Critical Local Stress Research Articles

Formulas for determining the critical buckling stress of I-shaped members under pure bending

Steel structures are widely used in construction, and the stability conditions for these structures are of greater concern due to their long and slender characteristics. When a plate element is subjected to axial compression, bending, shear, or a combination of these forces in its plane, the plate may buckle locally before the memberas a whole becomes unstable or before the yield stress of the material is reached. This local buckling behaviorcauses the plates in the cross-section of the steel member to interact with each other. Therefore, it is necessary to consider this interaction when calculating or checking for stability conditions. In this research, the proposed formulas determine the buckling coefficient as well as the local critical stress for I-shaped steel beams, accounting for the flange-web interaction when the flange-thickness to web-thickness ratio changes. Additionally, the buckling analysis results indicate that local buckling stress does not depend on the length-to-height ratio but is impacted by the height-to-width and thickness-to-width ratios. Comparisons between the proposed formulas and numerical results show that the suggested formulas have high reliability when the coefficient of variation is small and the coefficient of determination is very high.

Effect of macro- and micro-morphology on fluid film properties based on plasto-elastohydrodynamic lubrication

Purpose The developed plasto-elastohydrodynamic lubrication (PEHL) model is used to demonstrate the permanent change of macro morphology by critical high local stress at micro asperities in contact, which may further affect the fluid-film characteristics. Design/methodology/approach Geometric morphology is integrated into the PEHL model to elucidate the fluid-film properties governed by both macro- and micromorphologies. Findings Results show the model, accounting for combination of elastic and plastic deformations, realistically reveals fluid film distribution affected by the significant pressure highly concentrated within surface micro roughness interaction. The designed macroscopic textured surface mitigates the fluid film rupture phenomenon and prevents accumulated wear degradation from plastic deformation. Originality/value The PEHL model takes into account both elastic and plastic deformations and realistically reveals the fluid film distribution affected by large pressures that are highly concentrated in surface micro-roughness interactions. The macro-textured surfaces are designed to mitigate fluid film rupture phenomena and prevent cumulative wear caused by plastic deformation. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2024-0170/

A novel analytical method for local buckling check of box sections with unequal wall thicknesses subjected to bending

This study develops a novel analytical method to evaluate if box sections, with unequal wall thicknesses under bending, will undergo local buckling prior to reaching their yield strength since the analytical determination of critical local buckling stresses for such sections remains unexplored due to the lack of local buckling coefficients, warranting further investigation in scholarly discourse. Despite not directly computing the local buckling stresses, the developed method specifies a possible critical local buckling stress range by incorporating reference, critical, and equivalent section models, all formulated and developed with uniform wall thicknesses. The formulated method proficiently discerns the occurrence of local buckling by conducting a comparative assessment of the yield strength of the box section material against both the lower (min) and upper (max) bound stresses of the critical local buckling stress range. If local buckling persists unclear after the initial benchmark, the method reaches the final conclusion by comparing the constant wall thickness of the critical section with the web thickness of the box section. The developed method validated against finite element results obtained from linear elastic eigenvalue buckling analyses can be applied to the problem of determining whether such box sections subjected to bending will experience local buckling.

Formulas determining the local critical stress of I-shape sections under axial compression

The I-shaped steel sections should be checked for local buckling conditions during design. When local buckling occurs, there is interaction between thin-walled components of the section. Design codes have provided formulas to determine local critical stress for I-shaped steel sections, but they do not account for this interaction. This paper proposes equations for determining the local ultimate stress of I-shaped sections under axial compression, considering web and flange interaction when ratios between the height and width of the section, the flange thickness and web thickness change. The local critical stress is determined by the semi-analytical finite strip method carried out in the CUFSM program. The equations are proposed based on the parametric study. The reliability of formulas is confirmed when comparison to published and numerical results.

Effect of grain size and segregation on the cryogenic toughness mechanism in heat-affected zone of high manganese steel

High manganese steels have been nominated as desirable materials used for various cryogenic applications due to their excellent cryogenic toughness caused by twinning. High manganese steel welded joints were obtained through gas metal arc welding, and the microstructural differences at three subzones of heat-affected zone (HAZ) were utilized. The aim was to investigate the effect of grain size and Mn/C/Cu segregation on the cryogenic toughness mechanism of high manganese steel welded joints. The results indicate that the average impact absorbed energies at −196 °C for 1.0, 3.0, and 5.0 mm from the fusion line (denoted by FL + 1, FL + 3, and FL + 5) is 118.6 J, 102.4 J, and 117.2 J, respectively. Compared with base metal, the embrittlement occurred in HAZ. Large grains improve toughness, while small grain boundaries, segregation, and precipitation in HAZ deteriorate toughness. Larger grain size facilitates the primary twins with thinner inter-twin spacing and twin thickness, and the high density of these primary twins inhibits the activation of secondary twins. This, in turn, enhances cryogenic impact toughness. Although the stacking fault energy (SFE) throughout the welding joint lays within the range for the twinning-induced plasticity effect, the enrichment of Mn/C/Cu slightly increases the local SFE and critical resolved shear stress for twining within the segregation zone. This phenomenon makes the activation of primary twins more challenging. Furthermore, the C segregation at grain boundaries leads to the precipitation of fine Cr23C6 carbides. These carbides serve as crack initiation points during impact tests, contributing to degradation in cryogenic impact toughness.

Development of a Eurocode-based design method for local and distortional buckling for cold-formed C-sections encased in ultra-lightweight concrete under compression

An innovative direction in the field of light-gauge building systems has been presented in recent years when the cold formed steel (CFS) C-sections are encased in an ultra-lightweight material. The advantages of the two materials are integrated, resulting in a unique complex structure in which the encasing material provides heat insulation and fire protection. In addition, this material supports the CFS parts, which leads to an increase in their resistance to stability failures. This paper presents an innovative design procedure for encased CFS elements based on the specifications of Eurocode by applying the effective width method. The new design is based on analytical and numerical basis, incorporating the continuous bracing action of the encasing material by an elastic half-space-model, similar to sandwich beam theory. Close-form equations are derived to calculate the encased CFS's local and distortional critical stress. Furthermore, the applicability of the new design is demonstrated using a large set of experimental data of newly tested members and previously published ones. Results show that the trend of calculated and measured results matches well, making the proposed design method applicable in the investigated domain.

Experimental and numerical study on press-fitted railway axles: Competition between fretting and plain fatigue

To investigate the competitive relationship between plain and fretting fatigue in press-fitted railway axles, the plain fatigue limit and fretting fatigue strength were tested, respectively, by changing the depth of the stress relief groove. Next, detailed information on fretting and plain fatigue, as well as on fretting wear, was gathered. Finally, an evaluation methodology integrating the finite element (FE) simulation with the Modified Wöhler Curve Method (MWCM) was established to evaluate the damage in both fretting and plain fatigue scenarios. It was found that as the groove depth increased, the plain fatigue limit decreased while the fretting fatigue strength increased. The optimal groove depth, hopt, that equalized the anti-fatigue capabilities of the groove and wheel seat, was affected by the number of test cycles. For this press-fitted railway axle, hopt was 0.2 mm < hopt < 0.4 mm for 107 test cycles, and hopt > 0.6 mm for 108 cycles. The calculated critical local stress condition, σCri, required for initiating a crack, was 161.8 MPa, which almost agreed with the theoretical value. The calculated σMWCM values can be used to characterise the fretting and plain fatigue damage. The local stress condition for determining an optimal groove depth was: σMWCM in the wheel seat and groove root simultaneously reached σCri.

Elastic critical local buckling stress in cold-formed lipped channel and hat sections under uniform compression

The classical design approach for the elastic critical local buckling load of the cold-formed open section (CFOS) neglects the plate element interaction at the cross-section, which compromises the benefits of CFOSs designed for high performance. To derive a novel formula for the local buckling coefficient, taking into account the plate element interaction at the cross-section, a series of displacement functions for expressing the buckling deformations of the web, flanges, and lips caused by local buckling in CFOSs is proposed in this paper. The effect of cross-sectional geometry on the buckling coefficient was investigated using the proposed formula derived from Timoshenko’s plate buckling theory. Further, simplified formulae were proposed for the buckling coefficient and half wavelength of the elastic critical local buckling for practical use. The reliabilities of the proposed formulae were verified by comparing the results obtained from the proposed formulae with the analysis results based on the finite element method and finite strip method.

Cryogenic ductile and cleavage fracture of bcc metallic structures – Influence of anisotropy and stress states

The anisotropic cryogenic ductile and cleavage fracture properties of a body-centered cubic (bcc) steel at −196°C have been investigated under a broad spectrum of loading conditions, crossing stress triaxiality range from −1/3 to 1.5, and along three loading directions. Fracture is completely impeded in uniaxial compression tests. Conventional brittle behavior is only observed in high triaxiality conditions for the investigated bcc steel, and on the contrary ductile fracture with shear and void coalescence as underlying mechanisms takes place in low (simple shear) and moderate triaxiality (uniaxial tension) at −196°C. Cleavage fracture occurs after significant plasticity at −196°C under moderate triaxiality conditions during tensile tests using flat-notched specimens under plane-strain tension. For all the stress states, anisotropy has shown a profound influence in ductile fracture, brittle fracture, and, particularly in the transition region mixed with two failure types. It is concluded that the reason for the anisotropic transition of activated failure mechanisms crossing stress states at −196°C is because strain hardening capacity, Lankford coefficients, fracture initiation strain as well as cleavage fracture strength are all dependent on loading orientations. Based on the collected local critical stress and strain variables from finite element simulations using an evolving anisotropic plasticity model, an anisotropic unified fracture criterion revealing the underlying failure mechanisms is developed and demonstrates distinguished predictive capability in describing cryogenic ductile and cleavage fracture properties under different stress states and loading directions.

Hot tearing behavior of AZ91D magnesium alloy

Hot tearing is a serious destructive solidification defect of magnesium alloys and other casting metals. Quantitative and controllable measurements on the thermal and the mechanical behavior of an alloy during its solidification process are crucial for the understanding of hot tearing formation. We developed a new experimental method and setup to characterize hot tearing behavior via controlled cooling and active loading to force hot hearing formation on cooling at selected fractions of solid. The experimental setup was fully instrumented so that stress, strain, strain rate, and temperature can be measured in-situ while hot tearing was developing. An AZ91D magnesium alloy, which is prone to hot tearing, was used in this study. Results indicate that when hot hearing occurred, the local temperature, critical stress, and cumulative strain were directly affected by strain rate. Depending on the applied strain rate, hot tearing of the AZ91D magnesium alloy could occur in two solidification stages: one in the dendrite solidification stage (fS ∼ 0.81–0.82) and the other in the eutectic solidification stage (fS ∼ 0.99). AZ91D alloy exhibited distinct mechanical behaviors in these two ranges of fraction solid.

Estimate of Coffin-Manson Curve Shift for the Porous Alloy AlSi9Cu3 Based on Numerical Simulations of a Porous Material Carried Out by Using the Taguchi Array.

In real engineering applications, machine parts are rarely completely homogeneous; in most cases, there are at least some minor notch effects or even more extensive inhomogeneities, which cause critical local stress concentrations from which fatigue fractures develop. In the present research, a shift of the Coffin–Manson εa–N material curve in a structure with random porosity subjected to dynamic LCF loads was studied. This allows the rest of the fatigue life prediction process to remain the same as if it were a homogeneous material. Apart from the cyclic σ–ε curve, which is relatively easy to obtain experimentally, the εa–N curve is the second most important curve to describe the correlation between the fatigue life N and the strain level εa. Therefore, the correct shift of the εa–N curve of the homogeneous material to a position corresponding to the porous state of the material is crucial. We have found that the curve shift can be efficiently performed on the basis of numerical simulations of a combination of five porosity-specific geometric influences and the associated regression analysis. To model the modified synthetic εa–N curve, five geometric influences of porosity by X-ray or μ-CT analysis are quantified, and then the porosity-adjusted coefficients of the Coffin–Manson equation are calculated. The proposed approach has been successfully applied to standard specimens with different porosity topography.

Axial compression behaviour of cruciform cold-formed steel built-up columns: Shape optimization and experimental study

In this paper, the cruciform CFS built-up cross sections are formed through four identical multi-roll lipped channels connected at their webs with high-strength bolts and filler plates. An optimization algorithm is primarily proposed that integrates sequential quadratic mathematical programming methods and finite strip analysis. It is desirable to effectively improve the buckling behaviour of cruciform CFS built-up columns without increasing the material volume. Eight different areas of built-up sections were optimized, each built-up open section was formed by fold-lines of the steel plate, and the width and angle of the constituent elements of the built-up section were selected as the main design variables. To simplify the optimization task and provide more practical structural components, usage constraints and practical manufacturing limits were imposed on the selected built-up sections during the optimization process. The results show that the adopted optimization process significantly increased the critical local buckling stress of the cruciform CFS built-up columns by 26.2%–58.9%. The design strength calculated according to the AISI standard was increased by 2.76%–18.15%. The axial compression bearing capacity tests with two different optimized cross sections were conducted, and the test loading capacities and failure modes of each specimen were obtained. The test results show that the failure modes were mainly driven from local and distortional buckling to torsional and flexural buckling with increasing slenderness, and the deformations were concentrated in the region near the end of column. Finally, the axial compression strengths of such cruciform CFS built-up columns obtained from the tests were used to assess the applicability of AISI standards. For columns failed by local and distortional buckling, AISI standard were un-conservative, whereas for torsional and flexural, AISI standard were conservative.

Cleavage Fracture of the Air Cooled Medium Carbon Microalloyed Forging Steels with Heterogeneous Microstructures.

Cleavage fracture of the V and Ti-V microalloyed forging steels was investigated by the four-point bending testing of the notched specimens of Griffith-Owen’s type at −196 °C, in conjunction with the finite element analysis and the fractographic examination by scanning electron microscopy. To assess the mixed microstructure consisting mostly of the acicular ferrite, alongside proeutectoid ferrite grains and pearlite, the samples were held at 1250 °C for 30 min and subsequently cooled instill air. Cleavage fracture was initiated in the matrix under the high plastic strains near the notch root of the four-point bending specimens without the participation of the second phase particles in the process. Estimated values of the effective surface energy for the V and the Ti-V microalloyed steel of 37 Jm−2 and 74 Jm−2, respectively, and the related increase of local critical fracture stress were attributed to the increased content of the acicular ferrite. It was concluded that the observed increase of the local stress for cleavage crack propagation through the matrix was due to the increased number of the high angle boundaries, but also that the acicular ferrite affects the cleavage fracture mechanism by its characteristic stress–strain response with relatively low yield strength and considerable ductility at −196 °C.

Investigation of Pop-in Formation Mechanism in Fracture Toughness Test of Welded Joint and Improvement of Acceptance Criteria

A pop-in is a small, arrested brittle crack that occurs during a fracture toughness test. This is one of the important factors of the CTOD assessment of a welded joint because the fracture toughness of material differs by the significance of the pop-in. The current standard of the pop-in is said to be too conservative because of the reasons below; the absence of the test methodology which ensures the generation of pop-ins, and the difference of the loading mode between the CTOD test and the real structures. The objective of this study is to investigate the mechanism of the pop-in formation and to improve the pop-in acceptance criteria. This study is aimed to come up with a new standard of pop-in significance determination with the idea of the local critical stress criterion and newly proposed crack propagation model incorporating energy consumption theory. That is, the CZM considering that the critical stress works as the local crack propagation criterion, and the fracture surface energy expressing plastic dissipation beneath the running crack wake is defined in each propagation, has been proposed. When the stress of the crack tip approaches the critical fracture stress, the cohesive strength is lost, and the fracture surface is created. When the cohesive strength is lost, it takes away the fracture surface energy. In the physical aspect, the fracture surface energy is increased as the fracture surface roughness increases. The Charpy test with the three-sided specimen is conducted to find the relationship between the fracture surface roughness and the fracture surface energy. The appropriate value or function of the fracture surface energy is determined by the roughness of the fracture surface and trial and error of the FEM analysis. The result of the FEM analysis is well validated with the experimental data. Finally, the authors calculate many extrapolated conditions of toughness distribution and LBZ width and conclude the current pop-in judgment criterion is too severe and propose a new rational one.

Local buckling of thin-walled circular hollow section under uniform bending

This article presents a semi-analytical finite strip method based on Marguerre’s shallow shell theory and Kirchhoff’s assumption. The formulated finite strip is used to study the buckling behavior of thin-walled circular hollow sections (CHS) subjected to uniform bending. The shallow finite strip program of the present study is compared to the plate strip implemented in CUFSM4.05 program for demonstrating the accuracy and better convergence of the former. By varying the length of the CHS, the signature curve relating buckling stresses to half-wave lengths is established. The minimum local buckling point with critical stress and corresponding critical length can be found from the curve. Parametric studies are performed to propose approximative expressions for calculating the local critical stress and local critical length of steel and aluminum CHS.

A numerical study on nanometric cutting mechanism of lutetium oxide single crystal

It is hard for ultra-precision machining to realize nanometric accuracy on lutetium oxide single crystal. However, molecular dynamics analysis can be employed to reveal the atomic scale details of material removal process, providing a theoretic basis. This article focuses on both cutting speed and cutting depth, analyzing the influence on cutting force, stress distribution, subsurface deformation and crack formation. The results show that amorphization takes place in the region which undergoes a high compressive stress. Crack initiation emerges with a release of tensile stress and is always accompanied with a sharp drop in cutting force. A higher cutting speed and larger cutting depth result in a larger critical local tensile stress for crack initiation. Cutting zone and interface area are prone to damage concentration. Once these damages combine together, there would be a visible bulk material peeling off.

Critical Stresses in Materials with Cracks

The fracture mechanics concepts, as well as the concepts introduced on the basis of principle of critical energy, correlated with strength of materials with cracks is analysed. The equivalent stress method of strength was applied to cracked materials, by using the concept of local critical stress. This one depends on the material behavior and the deterioration due to crack. Experimental results have been obtained with specimens of OL304 steel with different cracks. The influence of crack depth and crack width is put into evidence.

Strength and Fracture Toughness of Hardox-400 Steel

This paper presents results of strength and fracture toughness properties of low-carbon high-strength Hardox-400 steel. Experimental tests were carried out for specimens of different thickness at wide temperature range from −100 to 20 °C. The dependences of the characteristic of material strength and fracture toughness on temperature based on experimental data are shown. Numerical calculation of the stress and strain distributions in area before crack tip using the finite element method (FEM) was done. Based on results of numerical calculation and observation of the fracture surfaces by scanning electron microscope (SEM), the critical local stress level at which brittle fracture takes place was assessed. Consideration of the levels of stress and strain in the analysis of the metal state at the tip of the crack allowed to justify the occurrence of the brittle-to-ductile fracture mechanism. On the basis of the results of stretch zone width measurements and stress components, the values of fracture toughness at the moment of crack initiation were calculated.

A refined model for local buckling of rectangular CFST columns with binding bars

This paper presents a refined model for local buckling of rectangular concrete-filled steel tubular (CFST) columns with binding bars under axial compression due to a deficiency in the previous model i.e. the influences of horizontal spacing and diameter of binding bars were not considered. The influences of longitudinal spacing, horizontal spacing and diameter of binding bars on the critical local buckling stress can be reasonably considered in the proposed model, which is applicable to both elasto-plastic phase and elastic phase. The refined model is verified against the experimental results, showing better agreement than the previous model. Then, the proposed model is employed to investigate the influences of longitudinal spacing, horizontal spacing, diameter of binding bars and cross-sectional aspect ratios on the critical local buckling stress. It is found that the critical local buckling stress increases considerably with the decrease of the spacing of binding bars. Furthermore, the influence of longitudinal spacing of binding bars on the critical local buckling stress is more significant than that of horizontal spacing. It is also found that the critical local buckling stress increase modestly with the increase of diameter of binding bars in the case of small spacing of binding bars. In addition, the cross-sectional aspect ratio have little influence on the critical local buckling stress, which can be ignored. Aiming at delaying the occurrence of local buckling of steel plates in rectangular CFST columns with binding bars, it is suggested that decreasing longitudinal spacing as an efficient measure has priority over other measures.

On the phase field modeling of crack growth and analytical treatment on the parameters

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is utilized to solve the complete system of crack phase field and mechanics equations. The analytical expressions for the crack surface profile and the crack tip velocity are verified with the numerical solutions. It is shown that under mode I cracking and proper calibration of parameters, phase field models always agree with Griffith’s theory.