM) of AlScN(002) rocking curves at 2.2 ± 0.1° over the whole coating area when deposited with higher share of unipolar pulse mode during film growth. For a higher share of bipolar pulse mode, the films showed a much larger c-lattice parameter in the center of the coating area, indicating high in-plane compressive stress in the films. Rocking curve FWHM also showed similar values of 1.5° at the center to 3° at outer edge. The piezoelectric characterization method revealed homogenous d33,f of 11–12 pm/V for films deposited at a high share of unipolar pulse mode and distribution of 7–10 pm/V for a lower share of unipolar pulse mode. The films exhibited ferroelectric switching behavior with coercive fields of around 3–3.5 MV/cm and polarization of 80–120 µC/cm².

High External Quantum Efficiency Green Light Emitting Diodes on Stress-Manipulated AlNO Buffer Layers

We demonstrated high-brightness InGaN/GaN green light emitting diodes (LEDs) with ex-situ sputtered stress-manipulated AlNO buffer on 4-inch patterned sapphire substrates. The lattice constant of the AlNO buffer was adjusted by oxygen flow. As a result, the dislocation density and the in-plane compressive stress caused by lattice mismatch were greatly reduced, while the interface quality of the InGaN/GaN multiple quantum wells and the uniformity of the indium composition were greatly improved. At 20A/cm², the external quantum efficiency and wall plug efficiency of the 526.4-nm-green LEDs grown on the sputtered AlNO buffer reached 46.1% and 41.9%, which were both higher than reported values.

Thermal stress control of the polymorphic transformation in MnTe semiconductor films

The polymorphic transformation of the compound MnTe between its wurtzite-type (β) and nickeline-type (α) crystalline phase results in a significant change in its physical properties. In this study, the effect of thermal stress on the β→α transformation in MnTe films was investigated by varying the materials used for the MnTe film's capping layers (Ni, Ti, Mo, W, and SiO2). The capping layer/β-MnTe stacked films were heated above the transformation temperature, and the volume fraction of the material that transformed during the heating was evaluated using XRD measurements. In-plane compressive thermal stress observed at the interface between the MnTe film and capping layer promotes the β→α transformation. The in-plane thermal stress at the interface that induces the β→α transformation has linear temperature dependence, and the gradient of this dependence was estimated to be around −20.5 MPa K−1. The obtained results indicate that the polymorphic transformation of the MnTe film can be controlled by the thermal stress generated by mechanical constraints induced by the surrounding layers. The results of this study offer new insights into the design of MnTe-based phase-change devices and the application of straintronics in semiconductor films.

Critical limit of diameter-to-thickness ratio for inner tubes of DSSTCC columns

To improve the confinement efficiency of steel tubes to the sandwiched concrete, the concept of double skin steel tubes confined concrete (DSSTCC) columns was proposed. This paper aims to theoretically investigate the local stability of inner steel tubes in DSSTCC columns. Firstly, considering that the stress state and failure mode of the inner steel tube are similar to those of the fixed circular arch subjected to a uniform radial load, the arc section of the inner steel tube was simplified into a circular arch for stress analysis. Secondly, the expected value of the in-plane elastic ultimate axial compressive stress of the circular arch was solved by the Monte Carlo method, and the ratio of its value to the yield stress was used to characterize the stable state of the inner tube. Then, the influence of the maximum included angle corresponding to the formed circular arch on the result was discussed, and an empirical formula was given to obtain a reasonable estimation of the critical limit of diameter-to-thickness ratio. Finally, it can be seen from the analysis that the method proposed in this paper is suitable for inner tubes made of the material with an elastic perfectly-plastic model, a bilinear model, or a bilinear plus nonlinear hardening model. These results are a contribution to the buckling analysis of inner tubes.