Plastic Collapse Analysis Research Articles

Plastic collapse analysis in multiaxially loaded defective pipe specimens at different temperatures

A comprehensive numerical investigation is carried out using a newly developed constitutive model to describe failure at low temperatures in multiaxially loaded cracked pipes made of 316L stainless steel. The kinetic phase transformation and the temperature-dependent fracture criterion are implemented to accurately capture the mechanical response at different temperature levels. Although experimental observations of these simulations were not available, their results were quite consistent with some already published results obtained on similar materials and loading conditions at room temperature. The results indicate that the existing multiaxial plastic collapse failure criterion, including shearing, still provides a fail-safe design margin for low temperature loading conditions, including internal pressure. Moreover, martensite kinetic phase transformation plays an important role, especially during straining at low temperatures.

Plastic Collapse Analysis in Multiaxially Loaded Defective Pipe Specimens at Different Temperatures

Plastic Collapse Analysis in Multiaxially Loaded Defective Pipe Specimens at Different Temperatures

Reconciling fracture toughness parameter contradictions in thin ductile metal sheets

AbstractThe well‐known trade‐off between strength and fracture toughness in bulk specimens is often used to explain the low fracture toughness of very thin ductile face‐centred cubic metal specimens, but this interpretation contradicts the relative length scales of thickness‐dependent strength and thickness‐dependent fracture toughness. This study uses the concept of similitude to demonstrate that linear elastic fracture mechanics analysis of 25.4 μm thick annealed aluminium is invalid, although the resulting fracture toughness measurements fit well with the existing literature and idea of a strength/fracture toughness trade‐off. Similarly, an elastic plastic fracture mechanics analysis is sensitive to out‐of‐plane deformation that cannot be practically eliminated or corrected for with a model. However, a plastic collapse analysis using a critical net section stress criterion is demonstrably valid by the concept of similitude, is insensitive to out of plane deformation, and agrees with the evidence of extensive plasticity in the fracture surfaces.

Plastic collapse and energy absorption of circular filled tubes under quasi-static loads by computational analysis

This study presents the finite element analysis of plastic collapse and energy absorption of polyurethane-filled aluminium circular tubes under quasi-static transverse loading. Increasing focuses were given to impact damage of structures where energy absorbed during impact could be controlled to avoid total structure collapse of energy absorbers and devices designed to dissipate energy. ABAQUS finite element analysis application was utilized for modelling and simulating the polyurethane-filled aluminium tubes, different set of diameter-to-thickness ratios and span lengths, subjected to transverse three-point-bending load. Different sets of polyurethane-filled aluminium tubes subjected to the transverse loading were modelled and simulated. The failure modes and mechanisms of filled tubes and its capabilities as energy absorbers to further improve and strengthening of empty tube were also identified. The results showed that plastic deformation response was affected by the geometric constraints and parameters of the specimens. The diameter-to-thickness ratio and span lengths had shown to play crucial role in optimizing the PU-filled tube as energy absorber.

An adaptive selective ES-FEM for plastic collapse analysis

Abstract We present a selective edge-based smoothed finite element method (sES-FEM) of kinematic theorem for predicting the plastic limit loads in structures. The basic idea in this method is to use two levels of mesh repartitioning for the finite element limit analysis. The master level begins with an adaptive primal-mesh strategy guided by a dissipation-based indicator. The slave level consists of further subdividing each triangle into three sub-triangles and creating a dual mesh through a careful selection of a pair of two sub-triangles shared by the corresponding common element edge. By applying a strain smoothing projection operator to the strain rates on the dual mesh, the flow rule constraint is enforced over the edge-based strain smoothing domains, and likewise everywhere in the problem domain. This numerical procedure is performed for a cohesive-frictional material. This numerical procedure is also performed necessarily to avoid the volumetric locking problem for a purely cohesive material. The optimization formulation of limit analysis is next presented by the form of a second-order cone programming (SOCP) for the purpose of exploiting the efficiency of interior–point solvers. The present method uses linear triangular elements and handles a low number of optimization variables. This leads to a convenient way to design and solve the large-scale optimization problems effectively. Several numerical examples are given to demonstrate the simplicity and effectiveness of the proposed method.

Plastic collapse analysis of Mindlin-Reissner plates using a composite mixed finite element

Summary The paper proposes a mixed finite element model and experiments its capability in the analysis of plastic collapse Mindlin–Reissner plates. The model is based on simple assumptions for the unknown fields, ensuring that it is easy to formulate and implement. A composite triangular mesh is assumed over the domain. Within each triangular element, the displacement field is described by a quadratic interpolation, while the stress field is represented by a piece-wise constant description by introducing a subdivision of the element into three triangular regions. The plastic collapse analysis is formulated as quadratic and conic mathematical programming problem and is accomplished by an interior-point algorithm, which furnishes both the collapse multiplier and the collapse mechanism. A series of numerical experiments shows that the proposed model performs well in plastic analysis, where it takes advantage of the absence of locking phenomena and the possibility of simply described discontinuities in the plastic deformation field within the element. Copyright © 2015 John Wiley & Sons, Ltd.

A composite mixed finite element model for plane structural problems

The paper proposes a mixed finite element model and experiments its capability in the analysis of elastic and plastic collapse plane problems. The model is easy to formulate and implement because it is based on simple assumptions for the unknown fields. A composite triangular mesh is assumed over the domain. Within each triangular element the displacement field is described by a quadratic interpolation, while the stress field is represented by a piece-wise constant description by introducing a subdivision of the element into three triangular regions. The elastic solution is constructed through the stationarity condition of the mixed Hellinger–Reissner functional. The plastic collapse analysis is formulated as a mathematical programming problem and is accomplished by an Interior Point algorithm which furnishes both the collapse multiplier and the collapse mechanism. A series of numerical experiments shows that the proposed model performs well in elastic problems and achieves the favorite context in plastic analysis, where it takes advantage of the absence of volumetric locking and the piecewise constant interpolation of the stress field within the element.

Plastic collapse analysis of cracked structures using extended isogeometric elements and second-order cone programming

We investigate a numerical procedure based on extended isogeometric elements in combination with second-order cone programming (SOCP) for assessing collapse limit loads of cracked structures. We exploit alternative basis functions, namely B-splines or non-uniform rational B-splines (NURBS) in the context of limit analysis. The optimization formulation of limit analysis is rewritten in the form of second-order cone programming (SOCP) such that interior-point solvers can be exploited efficiently. Numerical examples are given to demonstrate reliability and effectiveness of the present method.

Plastic collapse analysis of CFRP strengthened and rehabilitated degraded steel welded RHS beams subjected to combined bending and bearing

Innovative techniques using the lightweight, high strength and corrosion resistance of carbon fibres reinforced polymers (CFRP) composites have been proposed in a recent paper by the author. The present paper presents plastic mechanism analyses of CFRP strengthened and rehabilitated rectangular hollow sections (RHS) under quasi-static large deformation 3-point bending. The strengthening series was for un-degraded RHS beams from the manufacturer reinforced using externally wrapped CFRP sheets. The rehabilitation series was for artificially degraded RHS beams repaired using externally wrapped sheets or bonded plates. The main parameters examined in this paper were the section type, section and member slenderness and the type and number of the CFRP sheets. Three different phases of plastic deformation were observed during the test, namely, denting, denting and bending, and structural collapse. Two methods were used to model the large plastic deformation measured during plastic collapse of the composite RHS beams, namely, equilibrium and energy methods of analysis. It was found that the predicted collapse curves using the equilibrium approach were in good agreement with the measured curves for the bare and composite specimens examined in the strengthening and rehabilitation series, particularly for the latter series. This may be caused by a number of factors such as the specimens in the rehabilitations series were comparatively longer and had larger bearing width. The energy theory was found to have deficiencies represented in the simplified linear polygon shape adopted for the mechanism geometry, and adopting the plastic 1/2-wave length used for I-sections, as well as the use of a simplified formulae to describe the relationship between the local denting displacement and global bending rotation angle for the three phases of deformation observed during the test.

Mechanics of anisotropic hierarchical honeycombs

Abstract Anisotropic hierarchical honeycombs of uniform wall-thickness are constructed by repeatedly replacing each three-edge vertex of a base hexagonal network with a similar but smaller hexagon of the same orientation, and stretching the resulting structure in horizontal or vertical directions to break the isotropy. The uniform overall thickness is then adjusted to maintain the constant average density. The resulting fractal-appearing hierarchical structure is defined by the ratios of replacement edge lengths to the underlying network edge length and also the cell wall angle. The effective elastic modulus, Poisson׳s ratio and plastic collapse strength in the principal directions of hierarchical honeycombs were obtained analytically as well as by finite element analyses. The results show that anisotropic hierarchical honeycombs of first to fourth order can be 2.0–8.0 times stiffer and at the same time up to 2.0 times stronger than regular honeycomb at the same wall angle and the same overall average density. Plastic collapse analysis showed that anisotropic hierarchical honeycomb has the larger plastic collapse strength compared to regular hierarchical honeycomb of the same order at certain oblique wall angles. The current work provides insight into how incorporating anisotropy into the structural organization can play a significant role in improving the mechanics of the materials structure such as regular or hierarchical honeycombs, and introduces new opportunities for development of novel materials and structures with desirable and actively tailorable properties.

Plastic collapse of lattice structures under a general stress state

We present a numerical minimization procedure to determine the macroscopic ‘plastic collapse strength’ of a tessellated cellular structure under a general stress state. The method is illustrated with sample cellular structures of regular and hierarchical honeycombs. Based on the deformation modes found by minimization of plastic dissipation, closed-form expressions for strength are derived. The current work generalizes previous studies on plastic collapse analysis of lattice structures, which are limited to very simple loading conditions.

Finite Element Analysis of Plastic Collapse and Crack Behavior of Steel Pressure Vessels and Piping Using XFEM

This article aims to study the plastic collapse and crack behavior of steel pressure vessels and piping using the extended finite element method (XFEM). First, the plastic collapse loads of steel cylinders under the internal pressure are predicted, and the numerical results are compared with experimental data. In addition, the computational efficiency and accuracy using different methods including the XFEM, nonlinear stabilization algorithm, and arc-length algorithm are compared. Particularly, effects of different initial crack configurations, element sizes, damage initiation, and evolution criteria on the crack behaviors are investigated. Second, the crack initiation and propagation properties of buried pipelines due to deflection in the landslide area are explored, and the numerical results are compared between testing data and current study. Besides, the effects of internal pressure, wall thickness, soil property, and width of landslide area on the critical deflection displacement of buried pipeline are studied. This research provides a fundamental support for safety evaluation and life prediction of pressurized structures.

Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines

In the framework of the finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to the internal pressure is conducted on the basis of the unified strength criterion (USC). An analytical solution of the burst pressure for pipes with capped ends is derived, which includes the strength differential effect and takes the influence of strength criterion on the burst pressure into account. In addition, a USC-based analytical solution of the burst pressure for end-opened pipes under the internal pressure is obtained. By discussion, it is found that for the end-capped pipes, the influence of different yield criteria and the strength differential effect on the burst pressure are significant, while for the end-opened pipes, the burst pressure is independent of the specific form of the strength criterion and strength difference in tension and compression.

Plastic collapse analysis of thin-walled pipes based on unified yield criterion

Based on a unified yield criterion (UYC), the plastic collapse analysis of thin-walled pipes is conducted in the framework of finite strain. A unified analytical solution for the burst pressure of end-capped defect-free pipes is derived, which is fit for various kinds of non-SD (strength differential) materials. A series of solutions can be deduced from this unified solution, and those solutions of burst pressure on the basis of Tresca, von Mises, ASSY, and TS criteria are special cases of it. By comparing with existing test result, it is found that the present unified solution is very convenient and effective for the prediction of burst pressure.

A comparison of plastic collapse and limit loads for single mitred pipe bends under in-plane bending

This paper presents a comparison of the plastic collapse loads from experimental in-plane bending tests on three 90° single un-reinforced mitred pipe bends, with the results from various 3D solid finite element models. The bending load applied reduced the bend angle and in turn, the resulting cross-sectional ovalisation led to a recognised weakening mechanism. In addition, at maximum load there was a reversal in stiffness, characteristic of buckling. This reversal in stiffness was accompanied by significant ovalisation and plasticity at the mitre intersection. Both the weakening mechanism and the post-buckling behaviour are only observable by testing or by including large displacement effects in the plastic finite element solution. A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour. The plastic collapse finite element solution, with large displacements, produced excellent agreement with the experiment. Sufficient experimental detail is presented for these results to be used as a benchmark for analysts in this area. Given the robustness of non-linear solutions in commercial finite element codes and the ready availability of computing resources, it is argued that pressure vessel code developers should now be recommending large displacement analysis as the default position for limit and plastic collapse analyses, rather than expecting engineers to anticipate weakening mechanisms and related non-linear phenomena.

Potentials for the modified Cam-Clay model

Energy and dissipation pseudo-potentials are employed to derive constitutive relationships, in the context of thermodynamic concepts, for the widely used Modified Cam-Clay (MCC) model for soil mechanics. A variational formulation of the MCC evolution equations is proposed in this paper. Since plastic collapse of MCC soils cannot be embedded in the classical limit analysis theory, finding the critical amplification of the load that produces plastic collapse is formulated in the form of a system of equations and inequalities. Then, a mixed minimization principle is proposed for the plastic collapse analysis of MCC soils. This principle is obtained by the application of the variational formulation for the flow law introduced in the first part of the article.

Plastic collapse analysis of thin-walled circular tubes subjected to bending

Circular tubes have been widely used as structural members in many engineering applications. Therefore, its collapse behavior has been studied for many decades, focusing on its energy absorption characteristics and collapse mechanism. In order to predict the collapse behavior of members, one could rely on the use of finite element codes or experiments. These tools are helpful and have high accuracy but are costly and require extensive running time. Therefore, an approximate model of tubes collapse mechanism is an alternative especially for the early step of design. This paper is also aimed to develop a closed-form solution to predict the moment–rotation response of circular tube subjected to pure bending. The model was derived based on the principle of energy rate conservation. The collapse mechanism was divided into three phases. New analytical model of ovalisation plateau in phase 2 was derived to determine the ultimate moment. In phase 3, the Elchalakani et al. model [Int. J. Mech. Sci. 2002; 44:1117–1143] was developed to include the rate of energy dissipation on rolling hinge in the circumferential direction. The 3-D geometrical collapse mechanism was analyzed by adding the oblique hinge lines along the longitudinal tube within the length of the plastically deformed zone. Then, the rates of internal energy dissipation were calculated for each of the hinge lines which were defined in terms of velocity field. Inextensional deformation and perfect plastic material behavior were assumed in the derivation of deformation energy rate. In order to compare, the experiment was conducted with a number of tubes having various D/ t ratios. Good agreement was found between the theoretical prediction and experimental results.

Plastic buckling and collapse of thin shell structures, using layered plastic modeling and co-rotational ANDES finite elements

This study reveals an analysis of plastic buckling and collapse of thin shell structures. For this purpose, the co-rotational and layered plastic model as well as ANDES (Assumed Natural Deviatoric Strain) finite element formulations are used. The co-rotational kinematics formulation splits the translational and rotational deformations in a small deformation analysis. The ANDES finite element is modified to elastoplastic ANDES finite element by the introduction of the von Mises yield criterion elastoplastic formulation on its original deformation model. In order to accommodate the plasticity formulation, the Gauss point layered integration is inserted through of thickness of the element to produce the internal force vector and material stiffness matrix. Special effort is devoted to maintain the consistency of the internal forces and tangent stiffness as well as to enhance the robustness of element level computations. The arc-length method is used to follow the postbuckling equilibrium path. Results are presented for several benchmark elastoplastic shell problems available in the present literature, which are generally in agreement with the present work.

Calculations of plastic collapse load of pressure vessel using FEA

This paper proposes a theoretical method using finite element analysis (FEA) to calculate the plastic collapse loads of pressure vessels under internal pressure, and compares the analytical methods according to three criteria stated in the ASME Boiler Pressure Vessel Code. First, a finite element technique using the arc-length algorithm and the restart analysis is developed to conduct the plastic collapse analysis of vessels, which includes the material and geometry non-linear properties of vessels. Second, as the mechanical properties of vessels are assumed to be elastic-perfectly plastic, the limit load analysis is performed by employing the Newton-Raphson algorithm, while the limit pressure of vessels is obtained by the twice-elastic-slope method and the tangent intersection method respectively to avoid excessive deformation. Finally, the elastic stress analysis under working pressure is conducted and the stress strength of vessels is checked by sorting the stress results. The results are compared with those obtained by experiments and other existing models. This work provides a reference for the selection of the failure criteria and the calculation of the plastic collapse load.

Influence of flow stress choice on the plastic collapse estimation of axially cracked steam generator tubes

The influence of the choice of flow stress on the plastic collapse estimation of axially cracked steam generator (SG) tubes is considered. The plastic limit and collapse loads of thick-walled tubes with external axial semi-elliptical surface cracks are investigated by three-dimensional non-linear finite element (FE) analyses. The limit pressure solution as a function of the crack depth, length and tube geometry has been developed on the basis of extensive FE limit load analyses employing the elastic–perfectly plastic material behaviour and small strain theory. Unlike the existing solutions, the newly developed analytical approximation of the plastic limit pressure for thick-walled tubes is applicable to a wide range of crack dimensions. Further, the plastic collapse analysis with a real strain-hardening material model and a large deformation theory is performed and an analytical approximation for the estimation of the flow stress is proposed. Numerical results show that the flow stress, defined by some failure assessment diagram (FAD) methods, depends not only on the tube material, but also on the crack geometry. It is shown that the plastic collapse pressure results, in the case of deeper cracks obtained by using the flow stress as the average of the yield stress and the ultimate tensile strength, can become unsafe.