Complex Three-dimensional Stress State Research Articles

Analysis of test method for physical model test of mining based on optical fiber sensing technology detection

Abstract The common utilization research methods in mining engineering include theoretical analysis, mechanical modeling, similarity model test, numerical simulation, and field test. And physical similarity model test is one of the main research methods for mining engineering problems. Underground engineering is often in the complex three-dimensional stress state. Compared with plane model, three-dimensional model can actually reflect the stress state of surrounding rock. Nevertheless, traditional measurement methods can’t achieve internal deformation of the model with multi-scale distributed monitoring. Optical fiber sensing technology provides a solution to these problems. The sensing fibers are arranged in the plane model with the size of 3000 × 200 × 1280 mm and the three-dimensional model with the size of 3600 × 2000 × 2000 mm, and the strain distribution of the model has been analyzed with the consideration of different positions relationship between the working face and the optic fiber. The results show: the strain coefficient of the test optic fiber with 2 mm diameter calibrated by the uniform strength beam experiment is 0.0497 MHz/μe. The frequency shift of the optic fiber is positive when the fiber is under tension state, and the result is opposite when under compression; In physical model tests, when the working face is close to the sensing fiber, the strain curve shows a negative step change caused by the abutment pressure. When the working face cross the fiber, the strain curve shows a positive step change due to the downward movement of broken rock layer; after the working face away from the fiber, the re-compaction of the broken rock block induced by gravity load causes the optical fiber to be under pressure, and the sensing fiber generates compressive strain. The three-segment distribution area of the strain curve corresponds to the “three-zone” height range of the overburden caused by mining, respectively. The test results could provide theoretical guidance for the application of distributed optical fiber in the determination of the caving zone and fractured zone range of overburden induced by coal mining.

GWFMM model for bi-modulus orthotropic materials: Application to mechanical analysis of 4D-C/C composites

This paper proposes a new constitutive model named general weighted flexibility matrix (GWFMM) material model for the analysis of structures made of bi-modulus orthotropic material in complex three-dimensional stress state. The material properties of the GWFMM model are assigned according to the positive–negative signs and magnitudes of the principal material stresses. General analysis modules of the orthotropic materials with different moduli of elasticity in tension and compression are developed. Comparing with Bert’s model for laminated materials, GWFMM model can obtain more accurate mechanical response of structures in complex three-dimensional stress states.

Nanotribology in austenite: Plastic plowing and crack formation

Especially during the run-in phase of metal friction, plasticity develops in the contact zone. If well controlled, the plasticity will lead to an improved microstructure that exhibits low wear rates during machine operation. We investigate the plasticity due to a single stroke of a micrometer-sized asperity to understand fundamentally tribology induced plasticity and microstructure formation. We find that the local crystal orientation has a significant influence on the development and spread of plasticity. Additionally, the complex three-dimensional stress state results in the formation of non-obvious plastic slip patterns. Finally, we observe crack formation in the scratch track even during the single stroke experiments.

A new specimen geometry to determine the through-thickness tensile strength of composite laminates

The tensile strength in thickness direction is one of the dimensioning parameters for composite load introductions, which are exposed to complex three-dimensional stress states, like e.g. composite lugs. In the present paper a simple test setup which introduces the load into the specimen by a form fit was chosen to determine the through-thickness tensile strength of quasi-isotropic carbon/epoxy laminates. By means of detailed finite element analyses a new quadrilaterally waisted specimen geometry was developed and validated by mechanical testing. The influence of the manufacturing process on the location of failure was investigated and recommendations for future tests are made. Compared to alternative state of the art methods the proposed test method leads to higher accuracy and reproducibility of the determined through-thickness tensile strength.

Three-dimensional invariant-based failure criteria for fibre-reinforced composites

A new three-dimensional failure criteria for fibre-reinforced composite materials based on structural tensors is presented. The transverse and the longitudinal failure mechanisms are formulated considering different criteria: for the transverse failure mechanisms, the proposed three-dimensional invariant-based criterion is formulated directly from invariant theory. Regarding the criteria for longitudinal failure, tensile fracture in the fibre direction is predicted using a noninteracting maximum allowable strain criterion. Longitudinal compressive failure is predicted using a three-dimensional kinking model based on the invariant failure criteria formulated for transverse fracture. The proposed kinking model is able to account for the nonlinear shear response typically observed in fibre-reinforced polymers. For validation, the failure envelopes for several fibre-reinforced polymers under different stress states are generated and compared with the test data available in the literature. For more complex three-dimensional stress states, where the test data available shows large scatter or is not available at all, a computational micro-mechanics framework is used to validate the failure criteria. It is observed that, in the case of the IM7/8552 carbon fibre-reinforced polymer, the effect of the nonlinear shear behaviour in the failure loci is negligible. In general, the failure predictions were in good agreement with previous three-dimensional failure criteria and experimental data. The computational micro-mechanics framework is shown to be a very useful tool to validate failure criteria under complex three-dimensional stress states.

Three-dimensional dissipative stress space considering yield behavior in deviatoric plane

Naturally deposited soils are always found in the complex three-dimensional stress state. Constitutive models developed for modeling the three-dimensional mechanical behavior of soils should obey the basic laws of thermo-mechanical principles. Based on the incremental dissipation function, a new deviatoric shift stress is derived and then introduced into the existing constitutive models to describe the yield behavior in the deviatoric plane for geomaterials. By adopting the proposed shift stress, the relationship between dissipative stress tensors and true stress tensors can be established. Therefore, the three-dimensional plastic strain can be calculated reasonably through the associated flow rule in the three-dimensional dissipative stress space. At the same time, three methods that are conventionally adopted for generalizing constitutive models to model the three-dimensional stress-strain relationships are examined under the thermo-mechanical framework. The TS (transformed stress) method is shown to obey the thermo-mechanical rules and the TS space adopted in TS method is actually a translational three-dimensional dissipative stress space. However, it is illustrated that the other two approaches, the method of using failure criterion directly and the method of using g(θ) function, violate the basic rules of thermo-mechanical theories although they may bring convenience and simplicity to numerical analysis for geotechnical engineering. Comparison between model predictions and experimental data confirms the validity of the proposed three-dimensional dissipative stress space.

Parametric Study and Design Recommendations for In-Span Hinges in Reinforced Concrete Box-Girder Bridges

In-span hinges (ISHs) are located at the bridge deck of reinforced concrete box-girder bridges and are used to transmit vertical loads between two adjacent parts of the deck. ISHs are disturbed regions because of the complex three-dimensional stress state caused by concentrated bearing loads and utility openings. The common modeling practice for ISHs is simplified two-dimensional idealization as short cantilevers following standard procedures. Such simplified analytical and design procedures lead to inefficient detailing because they do not take into account the realistic failure modes of ISHs; punching shear is one of these critical modes. In this study, the influence of reinforcement and geometrical detailing on the behavior and strength of ISHs is assessed using a computational approach. The computational model is calibrated based on previous experimental results and adopts nonlinear three-dimensional finite-element analysis (FEA), accounting for cracking of concrete and elastic–plastic behavior of reinforcement. The concrete material is modeled using the total strain rotating crack method, and the effect of compression softening is incorporated into the constitutive model. The reinforcing steel is modeled using embedded reinforcement formulation assuming a perfect bond between the concrete and the reinforcement. From the computational study, design guidelines are presented for better constructability of these disturbed regions. Findings from this study revealed that the strength of ISHs is mostly improved by increasing the amount of diagonal reinforcement in the seat and by increasing the bearing plate size.

Stress and failure analysis of thick-walled conical composite rotors

The high specific strength and stiffness of composite materials, as well as the possibility of creating a load-adapted property profile of them are ideally suited for the design of high-speed lightweight rotors. With respect to a load-adapted reinforcement structure of composite rotors, the rotor geometry has a significant influence on the optimum fibre orientation. In the case of conical rotors—the structural behaviour is strongly influenced by centrifugally induced bending effects in the rotor structure, which cause complex three-dimensional stress states in combination with the ordinary tangential and radial stresses. For analysis of the resulting complex stress states, an analytical method has been developed and verified numerically as well as experimentally. The novel method presented here is the basis for a realistic failure analysis and, in particular, serves as an efficient tool for extensive parameter studies and optimizations within the design process.

Stress and failure analysis of thick-walled conical composite rotors

The high specific strength and stiffness of composite materials, as well as the possibility of creating a load-adapted property profile of them are ideally suited for the design of high-speed lightweight rotors. With respect to a load-adapted reinforcement structure of composite rotors, the rotor geometry has a significant influence on the optimum fibre orientation. In the case of conical rotors—the structural behaviour is strongly influenced by centrifugally induced bending effects in the rotor structure, which cause complex three-dimensional stress states in combination with the ordinary tangential and radial stresses. For analysis of the resulting complex stress states, an analytical method has been developed and verified numerically as well as experimentally. The novel method presented here is the basis for a realistic failure analysis and, in particular, serves as an efficient tool for extensive parameter studies and optimizations within the design process.

Bending of filament wound composite laminated cylindrical shells

This paper presents a rigorous elasticity solution for filament wound composite laminated cylindrical shells subjected to out-of-plane bending. The material of the shell is assumed to be cylindrically anisotropic. Based on the theory of cylindrically anisotropic elasticity, coupled partial differential governing equations are developed using Lekhnitskii's stress functions. Homogeneous solutions are obtained using separation of variables and polynomial forms are used for particular solutions. To illustrate the fundamental nature of the problem, an example of off-axis composite shells is presented. Complex three-dimensional stress states, large stress gradients through the thickness and strong effect of fiber orientations are reported. Detailed stress distributions of two laminated shells [ 45 −45 ] s , [ 45 −45 ] are examined.

Process-Induced Residual Thermal Stresses in Advanced Fiber-Reinforced Composite Laminates

A study of process-induced stresses in advanced fiber-reinforced composite laminates is presented. An analysis of the residual thermal stresses is conducted on the basis of laminate thermoelasticity theory in conjunction with a quasi-three-dimensional finite element method. Formulation of the numerical method is briefly outlined in the paper. To illustrate the fundamental nature of the problem, numerical examples for a quasi-isotropic [0 deg/90 deg/ ± 45 deg]s graphite-epoxy composite system are presented. Complex three-dimensional stress states of significant magnitude are reported. Emphasis is placed on the interlaminar stress distributions along ply interfaces. Effects of laminate stacking sequence on the residual thermal stresses are examined in detail. Implications of the results on deformation and failure of composite laminates are discussed.