Inelastic Bending Research Articles

3‐D Structure and Development of a Metamorphic Core Complex in the Northern South China Sea Rifted Margin

AbstractThe 3‐D structure of continental metamorphic core complexes (MCCs) and their coevolution along with the associated extensional detachments are still not well understood. In this study, analysis of a newly acquired high‐resolution 3‐D seismic reflection volume reveals for the first time a well‐imaged MCC in the proximal northern South China Sea (SCS) rifted margin, the Kaiping MCC (KP MCC). These data provide a 3‐D view of the KP MCC and the associated KP detachment fault. The KP MCC is characterized by ascend of ductile midcrustal materials, and it is partially exhumed in the KP9 High. The KP detachment fault displays a domed low‐angle geometry, and is characterized by pronounced NS‐plunging corrugations, among which two megacorrugations of tens of kilometers are revealed. Evidence show that the KP MCC developed according to the classical rolling‐hinge model. A group of secondary normal faults and fractures, which are parallel to the axis of the KP MCC and offset the KP detachment surface at the crest of the MCC, developed in response to inelastic bending during progressive warping of the footwall. The migration of the domal seismic reflection layers provides a visual evidence for the kinematic process of the rolling‐hinge activity, during which the brittle‐ductile transition and the rolling hinge gradually migrate as the detachment fault slips. The origin of the KP MCC in the northern SCS margin is suggested to have been favored by the existence of a pre‐existing midcrustal ductile layer and basement structures within the upper brittle crust.

Analysis of Equivalent Flexural Stiffness of Steel–Concrete Composite Beams in Frame Structures

Vertical deflection of a frame beam is an important indicator in the limit-state analysis of frame structures, particularly for steel–concrete composite beams, which are usually designed with large spans and heavy loads. In this study, the equivalent flexural stiffness of composite frame beams is analysed to evaluate their vertical deflection. A theoretical beam model with a spring constraint boundary and varied stiffness segments is established to consider the influence of both the rotation restraint stiffness at the beam ends and the cracked section in the negative moment region, such that the inelastic bending deformation of the composite beams can be elaborately described. By an extensive parametric analysis, a fitting formula for evaluating the equivalent flexural stiffness of the composite beams, including the effects of the rotational constraint and the concrete cracking, is obtained. The validity of the proposed formula is demonstrated by comparing its calculation accuracy with those of existing design formulas for analysing the equivalent flexural stiffness of the composite beam members. Moreover, its utility is further verified by conducting non-linear finite element simulations of structural systems to examine the serviceability limit state and the entire process evolution of beam deflections under vertical loading. Finally, to facilitate the practical application of the proposed formula in engineering design, a simplified method to calculate the deflection of composite beams, which utilises the internal force distribution of elastic analysis, is presented based on the concept of equivalent flexural stiffness.

The Dahl’s Model for the Inelastic Bending Behavior of Textile Composite Preforms. Analysis of its Influence in Draping Simulation

Most of the numerical simulations of dry textile reinforcements forming are based on a macroscopic approach and continuous material models whose behavior is assumed to be elastic (linear or nonlinear). On the one hand, the experience shows that under loading/unloading stresses, residual inelastic deformations are observed. On the other hand, among the deformations that a woven reinforcement undergoes during forming, in most cases, only bending is subject to loading/unloading stresses. The first objective of this work is to highlight the inelastic bending behavior of textile reinforcements during a forming process and to find the possible origins of inelasticity. The second objective is to find the cases generating bending loading/unloading during forming as well as to study the influence of the bending inelasticity on forming simulation. For this purpose, the inelastic bending behavior was characterized by three-point bending tests. Then, the Dahl friction model was adapted to bending to describe the inelastic behavior. Finally, this model was implemented in a finite element code based on shell elements allowing the study of the influence of taking into account the inelastic behavior in bending on the numerical simulation of forming.

Investigation of the unsteady creep of reinforced plates of nonlinearly inherited materials, taking into account the weakened resistance by transverse shear

The problem of inelastic bending deformation of plates is formulated using the idea of the method of time steps in rectangular Cartesian and cylindrical coordinate frames based on two versions of the Tymoshenko theory and taking into account plates weakened resistance to transverse shears during plane-cross reinforcement and. The mechanical behavior of the materials of the components of the composition is described by the nonlinear-hereditary Rabotnov’s creep theory. The bending behavior under creep conditions of ring plates made of D16T aluminum alloy and axisymmetrically reinforced along boron and spiral-circular trajectories by boron fibers is studied. It is shown that under short-term loading the classical theory is quite acceptable for calculating the mechanical behavior of such composite structures. Under prolonged loading in the creep process, transverse shear deformations actively and rapidly develop in the binder material of the plate. Therefore, taking into account the weakened resistance to transverse shear after calculating the creep of thin-walled reinforced structural elements is needed. The compliance of the reinforced plates under long-term loading predicted by the classical theory and the first version of the Tymoshenko’s theory is significantly less than that determined by the second version of the Tymoshenko’s theory. Therefore it is recommended to use the second version of the Tymoshenko’s theory for adequate calculations of the creep of the reinforced plates.

Structural and Geomorphic Evidence for Rolling‐Hinge Style Deformation of an Active Continental Low‐Angle Normal Fault, SE Papua New Guinea

AbstractTo what degree low‐angle normal faults (LANFs) deform by a “rolling‐hinge” mechanism is still debated for continental metamorphic core complexes (MCCs). The Mai'iu fault in SE Papua New Guinea is one of the best preserved and fastest slipping active continental LANFs on Earth, providing an ideal setting in which to evaluate footwall deformation and doming in MCCs. We analyzed structural field data from the exhumed slip surface and subjacent footwall of the Mai'iu fault, together with geomorphic data interpreted from aerial photographs and GeoSAR‐derived digital terrain models. The exhumed part of the Mai'iu fault forms a smooth, continuous surface, traced at least 28 km in the slip direction. The fault emerges from the ground near sea level with a northward dip of ≤22°N and flattens southward over the crest of the Suckling‐Dayman Dome. Its most southern mapped portion dips ~12°S. Geomorphic and structural evidence indicates updip tectonic transport of the footwall and progressive back‐tilting of the exposed part of the fault and the underlying foliation through >26°. We infer that antithetic (northside‐up) dip slip on an array of steep‐dipping faults striking parallel to the Mai'iu fault accommodated some of the exhumation‐related inelastic bending of the footwall. The exhuming footwall was subject to late‐stage slip‐parallel contractional strain as recorded by a postmetamorphic crenulation foliation that strikes parallel to the curved Mai'iu fault trace, by folds of bedding in a large rider block that is stranded on the current footwall and by strike‐parallel warps in the exhumed fault surface. Geodynamic modeling predicts the observed footwall strain.

A closed-form analytical solution for the ratcheting response of steel tubes with wall-thinning under inelastic symmetric constant amplitude cyclic bending

Metallic tubes experiences a progressive accumulation of ovalisation, or ratchet, under cyclic inelastic bending. During their life time, the tubes may also suffer from different types of mechanically and/or chemically originated defects. The current paper discusses a closed-form solution for the response analysis of defective circular steel tubes under monotonic and cyclic inelastic bending. The defect in the tube is idealised as a uniform patch type wall thinning.The material model considers the cyclic hardening/softening features based on a combined non-linear hardening law. To account for the non-fading memory characteristics of the steel material, the hardening modulus in each half-cycle is introduced as a state variable. A modified version of the Bailey–Norton law is used for the cyclic growth (cyclic creep) in the ovalisation of the cross-section. In overall, the solution considers the geometrical non-linearity due to the ovalisation as well as the hysteresis effects.The study also includes monotonic and cyclic inelastic bending experiments on small-scale, thick-walled, high strength, low alloy carbon steel defective tubes. The analytical solutions for the inelastic monotonic and cyclic bending of the tubes are validated against these experimental data and reasonable agreements are noticed and reported.

Surface-modified steel sheets and corrugated panels in three-point bending

The structural behaviour of nano-structured materials produced by surface mechanical attrition treatment (SMAT) method under three-point bending is explored in this study. Theoretical models are developed to analyse beams of rectangular and corrugated cross-sections in elastic and inelastic bending. In these models, several material parameters are determined by curve fitting between analytical calculations and experiments. AISI 304 stainless steel sheets of selected thicknesses and corrugated panels with and without SMAT are designed, manufactured and tested. The experimental investigation reveals that the combination of corrugated shape and SMAT method gives the most significant increase in terms of bending stiffness, strength and hardening.

Inelastic Bending Performances of Laminated Bamboo Beams: Experimental Investigation and Analytical Study

Laminated bamboo (LB) is a processed bamboo-based composite fabricated by gluing bamboo strips under controlled temperature and pressure. It has many superior mechanical properties compared to commonly used wood products and is well suited for use as a construction material. The present work consisted of two parts. The first part aimed at studying the bending performances of LB beams. The stress-strain relationship of the LB composite had approximately perfect elasticity under tension, yet exhibited more complicated behavior under compression (i.e., linearity in the prior-proportional limit and nonlinearity in the post-proportional limit). The strength in tension was significantly higher than that during compression. Damage of LB beam began with the fiber yielding in the compressive zone until failure occurred when the fibers at the outermost part of the tensile zone broke. Hence, LB beams always underwent a long nonlinear process before failure. An empirical stress-strain relationship was proposed on the basis of a bilinear model. In the second part of the study, an analytical model for calculating the load-carrying capacity and deflection of LB beams was developed. Experimental results confirmed that the model had enough accuracy for design calculation.

Study on the Unsteady Creep of Composite Beams with an Irregular Laminar Fibrous Structure Made from Nonlinear Hereditary Materials

The creep of homogenous and hybrid composite beams of an irregular laminar fibrous structure is investigated. The beams consist of thin walls and flanges (load-carrying layers). The walls may be reinforced longitudinally or crosswise in the plane, and the load-carrying layers are reinforced in the longitudinal direction. The mechanical behavior of phase materials is described by the Rabotnov nonlinear hereditary theory of creep taking into account their possible different resistance to tension and compression. On the basis of hypotheses of the Timoshenko theory, with using the method of time steps, a problem is formulated for the inelastic bending deformation of such beams with account of the weakened resistance of their walls to the transverse shear. It is shown that, at discrete instants of time, the mechanical behavior of such structures can formally be described by the governing relations for composite beams made of nonlinear elastic anisotropic materials with a known initial stress state. The method of successive iterations, similar to the method of variable parameters of elasticity, is used to linearize the boundary-value problem at each instant of time. The bending deformation is investigated for homogeneous and reinforced cantilever and simply supported beams in creep under the action of a uniformly distributed transverse load. The cross sections of the beams considered are I-shaped. It is found that the use of the classical theory for such beams leads to the prediction of indefensibly underestimated flexibility, especially in long-term loading. It is shown that, in beams with reinforced load-carrying layers, the creep mainly develops due to the shear strains of walls. It is found that, in short- and long-term loadings of composite beams, the reinforcement structures rational by the criterion of minimum flexibility are different.

On the ratcheting of defective low-alloy, high-strength steel pipes (API-5L X80) under cyclic bending: An experimental study

Metallic tubes experiences a progressive accumulation of ovalisation, or ratchet, under cyclic inelastic bending. The current paper deals with the ratcheting behaviour of defective small-scale API X80 carbon steel tubes subjected to cyclic bending. The subject appears not to have received due previous attentions but is important in the design and mechanical integrity assessment of the piping systems. Right-angle uniform material loss is used to simulate an external corrosion patch in the test tubes.It is noticed that under inelastic cyclic bending the ovalisation ratchets both with the perfect and defective specimens. The rate of ratcheting increases and the number of cycles to failure decreases in the defective specimens as compared to those in the perfect ones. Both perfect and defective specimens show ratcheting in the circumferential strains, but this quickly ends in shakedown. The local deformation modes in the perfect specimens are characterised by diffusive wrinkling, but by inward kinking in the defective specimens. The perfect specimens demonstrate similar ratcheting rates in the sagging and hogging phases, but the defective specimens not. The modes of local deformation and failure for specimens with identical defects remain almost the same under cyclic and monotonic bending.

Rapid prediction of inelastic bending moments in RC beamsconsidering cracking

A methodology using neural networks has been proposed for rapid prediction of inelastic bending moments in reinforced concrete continuous beams subjected to service load. The closed form expressions obtained from the trained neural networks take into account cracking in concrete at in-span and at near the internal supports and tension stiffening effect. The expressions predict the inelastic moments (considering the concrete cracking) from the elastic moments (neglecting the concrete cracking) at supports. Three separate neural networks are trained since these have been postulated to represent all the beams having any number of spans. The training, validating, and testing data sets for the neural networks are generated using an analytical-numerical procedure of analysis. The proposed expressions are verified for example beams of different number of spans and cross-section properties and the errors are found to be small. The proposed expressions, at minimal input data and computation effort, yield results that are close to FEM results. The expressions can be used in preliminary every day design as they enable a rapid prediction of inelastic moments and require a computational effort that is a fraction of that required for the available methods in literature.

Inelastic Test and Design Method of Cold-formed Steel Lipped Channel Members in Bending

The aim of this paper is to investigate the inelastic bending capacity and design method of cold-formed steel lipped channel bending members. The bending tests were conducted on 30 cold-formed steel lipped channel members. The nominal yield stress and the nominal thickness of the bending members were 235 MPa and 2mm. The theoretical global buckling stress was higher three times than the yield stress which can make sure the failure of members were in inelastic stage. For each specimen, an analytical analysis using Finite Element Method (FEM) was also conducted considering the influence of the boundary, the ultimate bending capacity, and the failure mode could also be captured. The test results show that the Chinese cold-formed steel specification Technical code of cold-formed thin-walled steel structures (GB50018-2002) is conservative for lipped channel bending sections in inelastic stage. The test results are used to put forward to a revised design method based on effective width method for the current Chinese cold-formed steel specification. The comparison on the bending capacity between the test results and the calculated results by using the proposed method, effective width method and direct strength method in North American cold-formed steel specification (AISI-S120-2016(draft)) shows that the proposed method can consider the inelastic reserve capacity of bending members well. The failure modes and bending capacity of bending members obtained using the idealized shell finite element model, which are close to the experimental results, shows that the idealized model is very well to model the buckling behavior and calculate capacity of bending members.

On the ratcheting response of circular steel pipes subject to cyclic inelastic bending: A closed-form analytical solution

The current paper deals with the cyclic plastic response and strain ratcheting of circular steel tubes under repeated inelastic pure bending. A closed-form solution is proposed for the problem. The cyclic softening/hardening behaviour of the material is modelled using a combined bilinear kinematic/nonlinear isotropic hardening rule. The relative hardening modulus in each half-cycle is considered as an extra state variable to account for the non-fading memory characteristics of the material. The cycle by cycle growth (creep) in the ovalisation of the cross-section is modelled using a modified version of the Bailey–Norton creep law. The solution considers the material nonlinearity, the cyclic plasticity effects and the geometrical nonlinearity due to the ovalisation of the cross-section. The model predictions are examined against a number of available test data on the inelastic monotonic and cyclic bending of tubes and reasonable agreements are observed.

A higher-order Eringen model for Bernoulli–Euler nanobeams

Small-scale effects in carbon nanotubes are effectively assessed by resorting to the methods of nonlocal continuum mechanics. The crucial point of this approach consists in defining suitable constitutive laws which lead to reliable results. A nonlocal elastic law, diffusely adopted in literature, is that proposed by Eringen. According to this theory, the elastic equilibrium problem of a nonlocal nanostructure is equivalent to that of a corresponding local nanostructure subjected to suitable distortions simulating the nonlocality effect. Accordingly, transverse displacements and bending moments of a Bernoulli–Euler nonlocal nanobeam can be obtained by solving a corresponding linearly elastic (local) nanobeam, subjected to the same loading and kinematic constraint conditions of the nonlocal nanobeam, but with the prescription of suitable inelastic bending curvature fields. This observation leads naturally to the definition of a higher-order Eringen version for Bernoulli–Euler nanobeams, in which the elastic energy is assumed to be dependent on the total and inelastic bending curvatures and on their derivatives. Weak and strong formulations of elastic equilibrium of first-order gradient nanobeams are provided by a consistent thermodynamic approach. Exact solutions of fully clamped and cantilever nanobeams are given and compared with those of literature.

An Evaluation of Energy Absorption under Three-Point Bending Deformation at Higher Deflection Rate for TRIP Steel

In the last few decades, energy absorption of materials becomes an critical issue in a design process of a vehicle because risks of primary and secondary accidents against pedestrians, other road users and structures can be reduced by a performance of absorbing energy in its support structures. Among various materials used for the structures, TRIP steel with favorable mechanical properties such as excellent formability and higher impact energy absorption is attractive to automotive industries. Huge numbers of research works have been carried out to investigate deformation behavior of TRIP steel. However, just few studies can be found on the performance in TRIP steel, especially, at higher deformation rate during the crash of the vehicle. Kinetic energy by higher speed of the vehicle will be consumed by inelastic bending deformation of components. Thus, a consideration of bending deformation at high impact velocity is required for the evaluation of the performance. In this study, the performance in TRIP steel at high deformation rate is clarified by conducting both quasi-static and impact three-point bending tests for pre-cracked specimen.

Section classifications for cold-formed channel steel

The inelastic reserve capacity, which is the additional capacity of a member beyond the first yielding, is very important for limit-state design of frame structures. The aim of this work was to investigate the inelastic bending capacity of cold-formed channel sections according to European standards and to propose revisions to current design rules. An extensive experimental and analytical analysis of 42 cold-formed channel sections was conducted. Material properties of the tested sections were examined using tension tests on metal coupons. The sections were cold-formed from G450 steel with a nominal thicknesses of 1·6 mm, and varying theoretical buckling stresses ranging between elastic and seven times the yield stress. The results from the pure bending experimental investigations and the European design standards for steel structures were compared. It is concluded that the section classifications defined in Eurocode 3 are not accurate for cold-formed channel sections. Therefore, modifications to the section classifications that have been derived for hot-rolled sections are required in the case of cold-formed sections to maintain accuracy (based on the presented test series). Design rules are developed to account for such behaviour.

Design of a four-point bend test for ultra-low cycle fatigue of pipelines under inelastic bending

This master thesis is situated in the research domain dealing with the ductile failure of pipelinesunder extreme loading conditions. It is part of an umbrella research aiming to develop innovativeexperimental and computational methodologies to simulate fracture of steel structural elements under ultralow cycle fatigue. The focus of this study is on steel pipeline applications. The objective of this thesis is todesign a large-scale four-point bend test setup to cyclically bend pipes. The feasibility of instrumentationwill be evaluated using small scale test specimens. In this paper some ideas, constraints and opportunitiesfor the design are considered, based on a literature review of several test setups for other applications. Thedesign parameters have been calculated to compose the design windows and an initial overview of thepossible instrumentation is given.

Slenderness limits for cold-formed channel sections in bending by experimental methods

Inelastic design methods allow for larger application of loads on sections than elastic design methods, due to the redistribution of yield stress through the depth of the section. Sections that can reach the full plastic capacity and maintain it for sufficient rotation are considered applicable for plastic mechanism design, resulting in more economical structural solutions. Cold-formed steel channel sections are used extensively in portal frame structures in agricultural and light industrial/commercial applications, structures well suited to plastic design, however may currently only be designed elastically. To address this limitation in design standards, experimental and numerical analyses on the inelastic bending capacity of cold-formed channel sections are performed, and design rules to account for such behaviour are developed. Design rules are prepared using the hot-rolled steel specification methodology of classifying a section as compact, non-compact or slender (according to the Australian Standards) and Classes 1, 2, 3 and 4 (according to the European Standards). Proposals for the Australian standard are shown to provide accurate and reliable capacity predictions for cold-formed steel channel sections whose bending capacity exceeds the elastic limit.

Inelastic Bending Capacity of Cold-Formed Steel Members

AbstractThe objective of this paper is to provide and verify a general design method for prediction of inelastic bending capacity in cold-formed steel members potentially subject to local, distortional, and/or lateral-torsional buckling modes. An extensive experimental database of tested cold-formed steel beams is collected and indicates that inelastic reserve in the bending capacity of thin-walled cold-formed steel members is more common than typically assumed. Elementary mechanics for inelastic reserve are reviewed and simplified expressions provided for connecting the strain demand to the inelastic bending capacity in the range between the yield moment and the fully plastic moment. The strain capacity that can be sustained in inelastic local and inelastic distortional buckling is investigated through existing experiments coupled with nonlinear finite-element (FE) analysis. The nonlinear FE models provide a comprehensive means to investigate the relationship between cross-section slenderness, normalized...

Inelastic behaviour and design of cold-formed channel sections in bending

The aim of this paper is to investigate the inelastic bending capacity of cold-formed channel sections, and provide design rules to account for such behaviour. An extensive experimental and analytical analysis of 42 cold-formed channel sections in three different geometric categories is conducted, including simple channel sections, channel sections with simple edge stiffeners and channel sections with complex edge stiffeners. The sections were cold-formed from G450 steel with nominal thickness of 1.6 mm, and varying theoretical buckling stresses ranging between elastic to seven times the yield stress. The results of the pure bending experimental investigations show that current international cold-formed steel specifications are conservative, for channel sections with low slenderness values. The experimental results are used to propose revisions to current international cold-formed steel specifications.