Elasto-plastic Stress Analysis Research Articles

Elastoplastic Stress Analysis and Residual Stresses in Metal-matrix-laminated Plates under In-plane and Transverse Loading

Fiber-reinforced metal-matrix composites provide high strength, ductility, specific stiffness, yield point, and a good temperature performance. In this study, steel fiber-reinforced aluminum metal-matrix composite-laminated plates are loaded under in-plane and transverse forces. The finite element method is used for obtaining the solution. The Tsai-Hill theory is used as a yield criterion. The laminated plates are oriented symmetrically and antisymmetrically. The orientation angles are chosen as (0/90)2, (15/15)2, (30/30)2, (45/45)2, (60/60)2, (75/75)2, (0/15)2,(0/30)2,(0/45)2,(0/60)2, and (0/75)2 for the in-plane loading. The stress components are calculated for 500 and 700 load steps. The in-plane force is increased 0.08 (N/mm) per step. The transverse loading is carried out on symmetric and antisymmetric (0/90)2, (30/30)2, (45/45)2, and (60/60)2 laminated plates. The expansion of the plastic region is carried out for 100, 300, and 500 load steps. The magnitude of the residual stress components at the midpoint of the plates for different orientation angles are calculated.

An Elastoplastic Stress Analysis of Aluminum Alloy Metal-Matrix Composite Beams under a Transverse Linearly Distributed Load by Use of Anisotropic Elasticity Theory

Beams are structural elements loaded transversely in general conditions. This loading causes shear forces and bending moment. In this study, an analytical elastoplastic stress analysis is carried out on simply supported stainless steel fiber-reinforced aluminum alloy metal-matrix composite beams under linearly distributed load by use of anisotropic elasticity theory. In the elastoplastic solution, the material is assumed to be perfectly plastic. Sample problems are given for various angles analytically. The yielding begins at the upper and lower surfaces of the beam at the same distances from the ends. The intensity of residual stress component of σ x is a maximum at the upper and lower surfaces whereas the residual stress component of τ xy is maximum on the x axis of the beam. The composite beams can be strengthened by using the residual stresses.

An Elasto-Plastic Stress Analysis in a Polymer–Matrix Composite Beam Supported from Two Ends under Transverse Linearly Distributed Load by Use of Anisotropic Elasticity Theory

An analytical elasto-plastic stress analysis is carried out in a low-density polyethylenethermoplastic beam supported from two ends under transverse linearly distributed load reinforced by Cr–Ni steel fibers analytically. The material is assumed to be perfectly plastic for the elasto-plastic solution. The intensity of the uniform force is chosen at a small value; therefore, the normal stress component y is neglected in the elastic–plastic solution. The expansion of the plastic region and the residual stress component of σx and τxy are determined for 0, 30, 45, 60, and 90 orientation angles. The yielding begins at the upper and lower surfaces of the beam at the same distances from the ends. The intensity of residual stress component of x is maximum at the upper and lower surfaces but residual stress component of τxy is maximum on the x axis of the beam. The strength of the beam is increased by residual stresses.

An Elasto-plastic Stress Analysis of Aluminum Metal-Matrix Composite Beam Subjected to Transverse Linearly Distributed Load

An analytical elasto-plastic stress analysis is carried out on metal-matrix composite beams supported from two ends under transverse linearly distributed load. The composite beam consists of stainless steel fiber and aluminum matrix. The material is assumed to be perfectly plastic for the elasto-plastic solution. The expansion of the plastic region and the residual stress component of x and τxy are determined for 0, 30, 45, 60, and 90 orientation angles. The yielding begins at the upper and lower surfaces of the beam at the same distances from the ends. The intensity of residual stress component of x is maximum at the upper and lower surfaces but residual stress component of τxy is maximum on the x axis of the beam. The strength of the beam is increased by residual stresses.

Elasto-plastic Stress Analysis in a Thermoplastic Composite Laminated Plate with Open Circular Hole Loaded Transversely

In the present study an elastic-plastic stress analysis is carried out for long stainless steel fiber-reinforced homogeneous polyethylene thermoplastic composite laminated plates with open circular hole by using finite element technique.The thermoplastic composite layer reinforced by long stainless fiber is manufactured using molds under a pressure of 15 MPa and heating up to 170 C by electrical resistance. The laminated plates with open hole consist of four layers and bonded symmetrically and antisymmetrically. Each layer with constant thickness is meshed into 48 elements and 228 nodes with simply supported. The expansion of plastic zone and residual stress are determined in the symmetric and antisymmetric cross-ply and angle-ply laminated plates for small deformations. The load is increased by 0.01 N/mm at each step. Iteration numbers are chosen as 150, 300, and 600. The intensity of the residual stress is maximum near the open circular hole and the yield points in symmetric laminates are higher than those in antisymmetric laminates.

An Elastic-plastic Stress Analysis in a Polymer Matrix Composite Beam of Arbitrary Orientation Supported from Two Ends Acted Upon with a Force at the Mid Point

Polymer matrix composite beam of arbitrary orientation supported from two ends acted upon with a force at the mid point is studied by an analytical elasto-plastic stress analysis. In the elasto-plastic solution, the material is assumed to be perfectly plastic. The expansion of the plastic region and the residual stress component of σ x are determined for 0, 30, 45, 60 and 90° orientation angles. The yielding begins for 0 and 90° orientation angles at the upper and lower surfaces of the beam at the same distances from the mid point. But, it starts first at the lower surface for 30, 45 and 60° orientation angles. The intensity of the residual stress component of xy is maximum on or around the x axis of the beam but the residual stress component of τ x is maximum at the upper and lower surfaces.The beam can be strengthened by using the residual stress.

Boundary element analysis of 3-D elasto-plastic contact problems with friction

In this paper, a boundary element method for three-dimensional elasto-plastic stress analysis of frictional contact problems in the framework of small strains and small displacements is presented. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial strain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the ceramic femoral head frictional contact problem.

Elasto-plastic static stress analysis of 3D contact problems with friction by using the boundary element method

In this paper, a boundary element method for three-dimensional elasto-plastic stress analysis of frictional contact problems in the framework of small strains and small displacements is presented. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial strain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the ceramic femoral head frictional contact problem.

Elasto-plastic Stress Analysis with Nested Finite Element Method

Nested-finite-element methodology (NFEM) is an improved finite-element method to evaluate local concentrations of stress with nested sub-elements. NFEM was applied only to elastic and explicit inelastic problems, because it is unable to calculate residual forces accurately from stresses at integral points. I thus developed an algorithm that would allow implicit analysis of the elastic-plastic problem on the basis of NFEM. The algorithm has the following steps : (1) Calculate the displacements of nodes with elastic NFEM. (2) Calculate stresses at each integral point. (3) Modify stresses at “yielded” integral points in main-elements and sub-elements. (4) Extrapolate stresses from integral points in sub-elements to integral points in main elements, and (5) Calculate residual forces at nodes from stresses. All steps are repeated until the residual forces converge to an allowable limit. The stress extrapolation scheme is the most important part of the method. I developed the extrapolation algorithm based on the shape functions of an iso-parametric element. To conclude, elastic-plastic NFEM can be used to implicitly analyze the stress of inelastic materials.

An Elasto-Plastic Stress Analysis of Simply Supported Thermoplastic Composite Beams under a Transverse Linearly Distributed Load

An Elasto-Plastic Stress Analysis of Simply Supported Thermoplastic Composite Beams under a Transverse Linearly Distributed Load

The effects of overlap length and adherend thickness on the strength of adhesively bonded joints subjected to bending moment

In this work, elasto-plastic stress analysis of a Single Lap Joint (SLJ) subjected to bending moment was investigated using 2D non-linear Finite Element Analysis (FEA). The SLJs, consisting of hardened steel as the adherend bonded by two adhesives, one stiff and one flexible, with very different mechanical behaviors were analyzed. In order to determine the effect of geometrical parameters on the performance of the SLJs, four different adherend thicknesses and overlap lengths for each adhesive were used. For verification of the analysis, the FEA results were compared with experimental results. It was observed that there was a significant effect of adherend thickness on the strength of the joint with both adhesives. However, the load carried by the SLJ with the flexible adhesive increased with increasing overlap length.

Elasto-plastic element-free Galerkin method

In this paper the element free Galerkin method (EFGM) has been extended to be used in the elastoplastic stress analysis. The developed method has been examined in planar stress analysis around the tip of a crack and in its opening mode of loading. To do this, at the first step by using the incremental relations of plastic deformation a system of elastoplastic EFGM equations has been derived. Since the obtained relations are nonlinear, a nonlinear solution technique has been chosen. To examine the validity of this technique, stress fields in two different plates with and without a crack have been calculated and the results have been compared with other similar analytical works in the literature. In doing so the power law work hardening behavior has been employed and the value of J-integral has been used as a base for comparison of the results.

THE BAUSCHINGER AND HARDENING EFFECT ON RESIDUAL STRESSES IN THICK-WALLED CYLINDERS OF SUS 304

A thick-walled cylinder of strain hardening material with closed ends, which is assumed to obey Von-Mises yield criterion is considered. An elastoplastic and residual stress analysis of thick-walled cylinders is performed with the incremental theory of plasticity. Critical pressures of direct and reverse yielding are investigated using the Von-Mises yield criterion as well as the Bauschinger effect factor (BEF). The material selected is SUS 304 stainless steel. The material's loading and unloading properties including the (BEF) are obtained experimentally and represented mathematically as a continuous function of effective plastic strain. The material model and the BEF have been incorporated in an analytical-numerical model so as to predict the cylinders plastic and residual stresses as well as the critical pressures of direct and reverse yielding. The analytical-numerical model for the prediction of critical inner pressure, plastic stress distributions and the subsequent residual stresses of thick-walled cylinders is validated by using experimental results. Residual stresses with and without the BEF are obtained and the corresponding results are compared. In the case study of a specific cylinder (Radii ratio of β=2), it has been concluded that residual stresses subsequent to a 45% overstrained condition are at the onset of reverse yielding when the BEF is considered.

The effect of ply number, orientation angle and bonding type on residual stresses of woven steel fiber reinforced thermoplastic laminated composite plates subjected to transverse uniform load

This paper is concerned with the numerical results of the elasto-plastic stress analysis and residual stresses in woven steel fiber reinforced thermoplastic laminated composite plates for transverse uniform loads. The effects of ply number, orientation angle and bonding type on the residual stresses of laminated composite plates are investigated. Elasto-plastic stress analysis is carried out in the laminated plate by using the finite element technique. The finite element code ANSYS is used to perform the numerical analyses using an eight-node layered shell element. Yielding loads and residual stresses are obtained for symmetric and anti-symmetric laminated plates with simply supported boundary conditions. Different stacking sequences of laminated composites are used in analysis and the results are compared with each other. Three load steps are carried out for each analysis consecutively. In the first load step, the yielding transverse load is applied. Secondly, a series of load increments is added until the load reaches “Yielding Load+0.005 MPa”. In the last step the external load is released to obtain the residual stress components.

An Elasto-Plastic Stress Analysis in a Polymer Matrix Composite Beam of Arbitrary Orientation Subjected to Transverse Linearly Distributed Load

An elasto-plastic stress analysis is carried out in a low density polyethylene thermoplastic cantilever beam of arbitrary orientation subjected to transverse linearly distributed load reinforced by Cr-Ni steel fibers analytically. In the elasto-plastic solution, the material is assumed to be perfectly plastic. The expansion of the plastic region and the residual stress component of σ x are determined for 0°, 30°, 45°, 60° and 90° orientation angles. The yielding begins at the upper and lower surfaces of the beam at the same distances from the free end. The intensity of residual stress component of σ x is maximum at the upper and lower surfaces but residual stress component of τ xy is maximum on the x axis of the beam. Sample problems are given for various angles, x axis of the beam is used to obtain the location of the elasto-plastic boundary and to calculate elastic, elasto-plastic and residual normal and shear stresses.

Thermal Elastic-Plastic Stress Analysis in Simply Supported Thermoplastic Laminated Plates

In the present study, an analytical elasto-plastic stress analysis is carried out on symmetric cross-ply [0°/90°]2 and symmetric angle-ply [30°/-30°]2, [45°/-45°]2, [60°/-60°]2, thermoplastic laminated plates. Composite laminated plates are simply supported and subjected to constant temperature change through the thickness. The analytical solution is performed for satisfying thermoelastic-plastic stress-strain relations and boundary conditions for small plastic deformations. The composite materials are assumed to be linearly hardening. The Tsai-Hill theory is used as a yield criterion. Residual stress components (σ x) r and (σ y) r for cross-ply laminated plates have some magnitudes but (τ xy) r are zero. The intensity of residual stress components increase gradually depending on the temperature increment. For symmetric angle-ply laminated plates, all residual stresses are found zero.

Plasticity in constrained layers: model with point forces

An elasto-plastic stress analysis is carried out to determine the stresses and deformations within a thin ductile layer sandwiched between two semi-infinite elastic blocks. The layer is assumed to contain a crack much longer than the layer thickness and to have a much lower elastic modulus than the constraining blocks. The development of plasticity within the layer is examined for an increasing applied stress normal to the layer, leading to mode I conditions at the crack tips. The normal stress σ yy within the layer is found to rise approximately linearly from about 3 σ Y up to 6 σ Y in some cases, while the stress difference σ yy − σ xx remains approximately constant within that zone. The plastic deformation is restricted to a narrow zone, coplanar with the crack, appearing to suite a line representation such as the Dugdale model. However, the conventional Dugdale model predicts σ yy = σ xx along the plastic zone. This limitation is shown to be overcome by adding a distribution of point forces to the distribution of climbing edge dislocations which is effectively used in the Dugdale model. These point forces act in the plane of the crack and must satisfy the overall equilibrium requirement that there is no net force on the crack.

3D Elasto-Plastic Stress Analysis by the Method of Arbitrary Lines

The method of arbitrary lines (MAL) constitutes a general dimensional reduction methodology for elliptic boundary value problems (BVP) in arbitrary two- and three-dimensional domains by solving systems of one-dimensional boundary value ordinary differential equations (ODEs). It has been already applied to two-dimensional problem, and the good results have been reported. In this work, we consider the extension of the MAL to three-dimensional elasto-plastic stress analysis. We first give the MAL formulation of three-dimensional elasto-plastic problems. Although the MAL formulation is derived from the principle of three-dimensional increment virtual work as well as the finite element method (FEM), the MAL is different from FEM in that displacement increment and virtual displacement increment are expressed continuous functions along one direction and shape-functions along other two directions. Substituting displacement increment and virtual displacement increment into the principle of three-dimensional increment virtual work, we have a system of ODEs. The three-dimensional elasto-plastic analysis of BGA model, which was a method of the solder joints of electronic component, was carried out. As results, it was confirmed that to solve 3D elasto-plastic problem at the good accuracy was possible by the MAL.

An Elasto-Plastic Stress Analysis on a Metal Matrix Composite Beam of Arbitrary Orientation Supported from Two Ends under a Transverse Uniformly Distributed Load

An analytical elastic-plastic stress analysis is carried out on a metal-matrix composite beam of arbitrary orientation supported from two ends under a transverse uniformly distributed load. The composite layer consists of stainless steel fiber and aluminum matrix. The material is assumed to be perfectly plastic in the elasto-plastic solution. The intensity of the uniform force is chosen at a small value; therefore the normal stress component of σy is neglected during the elasto-plastic solution. The expansion of the plastic region and the residual stress component of σx are determined for 0°, 30°, 45°, 60° and 90° orientation angles. Plastic yielding occurs for 0° and 90° orientation angles on the lower and upper surfaces of the beam at the same distances from the mid point. However; it starts first at the lower surface for 30°, 45° and 60° orientation angles. The intensity of the residual stress component of σx is found maximum at the lower and upper surfaces. However; the intensity of residual stress component τxy is maximum on or around the x axis of the beam.

Elasto-Plastic Stress Analysis of Aluminum Metal Matrix Laminated Plates with a Circular Hole under Transverse Loading

Elasto-Plastic Stress Analysis of Aluminum Metal Matrix Laminated Plates with a Circular Hole under Transverse Loading