Papers by Keyword: Plane Stress

Abstract: There are materials whose forward flow curve is practically independent of plastic strain (perfect plasticity) but the Bauschinger effect reduces the elastic range with flow reversal. A new model that is capable of describing such behavior of material under plane stress conditions has been recently proposed. An important class of structures in which the state of stress can often be accurately approximated by plane stress conditions is thin hollow discs. It is therefore of interest to use the new model for determining the distribution of residual stresses in thin discs subject to various loading conditions, followed by unloading. This paper presents a solution for the residual stresses and strains in a hollow hyperbolic disc loading by external pressure, followed by unloading.

Abstract: Thin compact tension specimens made of direct quenched ultra-high strength steel were tested under constant rate uniaxial tensile load. The length of the crack was monitored using optical microscopes on both sides of the specimens during the fatigue pre-cracking (using a chevron V-notch). Deformations during the crack lengthening were recorded by a full-field measurement technique using a set of digital cameras to check the effect of side grooves on reduction of surface deformation. The Specimen without side grooves showed a high level of plasticity, thickness reduction, and crack growth along a deviating path. In addition, the fracture surface showed excessive failure along the inclined plane. The presence of side grooves, however, led to the decrease of the maximum applied force at final fracture while the force prior to crack tearing was almost the same as the specimen without side grooves. Grooves significantly reduced the inclination of the fracture plane and plastic deformation due to removal of low stress triaxiality on the surface. They led to the fracture along a straight path and approximately even surface which makes them beneficial especially when compliance method is used in plane stress fracture tests.

Abstract: In this article, we used standard dumbbell specimen (SDS), compact tension specimen (CTS) and Double edge notched specimen (DENS) which made of materials of modified double-base propellant to do the uniaxial tensile experiments under different tensile rates. In comparison, three kinds of specimen whoes geometric features are similar with the specimen above but the thickness is smaller, were also used to get the relationship of force (F) and displacement (l). After analysis of these relationship, we confirmed that the plane stress and stress concentration influence the use of EWF method. The experimental results prove that the geometric features of the specimen which are proposed by B.cotterell and J.K.reddel are absolutely right. But for the thicker specimen used by GUAN GONG and other researchers, we can just know the trend is correct, and should do further research to know the influence which specimen’s geometric characteristics bring to experiment.

Abstract: The paper investigates by numerical modeling the effects of crystallographic texture and grain shape on the shape of the yield surface of aluminum sheet material at small strains. Different representative volume elements (RVEs) of the material are considered. Plane stress state is assumed in the sheet. A rate-dependent model of crystal plasticity (CP) is used in combination with either the full-constraint (FC) Taylor model or the finite element method (FEM) to compute the volume averaged stress of the material. The effect of different crystallographic textures observed in aluminum alloys on the shape of the yield surface is firstly investigated. An analytical yield function is used to generate yield surfaces for the different crystallographic textures. The deviation between the stress states at yielding computed by FC-Taylor model and the analytical yield surface is used to evaluate the capability of the yield function to fit the anisotropic yield surfaces representing different strong crystallographic textures. Two different shapes of the grains are introduced in the RVEs of CP-FEM in order to study the effect of the grain morphology. Small effects of grain shape are found at small strain compared with the marked influence of crystallographic texture.

Abstract: This paper presents new design of the structural specimen for plane stress analysis. Requirement was that the specimen is loaded by universal tensile testing machine without any special equipment. Specimen was analyzed using finite element method in ANSYS Workbench software. Finite element method was also used for simulation of strain gauge measurement to determine principal stresses, equivalent von Mises stress and orientation of the principal axes in the center of specimen. Finally, experimental stress analysis using strain gauges was performed on real specimen. Results from experimental measurements and numerical simulations were compared.

Abstract: A small rectangular strip of fcc Cu, containing a through crack on the nanoscale and subjected to loading under displacement control, is simulated using molecular dynamics (MD). The geometry is highly constrained and chosen to mimic that of a thin strip between two stiff layers. The Lennard-Jones pair potential is used for the inter-atomic forces. The centrally placed crack shaped void is created by removing a few atoms inside the specimen. The crack is loaded perpendicular to the crack plane and the tensile stress is studied as it varies over the thickness of the strip. Comparisons with finite element calculations are made and the goal is to find a limit in model size beneath which the finite element (FE) solutions and linear elastic fracture mechanics (LEFM) lose their accuracy.

Abstract: Heavy steel plates are among the most essential construction elements for plant and heavy machinery. Their production involves hot rolling, followed by accelerated cooling and leveling. In this work, the focus is put on modelling the accelerated cooling step. It is the goal to build an algorithm which can be used for a virtual design of the accelerated cooling process in order to minimize distortion. Simulation of accelerated cooling requires a complex material model since various physical effects are involved, when plates are cooled down from 850°C to room temperature. Above all, the material undergoes a phase transformation from the austenitic parent phase to the bainitic product phase. The phase transformation is accompanied by metallurgical strains as well as transformation induced plasticity [1]. The highly nonlinear material behavior calls for implicit local integration. To this end, an implicit procedure is formulated within the plane stress theory accounting for plasticity and TRIP. Moreover, it provides the consistent elasto-plastic material stiffness. The global level normally requires an excessive number of DOFs for reliable predictions. It is a challenging task to make accurate predictions about the plate behavior (especially curvature) at the same time avoiding an excessive number of DOFs. A 3D calculation (Fig. 1) is still needed to verify the assumptions that are permitted to reduce the number of DOFs without losing accuracy. Eventually, the fast computation algorithm describes the approximate deformation of the plate by 3 DOFs only, enabling a reduction of computation time by several orders of magnitude. Due to its speed the algorithm can be used as an efficient tool for a virtual process design to obtain minimized distortion at the end of the cooling step (Fig. 2).

Abstract: This report is about the spatial stress analysis of a large underground civil air defense projects in Guangdong province. Aiming at the problems of plane stress models, spatial calculation models are built and the results are compared to those of plane stress calculation models, revealing how internal force of the spatial structure models change in different conditions.

Abstract: Continuous (or generalized) octahedral element bodies can be obtained by intercepting a cube with three groups of failure (or yield) planes successively under true triaxial stress state, on which the stresses are twin stresses. Among the resulting polyhedral characteristic element bodies, isoclinal octahedron and orthogonal octahedron are of particular importance. Strength models of continuous octahedrons are then derived by stress analysis to arbitrary inclined sections in three dimensional stress space, and strain models by the principle of strain analysis, so the plane constitutive relations of concrete can be understood by plane problems transformed by stress-strain space according to the symmetry of an orthogonal octahedral octahedron where an arbitrary oblique plane is parallel to one of three rectangular coordinate axes.

Abstract: An elastic-viscoplastic constitutive mode was adopted to analyze asymptotically the tip field of a mode I quasi-statically propagating crack in rate-sensitive materials under plane stress condition. Under the assumption that the viscosity coefficient is a power law function of the rate of effective plastic strain, it was obtained through dimension match that the crack tip field possesses power law singularity. And the singularity exponent is uniquely determined by the power law exponent in the supposed viscosity coefficient. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. Variations of crack tip field characters according to each material parameter were discussed by means of numerical computation. The stress intensity is dominated by the material viscosity whereas the hardening coefficient has less significant influence on tip field. Furthermore, the solution can be transformed to the elastic-nonlinear-viscous one of Hui and Riedel if the limit case of zero hardening coefficient is considered.