Plane Stress Conditions Research Articles

Computing Stresses from Measured In-plane Strains in Viscoelastic Body under Plane Stress Condition

Computing Stresses from Measured In-plane Strains in Viscoelastic Body under Plane Stress Condition

Correlation structure in the elasticity tensor for short fiber-reinforced composites

The present work provides a profound analytical treatment and numerical analysis of the material properties of SFRC on the mesoscale as well as the resulting correlation structure taking into account the probabilistic characteristics of the fiber geometry. This is done by calculating the engineering constants using the analytical framework given by Tandon and Weng as well as Halpin and Tsai. The input parameters like fiber length, diameter and orientation are chosen with respect to their probability density function. It is shown, that they are significantly influenced by the fiber length, the fiber orientation and the fiber volume fraction. The verification of the analytically obtained values is done on a numerical basis. Therefore, a two-dimensional microstructure is generated and transferred to a numerical model. The advantage of this procedure is, that there are several fibers with different geometrical properties placed in a preset area. The results of the numerical analysis meet the analytically obtained conclusions. Furthermore, the results of the numerical simulations are independent of the assumption of a plane strain and plane stress state, respectively. Finally, the correlation structure of the elasticity tensor is investigated. Not only the symmetry properties of the elasticity tensor characterize the correlation structure, but also the overall transversely-isotropic material behavior is confirmed. In contrast to the influencing parameters, the correlation functions vary for a plane strain and a plane stress state.

Dynamic shear instabilities in metallic sheets subjected to shear-compression loading

This paper presents an investigation on the formation of adiabatic shear bands in metallic sheets subjected to dynamic shear-compression loading under plane-stress conditions. For that purpose, we have developed a theoretical model based on perturbation analysis, and have performed finite element calculations. The material behavior has been modeled with von Mises plasticity, and the evolution of the yield stress has been considered dependent on plastic strain, plastic strain rate, and temperature. The theoretical model extends the linear stability analysis for simple-shear formulated by Molinari (1997) to shear-compression loading. The numerical simulations have been performed in ABAQUS/Explicit (2016) using a unit-cell model based on the work of Rodríguez-Martínez et al. (2015) in which the shear band formation is favored introducing geometric and material imperfections. Moreover, we have developed a calibration procedure for the stability analysis that enables to make qualitative and quantitative comparisons with the finite element calculations. Both stability analysis predictions and finite element results display the same overall trends, and show that any small negative triaxiality has a profound stabilizing effect on the material behavior delaying, or even preventing, the formation of a shear band. This key outcome has been substantiated for a wide range of strain rates and for materials with different strain hardening coefficients, strain rate sensitivities, and thermal softening behaviors.

Limit curves for brittle fracture in key-hole notches under mixed mode I/III loading based on stress-based criteria

In this research, with the aim to estimate the onset of fracture in key-hole notched components, made of brittle materials and subjected to combined tension-tear loading, the fracture limit curves are developed in terms of the notch stress intensity factors (NSIFs) based on the maximum tangential stress (MTS) and mean stress (MS) criteria. In order to verify the curves developed, a series of fracture tests are carried out on key-hole notched specimens made of PMMA using an improved loading configuration. The samples are prepared with three various notch tip radii for the sake of evaluating the influence of the notch tip radius on the fracture toughness of the key-hole notched samples. It is shown that for all notch tip radii, the fracture limit curves for both MTS and MS criteria are in very good consistency with the experimental data. No meaningful difference is found between the curves of MTS and MS criteria, especially under plane-stress conditions. It is also observed that the notch fracture toughness of the PMMA specimens could be well estimated under both plane-stress and plan-strain conditions.

A non-quadratic pressure-sensitive constitutive model under non-associated flow rule with anisotropic hardening: Modeling and validation

A non-associated flow rule (non-AFR) constitutive model is proposed to describe the evolving yield stress and plastic potential surfaces of sheet metal under plane stress conditions. The yield stress function is a multiplication of two yield functions, within the first part includes an asymmetric pressure-sensitivity that considers anisotropic and asymmetric yielding of sheet metals. This yield stress function can describe anisotropic hardening behavior by directly employing the hardening functions under seven different loading conditions, i.e., uniaxial tension along 0°, 45°, 90° to the rolling direction (RD) of sheet metal, uniaxial compression along the same orientations and equi-biaxial tension without any interpolation or optimization procedure at a discrete level of equivalent plastic strain. The second part is a non-quadratic isotropic function, which is the sum of two isotropic yield functions with high flexibility in shaping the yield surface. A new plastic potential function is proposed to capture the differential Lankford coefficients (r-values) between uniaxial tension and compression obtained from mechanical testing. Eight parameters in the plastic potential function were calibrated from seven r-values under the same loading conditions and one yield stress as calibrating parameters for the yield stress function. The proposed constitutive model was validated by experimental data of three engineering sheet metals, i.e., one dual-phase steel DP980, one TRIP-assisted steel QP980 and one aluminum alloy AA5754-O and compared with several classical yield criteria. The evolving yield behavior was accurately described by the proposed non-associated flow rule (non-AFR) constitutive model.

Forming Limit Prediction of Anisotropic Aluminum Magnesium Alloy Sheet AA5052-H32 Using Micromechanical Damage Model

This paper focuses on the implementation and applicable evaluation of a modified Gurson–Tvergaard–Needleman (GTN) damage model for predicting forming limit diagram of anisotropic aluminum alloy sheet, in which its elasto-plastic behavior is assumed to obey a non-quadratic anisotropic yield criterion. The original porous ductile material model is heuristically enhanced to suit anisotropy of sheet metal, and then, it is implemented via a user material subroutine using finite element codes of ABAQUS/Explicit software package. The material damage model is calibrated and applied to predict forming limit diagram of commercial aluminum alloy sheet AA5052-H32 via the Nakajima drawing tests under plane stress condition. To obtain various strain paths, the Nakajima tests are conducted for seven specimens, which are designed in accordance with standard ISO 12004-2-2008. The influence of material anisotropy on the predicted forming limit is also considered and discussed. The numerical simulation results obtained from the proposed damage model showed a good agreement with those of the experimental data.

Defining relations of creep theory for a polymer composite material

Simplified defining relationships are being developed that will make it easier to determine the mechanical characteristics of PCM. The creep strain of a PCM in a plane-stress state is considered. The constitutive relations for PCM are obtained using the asymptotic analysis method.For the case of a complex stress state, the defining relations contain a large number of arguments (SSS invariants) of a different order of smallness, then they will be simplified by asymptotic analysis methods. To determine the parameters included in the constructed relationships, new approaches (parametric identification methods) to solving inverse problems will be adapted or developed.

B EFFECT OF BOUNDARY CONDITIONS ON BUCKLING LOAD FOR LAMINATED COMPOSITE DECKS PLATES

Finite element (FE) method is presented for the analysis of thin rectangular laminatedcomposite decks plates under the biaxial action of in – plane compressive loading. Theanalysis uses the classical laminated plate theory (CLPT) which does not account for sheardeformations. In this theory it is assumed that the laminate is in a state of plane stress, theindividual lamina is linearly elastic, and there is perfect bonding between layers. The classicallaminated plate theory (CLPT), which is an extension of the classical plate theory (CPT)assumes that normal to the mid – surface before deformation remains straight and normal tothe mid – surface after deformation. Therefore, this theory is only adequate for bucklinganalysis of thin laminates. A Fortran program has been developed. New numerical results aregenerated for in – plane compressive biaxial buckling which serve to quantify the effect ofboundary conditions on buckling loading. It is observed that, for all cases the buckling loadincreases with the mode number but at different rates depending on whether the plate is simplysupported, clamped or clamped – simply supported. The buckling load is a minimum whenthe plate is simply supported and a maximum when the plate is clamped. Because of therigidity of clamped boundary condition, the buckling load is higher than in simply supportedboundary condition. It is also observed that as the mode number increases, the plate needsadditional supp

ПОЛНОЕ РЕШЕНИЕ ЗАДАЧИ ЛЯМЕ ДЛЯ ТОЛСТОСТЕННОГО В СРЕДНЕМ ИЗОТРОПНОГО ЦИЛИНДРА ИЗ НЕЛИНЕЙНО-ДЕФОРМИРУЕМЫХ МАТЕРИАЛОВ

the paper deals with the boundary value problem for the nonlinearly deformable composite cylinder with different types of boundary conditions. The stresses and displacements on both boundaries of the cylinder are constant, so their boundary average values for any area are constant and equal to the initial values. It should be noticed, that the solution of the boundary value problem is obtained without using nonlocal hypotheses about the composite material volume smallness by the angle for which the effective characteristics are calculated. In addition, the assumption of the composite material element smallness in the radial direction with respect to the thickness of the cylinder is used. It is established, that there is no possibility to consider plane stress state and plane strain of the cylinder separately from each other. Both of these states should be studied for analysis of stress-strain state according to Voigt and Reuss hypotheses. It is also shown that the solution of the Lame problem for a cylinder, which is derived, based on Voigt and Reuss hypotheses, is self-sufficient. Formulas, which describe stress-strain state of the composite cylinder, are derived based on this approximation.

Üçayaklı Ayna İle Tutulan Parçaların Üretim Sonrası Delik Profillerinin Tahmin Edilmesi

Estimating bore profile is important to select an appropriate tool for precision manufacturing in the process planning stage. Also, it helps in reducing the rejection rate of the process. A manufacturer might not be well-equipped and want to make their best with the resource on hand. Three-jaw chuck allows machining a wide range of workpiece, mostly circular parts in a lathe. However, clamping via a three-jaw chuck distorts the workpiece. In this study, the deformation of the bore profile was investigated numerically for circular parts. Finite element analyses were performed to examine dimensional variation for various materials and different wall thicknesses under fully elastic plane stress conditions. The stressed workpiece had a triangular form. Results showed that wall thickness and materials are important parameters on the triangulation of bore diameter. A simple calculation method based on thick-walled vessel theory was proposed to estimate the tolerance grade of the workpiece. This simple method provides the opportunity to reduce the rejection rate in the mass production of circular parts.

On loading paths followed inside plastic simple waves in two-dimensional elastic-plastic solids

Although the solution of hyperbolic partial differential equations in elastic-plastic media is of major importance in solid mechanics, the mathematical complexity of such problems increases with the space dimensionality. As a result, the development of analytical solutions is in general not possible. Whereas the wave structure resulting from given external loads is known and well understood for one-dimensional problems, several gaps still need to be filled for problems with more space dimensions. Indeed, the literature related to the propagation of simple waves in elastic-plastic solids is rather sparse since only particular two-dimensional and three-dimensional problems have been considered. Following the general three-dimensional framework of Mandel (1962), the object of the paper is to construct the loading paths followed inside the simple waves under plane strain and plane stress conditions. It is believed that the mathematical and numerical studies of the waves presented here could help define the characteristic structure involved in a Riemann problem.

Fatigue Crack Growth from Notches: A Numerical Analysis

A numerical approach based on plastic crack tip opening displacement (CTOD) was followed to study fatigue crack growth (FCG) from notches. The identification of fundamental mechanisms was made considering notched and unnotched models, with and without contact of crack flanks. Different parameters were studied, namely, notch radius, crack length, stress state, and material. The notch increases the plastic CTOD, and therefore fatigue crack growth rate, da/dN, as expected. The reduction of notch radius increases da/dN but reduces the notch affected zone. Ahead of the notch affected zone, da/dN increases linearly with crack growth, with a rate that increases linearly with the plastic CTOD. The crack closure phenomenon has a dramatic effect under plane stress conditions but a limited effect on plane strain conditions. In the former case, the contact of crack flanks reduces substantially the effect of notch radius and the size of the notch affected zone. These trends are associated with the increase of crack closure level with notch radius. The material does not affect the global trends, but the reduction of yield stress increases the level of plastic deformation and therefore da/dN. The effect of material, and also of stress state, is mainly associated with crack closure.

Experimental research of the stress-strain state when drawing aluminum-copper bimetal parts rectangular in plan

The stress-strain state of the aluminum-copper bimetal blank flange was studied when extracting boxes rectangular in plan. The studies were carried out using the grid method with assumptions about the material isotropy and incompressibility; uniform deformation within each cell; monotonous deformation, plane stress and three-dimensional strain state, while elastic strains were neglected. A CAD modeling program was used to minimize coordinate grid measurement errors and reduce the time for processing the information obtained. The blanks were rectangles of certain sizes with an explosion-welded AD aluminum and M4 copper layers subjected to preliminary heat treatment before the drawing operation. Rectangular blanks were successively drawn to a height of 10 mm with grid and test sample thickness measurements after drawing. Blank samples were photographed with the same focal length and loaded into the application program. In the program, coordinate points were applied to grid nodes with the distances and coordinates of these points measured before and after strain. According to measurement results, the highest strain was observed in the blank corner areas where compressive stresses increased from the angle bisector to the walls. These stresses led to bimetallic blank stratification and corrugations formed along the copper layer. 20 blanks were drawn, and corrugation was observed on the flange in each case. Varying the hold-down pressure from 0.25 to 0.5 MPa gave no positive results. The highest strain intensity is observed at the end part of the box flange, and this value decreases by 20 % at the approach to the die hole. The effect of angular shear stresses leads to a discontinuity in the transition zone featuring by the presence of an intermetallic layer with reduced plastic properties.

Analytical formulation of the contact pressure evolution for interference joints under creep regime

An analytical formulation to evaluate the contact pressure evolution in interference fit joints working under high temperature regime, is proposed. The phenomenon is mainly due to the stress relaxation related to the creep behaviour of materials used to realize this kind of joints. Despite extensive researches on the topic, the decay of contact pressure due to creep relaxation is commonly not considered or evaluated only by numerical methods. The proposed analytic solution correlates the contact pressure to the creep material properties and could be largely used to improve the design or the fitness-for-service assessment of joints that transmit load thanks to the interference fit. The formulation assumes the plane strain condition for the inner element and the plane stress condition for the outer one. It was validated by finite element analysis (FEA) and gives accurate prediction of the contact pressure evolution both in plane and axisymmetric simulations.

Adaptive extended isogeometric upper-bound limit analysis of cracked structures

Limit analysis, without the complicated elasto-plastic computation, is an efficient method for estimating safety load of engineering structures. This paper develops a novel computational approach by integrating second-order cone programming (SOCP) into adaptive extended isogemetric elements (XIGA) for upper-bound limit analysis of cracked structures. The advantage of XIGA is to model cracks without considering the location of crack faces by introducing enrichment functions. The local refined (LR) B-splines, which have versatile and flexible local refinement ability, are adopted as basis functions in the XIGA. We use structured mesh refinement strategy to implement local refinement based on the indicator of L2-norm of plastic strain rates. Cracked structures are assumed under plane stress condition, and the von Mises yield criterion is used. Kinematic formulation of the limit analysis is translated into the form of SOCP, then is solved by the Mosek tool. The developed model is implemented and its accuracy and effectiveness are illustrated through several numerical examples. In addition, numerical results illustrate that the convergence rate of adaptive XIGA is faster than that of traditional XIGA.

A compact plane stress yield function formulation

The construction of anisotropic yield function by introducing linear transformations is a common practice with many phenomenological yield criteria. Based on the K1 − K2 representation method of principle stresses (represented by Barlat89 yield function), a compact 13-parameter plane stress function is proposed. The new yield function consists of five different linear transformations, and is designed to have a certain symmetry in both the overall structure and the distribution of linear transformation matrix components. The new 13-parameter yield function is applied to predict the yield surfaces (loci), plastic strain rate directions, flow stresses and r-values for both fcc and bcc materials. Compared with the yield functions of Yld2004-18p and CPB06ex2 (both reduce to 14 parameters in symmetric plane stress condition), the new yield function can achieve similar prediction accuracy with fewer parameters.

Mesoscopic aspects of the computational homogenization with meshless modeling for masonry material

SummaryThe multiscale homogenization scheme is becoming a diffused tool for the analysis of heterogeneous materials as masonry since it allows dealing with the complexity of formulating closed‐form constitutive laws by retrieving the material response from the solution of a unit cell (UC) boundary value problem (BVP). The robustness of multiscale simulations depends on the robustness of the nested macroscopic and mesoscopic models. In this study, specific attention is paid to the meshless solution of the UC BVP under plane stress conditions, comparing performances related to the application of linear displacement or periodic boundary conditions (BCs). The effect of the geometry of the UC is also investigated since the BVP is formulated for the two simpliest UCs, according to a displacement‐based variational formulation assuming the block indefinitely elastic and the mortar joints as zero‐thickness elasto‐plastic interfaces. It will be showed that the meshless discretization allows obtaining some advantages with respect to a standard FE mesh. The influence of the UC morphology as well as the BCs on the linear and nonlinear UC macroscopic response is discussed for pure modes of failure. The results can be constructive in view of performing a general Fe·Meshless or Meshless2 analysis.

Making ultrastrong steel tough by grain-boundary delamination.

Developing ultrahigh-strength steels that are ductile, fracture resistant, and cost effective would be attractive for a variety of structural applications. We show that improved fracture resistance in a steel with an ultrahigh yield strength of nearly 2 gigapascals can be achieved by activating delamination toughening coupled with transformation-induced plasticity. Delamination toughening associated with intensive but controlled cracking at manganese-enriched prior-austenite grain boundaries normal to the primary fracture surface dramatically improves the overall fracture resistance. As a result, fracture under plane-strain conditions is automatically transformed into a series of fracture processes in "parallel" plane-stress conditions through the thickness. The present "high-strength induced multidelamination" strategy offers a different pathway to develop engineering materials with ultrahigh strength and superior toughness at economical materials cost.

On rotational instability within the nonlinear six-parameter shell theory

Within the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which occurs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we considered here both large translations and rotations. The constitutive relations contain some additional micropolar parameters with so-called coupling factor that relates Cosserat shear modulus with the Cauchy shear modulus. The discussed instability relates to the bifurcation from the static solution without rotations to solution with non-zero rotations. So we call it rotational instability. We present an elementary discrete model which captures the rotational instability phenomenon and the results of numerical analysis within the shell model. The dependence of the bifurcation condition on the micropolar material parameters is discussed.

Damage Accumulation Kinetics in Heat-Resistant Steels at the Plane Stress State Under Cyclic Loading at Different Temperatures

Experimental results are presented for damage accumulation in 10GN2MFA and 15Kh2MFA steels studied with the LM-hardness method at different stress states under cyclic loading at room and elevated temperatures that are consistent with the service conditions of structure elements. Damage accumulation kinetics is examined at primary and secondary creep stages in view of the multiaxial stress state and creep strain effects on the homogeneity coefficient. A higher level of initial strain on cyclic creep gives rise to more intensive damage accumulation in the metal, leading to the earlier onset of fracture in comparison with the smaller initial strain. Experimental critical homogeneity coefficients are given that correspond to the plastic strain stability loss when the stable deformation of the metal with its further fracture is affected by the reduction in the cross-section area and hardening modulus. The rate of homogeneity change in examined steels at different ratios of principal cycle stresses on cyclic creep is evaluated. The significant effect of a stress state at equilibrium between strain hardening and softening of the structure (specimen) metal at the secondary creep stage, is demonstrated. The effect of a stress state and temperature on damage accumulation kinetics of examined materials, in particular on the useful life of the metal on cyclic creep is established.