Saint-Venant Effects Research Articles

Estimating Stress Concentration near Grips by the Tension of Polymer Composite Samples

This work aims at the problem of justification of the tensile strength test of flat glass- and carbon-fiber-reinforced plastic samples. Any technique of sample holding causes a concentration of stress and influences negatively on the strength; quantitative estimates of this effect are presented in this work. Based on a simplified equation of shear analysis, the stress distributions in the samples were calculated by different ways of simulation of the diagram of shear stresses applied from the grip side. The advantage of the analytical solution consists in the fact that a clear description of the influence on strength of the following factors is possible, namely, the lengths of the grips and the working part and, particularly, the sample thickness. A similar scale effect is often explained in terms of statistical strength theory, but the analysis shows that the decrease in strength observed with an increase in the sample thickness can be explained by the effect of nonuniformity of the stress field near the grips. The appearance of this edge effect like a Saint-Venant effect is especially pronounced in polymer composites with a low ratio (as compared with metals) of the interlaminar shear modulus to the longitudinal Young’s modulus.

Edge Effect in a Two-layer Orthotropic Strip

The article discusses the edge effect (boundary layer, Saint-Venant effect) of a two-layer strip of orthotropic materials. Two methods are used to solve the problem of plane elasticity (solution in stresses and displacements). Both methods are constructed in such a way that they can describe the edge effect. This allows us to construct a theory for calculating the edge effects of single-layer strips based on which we manage to solve the problem of calculating the edge effect of two-layer strips analytically accurately. In fact, the problem can be summarized by saying that it is calculation of a single-layer strip. The obtained numerical results show that both methods of solution lead to the completely coinciding results.

Specific characteristics of numerical determination of the boundary effect stress-strain state for an orthotropic strip

The paper deals with the problem of determining the stress-strain state near the boundary of a one-layer strip made of an orthotropic material subjected to a self-balanced load applied at the end of the strip (Saint-Venant effect, boundary effect, and boundary layer). A comparative analysis of two methods for determining the boundary effect is carried out. The first method, i.e., the solution in stresses (with respect to σy), was developed by L. A. Agalovyan and gives good results of one-layer strips. The second approach, i.e., the solution in displacements, was developed by the author, and its results for the one-layer strip practically coincides with the solution in stresses. The obtained results were also verified by FEM. But the solution of the problem of elasticity in displacements is much more promising when analyzing multilayer strips.

Cr50Cu50 alloys produced from submicrometre structured powders through hot pressing at different pressures

In this study, two different compositions of submicrometre copper and chromium powders were mixed and the Cr50Cu50 alloys were fabricated via the powder metallurgy technique. The research imposed various hot pressing pressures, while the temperature was maintained at 1050°C for 1 h, respectively. The experimental results showed that the Saint Venant's effect obviously appeared in 1050°C, 48 MPa, 1 h hot pressing Cr50Cu50 alloys, which led to differences in the surface and internal hardness of the specimens. As a result, the optimal parameters of hot pressing of Cr50Cu50 alloys were 1050°C, 36 MPa for 1 h possessing the highest transverse rupture strength value (921.69 MPa). Moreover, the surface hardness increased to HV0.2 221.78 (HRB 95.4), the relative density reached 97.15% and apparent porosity decreased to 0.10%, respectively. Furthermore, the resistivity decreased to 5.28 × 10−6 Ω cm, and ICAS was enhanced to 32.65% after the optimal procedure.

Layer-wise finite-element analysis of a functionally graded hollow thick cylinder with a piezoelectric ring

In this work, a layer-wise finite-element formulation is developed for the analysis of a functionally graded material (FGM) hollow thick cylinder with one piezoactuator ring. The cylinder and ring is divided into many sublayers in the thickness direction and the full layer-wise shell theory is used to model a discretely stiffened FGM cylinder. In this model, the displacements are approximated linearly through each mathematical layer. This accounts for any discontinuities in the derivatives of the displacement at the interface of the ring and the cylindrical thick shell. This formulation is derived from the virtual work statement which includes the total structural potential energy and the electrical potential energy of the piezoelectric ring. Assembling stiffness and mass matrices, at each interface between two elements, stress and displacement continuity are forced, and then the finite-element model is solved. Static and dynamic responses of a functionally graded thick cylinder to electrical and mechanical loads with different exponent ‘ n’ of FGM are determined to show the significant influence of the material in homogeneity. The results obtained at a distance far from the ring are compared with the mechanical behaviour of an FGM cylindrical shell without a ring. Because of the Saint Venant effects, the piezoelectrically induced deformation of the shell is confined to a region close to the piezoelectric ring; thus agreements between these two results are observed.

Improved analysis of unidirectional composite delamination specimens

Generally, the delamination testing of composite specimens involves the analytical determination of the compliance and the energy release rate for the actual configuration. In this work an improved analysis for unidirectional composite delamination specimens is presented, which is based on the results of the last 30 years. The main goal of the present model is the improvement of the global mode decomposition method including four mechanical deformations apart from simple beam theory: Winkler–Pasternak foundation, transverse shear, Saint–Venant effect and crack tip shear deformation, respectively. These effects are investigated separately using a general loading scheme and at the final stage their results are superimposed. The derived model is applied to the mixed-mode I/II single-cantilever beam, the single-leg bending and the universal mixed-mode bending specimens. Beside the present solution three other ones are adopted to compare the results for the compliance and energy release rate of the mentioned specimens. Although the present model shows similar results to the most accurate finite element model, it is simpler and helps us to understand better the mechanisms of the delamination process.

Over-leg Bending Test for Mixed-mode I/II Interlaminar Fracture in Composite Laminates

In this work the over-leg bending (OLB) specimen is developed for mixed-mode I/II delamination characterization in composites. The traditional single-leg bending (SLB) specimen is modified by introducing the load eccentrically between the two supports of a three-point bending setup. The modified configuration is analyzed by using linear beam theories. The theories of transverse shear, Winkler-Pasternak-type elastic foundation, Saint-Venant effect, and crack tip shear deformation are incorporated in the analysis. Also, experiments are carried out on glass/polyester unidirectional specimens. Comparison between the results of analysis and experiment shows very good agreement. The traditional SLB and the novel OLB coupons are compared, and their advantages and drawbacks are highlighted. The newly developed OLB setup is relatively easier to perform and crack propagation may be simply investigated under displacement control.

Mode-II Fracture in E-glass-polyester Composite

In this work a novel beam analysis of the end-loaded split (ELS) and over-notched flexure (ONF) specimens are presented. New compliance and strain energy release rate equations are developed incorporating crack tip deformation and transverse shear analysis. The Saint Venant effect at the clamped end of the ELS specimen is also considered. Unidirectional glass-polyester specimens are manufactured and experimental (initiation and propagation) tests are performed to confirm the theoretical models. The experimental data is evaluated by means of four reduction techniques: the exact beam theory, virtual crack closure technique, compliance calibration method, and direct beam theory. It is shown that the results by the four methods agree quite closely; however, the compliance calibration method is not recommended for initiation data reduction in the case of the ONF specimen. The ELS specimens suffer from relatively large displacements. Thus, propagation tests are not possible to be performed. The ONF test seems to be a better tool to evaluate the mode-II toughness of composite materials with low flexural modulus.

Study of a Three-Point Bending Specimen for Shear Characterisation of Sandwich Cores

A sandwich beam loaded in three-point bending (TPB) was employed for the shear characterization of foam cores destined to structural sandwich application. In the design of the specimen, particular care was taken to avoid measurement errors deriving from the flexural component of the displacement and from the de Saint Venant's effects, yet retaining the simplicity in the formulae for data reduction. Using the new method, experimental tests were carried out on a PVC foam 55 Kg/M3 in density. For comparison, shear characterization tests were also performed according to ISO 1922. The results obtained demonstrate that, when the core shear modulus is considered, TPB and ISO 1922 can provide practically coincident results. However, TPB yielded a shear strength about 20% higher than the ISO Standard, together with a shear strain at failure that is 10% lower. The failure modes observed suggest that the core shear behavior is better represented by TPB, whereas ISO 1922 is unsuitable to correctly measure the core shear strength.

Saint-Venant Effects in the Iosipescu Specimen

The main purpose of this paper is to explain the shear strain differences observed between the two faces of certain Iosipescu specimens. The different parasitic moments that can act on the specimen are investigated and their effects assessed. Different Iosipescu fixtures from the literature are checked for these parasitic moments and it is shown that modification of the Wyoming fixture can lead to the elimination of its parasitic in-plane and out-of-plane movements. Finally, it is shown that the strain differences that remain are caused by Saint-Venant effects due to the proximity of the loading points to the notch line but that averaging the strains between the two faces eliminates this effect. This is an important feature since for certain material configurations (thick and transversely stiff specimens), preventing twisting of the fixture is not sufficient to enable the use of only one strain gauge.

A refined model for three-point bending of sandwich panels 2. Transverse stresses

According to the relationships derived in [1], transverse normal and tangential stresses in a sandwich panel have been analyzed. Asymptotic formulas for the stress concentration area in the vicinity of point forces are derived. Analytical estimates of a normal stress at the central and end sections of the panel are deduced. The Saint-Venant effect of the degeneration of a panel of finite length into an infinite strip is studied. For the estimation of the concentration of the transverse tangential stress, the possibility of a superposition of the solution of the slippage problem of the face layers and the classical solution allowing for shear is substantiated. It is shown that the local Reissner-type effects are specified by reducing the concentration of the tangential stress in the face layers along the longitudinal coordinate and transition to the steady tangential stress state in the filler layer. The concentration coefficients of the tangential stress are derived as functions of the dimensional parameters of the panel section.

Response of segmented-stiffness composite cylinders to axial end shortening

Composite fuselage structures that utilize different laminates in the crown, sides and keel may be part of future aircraft designs. Here exact, approximate and finite element solutions for the geometrically linear response to axial end shortening of cylinders constructed in this segmented fashion are investigated. It is concluded that circumferential displacements are the feature that distinguishes these designs from more conventional single-laminate designs. Additionally, it is the difference in effective laminate Poisson's ratios from one segment to the next, as opposed to the difference in effective laminate extensional or shear moduli, that is responsible for the circumferential displacement. However, for short cylinders ( L R = 2) with clamped boundaries, the circumferential displacement is greatly suppressed relative to the case of longer cylinders ( L R = 20) , while the radial displacement is not as dramatically influenced by length. This trait can be traced to the wavelengths that govern circumferential and radial responses, and can be interpreted as the Saint-Venant effect for circumferential displacement having a different characteristic length than the Saint-Venant effect for radial displacement.

A simplified improved beam analysis of the DCB specimen

Large deviations from the simple cantilever beam model have been observed when analysing double cantilever beam tests in composite materials. In the present paper a simplified improved beam model is proposed. The cracked part of the specimen is analysed by means of shear-corrected classical beam theory. The uncracked part is analysed by considering Saint Venant effects and deformation of a beam on an elastic foundation. Superposition of compliances results in a simple closed form expression which can be used to isolate the effects of different material parameters and analytical simplifications. Crack length corrections are discussed as well as the corrections that have to be made when calculating the strain energy release rate. An extensive numerical comparison is made with the more elaborate solutions of Whitney and Williams. Finally, a discussion is made on the relevance of one-dimensional analysis as compared with two- and three-dimensional analyses. The discussion is supported by numerical comparisons.

A New Approach to Linear Buckling of Thin Circular Cylindrical Shells

Adopting an end-problem approach to static displacement equations of thin circular cylindrical shells, a type of coupled eigenvalue problem is developed which integrates the eigenvalue problem of bending as well as that of linear buckling. This is shown to provide an alternative mathematical criterion of linear bifurcation buckling. In addition, it provides new insight into the nature of Saint Venant effects. Numerical illustrations for an isotropic shell are worked out to demonstrate the structure of the proposed eigenvalue problem.