Plane Stress Loading Research Articles

The yield condition strongly influences the formation of Dugdale plastic strips ahead of crack tips under tensile plane stress loading conditions

AbstractA finite element analysis indicates a good correlation between the Dugdale plastic strip model and a linear elastic/perfectly plastic material under plane stress loading conditions for a flow theory of plasticity based on the Tresca yield condition. A similar analysis under the von Mises yield condition reveals no plastic strip formation.

Mechanical Performance of Composite Laminate with Oblique Splicing Ply

In order to determine the mechanical properties of the carbon/polyurethane composite laminate with splicing ply, the tensile testing were performed on laminate specimens which has been designed specially. The tensile elastic modulus and tensile strength were obtained from the experimental datum. The breakage happened in place of joint gap. The stiffness of the composite laminate was affected by the oblique splicing ply significantly, but the strength is mainly determined by the continuous layers. The laminate is failure in low load. The numerical analyses using linear elastic and progressive damage model were conducted with the commercial the finite element model (FEM) software ABAQUS. The linear elastic FEM is established to calculate the inter-laminar stress. The progressive model is used to predict the strength on the basis of numerical computation. There are three different criteria used here in the strength prediction. By combining the damage model with classical lamination theory, the behavior of laminates under plane stress loading is predicted. The results show that the experimental tests are in good agreement with the finite element simulation.

Modeling of scattered damage accumulation kinetics under combined stress

An analysis of the reliability and range of application of a number of phenomenological damage models has been performed on the basis of experimental research carried out into the kinetics of damage accumulation in metallic structural materials under plane stress and active loading. Damage models are based on the main postulates of irreversible thermodynamics and continuum damage mechanics. The laws governing the effect of the type of stress state on scattered damage accumulation kinetics have been established.

Parametric analysis of the strain-dependent behavior of a metamaterial electric resonator

In this paper, we describe the strain-dependent behavior of an electric-LC (ELC) resonator unit cell, commonly used in metamaterial designs. We leverage analytic expression to understand the way strain manifests itself in a change in electromagnetic (EM) response. We verify the simplified physical models using full-wave simulations and generalize the trends to accommodate the strain profile for any arbitrary plane-stress loading scenario.

Investigation on the strain-path dependency of stress-based forming limit curves

Path-dependent forming limits have been computed for sheet metals undergoing various combinations of plane stress loading conditions. This paper presents a theoretical model for prediction of stress-based forming limit curves (SFLC) based on the Marciniak and Kuczynski (MK) model. Acceptable agreement was observed between calculated forming limit curves (FLC) and experimental data for AISI-1012 steel (Molaei 1999) and AA-2008-T4 alloys (Graf and Hosford Metallurgical Trans 24A:2503–2512, 1993). In this paper, the path dependency of SFLCs predicted for different non-proportional loading histories has been investigated. For a range of prestrain values in different bilinear loading paths, the SFLC remains practically unchanged. However, some strain path dependency is observed for large values of prestrain (\( \bar{\varepsilon } \geqslant 0.35 \) for AISI-1012 steel) and for abrupt changes in strain path. Nevertheless, the SFLC remains a good failure criterion for virtual forming simulations because the path dependency of SFLCs is much less significant than that of strain-based FLCs.

Crack observation methods, their application and simulation of curved fatigue crack growth

Abstract The observation of cracks with curved crack path has to be done optically. It is shown that a modified commercial flat bed scanner and a combination of a high-resolution scanner camera system with 10,000 × 10,000 pixels with a telecentric lens are appropriate for high-resolution (up to 8 μm/pixel) optical recording of multiple crack ends on sample areas up to 210 mm × 290 mm. The high-resolution photographs are suitable for determination of crack lengths. It is also possible to observe crack paths or geometrical crack tip parameters and strain fields by image correlation. The method is used to determine static crack resistance and cyclic crack growth curves on center crack tension and biaxial cruciform samples. Furthermore, the paper presents an improved finite element technique for the simulation of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under biaxial plane stress loading applying a predictor–corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method including the consideration of the plastic limit loads. For this, the program PCCS-2D was extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the failure assessment diagram procedure in combination with a numerical crack path simulation. Finally, the simulation is verified experimentally.

A novel method for evaluating plane stress dynamic fracture toughness of 0Cr18Ni10Ti stainless steel welded joints

A novel method was proposed for the evaluation of Mode I dynamic fracture toughness (DFT) under plane stress and small scale yielding conditions for welded joints of stainless steel (SS), 0Cr18Ni10Ti. In a hybrid experimental-numerical approach, the experiments were carried out on the Hopkinson pressure bar apparatus, and three dimensional (3D) transient numerical simulations were performed by a finite element (FE) computer program. Macroscopical plastic deformation was observed at the loading and supporting points, on the specimens, after the test, which could cause a large error if omitted in the numerical simulation. Therefore, elastic-viscoplastic analysis was performed on the specimen by adopting the Johnson-Cook (J-C) model to describe the rate-dependent plastic flow behavior of the material. The material heterogeneity in the mismatched welded joints, induced by the difference in the base metal (BM) and the weld metal (WM) in yield stress, has also been taken into consideration by using the J-C models separately. Good accordance was obtained between the experimental and the computational results by the present approach. The relationship between plane stress DFT and loading rate was also obtained on the order of 106 MPa·m 1/2 ·s -1 .

Path Independent Integral for an Elliptical Hole in a Plate under Tension for Plane Stress Deformation Theory

An exact expression is derived for a path independent integral surrounding an elliptical hole in an infinite plate with tensile tractions at infinity for plane stress loading conditions. The plate is composed of a non-work-hardening material satisfying the Tresca yield condition under proportional loading and small strain assumptions. This problem may serve as a simple classroom example for the derivation of a relationship between crack opening displacement and path independent integral for a nonlinear elastic material satisfying the Tresca yield condition.

A new generalized fracture criterion of elastomers under quasi-static plane stress loadings

The aim of this paper is to propose a new fracture criterion of rubber-like materials under plane stress loading. Our experimental data already published [A. Hamdi, M. Naït Abdelaziz, N. Aït Hocine, P. Heuillet, N. Benseddiq, Fracture criteria of rubber like-materials under plane stress conditions. Polym. Test. 25(9) (2006) 994–1005] are herein completed by results obtained from pure shear tests and then further analysed. In this analysis, we used a theoretical approach based on a reference axis change principle, introduced earlier by Nevière et al. [A strain based design criterion for solid propellant rocket motors. Proceedings OTAN, Symposium on Combat Survivability of Air, Sea and Land Vehicles, Alborg, Denmark, 2002, pp. 23–26] for the case of solid propellant materials. Logarithmic extensions evaluated in a specific coordinates system were introduced in the analytical development, which leads to identifying a relevant rubber fracture criterion. The ultimate experimental extensions were compared with the predictions of this criterion and good agreement was observed.

Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dugdale plastic strip model

A number of plane stress numerical analyses of the mode I elastoplastic fracture mechanics problem have been performed in the past using the Huber–Mises yield criterion. This study employs instead the Tresca yield condition using an incremental theory of plasticity for a stationary crack. A commercial finite element program is used to solve the opening mode of fracture problem (mode I) for a square plate containing a central crack under generalized plane stress loading conditions. A biaxial uniform tensile traction is applied to the edges of a thin plate composed of a linear elastic non-work hardening material under small strain assumptions. The finite element results are compared with the analytical predictions of the Dugdale plastic strip model for a crack in an infinite plate subject to a biaxial uniform load at infinity.

Numerical Simulation of Fatigue Crack Growth for Curved Cracks Emanating from Fastener Holes in Sheets by the MVCCI Method

The paper presents the results of a continued study of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under plane stress loading. The predictor-corrector method (PCM) was extended in order to analyse the growth of multiple crack systems in a finite 2D structure. Together with the recently proposed improved modified virtual crack closure integral (MVCCI) method we can obtain accurate SIF values also for interacting cracks, and furthermore we can simulate fatigue crack growth of multiple crack systems in plane sheets under proportional mixed mode loading conditions. As a result, the program PCCS-2D is written to run within ANSYS to simulate interacting curved cracks. In order to check the accuracy and efficiency of the proposed method several example problems are solved. Especially curved cracks emanating from loaded fastener holes in sheets are analysed.

Prediction of Necking in Tubular Hydroforming Using an Extended Stress-Based Forming Limit Curve

This paper presents an extended stress-based forming limit curve (XSFLC) that can be used to predict the onset of necking in sheet metal loaded under non-proportional load paths, as well as under three-dimensional stress states. The conventional strain-based ϵFLC is transformed into the stress-based FLC advanced by Stoughton (1999, Int. J. Mech. Sci., 42, pp. 1–27). This, in turn, is converted into the XSFLC, which is characterized by the two invariants, mean stress and equivalent stress. Assuming that the stress states at the onset of necking under plane stress loading are equivalent to those under three-dimensional loading, the XSFLC is used in conjunction with finite element computations to predict the onset of necking during tubular hydroforming. Hydroforming of straight and pre-bent tubes of EN-AW 5018 aluminum alloy and DP 600 steel are considered. Experiments carried out with these geometries and alloys are described and modeled using finite element computations. These computations, in conjunction with the XSFLC, allow quantitative predictions of necking pressures; and these predictions are found to agree to within 10% of the experimentally obtained necking pressures. The computations also provide a prediction of final failure location with remarkable accuracy. In some cases, the predictions using the XSFLC show some discrepancies when compared with the experimental results, and this paper addresses potential causes for these discrepancies. Potential improvements to the framework of the XSFLC are also discussed.

The effect of compressive biaxial stress on vacancy clustering in thin Si–Ge layers

The paper presents the results of the study of elastic interaction and clustering of vacancies in Si 75Ge 25 and Si 50Ge 50 alloys under plane stress loading, as appropriate to thin SiGe layers grown coherently on top of a bulk silicon substrate. The first-principles calculation of the total energies of vacancy–vacancy and vacancy–Ge atom pairs predicts that the energy of a vacancy pair is sensitive to the pair orientation with respect to the principal crystalline axes. Lattice kinetic Monte-Carlo simulation of vacancy annealing demonstrates that such orientational dependence of vacancy interaction noticeably influences both the kinetics of vacancy annealing at elevated temperatures and the shape of the resulting vacancy clusters.

A continuum damage model for fiber reinforced laminates based on ply failure mechanisms

A ply-level damage model for simulation of stiffness degradation due to progression of damage in fiber reinforced laminates is presented. The proposed damage model is based on damage mechanisms observed at the ply level and hypotheses regarding their effect on material stiffness. Focusing on matrix dominated failure modes, the damage behavior is split into two contributions, damage evolution and damage effect. The prior describes the progression of damage as a function of load, while the latter predicts the effect of this damage by a fourth order tensor relation as function of the current failure mode and stress state. The model relies on six material parameters, whose identification by standard tests is addressed. By combining the damage model with classical lamination theory, the behavior of laminates under plane stress loading is predicted. The capabilities of the proposed damage model are assessed based on comparison to experimental data from the literature.

A Complete Perfectly Plastic Solution for the Mode I Crack Problem Under Plane Stress Loading Conditions

A continuous stress field for the mode I crack problem for a perfectly plastic material under plane stress loading conditions has been obtained recently. Here, a kinematically admissible velocity field is introduced, which is compatible with the continuous stress field obtained earlier. By associating these two fields together, it is shown that they constitute a complete solution for the uncontained plastic flow problem around a finite length internal crack, having a positive rate of plastic work. The yield condition employed is an alternative criterion first proposed by Richard von Mises in order to approximate the plane stress Huber-Mises yield condition, which is elliptical in shape, to one that is composed of two intersecting parabolas in the principal stress plane.

Formation of Vacancies and Divacancies in Plane-Stressed Silicon

The effect of compressive and tensile plane-stress loading on formation energies and electronic properties of vacancies and divacancies in silicon are studied by first-principles approach for in-plane strains up to 0.7%. It is demonstrated that contributions to defect formation energies from the elastic lattice relaxation and from the band structure modification respond to stress in a different manner, leading to noticeable different behaviour of formation energies for different charges states. The most stable vacancy charge states at different Fermi level are shown to be sensitive to strain magnitude and sign. This results in the strain-induced shifts and even disappearance of some of thermal ionization levels of vacancies and divacancies in the band gap.

Perfectly plastic caustics for the opening mode of fracture

Exact expressions for the caustics generated by the reflection of light surrounding crack tips in perfectly plastic materials under plane stress loading conditions and tensile tractions at infinity (mode I) are derived. Two individual cases are examined involving two different yield criteria. The first case uses an approximation of the Mises yield condition, where in the principal stress plane two intersecting parabolas replace the standard ellipse. The second case uses the Tresca yield condition where the mode I caustic is obtained as a limit of an elliptical hole in a perfectly plastic material. In both cases, kinematically admissible velocity fields are employed to obtain strain fields from which the theoretical caustics are predicted.

Crack growth in a new nickel-based superalloy at elevated temperature

Crack growth at elevated temperature has been simulated using the finite element method for sustained and cyclic loading conditions, representative of time-dependent and time-independent crack growth. Elastic-creep (EC) and elastic-plastic-creep (EPC) models have been used to simulate the crack growth under sustained loads at 650 and 725°C. Crack mouth opening displacements as well as the evolution of the inelastic zones due to creep and plasticity have been obtained. Elastic-plastic finite element analysis has been carried out to simulate the crack growth under cyclic load using a constitutive model. Fatigue crack growth was simulated for plane stress, plane strain and generalized plane strain loading conditions. The influence of plasticity on the effective crack driving force was also examined. Creep damage was found to be very limited at both temperatures for this alloy. Plasticity-induced crack closure was found to be absent in plane strain or generalized plane strain conditions, overestimated in plane stress loading conditions by the conventional compliance method.

Wrinkling of anisotropic metal sheets under deep-drawing: analytical and numerical study

The onset of wrinkling in sheet metal forming is investigated using an analytical approach and finite element (FE) simulations. In both cases the yield criterion proposed by Ferron et al. [Int. J. Plast. 10 (1994) 431] for orthotropic sheets is employed. The analytical approach is developed on the basis of the bifurcation criterion developed by Hutchinson [J.W. Hutchinson, Plastic buckling, in: C.-S. Yih (Ed.), Advances in Applied Mechanics, vol. 14, 1974, pp. 67–144] for thin and shallow shells submitted to a biaxial plane stress loading. Wrinkling limit curves obtained with the bifurcation analysis are drawn for different orientations of the orthotropic axes with respect to the principal stress axes, assuming also different orientations with respect to the geometric axes of principal curvatures. The numerical simulations are performed with the FE code ABAQUS/Explicit. Experimental results of deep-drawing processes taken from the literature are also analysed to check the reliability of the wrinkling predictions obtained with the bifurcation analysis and with the FE simulations. Both analytical and numerical predictions compare reasonably well with experiments.

Scale dependent crystal plasticity framework with dislocation density and grain boundary effects

The geometrically non-linear scale dependent response of polycrystal FCC metals is modelled by an enhanced crystal plasticity framework based on the evolution of several dislocation density types and their distinct physical influence on the mechanical behaviour. The isotropic hardening contribution follows from the evolution of statistically stored dislocation (SSD) densities during plastic deformation, where the determination of the slip resistance is based on the mutual short range interactions between all dislocation types, i.e. including the geometrically necessary dislocation (GND) densities. Moreover, the GND's introduce long range interactions by means of a back-stress measure, opposite to the slip system resolved shear stress. The grain size dependent mechanical behaviour of a limited collection of grains under plane stress loading conditions is determined using the finite element method. Each grain is subdivided into finite elements and an additional expression, coupling the GND densities to spatial crystallographic slip gradients, renders the GND densities to be taken as supplemental nodal degrees of freedom. Consequently, these densities can be uncoupled at the grain boundary nodes, allowing for the introduction of grain boundary dislocations (GBD's) based on the lattice mismatch between neighbouring grains and enabling the obstruction of crystallographic slip perpendicular to the grain boundary.