Spread Of Plastic Zones Research Articles

Tension-compression asymmetry effects on the plastic response in bending: new theoretical and numerical results

At present, the analysis and interpretation of the bending response of isotropic elastic/plastic metallic materials is done based on the assumption that yielding and subsequent plastic deformation under tension and compression are the same. In this paper, we put into evidence analytically and verified through F.E. analyses that even a slight tension-compression asymmetry in yielding of isotropic pressure-insensitive materials leads to very specific behaviour under four-point bending. For this purpose, the isotropic version of Cazacu et al. [1] yield criterion is used. This yield criterion is pressure-insensitive, accounts for third-invariant effects, and involves a unique parameter k which depends solely on the ratio between the yield stress in simple tension and compression, σT/σC; k = 0 corresponding to the von Mises criterion. The theoretical analysis shows that for a material with σT < σC, yielding first occurs in tension at the bottom outer fiber while for a material with σT > σC yielding sets in at the top outer fiber. As the moment is further increased, a single plastic zone spreads into the cross section starting from the fiber where min (σT, σC) is first reached, the neutral axis being no longer located at the mid-height of the beam, but moving continuously during bending. If the applied load is sufficiently large, yielding also occurs at the other outer fiber and the plastic domain is comprised of two zones, one in tension and the other in compression. The extent of the plastic zones in tension and compression is not the same, namely the extent of each zone and the critical value of the moment when these two zones join being dictated by the tension-compression asymmetry ratio of the material. Most importantly, the stresses in the cross section during loading, and consequently the distribution of residual stresses that remain after unloading are completely different than in the case of a von Mises material. To the author's knowledge these features of the plastic response in bending, which are confirmed by F.E. analyses, have not been previously identified or reported.

Prediction of Yielding Onset and Spread Pattern in Functionally Graded Thick-Walled Cylindrical Vessel Subjected to Thermo-Mechanical Loading

This research is concerned with the prediction of yield behavior of functionally graded (FG) thick-walled cylindrical pressure vessel under the combination of internal pressure and temperature gradient. In order to obtain the yield onset location and plastic growth zone, we applied Von-Mises yield criteria besides Prantle-Reuss flow rule in plane strain condition. This approach results in defining new formulation in order to determine the elastic limit pressure. In such cases as internal pressure with /without thermal gradient, the start and the spread of plastic zone are predicted. Moreover, the distributions of stress components are obtained along with the radial direction in elastic and plastic regions. The analysis results show that both FG power index and temperature gradient influence the commencement of plastic deformation. Using the appropriate choice of the FG parameters and the specified thermal gradient, the plastic zone can commence simultaneously from inside, outside or intermediate radius.

Prediction of Residual Life Assesment Using Thermography and Crack Growth Analysis

The most important characteristics for service safety of complex metal structures are those describing crack initiation and growth caused by static or dynamic, variable loading. Crack initiation and growth is subject of numerous investigations by different methods. The paper shows the possibility of applying infrared thermography to the problems of fracture mechanics. The main aim of testing was to qualitative relate the temperature changes of the spacemen measured by infrared thermography with the evaluation of fatigue cracks in steel specimen. Based on the distribution of temperature on the surface of the sample, during the action of force, the spread of plastic zones and crack tip are determined. The increase of temperature produced by the plastic deformation at the crack tip has been measured by infrared camera Thermal CAM SC640, FLIR Systems. SE(B) specimens were tested in three-point bending (TPB), following the procedures of ASTM E1820, on electrical mechanical testing machine with crack tip opening displacement (CTOD) control, at room temperature. Numerical simulation of stress distribution on the same model under same condition is presented, too. The results showed that thermography is a method suitable for monitoring and prediction of crack initiation and growth, as well as critical stress in elastic and elastic-plastic deformations. Fatigue crack growth behaviour of cracked TPB specimen made of S355 J2 G3 steel using Paris relation is considered.

On elastic–plastic buckling of cones

The paper considers the buckling of short, and relatively thick, mild steel conical shells subjected to the combined action of external pressure and axial compression. Past results on axially compressed cones and on cones subjected to hydrostatic external pressure are compared with fresh test results on equivalent, axially compressed cylinder and with the equivalent cylinder subjected to external hydrostatic pressure. The paper contains both numerical and experimental results. Details about experiments, numerical modelling and computed estimates of the load carrying capacity of analyzed shells are given. Results of this study suggest that the concept of equivalent cylinders is not applicable to short master-cones. Combined stability plots have also been derived for the master-cone and equivalent cylinders. They provide not only the failure envelopes but also the yield envelopes and spread of plastic zones. The paper also brings into the light a useful design tool proposed by Esslinger and van Impe [8], and applicable to elastic–plastic buckling of cones subjected to external hydrostatic pressure.

Plastic Zones and Residual Stresses of Metal Reinforced Composite Laminated Rectangular Plates with a Hole under In-Plane Loading

The nonlinear stress analysis and the spread of plastic zones in layered woven steel fiber-reinforced thermoplastic-matrix laminated rectangular plates are examined using the Finite element method and the first-order shear deformation theory for small deformations. Composite structures consisting of woven Cr–Ni wire as the fiber and F2.12 low-density polyethylene as the thermoplastic matrix are manufactured by hot-press molding. The mechanical properties are experimentally determined. The effect of aspect ratio of rectangular plate and antisymmetric structure is investigated. It is assumed that the laminated plates are subjected to in-plane uniform loads. Loading is gradually increased from the yield point of the plate as 0.01MPa at each load step. Load steps are chosen as 300, 350, and 400 iterations. Residual stresses and expansion of plastic zone have been presented by means of tables and figures.

Ductile–brittle transition of pure Al-interlayer sandwiched by high strength Al alloy

Four point bending test (FPB) was conducted to investigate the unusual ductile–brittle transition (DBT) of pure Al sheet with decreasing thickness, sandwiched by 2024 alloy through explosive cladding. The results show that, with the decrease in thickness of Al-interlayer restricted by parallel interfaces, obvious differences appear for the measured load–displacement curves, and fracture toughness characterized by critical J integral drops down remarkably. Correspondingly, brittle cleavage patterns, mainly belong to {1 0 0} besides a very few {1 1 0}, were observed on the fracture surfaces and increase gradually in the fraction as decreasing in the thickness of Al-interlayer. A finite element simulation showed that the crack-tip plastic zone spreads rapidly in the Al sheet and advances along the ligament confined by the two interfaces. With either decreased thickness or increased load, the stress triaxiality and maximum principal tensile stress ahead of crack-tip continue to increase, which make the materials become more brittle.

Evolution of plastic zones in dynamically loaded plates using different elastic–viscoplastic laws

In the framework of viscoplastic theory many different laws were developed, accounting for material behaviors like creep, relaxation or evolution of overstresses. Though each model is able to predict in uni-axial material tests the values of stresses depending on plastic strains and plastic strain rates the question is if solutions of simulations are still realistic if the viscoplastic law is applied on structural deformations. In the present study strain rate sensitive metal plates are subjected to shock waves. The purpose is to compare simulation results obtained with different elastic–viscoplastic laws to experiments in order to determine the most appropriate material model. By subjecting circular metal plates experimentally to shock wave loadings realistic deformation histories are measured. The measurements are compared to simulation results obtained with different viscoplastic laws. The aim is to find out the accuracy of each model concerning the predictions of displacements, shape formings, spread of plastic zones and evolutions of inner bending moments.

Prediction of the Residual Stresses and Expansion of Plastic Zones in Simply Supported Thermoplastic Composite Laminated Plates Subjected to Transverse Loads

In the present study, the residual stresses and expansion of the plastic zones in simply supported thermoplastic composite laminated plates under uniform transverse loads are given by using FEM. Elastic-plastic stress analysis is carried out for small deformations. Low density homogeneous polyethylene (thermoplastic) and woven stainless steel are used as matrix and fiber materials, respectively. The effect of the reinforcement angle varying from [0 / 15]2 to [0 / 90]2 for [0 /]2 and from [15 / 15]2 to [45 / 45]2 for [/]2 on the residual stresses and the spread of plastic zones are presented. In this analysis, the first-order shear deformation theory is used. The transverse loads are gradually increased from the yield point of the plate by 0.0001 MPa at each load step. Load steps are chosen as 100, 200, 300, 400 and 500. The laminated plates of constant thickness are formed by stacking four layers bonded symmetrically or antisymmetrically.

Ultimate behavior of long-span steel arch bridges

Because of the increasing span of arch bridges, ultimate capacity analysis recently becomes more focused both on design and construction. This paper investigates the static and ultimate behavior of a long-span steel arch bridge up to failure and evaluates the overall safety of the bridge. The example bridge is a long-span steel arch bridge with a 550 m-long central span under construction in Shanghai, China. This will be the longest central span of any arch bridge in the world. Ultimate behavior of the example bridge is investigated using three methods. Comparisons of the accuracy and reliability of the three methods are given. The effects of material nonlinearity of individual bridge element and distribution pattern of live load and initial lateral deflection of main arch ribs as well as yield stresses of material and changes of temperature on the ultimate load-carrying capacity of the bridge have been studied. The results show that the distribution pattern of live load and yield stresses of material have important effects on bridge behavior. The critical load analyses based on the linear buckling method and geometrically nonlinear buckling method considerably overestimate the load-carrying capacity of the bridge. The ultimate load-carrying capacity analysis and overall safety evaluation of a long-span steel arch bridge should be based on the geometrically and materially nonlinear buckling method. Finally, the in-plane failure mechanism of long-span steel arch bridges is explained by tracing the spread of plastic zones.

Pseudoforce Method for Nonlinear Analysis and Reanalysis of Structural Systems

This paper develops a new solver to enhance the computational efficiency of finite-element programs for the nonlinear analysis and reanalysis of structural systems. The proposed solver does not require the reassembly of the global stiffness matrix and can be easily implemented in present-day finite-element packages. It is particularly well suited to those situations where a limited number of members are changed at each step of an iterative optimization algorithm or reliability analysis. It is also applicable to a nonlinear analysis where the plastic zone spreads throughout the structure due to incremental loading. This solver is based on an extension of the Sherman-Morrison-Woodburg formula and is applicable to a variety of structural systems including 2D and 3D trusses, frames, grids, plates, and shells. The solver defines the response of the modified structure as the difference between the response of the original structure to a set of applied loads and the response of the original structure to a set of pseudoforces. The proposed algorithm requires O(mn) operations, as compared with traditional solvers that need O(m2n) operations, where m = bandwidth of the global stiffness matrix and n = number of degrees of freedom. Thus, the pseudoforce method provides a dramatic improvement of computational efficiency for structural redesign and optimization problems, since it can perform a nonlinear incremental analysis no harder than the inversion of the global stiffness matrix. The proposed method's efficiency and accuracy are demonstrated in this paper through the nonlinear analysis of an example bridge and a frame redesign problem.

Elasto-plastic analysis using shell element considering geometric and material nonlinearities

An elasto-plastic finite element procedure using degenerated shell element with assumed strain field technique considering both material and geometric nonlinearities has been developed. This assumes von-Mises yield criterion, von-Karman strain displacement relations and isotropic hardening. A few numerical examples are presented to demonstrate the correctness and applicability of the method to different kinds of engineering problems. From present study, it is seen that there is a considerable improvement in the displacement valuse when both material and geometric nonlinearities are considered. An example of the spread of plastic zones for isotropic and anisotropic materials has been illustrated.

Plasticity effects on fracture normal to interfaces with homogeneous and graded compositions

This paper deals with the problem of a crack in a multi-layered material with a homogeneous or a compositionally graded interface. The effects of plasticity mismatch between the layers (which have no elastic mismatch) on the shielding or amplification of the crack tip driving force are examined by recourse to finite element analyses for the case of a crack perpendicularly approaching the interface between the layers. When the near-tip plastic zone spreads across the interlayer, the crack-tip J integral is smaller than the remotely imposed J integral, if the crack is situated in the plastically weaker material. For this situation, introducing an interlayer between two dissimilar solids provides greater crack-tip shielding than joining the two solids without an interlayer (i.e., with a sharp interface). An interlayer with a homogeneous yield behavior (i.e., where the yield strength of the interlayer is the average of that of the two constituent layers) provides a greater shielding effect than a graded interface within which the yield strength varies linearly from one end of the interlayer to the other. When the crack approaches the interlayer from the plastically stronger material, the crack tip driving force is amplified as the plastic zone spreads across the interlayer. This amplification is the maximum for the interlayer with homogeneous properties, and essentially the same for the situations with a graded interlayer or no interlayer. The dependence of the shielding and amplification effects on the thickness of the interlayer, on the distance from the crack-tip to the interlayer, and on the remote loading are systematically examined.

Elastic-plastic finite element analysis of metal matrix plates with edge notches

Abstract A two-dimensional finite element program has been developed for elastic-plastic analysis. Isoparametric quadrilateral element with four nodes is used and Lagrange polynomial has been chosen as interpolation function. In the finite element solution, an initial stress method (modified Newton-Raphson method) is used. Residual stresses have been shown in figures and the spread of plastic zones has been illustrated for steel-aluminum composite plates with edge notches.

Elastic-plastic analysis of stress state and spread of plastic zone around single edge-cracked plate by finite element method

A two-dimensional finite element model for estimating elastic-plastic displacements and stresses near a crack for the elastic-plastic situation of loadings is presented. Singularity effects near the crack tip are solved by introducing 12-node cubic isoparametric elements in the crack tip region and collapsing them into triangular elements. The proposed finite element model is used to determine the spread of the plastic zone and mouth opening displacements of an edge-cracked structural steel plate. The spread of the plastic zone is obtained by successive increments of applied nominal tensile stress transverse to the crack length. The mouth opening displacement values obtained by this model are also compared with those measured experimentally.

The deformation analysis of a ball by FEM.

In the design of machine structures it is very important to determine the stiffness of bolt joints. A bolt joint has contact surfaces and surface asperities. To examine the deformation of an asperity, it is assumed that the tip of an asperity is a ball-shape. In this study the deformation of a ball pressed by flat surface bodies is analyzed by F. E. M. Numerical results are compared with experimental results and good agreement is shown. From the numerical results, the shape of the pressed ball surface becomes flat at the contact zone. When the ball is loaded, the plastic zone spreads toward the center of the ball. When unloaded, only elastic deformation occurs. Isostress lines are shown when the ball is loaded and unloaded.

Fatigue behavior of titanium in vacuum

To study the fatigue micromechanism in vacuum, fatigue tests for the double notched pure titanium thin plate (0.2 mm thick) were carried out in plane bending at various controlled pressure levels ranging from 1.33 × 10 −3 to 10 5 Pa. A continuous time record of specimen temperature was obtained during the fatigue tests. It was found that a sharp increase in both fatigue life and fatigue limit occurred in the pressure range 1–10 Pa. In vacuum of less then 10 Pa, the specimen temperature was raised up to greater than 20 K above room temperature and then the spread of plastic zone was evidently observed around a main crack, when specimens were cyclically stressed at σ = ± 150 MPa. Fatigue deformability was found to be very sensitive to temperature changes slightly above room temperature. This tendency appeared to be more remarkable for higher purity titanium. The improvement of fatigue life in vacuum was discussed in association with the enhancement of plastic deformability due to internal heating as well as the kinetics of molecular adsorption at the tip of a growing crack.

Elastic-plastic analysis of laminated anisotropic shells by a refined finite element laminated model

This paper presents a refined finite element shell model for the numerical analysis of thick or thin anisotropic laminated shells. A layered approach is adopted for solution with displacement variables assumed at each laminate interface. Elastic-plastic numerical analysis is performed based on flow theory and a Huber-Mises yielding surface extended by Hill for fully three-dimensional anisotropic materials. Numerical results obtained for both nonlaminated and laminated shells are presented and the effects of boundary constraints on the load-boundary deformation characteristics and on the spread of plastic zones are discussed. Comparisons are made to show the effects of anisotropy and bending-stretehing coupling on the elastic-plastic response. The effects of lamina angle sequences on the structural characteristics are also illustrated.

Nonlinear dynamic analysis with a 48 d.o.f. curved thin shell element

AbstractThe developments of an existing 48 degrees‐of‐freedom (d.o.f.), curved, quadrilateral, thin shell element, for materially and geometrically nonlinear static analysis of shell structures, are extended for the study of dynamic responses of nonlinear shells. The variable‐order polynomial representations of the shell surface and the non‐axisymmetric definition of the shell boundaries allow the study of the dynamic behaviour of a class of shell structures more general than those treated by using flat plate elements and elements with assumptions of axisymmetry. The equations of motion are based on a Lagrangian frame of reference. A combination of step‐by‐step and iterative procedures is used for the solution of nonlinear equations. The incremental equations of motion are linearized for computation purposes, and an algorithm for numerical integration based on Newmark's generalized operator for dynamic analysis, using optional iteration, is adopted. The flow theory of plasticity is used in the inelastic range, and perfectly plastic or isotropic strain hardening materials are considered. The spread of plastic zones in the thickness direction is treated by using a layered model. Numerical examples presented include the dynamic analyses of a square plate, a circular annulus, a cylindrical panel and a spherical cap. Comparisons with existing solutions demonstrate the validity and accuracy of the present developments.

A curved quadrilateral element for static analysis of shells with geometric and material nonlinearities

AbstractA 48 degrees‐of‐freedom quadrilateral element, including the effect of both material and geometric nonlinearities, is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures. The element surface is described by a variable‐order polynomial in curvilinear co‐ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co‐ordinates. Without being confined to the assumption of axisymmetry, this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones. In the formulation for geometric nonlinearity, the total Lagrangian approach is adopted. Only small strains and small rotations are allowed. In the formulation for plastic deformation, the concept of a layered element model is used. In the inelastic range, the material is assumed to obey the Von Mises yield criterion and the Prandtl–Reuss flow rule. A tangential stiffness formulation is combined with the modified Newton–Raphson iteration method for the solution of nonlinear problems. A systematic choice of examples ranging from fiat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency.

Incremental analysis of elastic-plastic frames at finite spread of yielding zones

In elastic-perfectly plastic frames finite zones of yielding develop under monotonically increasing loads. The classical deformation analysis assumes that the elastic rigidity reduces locally to zero at the generalized yield hinges only. Such an approach underestimates the deformations during the loading history and at collapse. A method is proposed in order to evaluate the displacements of elastic-plastic frames when the actual spread of plastic zones is included in the analysis. In comparison with the classical method the developed technique accounts for the axial and flexural stiffness variation along each beam member due to the partial yielding of cross-sections. The actual extent of plastic zones depends on the stress resultant distribution in the structure. The proposed method is based on an incremental analysis procedure formulated by means of the independent elastic-plastic kinematical compatibility equations, and casts a computeroriented technique for evaluating the influence of the finite extension of plastic zones, accounting for the interaction between axial force and bending moment, and for variable crosssections and loads along structural members. The evaluation of the stiffness reduction in the partially plastic elements is specified for Ishape cross-section and is performed according to two different concepts: (a) through an analytical evaluation of the elastic core size, by means of appropriate formulae developed for the cross-section shape under investigation; (b) through a step-wise linear rigidity variation, which requires a preliminary generation of interaction domains of equal stiffness in the space of the active stress resultants for standard profiles. The essential features of the method and those of the program application are illustrated in simple examples, showing the order of magnitude of the actual displacements in comparison with the results of the classical deformation analysis of elastic-plastic frames.