Maximum Stress Theory Research Articles

Hashin·Puck 파손기준 기반 적층 복합재료의 섬유 및 기지파손 평가에 관한 연구

In the present study, the fiber and matrix failure of composite laminates under arbitrary biaxial stresses were evaluated based on separate mode criteria such as Hasnin and Puck theories. There is a limitation to predict the fiber-dominant and/or matrix-dominant failures under arbitrary stress states using limit criteria (maximum stress and maximum strain theories) and interactive criteria (Tsai-Hill and Tsai-Wu theories). There is little literature for failure analysis of ships and offshore composite structures considering advanced failure theories such as Hashin and Puck theories. Furthermore, there is not enough practical commercial finite element analysis (FEA) code which is basically adopted the separate mode criteria. Hence, in the present study, the user-defined subroutine of commercial FEA code ABAQUS for evaluation of fiber and matrix failures of composite structures was developed based on Hashin and Puck failure criteria. And then, the proposed subroutine was validated by comparing with a series of experimental results of carbon- and glass-implemented composite laminates to guarantee the reliability and usefulness of the developed method.

Study on triaxial test method and failure criterion of asphalt mixture

Asphalt mixture is the most widely used pavement material all over the world. In China, more than 90% of service expressways are asphalt pavement. However, current asphalt pavement design method still has irrationality. Even though maximum tensile stress theory is used as failure criterion, pavement structure under the effects of wheel load is in three-dimensional complex stress state. Obviously, one-dimensional strength theory cannot reflect the failure characteristics and the resistance of pavement structure. So it is necessary to study the failure criterion of asphalt mixture under three-dimensional complex stress state. Due to limitations of test equipment, there are almost no studies in related area. Under this background, this paper develops a new triaxial test method, according to the investigation of strength characteristics of asphalt mixture under complex stress state through plane isobaric/axial tensile test, plane isobaric/axial compression test, plane tensile and compression/axial tensile test, to reveal the general rules of asphalt mixture's strength failure. The failure mode is divided into three types: tensile failure, shear failure and rheological failure. The tensile meridian and compression meridian in the stress space and strength envelope in the π plane where hydrostatic pressure is greater than zero are obtained, and the failure criterion of asphalt mixture under complex stress state is established, providing theoretical method and scientific basis for structure design as well as strength check of asphalt pavement under three-dimensional stress state.

In-plane shear failure properties of a chopped glass-reinforced polyester by means of traction–compression biaxial testing

We perform traction–compression biaxial testing in a chopped glass-reinforced polyester, applying in-plane perpendicular tensile–compressive loads to cruciform specimens. The purpose is to evaluate if this technique is suitable to perform shear tests and determine the shear strength and the shear failure strain of the composite. The failure properties obtained experimentally from this technique are compared with the analytical predictions of the Maximum stress, Maximum strain, Tsai-Hill and Tsai-Wu failure theories and the numerical results obtained by means of the Finite Element Method. The analysis is developed taking into account the different behaviour of the material under tension and under compression.

Strength models of bamboo scrimber for compressive properties

Ten groups of bamboo scrimber samples between 0° (parallel to the grain) and 90° (perpendicular to the grain) were chosen for compression test. The effect of different angles between load and grain on compressive properties of bamboo scrimber was studied. Fold failure, shearing failure and crushing failure were observed at 0–10°, 20–50° and 60–90°, respectively. From 0 to 90°, average ultimate strength and proportional limit strength decreased from 133.4 to 25.7 MPa and 113.9 to 14.9 MPa. The predictive accuracy of the Hankinson formula was higher comparing to the result of GB 50005 formula. The Norris criterion was inclusive for the majority of the testing values, making it secure during application. Furthermore, compressive properties could be predicted using maximum stress theory, which adequately explained the cause of different failure types for longitudinal compression strength, shear strength and transverse compressive strength. The study of strength models now provides a theoretical foundation for the rational use of bamboo scrimber.

Quasi-Static Simulation of Crack Propagation on Elastic Material with Material Discontinuous Zone

A numerical method to simulate the crack propagation based on the maximum circumferential stress theory is presented in this paper. The FEM method is used to estimate the influence of the material discontinuous zone on the propagation path of the crack placed in close to it in the matrix. When the crack grows, the FEM method uses the maximum circumferential stress theory to determine the propagation direction and the elements re-meshing program to ensure the accuracy of the crack-tip stress field. The crack propagation paths in the matrix with different material zone are simulated by the method. The simulation results show that the property of the material discontinuous zone influences the maximum deflection angle and its size influences the length of the deflected crack path.

Borehole Stability Logging Analysis in Zhenjing Oilfield, Ordos Basin, China

There is very important practical significance for borehole stability to oil and gas drilling and production. When the mud density is too large (mud column pressure too high),the formation will be fractured. When the the mud density is too low (mud column pressure too low), the borehole wall will be collapsed, and hole will be enlarged. In this paper, the fracture pressures of the formations were determined by using the maximum tensile stress theory. The formation collapse pressures were determined by using the Coulomb - Moore intensity criteria. According to the fracture pressure and collapse pressure to evaluate the borehole stability. The two wells stability evaluation examples were given, and the borehole security mud window were calculated.

Failure strain and stress fields of a chopped glass-reinforced polyester under biaxial loading

We perform experimental tests to obtain biaxial stress states in a chopped glass-reinforced polyester composite, applying in-plane perpendicular tensile loads to cruciform specimens. Three different specimens’ geometries have been considered for obtaining adequate failure modes with different loading cases. The scope is to estimate the strain and the stress failure states by measuring with gages the strains developed in the central zone, where a plane stress state with zero shear component occurs. We develop numerical simulations using the Finite Element Method in order to achieve a better understanding of the behaviour of the cruciform specimens under loading and to compare the numerical results with the experimental data. Maximum stress, Maximum strain, Tsai-Hill and Tsai-Wu biaxial failure theories are evaluated for the assumption of isotropic behaviour and contrasted with the experimental results.

Research on Test of Fracture Toughness and Fracture Criterion of Crack of Mixed Mode I and II of Steel Fiber Concrete

Steel fiber concrete is a new-type composite material of excellent property with broad application formed by common concrete mixed with disorderly oriented short steel fiber. Main action of steel fiber is to prevent broadening of interior micro crack in concrete and restrict occurrence and growth of macro crack. Based on basic theory of concrete fracture mechanics, this treatise adopts four-point shearing sampling material to conduct experimental research, having obtained critical fracture curve of crack of composite mode I, II of steel fiber concrete, setting up experimental formula of fracture criterion, probing into difference between fracture toughness of steel fiber concrete and that of common concrete, and discussing application of maximum tension stress theory in steel fiber concrete.

Micromechanics-based progressive failure analysis of composite laminates using different constituent failure theories

Predicting failure in a composite can be performed using ply level mechanisms and/or micro level mechanisms. This paper uses the generalized method of cells and high-fidelity generalized method of cells micromechanics theories, coupled with classical lamination theory, to study progressive damage in composites. Different failure theories, implemented at the fiber and matrix constituent level within a laminate, are investigated. A comparison is made among maximum stress, maximum strain, Tsai-Hill, and Tsai-Wu failure theories. To verify the failure theories, the Worldwide Failure Exercise experiments are used. The Worldwide Failure Exercise is a comprehensive study that covers a wide range of polymer matrix composite laminates. The objectives of this paper are to evaluate the current predictive capabilities of the generalized method of cells and high-fidelity generalized method of cells micromechanics theories for the progressive failure prediction of polymer matrix composite laminates and to evaluate the influence of four failure criteria applied at the fiber/matrix constituent scale. The numerical results demonstrate overall agreement with the experimental results for most of the composite layups examined, but also point to the need for more accurate resin damage progression models.

Effect of Timber Grain Orientation on Bonded-In Rod Connection Systems

Presented in this paper are the results of practical tests to determine some key material properties of engineered timber, in particular glulam. The results are discussed and compared with three known failure criterion, Hankinsons formula, The Tsai-Wu criterion and Maximum stress theory to determine if they are appropriate models for predicting the properties of glulam. The properties considered have been chosen with respect to a connection system for use in folded plate structures utilizing embedded rods. This paper considers the effect of the timber grain angle on the compression, tensile and steel dowel rod pull-out strengths. The test data shows that Hankinson and Tsai-Wu are both good models to predict both the compression and tensile behavior of engineered timber products at non-tangential angles, whereas maximum stress theory had less correlation and over predicts the results and would not be recommended for use in engineered timber materials.

Failure Analysis of Carbon Fiber Reinforced Polymer (CFRP) Bridge Using Composite Material Failure Theories

Portable bridges are very important for maintaining mobility in the aftermath of natural disaster or in the battlefield. This requirement has lead to the needs for light-weight bridging system for ease in launching, retracting, transporting, and storing. In this research, a foldable bridge with three sections of beam connected together using the hinges connection has been designed and analyzed. The bridge is constructed using sandwich Carbon Fiber Reinforced Polymer (CFRP) which consists of CFRP and Aluminum Honeycomb, as the skin and core, respectively. The uses of materials are expected will reduce the total weight of bridge without decreasing of overall performance. Failure theories of composite material such as Maximum Stress, Maximum Strain, Tsai-Wu and Tsai-Hill failure theories were selected to generate an allowable strength graph. From the graph, can be seen that, the material stresses are in the allowable stress-strain ranges, therefore, the bridge is capable of carrying the design load with sufficient safety factor.

Study on Tensile-Shear Failure of Fractured Rock Mass under Strong Seismic Load

Fractured rock mass endures tensile-shear and pressure-shear effects under horizontal seismic force. Based on rock fracture mechanics and the maximum circumferential stress theory, the extending condition (that is, the critical acceleration), the extending direction and the crack extension length under different direction of horizontal seismic force have been studied. The results are useful for judging the risk of dangerous rocks and providing a theoretical basis of pre-identification in the earthquake zone.

The Creep Rupture Numerical Simulation of Coal (Rock) Layered Slope

With rapid development of the national open mining coal resources, which generated lots of open-pit slope, and typically coal(rock) layered slope，under the external and internal structure function, it caused massive landslide with time increasing. Large coal(rock) slope deformation is not instantaneous, but rather the result of a long slow rheology, which is the main forms of creep; which is a serious threat to mining enterprise and the safety of workers. Appling the maximum tensile stress theory and establishing the creep rupture judgment criteria, And finite description of the creep cracks initiation, expansion and gathering. Based on FEPG software, programmed creep rupture module, it generated crack at the vertical direction of first principal stress vector, The crack propagation continue to find the maximum of the first principal stress, which achieved tensile strength and creep craze of elements, this process is continuously cycled. In Haizhou open-pit national mine-park, simulated the coal(rock) separation layer creep rupture, and the results of measurement and simulation was coincided; its study provided basis for prevention and disaster of coal (rock) slope.

Temperature dependence and fracture criterion of mixed mode I/II fracture toughness of phenolic resin for friction material

AbstractIn this study, the temperature dependence of the mixed‐mode fracture toughness of the phenolic resin for friction materials is investigated. For pure mode I, the fracture toughness decreases as the temperature increases, and it increases again after showing its minimum value. For pure mode II, the fracture toughness shows a similar trend but has its minimum value at a higher temperature. The temperature dependence of the mixed‐mode fracture toughness varies depending on the mode mixity, which is attributed to the different sensitivity to the relaxation phenomenon. At room temperature, as the fracture toughness for pure mode I and II are almost the same, the fracture locus shows a circular arc. At elevated temperatures, the locus becomes smaller and noncircular. At high temperature, the fracture locus shows an elliptical arc, where the fracture toughness for pure mode II is smaller than that for mode I. An empirical fracture criterion based on the time‐temperature dependence of the resin is proposed, and the proposed method successfully predicts the fracture toughness under various conditions of the temperature, time, and mode mixity. The crack initiation angles, on the other hand, are almost consistent regardless of the temperature, which agree with the maximum hoop stress theory. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Crack Growth Direction Analysis Based on Elastic-Plastic Property of Material

The finite element software ANSYS was employed to create a finite element model of the cracked wing beam integrated structure, and the stress field of the crack tip was got by the material nonlinearity (elastic-plastic) analysis method. Based on the maximum tensile stress theory criteria, the crack deflection angle was obtained. The crack deflection angles with different geometry parameters (crack length, wed thickness, the height-thickness ratio of the stringer, cross-sectional area, and the location of the stringer) of the wing beam integrated structure were calculated and compared with each other. So the influences of the geometry parameters of the wing beam integrated structure on the crack deflection were studied. The crack deflection angles obtained in elastic analyzing and elastic-plastic analyzing were compared to investigate the effects of the material property on the crack deflection angle.

Calculation Analysis on Cracking Load of New Type Composite Wall

New type composite wall is the main bearing member in Multi-ribbed Slab Structure (MRSS), whose cracking load is an important parameter to determine the restoring force model and damage index of the wall. Based on the twin shear unified strength theory, when the influence of intermediate principal stress σ2 and SD effect of materials are considered, the study on low-frequency cyclic lateral loading experiment of wall is proceed and the practical formula for the wall’s initial cracking load is deduced. The practical computing formulas for the wall’s initial cracking load based on twin shear unified strength theory and maximum tensile stress theory are contrastingly analyzed. The results show that, comparing the calculated values based on the twin shear unified strength theory and the values based on maximum tensile stress theory, the former are more closed to the experimental values, and it can provide more accurate, economic and applicable results for practical engineering.

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris’ law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena.

Applying failure criteria to the strength evaluation of 3-ply laminated veneer lumber according to grain direction by uniaxial tension test

The failure criteria from four theories — the Hankinson formula, Maximum stress theory, Tsai–Hill theory and Hyperbolic formula (modified Hankinson formula) — were applied to estimate the strength of laminated veneer lumber (LVL) by uniaxial tension test at various angles to the grain. The LVL strength predicted from these theories were compared with actual data to evaluate the accuracy of the criteria. The tensile strength rapidly decreased at orientations between 0 and 15°. In the Hankinson formula, the difference between the predicted strength with n = 2 and the measured data was very small, with a slight underestimation at grain angles of 15°, 30° and 45°. The Maximum stress theory predicted the LVL strength better at grain angles over 45°, but not under 45°. The predicted strength derived by the Tsai–Hill theory underestimated the strength at grain angles of 15°, 30°, and 45°, with the difference being the largest at a grain angle of 15°. The prediction of LVL strength using this theory may be somewhat misleading in small grain angle deviations. The Hankinson and Hyperbolic formulae showed good strength prediction according to grain variation, especially at small grain angles. These two formulae are more useful/practical in the estimation of engineered wood composites like LVL according to grain direction deviation between veneers in the lay-up process. Among the failure types of the tested LVL specimens, the shear failure parallel to the grain was predominant at each grain angle except for 0°. This resembles the cross grain tension failure type, while splintering tension failure was found at 0° and brash tension-like brittle fracture at 90°.

Fiber direction and stacking sequence design for bicycle frame made of carbon/epoxy composite laminate

According to the maximum stress theory and the results of strength-to-stress ratios, the fiber direction and stacking sequence design for the bicycle frame made of the carbon/epoxy composite laminates have been discussed in this paper. Three testing methods for the bicycle frame, i.e. torsional, frontal, and vertical loadings, are adopted in the analysis. From the finite element results, the stacking sequences [0/90/90/0] s and [0/90/45/−45] s are the good designs for the composite bicycle frames. On the contrary, the uni-directional laminates, i.e. [0/0/0/0] s , [90/90/90/90] s , [45/45/45/45] s and [−45/−45/−45/−45] s , are the bad designs. In addition, weak regions of failure occur at the fillets and connections of the frame, i.e. the stress concentration regions. All weak points occur at the inner or outer layer of the laminated composite tube. The 0°-ply and 90°-ply located on the inner and outer layer of the tube can effectively resist the higher stress at its location.

Development of Efficient Finite Element Software of Crack Propagation Simulation using Adaptive Mesh Strategy

The purpose of this study is on the determination of 2D crack paths and surfaces as well as on the evaluation of the stress intensity factors as a part of the damage tolerant assessment. Problem statement: The evaluation of SIFs and crack tip singular stresses for arbitrary fracture structure are a challenging problem, involving the calculation of the crack path and the crack propagation rates at each step especially under mixed mode loading. Approach: This study was provided a finite element code which produces results comparable to the current available commercial software. Throughout the simulation of crack propagation an automatic adaptive mesh was carried out in the vicinity of the crack front nodes and in the elements which represent the higher stresses distribution. The finite element mesh was generated using the advancing front method. The adaptive remising process carried out based on the posteriori stress error norm scheme to obtain an optimal mesh. The onset criterion of crack propagation was based on the stress intensity factors which provide as the most important parameter that must be accurately estimated. Facilitated by the singular elements, the displacement extrapolation technique is employed to calculate the stress intensity factor. Crack direction is predicted using the maximum circumferential stress theory. The fracture was modeled by the splitting node approach and the trajectory follows the successive linear extensions of each crack increment. The propagation process is driven by Linear Elastic Fracture Mechanics (LEFM) approach with minimum user interaction. Results: In evaluating the accuracy of the estimated stress intensity factors and the crack path predictions, the results were compared with sets of experimental data, benchmark analytical solutions as well as numerical results of other researchers. Conclusion/Recommendations: The assessment indicated that the program was highly reliable to evaluate the stress intensity factors and successfully predicts the cracks trajectories. Based on the results, it was recommended to add further development in the software to simulate crack propagation in elastoplastic materials.