Maximum Principal Stress Theory Research Articles

Numerical analysis of the impact of winding angles on the mechanical performance of filament wound type 4 composite pressure vessels for compressed hydrogen gas storage

Transportation relies heavily on petroleum products, forcing the adoption of alternative energy sources like hydrogen. Hydrogen is considered the cleanest fuel for the twenty-first century due to its water-based combustion and no CO2 emissions. However, challenges persist in production, utilization, and storage; employing composite material-based high-pressure storage vessels is increasing in the hydrogen storage sector. The paper analyzes the impact of the winding angles on the mechanical performance of the filament wound Type 4 composite pressure vessels (CPVs) for compressed hydrogen gas storage at 70 MPa. This work examines the individual winding angles and combined angles winding patterns to promote the efficiency of Type 4 CPVs by achieving maximum burst pressure, ensuring safe burst mode, and reducing CPV weight by applying maximum principal stress theory with the aid of the Ansys ACP Prep/Post and static modules. The weight and burst pressure of CPVs are significantly influenced by fiber orientation; a combination of positive and negative helical winding angles promotes higher burst pressure at a lower weight. A hoop angle and intermediate helical angles can be combined to create high-efficiency CPVs that provide mechanical performance comparable to that of a combination of high and low helical angles. Finally, a one-factor-at-a-time (OAT) sensitivity analysis was performed to determine how the winding angle and the thicknesses of layers affect the CPVs' performance. It was found that the performance of the CPVs is significantly influenced by the thicknesses of the wound layers.

Application of Fractography and Finite Element Analysis Adopting Elastic Foundation Stiffness to Improve Fatigue Life of Main Shaft in Mechanical Press

The main shaft of a mechanical press inevitably includes significant stress concentrations that can trigger severe mechanical damage and finally lead to failure under repetitive use. In this study, an efficient procedure to quantitatively evaluate the fatigue life of the shaft system including the main shaft and its support bearings, based on the macroscopic failure analysis of the main shaft broken during actual use, was investigated. For this purpose, the bearing support was modeled as an elastic foundation, and the elastic foundation stiffness value was varied to determine the optimal value that best simulates the failure behavior, especially with respect to the failure location and failure sequence, of an actual shaft. While the finite element mesh size was kept the same, only the effect of elastic foundation stiffness was investigated. The optimum value for the main shaft investigated in this study was approximately 60 N/mm³, and the fatigue life of the shaft was evaluated based on the conventional maximum principal stress theory. Based on this, two modified designs to enhance the fatigue life of the existing shaft are proposed.

Role of the Complex Interface Between Bi2Sr2CaCu2Ox Filaments and the Ag Matrix in the Mechanical and Electrical Behaviors of Composite Round Wires

For a superconducting Bi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Sr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> CaCu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> (Bi2212) multifilamentary composite round wire (RW), typically the interface between Bi2212 filaments and the Ag matrix become extremely complex after heat treatment, and all the time the question of how the unique interface structure affect the macro properties such as mechanical, electrical, and thermal behaviors has not been satisfactorily answered, mainly because it is very hard to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> measure the microstructure evolution and further evaluate its effect on these macro properties. Therefore, for this purpose, in this article, we made the modeling and numerical study on the role of the Bi2212/Ag interface in the mechanical and electrical behaviors of composite RWs. By using the randomly generated polygons method, we first reconstructed the cross section of Bi2212 composite RWs, especially in this reconstruction the complex Bi2212/Ag interface can be effectively characterized. On both of two models with and without the complex interface, we obtained the thermally residual stresses and strains due to cooling down from heat treatment, and then the mechanical response from the applied tensile strain. The comparative study further revealed that, for a practical Bi2212 RW with the complex interface, the distributions of the stress and strain are more uniform, which make the wire tend to safely and equivalently increase its limiting load capacity according to the maximum principal stress theory. In order to deeply understand the degradation of the critical current <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_c</i> under applied tensile strain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon $</tex-math></inline-formula> of Bi2212 RWs, we presented a current sharing model in which the current shares both in Bi2212 filaments and surrounding Ag matrix, taking into account the obstacle of cracks in the filament. By comparing the calculated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${I_c} - \varepsilon $</tex-math></inline-formula> curve with experimental data, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_c</i> degradation with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon $</tex-math></inline-formula> was very well interpreted by the mechanical damage and fracture of the microstructure of Bi2212 RWs.

Effects of mechanical stresses around single tube on ash shedding in pulverized coal combustor

In this study, the effects of mechanical stresses on the shedding of ash deposits in a coal-fired boiler were evaluated. We have confirmed that the shedding occurred because of the fracture within the initial deposit layer, which was formed by powdered ash residues. Therefore, assuming that the mechanical stress acting on the initial layer influenced the shedding, the distribution of the tensile stress and shear stresses acting on the initial deposit was calculated on the basis of elastic mechanism. Because the ash deposits were brittle in nature, it was assumed that the initial deposit failed on the basis of the maximum principal stress theory (MPST). The stress values were calculated based on the data for deposit shapes, which were obtained through previous ash deposition experiments on two bituminous coals, one subbituminous coal, and two lignite coals. The fracture strength of the deposit increased with a decrease in the ash fusion temperature. This result indicated that the strength of the deposit increased because of ash coalescence. Moreover, as the MPST, the starting point of fracture was estimated from the position where the principal stress became the largest, and the stress value was used to presume whether the fracture depended on tensile stress or shear stress. The deposit with a narrow adherence region failed because of tensile stress, and the signature of peeling due to tensile stress was observed in the cross-sectional scanning electron microscopy (SEM) image of the deposit after ash shedding. In contrast, the deposit with a wide adherence region failed because of shear stress. Therefore, peeling was not observed in the cross-sectional SEM image of the deposit after ash shedding. The results obtained from the analysis on the basis of the MPST well with the actual behavior of ash shedding.

Load capacity assessment of a braided textile composite bone plate under real-life condition

Bone plates are subjected to multi-axial stresses. Braided textile composites are suitable structures under severe load conditions. In this study, a bone plate was assumed to be made up of Bioactive Glass/Poly L-Lactic Acid (BG/PLLA) and analysed using the finite element method. Material properties obtained from our previous work were introduced into the model assuming an orthotropic mechanical behaviour. Combined loading, including tension/bending, torsion/bending and tension/bending/torsion, was effected into the model. The maximum principal stress theory was used to predict damage onset. Results from linear static analysis showed that the composite was able to properly fix the fractured site under physiological loading conditions. The plate was able to withstand a tension load of about 40 N together with a bending load of about 12 N and torsion of 0.5 N m. Therefore, under multiple loading conditions (real-life situation), it is necessary to control the level of the applied loads until healing.

Numerical investigation of insect wing fracture behaviour

The wings of insects are extremely light-weight biological composites with exceptional biomechanical properties. In the recent years, numerical simulations have become a very powerful tool to answer experimentally inaccessible questions on the biomechanics of insect flight. However, many of the presented models require a sophisticated balance of biomechanical material parameters, many of which are not yet available. In this article we show the first numerical simulations of crack propagation in insect wings. We have used a combination of the maximum-principal stress theory, the traction separation law and basic biomechanical properties of cuticle to develop simple yet accurate finite element (FE) models of locust wings. The numerical results of simulated tensile tests on wing samples are in very good qualitative, and interestingly, also in excellent quantitative agreement with previously obtained experimental data. Our study further supports the idea that the cross-veins in insect wings act as barriers against crack propagation and consequently play a dominant role in toughening the whole wing structure. The use of numerical simulations also allowed us to combine experimental data with previously inaccessible data, such as the distribution of the first principal stress through the wing membrane and the veins. A closer look at the stress-distribution within the wings might help to better understand fracture-toughening mechanisms and also to design more durable biomimetic micro-air vehicles.

Three-dimensional FEM stress analysis and strength prediction of scarf adhesive joints with similar adherends subjected to static tensile loadings

The interface stress distributions in scarf adhesive joints with similar adherends under static tensile loadings were analyzed using two-dimensional and three-dimensional finite element calculations for the two cases where adhesive length and width of the adherends were held constant. The effects of adhesive Young׳s modulus, the scarf angle and the adhesive thickness on the interface stress distributions were examined. In addition, the joint strength was predicted using the interface stress distributions based on the maximum principal stress theory and von Mises׳ stress criterion. It was found that when the scarf angle was around 60°, the singular stress at the edges of the interfaces was minimal in the 3-dimensional FEM calculations while the singular stresses vanished at 52° in the 2-dimensional FEM calculations. The value of the normalized maximum principal stress at the edges of the interfaces obtained from the 3-D FEM was larger than that from the 2-D FEM. It was found that the maximum principal stress increased at the edge of the interfaces as the scarf angle decreased. In addition, the effect of the adherends where the width was held constant was demonstrated. Experiments to measure strain and joint strengths were carried out. The measured strains were in a fairly good agreement with those obtained from the 3-D FEM calculations. Also, the measured joint strengths were fairly consistent with the predicted results based on the maximum principal stress theory. As a result, the maximum joint strength was observed when the scarf angle was around 60°. The difference in the interface stress distributions was demonstrated between the two cases.

Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones

Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σ(min)) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r(2) = 0.56). Under bending, FEA values of maximum principal stress (σ(max)) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r(2) = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ(torsion) were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.

Numerical Simulation of Fatigue Crack Growth of New-Material Track Rollers

Because of the excellent mechanical properties of Austempered Ductile Iron (ADI), track rollers can be made out of this material. The casting may lead to cracks forming inside rollers and there will also be some scratches in the surface when rollers work, which will greatly affect the lifespan of rollers. It is helpful to use crack propagation method based on the Finite Element Method (FEM) to simulate the crack growth. Firstly, define the position and the value of the force imposed on rollers. If the load is compressive, contact pairs should be set between the crack surfaces. After the model is established, Stress Intensity Factors (SIF) KI and KII can be calculated with the node displacement theory by using the commands of FEM software. With the maximum principal stress theory, crack growth direction can be determined. Since the values of KI and KII calculated by the software are positive, we should judge weather the values are positive or negative to get a right propagating angle. The analysis applies linear elastic fracture mechanics and FEM modeling the crack propagation in the elastic state.

Stress Analysis and Strength Evaluation of Scarf Adhesive Joints with Dissimilar Adherends Subjected to Static Tensile Loadings

The interface stress distributions in scarf adhesive joints with dissimilar adherends under static tensile loadings are analyzed using two-dimensional and three-dimensional finite element calculations. The effects of the adherends and adhesive Young's modulus, the scarf angle and the adhesive thickness on the interface stress distributions are examined. In addition, the joint strength is predicted using the interface stress distributions based on the maximum principal stress theory. It is found that when the scarf angle is around 60°, the singular stress at the edges of the interfaces is minimum in the 3-Dimensional FEM calculations. Furthermore, it is noticed that the strength of the joints with dissimilar adherends is smaller than that of the joints with similar adherends. For verification of the FEM calculations, the strains in the adherends and the joint strengths were measured in the experiments. The measured strains are in fairly good agreement with those obtained from FEM calculations. Also, the measured joint strength is fairly consistent with the calculated results.

Optimization of Crack-Free Polytypoidally Joined Si3N4–Al2O3 Functionally Graded Materials (FGM) Using 3-Dimensional Modeling

Joining Si3N4 and Al2O3 using 15 layers has been achieved by a unique approach that introduces SiAlON polytypoids as a functionally graded material (FGM) bonding layer. Previously, the hot press sintering of multilayered FGM with 20 layers, each 500 µm thick, has been achieved successfully. In the present study, the number of layers for FGM was reduced from 20 to 15 to increase optimization. Samples were fabricated by hot pressing at 48 MPa during the temperature ramp to 1650°C and cooling at 2°C/min to minimize residual stresses from sintering. Moreover, a finite element method (FEM) program based on the maximum principal stress theory and the maximum tensile stress theory was applied to design optimized and reduced FGM layers that produced a crack-free joint. The sample had a 3-dimensional cylindrical shape that was transformed to a 2-dimensional axisymmetric mode. By determining the expected thermal stress from the calculated elastic modulus and coefficient of thermal expansion, we were able to predict and prevent damage due to thermal stresses. These analyses are especially useful for FGM samples where it is very difficult to measure the residual stresses experimentally. Finally, oriented Vickers indentation testing was used to qualitatively characterize the strengths of the joint and the various interfaces. The indentation cracks were deflected at the SiAlON layers, implying weak interfaces. In other areas, cracks were not deflected, implying strong interfaces.

Reduction of Functionally Graded Material Layers for Si&lt;SUB&gt;3&lt;/SUB&gt;N&lt;SUB&gt;4&lt;/SUB&gt;-Al&lt;SUB&gt;2&lt;/SUB&gt;O&lt;SUB&gt;3&lt;/SUB&gt; System Using Three-Dimensional Finite Element Modeling

Numerical analysis method was used to reduce the number of functionally graded material (FGM) layers for joining Si3N4-Al2O3 using polytypoid interlayer by estimating the position of crack. In the past, hot press sintering of multi-layered FGMs with 20 layers of thickness 500 mm each have been fabricated successfully. In this paper, thermal residual stresses were calculated using finite element method (FEM) to find the optimized number of layers and its thicknesses of FGM joint. The number of layers for FGM was reduced to 15 layers from 20 layers. Thicknesses were varied to minimize residual stresses within the layers while reducing the number of FGM layers. The damage caused by thermal residual stress was estimated using maximum principal stress theory and maximum tensile stress theory. The calculated maximum stress was found to be axial stress of 430 MPa around 90% 12H/10% Al2O3 area. For each case, calculated strength of each FGM layer by linear rule of mixture was compared with computed thermal residual stresses. Thermal analysis results correctly predicted the position of crack, and this position agreed well with fabricated joints. Therefore, this numerical analysis method can be applied to reduced FGM layers of crack free joint. Finally, new composition profile of crack free joint was proposed using FGM method. [doi:10.2320/matertrans.MRA2007319]

Modeling the multiaxial strength of H-451 nuclear grade graphite

The core of a prismatic High Temperature Reactor (HTR) is constructed from an array of nuclear graphite components. Similarly, the core of a Pebble Bed HTR is confined by large graphite blocks which define the (annular) core geometry. In both HTR designs the large graphite components act as neutron moderator and reflector as well as providing mechanical support to the active core. During reactor operation the graphite components of the core are subjected to complex stress states. Consequently, core designers need a suitable theory of failure. Both deterministic (e.g., maximum principal stress theory) and probabilistic (e.g., Weibull failure theory) have been considered. To test candidate failure theories a multiaxial testing program was conducted at Oak Ridge National Laboratory on H-451 graphite. Large specimens (∼27 cm length) were subjected to combined axial stress (tension and compression) and internal pressure. A total of 59 specimens were tested at 9 stress ratios in the first and fourth stress quadrants. Here, we report the basis and performance of a microstructurally based graphite fracture model and multiaxial strength data for grade H-451 graphite, along with the application of the model to predict the failure envelope for H-451 graphite in the first and fourth multiaxial quadrants.

Passivation cracking analysis of integrated-circuit microstructures under aeronautical conditions

Passivation cracking is one of the main failures of integrated circuits (ICs). A major cause for these failures is the mismatch of thermal expansion coefficients, Young's modulus, and Poisson's ratios of the package materials. Here, the finite element simulations and the maximum principal stress theory are applied to investigate the effects of aeronautical conditions, mainly temperature and load cycles, on the local stress distribution in the passivation layers of IC microstructures. Passivation cracks are easy to initiate and to propagate because the aeronautical IC microstructures endure serious thermo-mechanical loading. The method also can be used to provide a basis for selecting passivation materials for aeronautical IC packages.

Effects of rheology of compound materials on passivation cracking of micro-structure of IC packages

Thermo-mechanical failures are the root cause of failures in integrated circuits. A major cause for these failures is the different coefficients of thermal expansion (CTE) of package materials. Compound material is necessary when assembling, which has different elastic modulus, poisson ratios and coefficients of temperature expansion under different temperatures. Therefore, the rheology of compound material used here is expected to have a pronounced influence on the local stress distribution in the passivation layer. The finite element simulations and the maximum principal stress theory are applied to investigate this influence, which paves the way for compound materials selection in IC packages.

Passivation Cracking Analyses of Micro-Structures of IC Packages

The passivation cracking of Micro-structures of IC packages is studied by maximum principal stress theory using a certain 2D FEM model with different design parameters, pitch of lines, width of line, thickness of epoxy, thickness of dielectric layer, thickness of glue, the glue material’s yielding stress and Aluminium yielding stress (following as “d”, “w”, “t_epo”, “t_Teos”, “t_glue” “sy_glue” and “sy_al” respectively). For different critical process steps, the final process temperature is acted as a representative parameter to analyze its impact. Furthermore, Response Surface Model (RSM) of principal stress is established using any two design parameters. Results show that “d”, “w”, “t_epo”, “sy_glue” and “sy_al” will have great influence on passivation cracking while “t_Teos” have a little impact.

Geometry Sensitivity Analyses of Microstructures of IC Packages on Passivation Cracking

Passivation crack is one of the main failures of micro-electronics. And the IC interconnect has a large varying range values comparing with its geometry size. In this paper, the influence of geometry values of micro-structures of IC packages on passivation cracking is studied by maximum principal stress theory using a certain 2D FEM model with different design geometry parameters, pitch of lines, width of line, thickness of epoxy, thickness of dielectric layer and the Aluminum yielding stress (following as “d”, “w”, “t_epo”, “t_Teos” and “sy_al” respectively). For different critical process step, here the final process temperature is acted as a representative parameter to analyze its impact. Furthermore, Response Surface Model (RSM) of principal stress is established using any two design parameters. Results show that width of line, thickness of dielectric layer and the Aluminium yielding stress will have great influence on passivation cracking while other parameters having little impact.

Fracture of plasma‐sprayed thick thermal barrier coatings under multiaxial stress states

ABSTRACTFailure behaviour of free‐standing plasma‐sprayed coatings was investigated under combined axial and shear loading. Thin‐walled tubular specimens were loaded with various combinations of tension/compression and torsion. This allows the failure surface to be established for loading situations where the two principal stresses are of opposite signs. Specimens failed in one of the two modes, a tensile failure perpendicular to the maximum principal stress or a compression shear failure through the thickness. Failure data were adequately described by the maximum principal stress theory. Stress–strain curves fall within a single scatter band depending on the failure mode. In situ deformation tests showed that the mechanism was microcrack closing and sliding in compression and microcrack opening, coalescence and the development of new microcracks in tension.

A numerical study of the behaviour of surface cracks under dry-sliding conditions

The shape and amount of the surface roughness of a machine part is based on the manufacturing processes. The irregularities cause serious stress concentrations due to the loads acting on the surface. When the loads effect on the surface repeatedly, the irregularities penetrate to turn into a crack. The load may act as normal and/or fractional forces. The latter is caused in general due to friction under rolling–sliding contact conditions. In this study, the behaviour of surface cracks under the normal and tangential loads were analysed. Three angular location for the crack is considered (i.e. −π/4, π/2 and π/4) The problem is considered under condition of linear elastic fracture mechanics and the finite element method was used for numerical solution. The intensity factors at crack tip, K I and K II , were calculated using displacement correlation method. Maximum principal stress theory was used to determine the direction of crack propagation. Effect of the friction coefficient on the stress intensity factors K I and K II and crack growth direction was also investigated.

Particle cracking in discretely reinforced materials with the voronoi cell finite element model

In this paper, a two dimensional small deformation Voronoi Cell finite element model is developed to model damage in heterogeneous materials by particle cracking or splitting. It incorporates a ductile elastic–plastic matrix material containing an arbitrary dispersion of brittle elastic inclusions. Inclusions may be of arbitrary shapes and sizes. Damage initiation by micro-cracking or splitting of the inclusions is assumed to follow a maximum principal stress theory or Rankine criterion. Complete particle cracking or splitting is assumed at the onset of damage. The model accounts for progressive particle fracture in complex microstructures without any user interference. Various microstructural morphologies are simulated to verify the effectiveness of the model.