Analytical Stress Distribution Research Articles

Controlled crack propagation of flexible Film/Substrate assembly by biaxial stress

Crack has long been regarded as a form of material failure. At the same time, it is also an effective processing method to create some patterns on the surface of objects. Currently, most crack-based processing methods are achieved by applying equai-biaxial thermal stress. However, the stress ratio of equi-biaxial stress state is fixed, and its flexibility is very limited. In this paper, a method is developed to control the crack propagation in thin film coated on substrate by using generalized biaxial stress. Under some reasonable assumptions on the shear stresses in the interface layer between the film and its substrate, an analytical stress distribution in film under biaxial stress state is obtained. Then, the strain energy density factor is used to predict the propagation direction of a prefabricated crack. By changing the biaxial stress state undergone by film, the crack propagation direction can be controlled. Some verification experiments are conducted, which are consistent with the theoretical prediction.

Failure behavior of horseshoe-shaped tunnel in hard rock under high stress: Phenomenon and mechanisms

A particle flow code (PFC) was first applied to examining the mechanical response of a horseshoe-shaped opening in prismatic rock models under biaxial compression. Next, an improved complex variable method was proposed to derive the stress distribution around the opening. Lastly, a case study of tunnel failure caused by rock burst in Jinping II Hydropower Station was further analyzed and discussed. The results manifest that a total of four types of cracks occur around the opening under low lateral confining stress, namely, the primary-tensile cracks on the roof-floor, sidewall cracks on the sidewalls, secondary-tensile cracks on the corners and shear cracks along the diagonals. As the confining stress increases, the tensile cracks gradually disappear whilst the spalling failure becomes severe. Overall, the failure phenomenon of the modelled tunnel agrees well with that of the practical headrace tunnel, and the crack initiation mechanisms can be clearly clarified by the analytical stress distribution.

Analytical stress solution and mechanical properties for rock mass containing a hole with complex shape

In this study, complex variable theory was employed to study the stress distribution for rock mass containing a hole with complex shapes. The method of mapping function calculation using optimization technique was investigated and improved. The shape-related mapping function was defined for parameter analysis. A new objective function for mapping function determination was developed to calculate related parameters without the consideration of restrictive conditions between boundary points in z-plane and ζ-plane, which significantly simplified the calculation process. In addition, the mapping function for planes containing a rotated hole was deducted to simplify analytical stress solution process for holes under complex stress conditions. Finally, for six kinds of holes with typical shapes in practical rock engineering, the mapping functions were determined, and the external analytical stress distribution were further presented. The analytical solutions combined with numerical and experimental results show that holes with arched boundaries suffer less stress concentration compared with those with corners. Hole shape mainly affects the stability of rock containing a hole via its influence on stress concentration extent around the hole.

Explicit fracture modelling of cemented tungsten carbide (WC-Co) at the mesoscale

Using Y-Geo software, the combined finite-discrete element method (FDEM) has been used for the first time to simulate fracture explicitly of cemented tungsten carbide (WC-Co). Although originally designed for geomechanical applications, this study has investigated the use of this numerical approach to model WC-Co material at the mesoscale. The composite material is modelled as a heterogeneous structure using fundamental mechanical properties of the respective phases. A series of simulations are validated against both analytical solutions and experimental observations; these cover both elastic and fracture behaviour of the model. Results show good agreement with both analytical stress distribution solutions and experimental fracture path results. For the first time the discrete fracture process, which has previously been described from experimental images, has been replicated by simulation. The study shows the potential of using the finite-discrete element method as a tool for studying fracture of WC-Co, although the paper also highlights areas of understanding that needs to be improved to achieve a robust model. Ultimately by being able to model fracture behaviour accurately, this would enable a systematic study of microstructural variables in isolation to optimise composition to improve fracture toughness, something which is difficult to do experimentally.

Two-dimensional analytical stress distribution model for unbalanced FRP composite single-lap joints

Abstract A two-dimensional analytical stress distribution model taking into account the effects of large deformation, bending-tension coupling and interfacial compliance on the quasi-static behavior of unbalanced FRP composite single-lap joints (SLJs) under tension is introduced in this paper. The model can accurately estimate the stress distributions in the adhesive layer of unbalanced composite SLJ. The analytical results are compared to numerical simulations from a nonlinear finite element model and results from existing models validating the accuracy of the introduced two-dimensional model. A parametric study investigating the influence of the tensile load, and the material properties on the stress distributions in the adhesive bond-line is performed with the newly introduced model. The results demonstrate that the geometrical nonlinearity of the SLJ configuration leads to the reduction of the peak values of normalized adhesive stress distributions, and the difference between two peak values of normalized adhesive stress distributions in the adhesive middle plane can be reduced by appropriate selection of the joint adherends.

Effect of material's behavior on residual stress distribution in elastic–plastic beam bending: An analytical solution

A considerable residual stress distribution can be produced while bending of parts. This stress distribution depends on material behavior. In this article, residual stress distribution has been determined through the thickness in beam bending. For three different models of elastic–plastic behavior, the stress distribution and maximum residual stress are derived analytically. The residual stress is compared for three different bending radii as a case study. Also, finite element analysis has been carried out for two material properties. The results show that material behavior has little effect on stress distribution for large value of bending radius. As the bending radius decreases, difference of stress distribution increases rapidly among three plastic behaviors. Comparing the results of finite element and analytical stress distribution shows good accuracy for suggested formulations.

Behavior of [0]8 woven composites under combined bending and tension loading: part - I experimental and analytical

The objective of this work is to investigate the mechanical properties of [0]8 woven glass fiber reinforced polyester (GFRP) composites under monotonic and combined tension/bending loading. The results show that the failure of combined test specimen was at its ends, which have zero deflection and maximum bending moment and stress. This behavior agrees with the analytical stress distribution along the specimen length. Adding a tensile load at the ends of woven composite beams that designed to carry pure bending loads, such as bridge decks, can duplicate bending capacity of the beam. The relationship between combined bending moment and tensile load was constructed.

Closed form ultimate strength of multi-rectangle reinforced concrete sections under axial load and biaxial bending

The analysis of prismatic members made of reinforced concrete under inclined bending, especially the computation of ultimate loads, is a pronounced non-linear problem which is frequently solved by discretizing the stress distribution in the cross-section using interpolation functions. In the approach described in the present contribution the exact analytical stress distribution is used instead. The obtained expressions are integrated by means of a symbolic manipulation package and automatically converted to optimized Fortran code. The direct problem-computation of ultimate internal forces given the position of the neutral axis-is first described. Subsequently, two kinds of inverse problem are treated: the computation of rupture envelops and the dimensioning of reinforcement, given design internal forces. An iterative Newton-Raphson procedure is used. Examples are presented.

Effect of End Tapering on Crack-Induced FRP Debonding from the Concrete Substrate

The technique of bonding fiber-reinforced plastic (FRP) plates on the tensile side of concrete members has been proved to be an effective method for structural strengthening. For a RC beam strengthened with FRP plates, failure may occur by concrete cover separation near the plate end, or crack-induced debonding initiated by an opening crack away from the plate end. Experimental investigations have shown that tapering of the FRP plate at its ends is effective in reducing the stress concentrations and increasing the loading for plate end failure to occur. However, with reduced averaged thickness of the tapered plate, crack-induced debonding is also easier to occur. To optimize plate tapering in practical designs, an approach to analyze crack-induced debonding of tapered FRP plates is required. In the present investigation, FRP debonding is first studied with the finite-element method. In the analysis, a three-parameter model is employed for the shear slip relation between concrete and the FRP plate. Based on the findings from FEM analysis, simplifying assumptions are derived and an analytical model is developed for calculating the stresses in the FRP plate and along the concrete-to-FRP interface. The analytical stress distributions show good agreement with those from the FEM analysis. Using the analytical model, the effect of FRP tapering is quantitatively assessed. Also, the effects of various parameters on the ultimate failure load are simulated.

Analytical evaluation of J-integral for elliptical and parabolic notches under mode I and mode II loading

In the present work the J-integral (indicated here as JVρ because two parallel flanks are not present) was calculated by using, along the free border, the exact analytical stress distribution for the ellipse and the asymptotic one for parabolic notches. The material was assumed as homogeneous isotropic and linear elastic. First, for an ellipse under remote tensile loading, the expression of JVρ has been analytically calculated on the basis of Inglis’ equations. The equations have been used to prove that, in terms of J-integral, the crack is the limit case of an equivalent elliptic notch. Furthermore, by distinguishing the symmetric and skew-symmetric terms, the well-known Stress Intensity Factors (SIF) of mode I and II for a crack in a wide plate under tension are obtained by adding a limiting condition. Second, by means of Creager–Paris’ equations, JVρ has been analytically calculated for a parabolic notch of assigned tip notch radius ρ. The asymptotic value of JVρ and the relationship between the peak stress and the relative SIF are the same as the ellipse. Finally, as an engineering application, we provide an accurate formula for the evaluation of the Notch Stress Intensity Factors of a crack, mainly subjected to tensile stress, from the peak stress of the equivalent ellipse under the same loading.

On the Elastic–Plastic Deformation of a Rotating Disk Subjected to a Radial Temperature Gradient

Elastic–plastic stress distribution in a nonisothermal rotating annular disk is analyzed by the use of Tresca and von Mises criteria. An energy equation that accounts for the convective heat transfer with a variable heat transfer coefficient is modeled. For a given angular velocity, the steady temperature distribution in the disk is obtained by the analytical solution of the energy equation. Tresca yield criterion and its associated flow rule are used to obtain the analytical stress distributions for a linearly hardening material. A computational model is developed to analyze elastic–plastic deformations of the disk using von Mises yield criterion and its flow rule. This model incorporates Swift's hardening law to simulate linear as well as nonlinear hardening material behavior. It is shown that the stress distribution in the disk is affected significantly by the presence of the temperature gradient.

An Analytical Model to Predict Fracture of Off-Axis Unidirectional Composites

An analytical model based on isotropic homogeneous material behaviour is proposed to predict fracture in unidirectional composites under general loading. The model calculates the internal stress distribution corresponding to the applied load. In conjunction with the respective strength values, the model is capable of assessing the dominant stress component for failure initiation. For uniaxial tensile loading a comparison of calculated analytical stress distributions reasonably agrees with results from FE-analysis. A comparison of the analytical predictions with fractographic results for different off-axis angles provides good agreement.

DYNAMIC STRESS ANALYSIS OF GAS TURBINE ROTOR AIRFOILS USING THERMOELASTIC TECHNIQUES

Summary The SPATE system provided a means for experimental ther-moelastic analysis of high frequency modes of vibration of a complicated turbine impeller which did not facilitate analysis with conventional methods due to low stress response and high modal density. Testing also demonstrated a unique experimental stress analysis technique which was applied to a blade and vane airfoil and exhibited excellent stress distribution correlation with an established experimental technique (brittle lacquer) and with analytical stress distributions predicted by NASTRAN. Full field dynamic stress analysis of gas turbine compressor airfoils accomplished using thermoelastic techniques provided an efficient method of determining optimum strain gage locations for monitoring rig and engine vibratory stress. Significant cost savings could be realized using this technique from: (1) reduction in the amount of instrumentation required to characterize airfoil dynamic behavior and (2) increased vibratory response mode coverage thereby preventing the re-running of engine test programs to measure vibratory stress response levels of unexpected resonances encountered during initial engine testing. Care is required when using SPATE results for vibratory modes resulting in high bi-axial stress distributions since the system output indicated stress magnitudes based on the sum of the principal stresses which could be significantly higher than either of the individual principal stresses.

有限要素法を用いたスパイクシューズの突き上げ評価法

Shoes used in field sports such as football, rugby and baseball have variable studs on the soles, and these studs are very important parts for players' performance. However, they cause high pressure areas on the foot sole, with pain which sometimes injure the foot. To decrease this feeling is a very serious issue in the designing of spike shoes. So far, pressure feeling has been measured only by sensory evaluational methods, which have had various observational errors. Accordingly, the estimation of pressure feeling by using a numerical approach will become an important key in the designing of spike shoes. In this study, the stress fields distributed on the foot sole when wearing spike shoes were simulated by the finite elements method. Then an evaluational method of pressure feel was proposed by using this analytical stress distribution. The analytical results were compared with experimental ones, focusing on pressure feeling and distribution. By doing this, the validity of this proposed analytical procedure was confirmed. Also, the effects of changing the stud configura tion and loading condition were discussed.

Strength design of the thin walled butt joint bonded with adhesive resin between dissimilar adherends.

The effects of the mechanical properties of adherend materials on the strength of adhesive joints were studied by applying a tensile and torsional load to the tubular butt joints of dissimilar adherends. The specimen materials used in the experiment were carbon steel, copper, brass, aluminium alloy for adherends and epoxy resin for adhesive. The strength of the cured adhesive joint under the tensile load was compared with that without curing to investigate the effect of the difference in the coefficient of thermal linear expansion on the strength of the adhesive joints. The strength of the cured joints was higher than that of the non-cured joints. This showed that there was no remarkable influence of the coefficient of thermal linear expansion on the joint strength. The effects of ratio of Young's modulus on the joint's strength under tensile load decreased when the difference in Young's modulus of adherends was larger. This decrease of the joint strength was discussed on the basis of the analytical stress distribution in the inter face between adhesive layer and the adherend.

Applications of isoparametric three-dimensional hybrid-stress finite elements with least-order stress fields

This paper investigates the factors relating to element stability, coordinate invariance and optimality in 8- and 20-noded three-dimensional brick elements in the context of hybrid-stress formulations with compatible boundary displacements and both a priori and a posteriori equilibrated assumed stresses. Symmetry group theory is used to guarantee the essential non-orthogonality of the stress and strain fields, resulting in a set of least-order selections of stable invariant stress polynomials. The performance of these elements is examined in numerical examples providing a broad range of analytical stress distributions, and the results are favourably compared to those of the displacement formulation and a stress-function based complete stress approach with regard to displacements, stresses, sampling, convergence and distortion sensitivity.

ＮＯＬリング引張試験法の検討

The so-called NOL ring test has been usually used as a testing method to measure the longitudinal tensile properties of filament-wound composites; however, it has a disadvantage to accompany an appreciable bending moment occurring at the split in the dee-fixture where the fracture takes place.The authors have proposed an improved ring having a form of race track (RT) with straight parts, as Dow noted prior to us. The tensile tests have been carried out to compare both types of ring specimens of carbon fiber reinforced plastics. They show a remarkable bending effect and a decrease of tensile strength with an increase in thickness.On the other hand, the analytical stress distributions in both types of ring specimens under separation of split-dee fixture are obtained by the finite element method. The correction by the numerical results leads to the nearly equal tensile strength and modulus, and the RT ring specimens are shown to be desirable to have the reliable tensile data with a substantial reduction in bending moment. Furthermore, the nonlinear analysis is done by taking into consideration the changes of ring configuration and of contact location with split-dee during elongation, which explains the nonlinear relation between load and bending strains.