Strength Of Materials Theory Research Articles

Functional failure criterion based on biaxial tensile testing of steel liners and its application to fragility analysis of nuclear containment under overpressure conditions

To investigate the mechanical behavior of the steel liner under bi-directional tensile loading, 39 cruciform tensile specimens made of P265GH steel liner are examined by biaxial tensile tests with different loading ratios. Based on the strength theory of materials and test results, an anisotropic tearing criterion for the steel liner is established. Subsequently, the proposed tearing criterion is applied to the fragility analysis of the containment under overpressure conditions. Finally, the differences between the proposed and existing tearing criteria are discussed. The results show that the strength of the steel liner under biaxial tensile loading is improved, while the deformation capacity is significantly decreased. The proposed tearing criterion is more consistent with the actual behavior of steel liners under bi-directional tensile loading. When evaluating the probabilistic performance of the containment, it is more practical and safer to predict the functional failure of the containment by using the proposed tearing criterion.

Evaluation of compressive strength of cement-stabilized rammed earth wall by ultrasonic-rebound combined method

It is difficult to guarantee the construction quality of rammed earth buildings, and there needs to be more guidance for the quality inspection of historical protection buildings. To facilitate the assessment of the quality of rammed earth walls, based on the establishment of concrete strength measurement curves, this study took the additive content and type with curing time as variables, and considered the rebound (R) values and ultrasonic pulse velocity (UPV) values in the dense and sparse zones. Based on the material strength theory, the strength measurement curve of cement-stabilized rammed earth was finally established in the sparse zone. The single-factor method and two-factor method were considered to evaluate the unconfined compressive strength (UCS), respectively. The results showed that the R value and UPV increased with the increase in cement content. With the increase in curing time, the R value increased and stabilized; the UPV increased, decreased, and finally stabilized. The difference in the R value of the sparse and dense zones is within ±1, and the difference in the UPV is within ±0.2 km/s. The single R method or UPV method predicts the UCS with poor accuracy, while the ultrasonic-rebound combined method can better predict the UCS. Finally, samples from the failed specimens were taken for scanning electron microscopy tests to further verify the test results on a microscopic level.

Research on Parameter Design Method and Motion Characteristics of a Ball Cage Flexible Joint

The flexible joint is an important part in ultra-short-radius drilling tools, and its structural parameters and motion characteristics are key factors affecting the success of drilling. In this work, a new type of ball cage flexible joint, which is applied in 5″ and 5.5″ cased wells, was proposed based on the working principle of the ball cage universal joint. A structural parameter design method for the ball cage flexible joint was established according to the geometric coordination relation and material strength theory. Using this new method, the length, diameter, and window size of the ball cage flexible joint were analyzed. The multi-body motion process was further analyzed using a multi-body dynamics method, and then the motion characteristics, such as impact contact force, isokinetic characteristics, transfer efficiency, deflection torque and so on, were studied. Based on the above analyses, the structural parameters of the designed joint were optimized by means of the orthogonal test method. Results demonstrate that the experimental ball cage flexible joint has excellent isokinetic transmission characteristic, which can effectively suppress vibration and shock caused by changes in rotational speed. The transmission efficiency of the structure was 89.8%, while the power loss rate was 0.102%. According to the orthogonal test analysis, the optimal structure of the flexible joint has a ball seat diameter of 80 mm, a ball head diameter of 62 mm, and a ball key diameter of 16 mm. It is important to note that the ball key diameter was the most influential factor on the flexible joint internal contact force. The ball key contact force varied periodically, and there was a significant phase difference between the contact forces of different balls. On the other hand, with an increase in the flexible joint working angle, the deflection torque increased gradually, and the vibration amplitude of the torque increased. This work can provide reference for the parameter optimization design of the new flexible joint.

Design Contributions to the Elaboration of New Modeling Schemes for the Buckling Assessment of Hydraulic Actuators

Hydraulic cylinders represent the main actuating/positioning element for standalone lifting equipment or equipment for various transport platforms. This type of actuator represents a structural component responsible for the operational safety of the equipment it serves. One of the most common and dangerous reasons concerning the end of life for this equipment is the buckling or loss of stability of the elastic equilibrium shape. This article aims to compare the classical approach of the problem in accordance with the strength of materials theory in relation to the numeric algorithms used in the applications for the analysis of structure behavior and the algorithms that are based on the finite element method. The subject of study is a hydraulic cylinder that is installed in a self-lifting platform and because of the manifestation of the phenomenon under analysis, it has led to a technical accident. For this purpose, an estimation of the value for the buckling critical load of the cylinder assembly was carried out.

A nondimensional framework for size dependent quasi-brittle fracture criteria

It is well known that the quasi-brittle fracture behaviors of plain specimens and cracked specimens with sufficiently long cracks can be predicted satisfactorily by the material strength theory and the linear elastic fracture mechanics, respectively. However, the transition between these two classical limits is relatively complicated and vague, so that intensive attentions have been paid to explain this size dependent phenomenon during the past three decades. Although the fracture process zone (FPZ) is a well-accepted mechanism for this size effect, the stress distribution in the FPZ is still not well understood, which usually results in introducing additional parameters supplementary to conventional material parameters to fit the testing data. In order to establish reasonable fracture criteria without additional parameters, this paper proposes a general construction framework based on the dimensional analysis, in which different stress distributions in the FPZ generate different trial functions. The criteria construction process is firstly demonstrated by using three uniform stress FPZ models. It is found that the well-known line method of the theory of critical distances is consistent with the modified Irwin’s model. Furthermore, a new criterion is established by constructing the stress gradient continuous model (SGCM), in which the stress distribution in the FPZ is not only continuous but also smooth. Finally, experimental results of different quasi-brittle materials are used to examine the validities of these criteria, some of which can achieve reasonable agreements with testing data without additional parameters, and the criterion based on the SGCM shows a better performance for certain cases. Therefore, one can envisage that optimized quasi-brittle fracture criteria could also be established based on the proposed general framework by adopting more realistic FPZ models for specific materials.

Failure mode maps of lap joints under the tensile shear testing condition

Failure modes in lap joints with or without the filler material under the tensile shear testing condition may include the interfacial shear fracture, the nearly normal fracture in the plate materials, and necking in various locations. The commonly adopted analyses by either material strength theory or fracture mechanics are problematic, since the shear or normal fracture forces are not far from that for necking and thus the entire damage evolution should be explicitly calculated. The classic Gurson–Tvergaard–Needleman model and a shear-extended Gurson model are employed here to calculate the void-growth-controlled ductile failure process, which facilitate the construction of failure mode maps with respect to geometric and material parameters.

Analysis on the Influence Factors of Propellant Tank Stress

The propellant tank is a vital structure for the liquid rocket, and the analysis of influence factors to the propellant tank stress can provide a significant reference to design the propellant tank. Through establishing the ellipsoid cylindrical tank model, the meridian stress and hoop stress distributions of tank roof, cylinder and bottom are analysed. And then the equivalent stress is defined based on the material strength theory. According to the parameters of a certain type tank, the equivalent stresses of tank roof, cylinder and bottom are worked out with different ellipsoidal norms, overload factors, tank radiuses and internal pressurizations, the effects of these influence factors on the tank stress are analysed, and the change laws of tank roof, cylinder and bottom equivalent stresses are determined to provide a reference for the design of propellant tank.

A concise review about fracture assessments of brittle solids with V-notches

A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched solids are discussed first. The concept of notch stress intensity factor is introduced. Combine the digital image correlation method with numerical computation techniques to analyze the stress distribution near the notches. Fracture criteria such as strain energy density, J-integral, theory of critical distance are used. However, various new materials are developed in different engineering fields, thus, the establishment of reliable and accurate material strength theory or failure criterion is imperative. Therefore, predicting fracture for various modern materials would require more experiments to infer material dependent parameters in the local fracture model.

General theory of cross-sections kinetics in calculating rod elements of structures. Cartesian coordinates

The applied mechanics of deformable bodies evolves to its more rigorously substantiated predominant empirical approaches, which significantly limit calculation possibilities. The most "severe" limitation is applying exclusively the hypotheses of non-warping cross-sections in calculating the structural rod elements. The research was carried out to expand the possibilities and to systematically generalize and complete a traditional approach within the theory of strength of materials, which is based on isolating a subsystem of points in a cross-sectional form. The presented theory is a synthesis of the theory of strength of materials and the applied theory of elasticity. The theory of strength of materials contributed with the paradigm of monitoring the behaviour of cross-sections as a subsystem of points of a deformable body. The theory of elasticity provided differential equations of internal constraints, modifiable according to the traditional assumptions of the theory of material strength, except for those relating to the behavior of cross-sections. The study touches upon the analytical issue of optimizing the forms of various rod junctions, such as threaded, toothed, and strained junctions, and also on the issue of stress concentration in the regions of curvilinear transitions.

General theory of cross-sections kinetics in calculating rod elements of structures. Cartesian coordinates

The applied mechanics of deformable bodies evolves to its more rigorously substantiated predominant empirical approaches, which significantly limit calculation possibilities. The most “severe” limitation is applying exclusively the hypotheses of non-warping cross-sections in calculating the structural rod elements. The research was carried out to expand the possibilities and to systematically generalize and complete a traditional approach within the theory of strength of materials, which is based on isolating a subsystem of points in a cross-sectional form. The presented theory is a synthesis of the theory of strength of materials and the applied theory of elasticity. The theory of strength of materials contributed with the paradigm of monitoring the behaviour of cross-sections as a subsystem of points of a deformable body. The theory of elasticity provided differential equations of internal constraints, modifiable according to the traditional assumptions of the theory of material strength, except for those relating to the behavior of cross-sections. The study touches upon the analytical issue of optimizing the forms of various rod junctions, such as threaded, toothed, and strained junctions, and also on the issue of stress concentration in the regions of curvilinear transitions.

Modified cantilevers to probe unambiguously out-of-plane piezoresponse

We demonstrate and investigate the coupling of contributions from both in-plane (IP) polarization and out-of-plane (OP) components in ${\mathrm{BiFeO}}_{3}$ (BFO) thin-film polarization probed by piezoresponse force microscopy (PFM). Such coupling leads to image artifacts which prevent the correct determination of OP polarization vector directions and the corresponding piezoelectric coefficient ${d}_{33}$. Using material strength theory with a one-dimensional modeling of the cantilever oscillation amplitude under electrostatic and elastic forces as a function of the tip length, we have evidenced the impact of IP piezoresponse to the OP signal for tip length longer than 4 \ensuremath{\mu}m. The IP polarization vector induces a significant longitudinal bending of the cantilever, due to the small spring constant of long tips, which provokes a normal deviation superimposed to the OP piezoresponse. These artifacts can be reduced by increasing the longitudinal spring constant of the cantilever by shortening the tip length. Standard cantilevers with 15-\ensuremath{\mu}m-long tips were modified to reach the desired tip length, using focused ion-beam techniques and tested using PFM on the same BFO thin film. Tip length shortening has strongly reduced IP artifacts as expected, while the impact of nonlocal electrostatic forces, becoming predominant for tips shorter than 1 \ensuremath{\mu}m, has led to a non-negligible deflection offset. For shorter tips, a strong electric field from a cantilever beam can induce polarization switching as observed for a 0.5-\ensuremath{\mu}m-long tip. Tip length ranging from 1 to 4 \ensuremath{\mu}m allowed minimizing both artifacts to probe unambiguously OP piezoresponse and quantify the ${d}_{33}$ piezoelectric coefficient.

Fully stressed design of beam cross-section: The analytical solution

In this paper, we find the exact form of the contour of a fully stressed double symmetrical beam cross-section, in the frame of strength of materials theory, and show that there exist two horizontal asymptotes, so that the cross-section contour is not a limited function but its area is finite.

Assumption tests regarding the ‘narrow’ rectangles dimensions of the open thin wall sections

Computer based analytic models that use the strength of materials theory are inheriting the accuracy given by the basic simplifying hypotheses. The according assumptions were rationally conceived hundreds of years ago in an age when there was no computing instrument, therefore the minimization of the necessary volume of calculi was an important requirement. An initial study was an attempt to evaluate how ‘thin’ may be the walls of an open section in order to have accurate results using the analytic calculus method. In this initial study there was compared the calculus of the rectangular sections loaded by twisting moments vs. a narrow section under the same load. Being compared analytic methods applied for a simple shape section, a more thorough study was required. In this way, we consider a thin wall open section loaded by a twisting moment, section which is discretized in ‘narrow’ rectangles. The ratio of the sides of the ‘narrow’ rectangles is the variable of the study. We compare the results of the finite element analysis to the results of the analytic method. The conclusions are important for the development of computer based analytic models which use parametrized sections for which different sets of calculus relations may be used.

A Statistical Theory of the Damage of Materials

A statistical theory of disperse damage of materials gained under loading is proposed. It is based on the idea of distribution of potential damage spots within a specimen similar to the distribution of the strength values found by testing a set of identical specimens. A relation between damage risk and the probability of damage of a single specimen is assumed. It conforms to the relation between risk and probability of strength distribution of a set of identical specimens, according to Weibull’s statistical theory of material strength. The damage risk just like the damage probability are assumed to be functions of loading and time. Damage is modeled regarding two mechanisms—thermo-fluctuation damage based on the kinetic theory of material strength, and damage depending on a parameter called loading degree (percentage), which depends on load and time. The first mechanism adopts two relations regarding energy barrier reduction due to loading. Equations of damage advance under short-term loading (with a constant rate of load increase) and under long-term (constant) loading are derived. Theoretical relations of damage development are compared with experimental evidence gained via specific tests on short glass fibre reinforced polyoximethylene. The damage itself consists of the accumulation of additional internal surfaces within the entire material volume as measured by small angle scattering X-ray refractometry. It is shown that the mechanism of damage as a function of loading degree where time participates implicitly, gains advantage over the kinetic mechanism where time is explicitly present. The cumulative functions derived for damage accumulation can be used to assess not only damage, but also for statistical analysis of the strength and other quantities.

The Thin Ice Layer Brittle Fracture Stress Model and de-icing Angle Optimization

Through the establishment of stress balance equation and analysis of stress status, de-icing model and brittle fracture model under the conditions of vertical scraping and tilt scraping are presented respectively. According to material strength theory, the thesis analyses necessary external force to eliminate ice layer and its influencing factors, and then gains energy consumption forecast formula of mechanical scraping deicing, which provides the basis for motor selection of ice-scraping mechanism. Conclusion shows that tilt scraping can greatly reduce deicing energy consumption, that the smallest scraping force and energy consumption are obtained with tilt angle of 40°.

Analysis of out-of-plane stresses in sandwich beams subjected to pure bending with large deflections

The classic strength of materials theory considers out-of-plane stresses in beams subjected to pure bending to be negligible. This work undertakes a theoretical analysis of this proposition by basing it on the development of the Airy’s functions in polar coordinates. The purpose of this research is studying the effect of this kind of stresses in structures fabricated with non-isotropic materials. Specifically, multi-component sandwich beams subjected to pure bending and large deflections have been studied. An analytical model is proposed that allows these out-of-plane stresses to be calculated according to the curvature change and other design parameters of the specific structure. The completed model was used to calculate the out-of-plane stresses for different design configurations, in order to study their effects. Finally, results are compared to a finite element model.

Initial deflection of silicon-on-insulator thin membrane micro-mirror and fabrication of varifocal mirror

Thin membranes fabricated from silicon-on-insulator (SOI) wafer are valuable for deformable mirrors. The mirror is controlled to generate a specific wave-front with precision smaller than a wavelength. Here, we investigate quantitatively the initial deflection of the thin membrane mirrors fabricated from SOI wafer, which are often used in micro-electro-mechanical systems. A 1-μm-thick and 450-μm-diameter mirror fabricated from SOI wafer deflects upward around the circumference at an angle of 0.12°. The maximum deflection of the mirror is 320 nm at the center. The stress conditions of the mirrors are analyzed on the basis of material strength theory. The deflection is explained by the residual stress of the buried oxide layer of SOI wafer. The in-plane stresses of the micro-mirrors of diameters from 450 μm to 860 μm range from compressive stress of 1.2 MPa to tensile stress of 2.1 MPa. Furthermore, based on the above experimental and theoretical analyses, a 1-μm-thick varifocal micro-mirror of the diameter of 400 μm is fabricated. The focus of the mirror is varied from −28 mm to 21 mm with the deviation smaller than 4 nm from parabola in the mirror central region.

Analytical calculation of stress intensity factor of cracked steel I-beams with experimental analysis and 3D digital image correlation measurements

An analytical method to calculate the stress intensity factor for cracked steel I-beams under both bending moment and axial load is presented. The method is based on the approach of crack surface widening energy release rate. The crack surface widening energy release rate is formulated by a G ∗-integral and elementary strength theory of materials. Comparisons between the analytical results and results available in the literature for specific cases demonstrate the validity of the methodology. Furthermore, the fatigue and fracture behavior of the steel I-beam are experimentally investigated. The fatigue crack growth rate, residual deflection and stiffness reduction of a cracked beam under cyclic loading are studied. A three-dimensional digital image correlation system is used to illustrate the stress evolution pattern and the plasticity zone around the crack tip using image processing technique, thereby providing further verification of the theoretical models.

Asymptotic analysis of laminated plates and shallow shells

It was noted long ago [1] that the material strength theory develops both by improving computational methods and by widening the physical foundations. In the present paper, we develop a computational technique based on asymptotic methods, first of all, on the homogenization method [2, 3]. A modification of the homogenization method for plates periodic in the horizontal projection was proposed in [4], where the bending of a homogeneous plate with periodically repeating inhomogeneities on its surface was studied. A more detailed asymptotic analysis of elastic plates periodic in the horizontal projection can be found, e.g., in [5, 6]. In [6], three asymptotic approximations were considered, local problems on the periodicity cell were obtained for them, and the solvability of these problems was proved. In [7], it was shown that the techniques developed for plates periodic in the horizontal projection can also be used for laminated plates. In [7], this was illustrated by an example of asymptotic analysis of an isotropic plate symmetric with respect to the midplane.

An Analytical Elasto-Creep Model of Solder Joints in Leadless Chip Resistors: Part 1—Development and Verification

A novel two-dimensional model is presented for multiaxial thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of solder joints in leadless chip resistor (LCR) assemblies. The model is applicable to both plane stress and plane strain conditions, and incorporates both global and local expansivity mismatches. Interfacial thermal stresses are approximated using elementary strength of materials theory under arbitrary time-dependent thermal loading. Partial differential equations are linearized through a simple finite difference discretization procedure. The model is mathematically straightforward, and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The paper presents comparisons with finite element results and considers the mechanics of solder creep accumulation and stress relaxation as predicted by the model.