Singular Loading Research Articles

Rate dependent C* fracture parameter using the optimized wedge-split test geometry and vision-based automated crack tip detection

Typical monotonic load-line displacement (LLD) control and crack mouth opening displacement (CMOD) control cracking tests are limited to singular loading rates and testing temperatures. These experimental protocols are not designed to derive a fundamental fracture parameter capable of relating to the viscoelastic property and cracking behavior of asphalt concrete (AC). On the other hand, a multi-rate LLD-control monotonic fracture experiment is capable of capturing the viscoelastic cracking behavior of AC by providing the rate-dependent fundamental C* fracture parameter as an output. Crack length and crack speed parameters are combined with reaction loads to calculate the rate-dependent C* parameter. The current C* experiment protocol implements manual processing of video images and exhibits high variability. The study aims to optimize the wedge-split geometry and improve the C* fracture parameter calculation protocol by applying an automated vision-based crack detection system and recording the crack growth path, considering the horizontal and vertical movement of the crack tip with higher accuracy. The three notch lengths (5, 15, and 30 mm) were evaluated. Plant and laboratory-produced mixes with varying stiffness and fracture characteristics were included in the testing program. An optimized notch length for the test geometry was determined based on the on-specimen strain field observed using the digital image correlation (DIC) technique and crack path analysis. The optimum notch length was found to be 15 mm due to consistent strain localization at the crack tip and less crack deviation in the horizontal direction. The main contribution of this paper is the proposed vision-based crack path detection method, which enables measuring the crack path's true crack length and maximum horizontal deviation. The developed protocol and optimization of the testing geometry led to a significant improvement of the existing C* testing protocol, resulting in higher data quality and consistent results. The proposed protocol was validated using three comparable and distinctively different lab-produced mixtures. The results show that the C* experiment effectively differentiated between the mixes based on crack speed and the C* parameter.

Large Deflection Analysis of Functionally Graded Beam by Using Combining Method

In this study, the large deflection behavior of a circular cross-section beam is examined using the Combining Method (CM). The CM is a numerical solution method that uses block diagrams in the Matlab-Simulink program and weighting coefficients in the Differential Quadrature Method (DQM). The beam material considered is Functionally Graded Material (FGM). Boundary conditions of the beam are taken as clamped-free (C-F) and a singular load is assumed to be applied from the free end of the beam. Geometric nonlinear analysis is performed while calculating the large deflection equations of the beam and performing numerical analysis. The effects of increasing the force applied to the beam, changing the beam cross-section in the longitudinal direction, and changing the material index of the FGM on the extreme deflection behavior of the beam were examined. For comparison purposes, the results obtained from CM are compared with the results obtained from both SolidWorks-Simulation and Ansys-Workbench programs. As a result of the analysis, increasing the applied force causes the x and y coordinates of the end point of the beam to decrease. The change in geometry and material index greatly affects the large deflection occurring in the beam.

Transverse Vibration Analysis of a Self-Excited Beam Subjected to Delayed Distributed and a Singular Load Using Differential Transformation Method

Transverse Vibration Analysis of a Self-Excited Beam Subjected to Delayed Distributed and a Singular Load Using Differential Transformation Method

Design and Calibration of an Instrumented Seat Post to Measure Sitting Loads while Cycling.

Traditional instrumented seat posts determine context-induced seat loads to analyze damping properties. This paper presents an enhanced instrumented seat post able to measure all six load components to resolve user-induced seat loads. User-induced cycling loads consist of all loads the user applies to the bicycle during cycling and is measured at the steer stem, the seat post, and the pedals. Seat loads are essentially uncharted territory, as most studies only address pedal loading to study cycling technique. In this paper, a conventional seat post is redesigned by equipping it with a u-shaped component and strain gauges. The instrumented seat post is straightforward thanks to (i) the simple design, (ii) the gravitational calibration method, and (iii) the permitted clearance on the strain gauge alignment. Analyzing mean seat loading in function of the pedal cycle can provide extra insights into cycling technique and the related injuries. It is an interesting addition to the universally adopted method of utilizing singular pedal loads.

Modeling and Control of Methanol Engine Speed with GT-Power and Simulink

With a 4-cylinder methanol engine as the research object, GT-Power was used to build a one-dimensional simulation model for the methanol engine and verify its accuracy. The PID and fuzzy PID control models were built based on MATLAB/Simulink, and the methanol engine model was coupled with the control models. The speed control effects of the methanol engine under different control strategies were compared and analyzed. The results showed that traditional PID control method could meet the control requirements under a singular load, but the overshoot of the engine speed step response curve under fuzzy PID control was decreased by about 12% compared with traditional PID controls methods, also showing significantly lower speed fluctuations. When the working conditions of the engine changed, the fuzzy PID control method had better engine speed control performancethe than the traditional PID control method.

The Effects of Loading Frequency, Sensitization, and Crack Length on Corrosion Fatigue of AA5456-H116

The effects of fatigue loading frequency (f), sensitization, and crack length on corrosion fatigue crack growth rates (da/dN) were investigated for AA5456-H116 under full immersion in 3.5 wt% NaCl. Results from fracture mechanics-based experiments conducted at a constant stress-intensity range (ΔK) and load ratio (R) suggest that highly sensitized AA5456-H116 microstructures (ASTM G67 nitric acid mass loss tests [NAMLT] value of 24 mg/cm2 and higher) exhibit increased da/dN over microstructures in the as-received condition (NAMLT 5 mg/cm2) and the onset of an inverse f-dependence. For a single, high level of sensitization (70 mg/cm2), da/dN increased 3.5× as f decreased from 10 Hz to 0.03 Hz. At a singular low loading f of 0.03 Hz, high sensitization levels (65 mg/cm2) accelerated da/dN fivefold over da/dN in the as-received condition. The da/dN of microstructures below a critical NAMLT value of 24 mg/cm2 were f-independent. Specifically, in microstructures with a low sensitization level (ASTM G67 NAMLT value less than 24 mg/cm2), there was no increase in da/dN as f decreased from 1 Hz to 0.03 Hz. At any singular f, sensitization up to 24 mg/cm2 did not accelerate da/dN over the rate in an as-received microstructure. Additional testing established that the inverse f-dependence of da/dN observed in highly sensitized microstructures cannot be attributed to crack length effects. Two hypotheses are discussed that may explain the observed inverse relationship between f and da/dN in microstructures at or above the critical NAMLT value of 24 mg/cm2.

Relationship between green's functions of tangential contact and crack problems for generally anisotropic bodies

It was proved by the author [5] that in the case of normal contact and crack problems for anisotropic bodies the kernels of the integral transforms of the responses to the singular loadings are inverse to one another. It does not look like this property was previously noticed by other authors. The case of the relationship between tangential contact and crack problems is obviously more complicated and deserves a separate investigation. Such relationship is established here. Several particular cases of anisotropy are considered as illustrative examples. It is also shown that the kernels of the governing integral equations can be computed exactly, using the theory of generalized functions.

Vibration of the bridge under moving singular loads - theoretical formulation and numerical solution

The paper presents the results of the numerical analysis of a simple vehicle passing over a simply supported bridge span. The bridge is modelled by a Euler-Bernoulli beam. The vehicle is modelled as a linear, visco-elastic oscillator, moving at a constant speed. The system is described by a set of differential equations of motion and solved numerically using the Runge-Kutta algorithm. The results are compared with the solution obtained in commercial FEM software using the Newmark method. The parameters of the system are taken from the existing bridge span and from the existing railway vehicle. Simulations are also performed with a concentrated force model of the vehicle.

On the Advantages of the Theories of Plasticity with Singular Loading Surface

This paper analyzes the peculiarities of plastic flow of metals for the case of non-proportional loading when the loading path consists of two portions—uniaxial tension and subsequent infinitesimal pure shear (torsion). The issue is discussed from the point of view of the hardening rules governing the kinetics of loading surface. Three cases are considered, flow plasticity theory with isotropic and kinematic hardening rule, as well as the synthetic theory of plastic deformation. As a result, the synthetic theory leads to the results that correlate with experiments, whereas the former two theories associated with smooth loading surfaces give a principal discrepancy with experimental data.

Analysis of partially embedded beams in two-parameter foundation

In this study, Pasternak foundation model, which is a two parameter foundation model, is used to analyze the behavior of laterally loaded beams embedded in semi-infinite media. Total potential energy variation of the system is written to formulate the problem that yielded the required field equations and the boundary conditions. Shear force discontinuities are exposed within the boundary conditions by variational method and are validated by photo elastic experiments. Exact solution of the deflection of the beam is obtained. Both foundation parameters are obtained by self calibration for this particular problem and loading type in this study. It is shown that, like the first parameter k, the second foundation parameter G also depends not only on the material type but also on the geometry and the loading type of the system. On the other hand, surface deflection of the semi infinite media under singular loading is obtained and another method is proposed to determine the foundation parameters using the solution of this problem.

On methods for the solution of integral equations of the theory of plasticity based on the concept of slip

We have proposed a modification of the methods for solving the system of integral equations [M. Ya. Leonov and N. Yu. Shvaiko, “Complex plane deformation,” Dokl. Akad. Nauk SSSR, 159, No. 2, 1007–1010 (1964); N. Yu. Shvaiko, “On the theory of slip with smooth and singular loading surfaces,” Mat. Metody Fiz.-Mekh. Polya, 48, No. 3, 129–137 (2005)]. These equations describe the development of plane plastic deformation for simple and complex loading processes. A characteristic feature of these equations lies in the presence of unknown functions both under the integral sign and in the integration limits. We have written analytical solutions for monotone deformation and in a small neighborhood of an angular point of the loading trajectory. For arbitrary piecewise smooth trajectories, we have reduced this problem to the Cauchy problem for a first-order differential equation with known initial conditions. The results obtained simplify significantly the construction of constitutive equations $ {\dot{\sigma }_{mn}} \sim {\dot{\varepsilon }_{mn}} $ and their use in applied problems of the theory of plasticity as compared with [N. Yu. Shvaiko, “On the theory of slip with smooth and singular loading surfaces,” Mat. Metody Fiz.-Mekh. Polya, 48, No. 3, 129–137 (2005); N. Yu. Shvaiko, Complex Loading and Problems of Stability [in Russian], Izd. DGU, Dnepropetrovsk (1989)].

Stress concentration analysis of interfacial micro-structural cracks under internal singular loading sources

Common characteristic of the structure of the crystalic or amorphous materials is the existence of micro-cracks. Reasons of the existence of micro-cracks are (a) the chemical composition of the material, (b) the kinetic mechanisms of the atoms or grains or atomic chains or dislocations or other structural elements during the solidification or forming or loading of a macroscopic material part. The dramatic effect of sub-critical crack growth on the mechanical integrity of structures was clearly brought to light by the often structural failures. As the micro-crack growth is the result of atomic bonds de-boding, the understanding of mechanisms and analysis of cracks is a useful tool for the chemistry to improve the chemical composition and the resulted micro-structure of materials in order to achieve better macroscopic fracture toughness. Due to the progress of the nanomechanics and the microelectronics, it is recognized today that the existence and growth of micro-cracks in the interface between thin layers such as thin films in electronic devices, sensors and actuators in smart materials or ceramic coating in machine components for wear or corrosion resistance, cause changes in the prescribed material properties and reduction of the material quality. In the present work, a mathematical analysis to determine the stress concentration areas in order strong particles to be inserted there (using chemical methods) for the material strengthening is attempted. To this scope, the equations describing the stress fields around interfacial micro-cracks in materials under internal singular loading sources are formulated. Numerical examples are included.

Singular layers for transmission problems in thin shallow shell theory: Rigid junction case

In this Note we study two-dimensional transmission problems for the linear Koiter's model of an elastic multi-structure composed of two thin shallow shells. This work enters in the framework of singular perturbation of problems depending on a small parameter ε. The formal limit problem fails to give a solution satisfying all boundary and transmission conditions; it gives only the outer solution. Both in the case of regular or singular loadings, we derive a limit problem which allows us to determine the inner solution explicitly.

Bridging Methods for Atomistic-to-Continuum Coupling and Their Implementation

Several issues connected with bridgingmethods for atomistic-to-continuum (AtC) coupling are examined. Different coupling approaches using various energy blending models are studied as well as the influence that model parameters, blending functions, and grids have on simulation results. We use the Lagrange multiplier method for enforcing constraints on the atomistic and continuum displacements in the bridge region. We also show that continuum models are not appropriate for dealing with problems with singular loads, whereas AtC bridging methods yield correct results, thus justifying the need for a multiscale method. We investigate models that involve multiple-neighbor interactions in the atomistic region, particularly focusing on a comparison of several approaches for dealing with Dirichlet boundary conditions. AMS subject classifications: 74B05, 74G65, 74S30, 74S05, 70-08, 70C20 PACS: 46.15.-x, 02.70.Ns, 02.70.-c, 46.25.-y, 02.70.Dh

Beam on viscoelastic foundation: an extension of Winkler’s model

Models in the field of Applied Mechanics originate less from thought experiments but rather from technical problems. So does the so-called Winkler model: elastic beam on deformable foundation. It stems from the then (1870) High Technology the railway system. The question was: What is the stress state in a continuously bedded beam, the sleeper, loaded by singular rail loads? Winkler came up with a convincing closed form solution by linearising the behaviour of the subgrade which consists of a compressed layer of stones. The Winkler model is time-independent. The extension is to make the subgrade time dependent, in the simplest case to make it viscous. This also applies to the problem of a wheel set consisting of a beam ring, a rigid disc, and in between a pre-stressed rubber sheet. Such wheel sets are or have been in use in nowadays tram and railway systems. In this paper an analysis of such a rotating wheel set under a singular load is given. It is shown that the stress state in the ring beam depending on rotational speed decreases linearly with increasing rotational speed.

Dynamic response of a circular plate to a moving load

An analytical series solution for the dynamic response of a circular, thin, isotropic plate under a moving singular load is given. The mass of the agent applying the force is ignored. The response of the plate is computed in two example cases, to illustrate the solution, including the force moving on a straight line through the plate, and also for a load moving on a circular trajectory on the plate.

Comparison of Stress Distributions of Dental Woven and Unidirectional Fiber-Reinforced Composite Crowns Under Different Loadings

The aim of this numerical study was to investigate and compare the stresses occurring in dental woven and unidirectional experimental fiber-reinforced composite (FRC) crowns under different thermal and singular force loading conditions. For this reason, finite element models of FRC crown and tooth systems were performed by using the ANSYS program. Stress analyses of the models were carried out under thermal loading conditions heated from 37 to 55°C, cooled from 37 to 5°C, and 450 N singular force loading conditions at different angles. The results indicated that high stresses occurred in both woven and unidirectional FRC crowns under horizontal loadings because of bending moment. Thermal stresses exhibited small values that did not cause any damage. It can also be concluded that since the stress component of σ z in the woven type FRC was smaller than that of unidirectional type FRC, use of the woven FRC might be beneficial in comparison with the unidirectional composite.

Comparative analysis of the theories of sliding with regular and singular loaded surfaces

We study the possibility of application of the versions of the theory of sliding [1] with regular and singular loading surfaces (Σ) under complex loads in the form of two-link paths and establish the relationships between the stress \((\dot \sigma _{ij} )\) and strain rates \((\dot \varepsilon _{ij} )\) in a small neighborhood of an angular point in the loading path. The advantages of the theory of sliding with singular surfaces are discussed and the impossibility of application of the theories of plastic flow with regular surfaces to the solution of the problems of stability of structural elements is demonstrated. However, their application to the solution of boundary-value problems of determination of the total strains can be reasonable.

Influence functions of the displacement discontinuity method for anisotropic bodies

In this study, the boundary element equations are obtained from the influence functions of a displacement discontinuity in an anisotropic elastic medium. For this purpose, Kelvin fundamental solutions for anisotropic media on infinite and semi-infinite planes are used to form dipoles from singular loads. Various combinations of these dipoles are used to obtain the influence functions of the displacement discontinuity. Boundary element equations are then derived analytically by the integration of these influence functions on a constant element which results in a linear system for unknown displacement discontinuities. The boundary integrals are calculated in closed form over constant elements. The obtained formulation is applied to a number of classical engineering problems.

各種特異項荷重下での多層だ円形介在物を有する横等方性圧電弾性体の解析理論

Piezoelectric materials are widely used in industrial areas from the excellent characteristic of mechanical and electrical couplings such as the sensors and actuators. On the other hands, cavities, inclusions, and dislocations in the materials affect fracture and strength of materials. So it is important to analyze mechanical and electrical fields around these defects. In this paper, two-dimensional electro elastic analysis is performed for transversely isotropic piezoelectric materials containing multilayered elliptical inclusion under several singular loads. General solutions of this study are obtained by using the complex potential functions and conformal mapping technique. And several numerical examples are shown by graphical representation. The effects of some condition of singular loads are discussed.