Plane Stress State Conditions Research Articles

Research of Mechanical Properties of the Aluminium Alloy Amag 6000 Under the Plane Stress State Conditions

Today's demands directly encourage to utilize the light alloy materials in industrial production. In the automotive industry, there is an increasing tendency to reduce the total weight of the car and thus also the weight of the individual car-body parts. A correct description of the material deformation behaviour with respect to the different stress states is very necessary for the own possibility to use these materials in the production. This paper describes a measurement of the mechanical properties and deformation behaviour of aluminium alloy Amag 6000 under the plane strain conditions. Thus these properties are monitored and evaluated by means of the plain strain tensile test. In this case, the plane strain is achieved by the shape concept of the testing specimen, which is loaded by the uniaxial tensile stress state using a standard testing device. The determined mechanical properties and the resulting stress-strain curves of the material under the plain stress state can be further used at defining material models for a more accurate description of the material deformation process during the sheet metal forming process.

The model of fiber-reinforced concrete element deformation under the conditions of plane stress state and subjected to radiation and its identification

A model of fiber-reinforced concrete element deformation was presented under the conditions of plane stress and subjected to radiation, leading to the change of fibre-concrete deformation diagram and radiation swelling. They proposed a model identification technique, which use determined the coefficients for the cases of nonlinear and linear approximation of deformation diagrams, and the approximation error for these cases was estimated. Using the given physical relationships and a number of additional hypotheses, a non-linear integral-differential resolution equation of a fiber-reinforced concrete plate on an elastic foundation is obtained under radiation conditions.

In-situ rock mass stress-state measurements in scales of mineral deposits: problem-solving

This paper describes the new method for in-situ measurements of the most large-scale stress fields that are comparable to dimensions of deposits and mining leases. The method considers open cast mines and collapse zones of underground mining as disturbing cavities. The calculation of stresses is carried out thru measured deformations for the conditions of plane stressed state from the measured displacements of survey marks on the earth surface. GPS or GLONASS technology is used for the measuring. The results of in-situ study deformations of pit edges Pipe Udachnaya Mine (Sakha Republic, Russia) have been presented as an example of practical application of the method.

Supercritical Deformation and Fracture of Bodies with Concentrators under Plane Stress State Conditions

The paper deals with experimental studies of inhomogeneous strain fields with regions of supercritical behavior of the material in the case of extension of plane specimens of steel 20 with concentrators of different geometry by using the method of digital image correlation. The use of a video system permits obtaining experimental data about the distribution of the fields of longitudinal, transverse, and shear components and the strain intensity. The previously considered criteria for the deformation process transition to the supercritical stage for different types of the stress–strain state were used to distinguish the regions of supercritical behavior and to analyze the evolution of the strain and temperature fields in their stable development.

Fatigue of VT1-0 Titanium Alloy with Vacuum-Plasma Coating Under a Plane Stress State

Fatigue testing of VO1-0 sheet titanium alloy specimens with TiN coating has shown that under plane stress state conditions, the hardening capacity of the coating is unchanged, resulting in a 15–20% increase in the fatigue limit, irrespective of the principal stress ratio σ2/σ1 ≥ 0. In order to predict the fatigue limit of thin sheet materials with coatings in the case where σ2/σ1 ≥ 0, the criterion σ2/σ1 ≥ 0. The σ − 1 = (σ 1 2 + σ 2 2 − σ 1 σ 2)/(σ 1 − vσ 2) is proposed, which has been earlier developed for uncoated materials.

Synthesis and forming characteristics of Al–TiO2 powder metallurgy composites during cold upsetting under plane stress state conditions

Aluminum-based metal matrix composites with various weight percentages of TiO2 reinforcement were synthesized by powder metallurgy technique and their forming characteristics were completely studied during cold upsetting under plane stress state conditions. The milled powders were characterized by scanning electron microscope, X-ray diffraction (XRD), and energy dispersive analysis using X-ray (EDAX) analysis. Green cylindrical compacts were made using a 400 kN hydraulic press using suitable punch and die, sintered at (590 ± 10)℃ for a period of 3 h, furnace cooled, and machined to obtain samples with 0.5 aspect ratio. The cold upset tests were carried out in steps of 10 kN and the true axial stress (σ z), the true hoop stress (σθ), the true hydrostatic stress (σ m), and the true effective stresses (σeff) were determined, and their behavior against the true axial strain (ɛ z) was thoroughly analyzed. It was observed that, the addition of TiO2 to the Al matrix material increases the strength coefficient ( K) and decreases the strain hardening index ( n). The decrease in densification and deformation characteristics was observed for the addition of more weight percentages of TiO2. The microstructure analysis was done for the cold upset samples and reported.

An Experimental Study of Ratcheting Effect Under Multiaxial Proportional Loading

The paper addresses the mechanical behavior of carbon steel 20 in asymmetric loading under the conditions of plane stress state that occurs in a thin-walled specimen in tension–compression and alternating torsion. The asymmetric cyclic loading of specimens was carried out in a stress-controlled mode along three paths with a frequency of 0.1 Hz with a base up to 1200 cycles. Cyclic stress–strain diagrams have been constructed for the specimens under tension–compression, alternating torsion, and proportional loading. The curves of von Mises equivalent ratcheting strains have been plotted. The highest ratcheting rate is shown to take place in the tension–compression loading case.

Postcritical deformation of steels in plane stress state

We study the laws determining the mechanical behavior of materials at the postcritical deformation stage. Proportional tension-torsion tests of thin-walled tubular specimens of structural steels were carried out for various deformation trajectories to obtain experimental data about the work softening of steels under plane stress state conditions. The obtained experimental data were analyzed to determine the instant of time in the deformation process at which the transition to the postcritical stage occurs.

The influence of the relationship between yield strength and temperature on the stress state in a thin hollow disk

A thin hollow elastoplastic or perfectly plastic disk placed in a rigid cylindrical container and subjected to the action of a temperature field is considered. The conditions of plane stress state are assumed. The Mises yield condition is satisfied in the plastic zone. The main feature of the problem formulation is in the relationship between yield strength and temperature, taken in arbitrary form. A parametric analysis of the solution is carried out for the linear relationship. It was shown that the relationship between yield strength and temperature needs to be taken into account for some materials to define the stress-strain state in the disk and to estimate the conditions of the transition of the whole disk to the plastic state.

Erratum to: “Plane stress state problems for notched bodies whose plastic properties depend on the form of the stress state”

We consider one possible approach to the problem of describing the dependence of material plastic strain characteristics on the stress hydrostatic component arising in many porous, fractured, and other inhomogeneous materials. The plastic strain of the media under study is investigated under the plasticity assumption in the corresponding generalized form with the use of the form parameter of the stress state. The plasticity constitutive relations are stated on the basis of the plastic flow law associated with the accepted plasticity condition. For the conditions of plane stress state in the framework of the material rigid-plastic model, a system of partial differential equations is obtained and conditions for its hyperbolicity are determined. The relations for determining the stress fields and velocity fields in plastic domains are obtained, and their properties are investigated. The problem of tension of a strip with symmetric angular notches is solved, where the stress fields are determined and the continuous displacement rate field is constructed. The problem of uniform symmetric tension of a plane with a circular hole is considered. The stress fields in a strip with symmetric circular notches are examined. A comparison with solutions for plastically incompressible media whose properties are invariant with respect to the form of the stress state is performed.

YIELD STRESS MODIFICATION IN THE STRIP YIELD MODEL

From among of the deterministic models for fatigue crack growth predictions suitable for metallic materials a Strip Yield (SY) model can be considered the most general and powerful crack growth prediction tool owing to its applicability to arbitrary variable amplitude load histories. The SY model based on the conception of plasticity at the crack tip accord­ing to Dugdale, modified to accounting for the crack closure phenomena. The original Dugdale model is only valid for plane stress state conditions at the crack tip. Accounting for the triaxial stress conditions at the crack tip requires the yield stress modification, what is usually realized by using the suitable constraint factors. In the paper several concepts of the yield stress modification in the SY model have been described and notified. As it has been concluded the another important role of the constraint factors, in addition to accommodating in the SY model the triaxial stress state, is cover­ing indirectly various processes which do affect crack growth, but cannot be treated in a rigorous way.

Bending of a two-layer beam with non-rigid contact between the layers

The bending, under plane stress state conditions, of a two-layer beam-strip with identical isotropic linearly elastic layers with non-rigid contact between them is considered. The effect of the contact interaction between the layers, simulated by an elastic or elastoplastic gasket of negligibly small thickness with a finite shear stiffness, on the deflection of the beam is studied. Absolute slippage and rigid contact between the layers are the two limiting values of the shear stiffness. The values of the flexural stiffness of the beam differ by a factor of four in these limiting situations. The problem is reduced to a one- dimensional problem in the case of harmonic external load and an asymptotic solution is constructed for it. In the case of a load of general form, the Kirchhoff - Love hypotheses are used to construct an approximate solution and the problem is reduced to a one-dimensional problem. The difficulties which arise in simulating of the interaction forces between the layers using Coulombic dry friction forces are discussed.

An experimental investigation on strain hardening behaviour of aluminium – 3.5% alumina powder metallurgy composite preform under various stress states during cold upset forming

An experimental investigation on instantaneous strain hardening behaviour of aluminium – 3.5% alumina powder metallurgy composite preforms for three different stress state conditions, namely, the uniaxial, the plane and the triaxial has been carried out. Sintered aluminium–alumina composite with three different aspect ratios (height to diameter ratio), namely, 0.35, 0.56 and 0.72 and two different initial preform relative densities of 0.80 and 0.90 were prepared, sintered at 550 ± 10 °C under the cover of protective indigenously developed ceramic coating for a period of 90 min in an electric muffle furnace and cooled inside the furnace itself. Sintered but mildly machined disc specimens were cold deformed under axial tests using mirror polished flat dies. The instantaneous strain hardening exponent ( n i ) and the instantaneous strength coefficient ( K i ) were determined for each aspect ratios for all three different stress state conditions and the results were analyzed in the present work. The analysis of the experimental results has shown that the instantaneous strain hardening exponent ( n i ) and the strength coefficient ( K i ) are greater for the triaxial stress state condition irrespective of the initial preform densities and the aspect ratios when compared to uniaxial and plane stress state conditions.

Influence of the intermediate material on the singular stress field in trimaterial junctions

By the method of eigenfunctions, we analyze the stresses formed at the vertex of a multicomponent wedge formed by homogeneous elastic wedges under the conditions of plane stress state or plane deformation. The exponent of the singularity of stresses in the case of opening and shift of the wedges is numerically determined. The singular stresses formed near the vertex are investigated both for softer and stiffer wedges.

Computational Model of Propagation of Fatigue Cracks in Hydrogenated Welded Joints

On the basis of the energy approach of fracture mechanics, we develop a computational model of propagation of fatigue cracks in thin-walled hydrogenated welded joints under the conditions of plane stressed state. A problem of diffusion with the corresponding boundary conditions for the analysis of the field of hydrogen concentration in the zone of welded joint in the case of variable temperature is posed and its numerical solution is found. It is shown that the computed kinetic diagrams of fatigue fracture are in good agreement with the available experimental data. The relations obtained by using the proposed model enable us to predict the path and the period of subcritical growth of fatigue cracks.

Tension of an elastoplastic disk. Part 2. Edge crack

Within the framework of the model of plasticity strips, we study the elastoplastic problem of fracture mechanics concerning the development of these strips near the tips of an edge crack in a circular disk. We assume that plastic deformations near the crack tip are localized along three plasticity strips (L 1,L 2,L 3) under the conditions of plane stressed state and along two plasticity strips (L 1,L 2) under the conditions of plane deformation. One of these strips (L 3) is modeled by a line of discontinuity of normal and tangential displacements and the remaining two strips (L 1,L 2) are modeled by the lines of discontinuity of tangential displacements. Their lengths and orientations are determined as a result of numerical solution of the problem by the method of singular integral equations. We also present the values of the crack-tip opening displacements.

Plasticity bands near the tips of edge cracks in a body with circular hole

Within the framework of the model of plasticity bands, we consider a two-dimensional elastoplastic problem of fracture mechanics for a body with one circular hole and two collinear cracks whose ends lie on the contour of the hole under the conditions of plane stressed state and plane deformation. It is assumed that plastic strains near each tip of the edge cracks are concentrated along three (for the plane stressed state) or two (under the conditions of plane deformation) plasticity bands. Their lengths and orientations are determined as a result of the solution of the problem. Numerical results are obtained for the cases of a biaxial tensile load acting at infinity and constant pressure applied to the contour of the hole and edge cracks (under the conditions of plane deformation).

Propagation of plasticity bands from the tip of a semiinfinite crack of mixed type

In the framework of the model of plasticity bands, we analyze an elastoplastic fracture-mechanics problem of propagating plasticity bands near the tip of a semiinfinite crack of mixed type. It is assumed that, under the conditions of plane stressed state, plastic strains near the tip of a semiinfinite crack are localized along three plasticity bands (L1,L2,L3) and, under the conditions of plane deformation, they are localized along two bands (L1,L2). One of these bands (L3) is simulated by a line of discontinuity of normal and tangential displacements. The remaining two bands (L1,L2) are simulated by the lines of discontinuity of tangential displacements. Their lengths and orientations are determined in the process of numerical solution of the problem by the method of singular integral equations. We also present the values of crack tip opening displacements.

Effect of stress state type on deformation process of austenitic steel under thermal cycling conditions

Analysis of the deformation process of an austenitic steel under the conditions of cyclic temperature variation has been made. The experiments were carried out on thin-walled tubular specimens loaded with axial force and torsional moment with the stress intensity kept constant and subjected to thermal cycling. The computed mean values of steady strain rate components, when compared with those obtained experimentally, showed that flow theory was in fairly good agreement with the experiment. Values of the exponent as well as the coefficient in the Norton-Bailey law depend however on stress state type. It was probably caused by interaction of two different failure mechanisms occurring under plane stress state conditions. It was also found that a type of criterion used for limit state description depends on stress intensity value.

Elastic-plastic strain of a titanium alloy under plane stress state conditions

Elastic-plastic strain of a titanium alloy under plane stress state conditions