Linear Stress Distribution Research Articles

Fatigue strength assessment of aluminium welded joints under variable amplitude loading using the Peak Stress Method

One of the simplest and most efficient ways to design lightweight structural components is the combination of welding and aluminum alloys. However, welded joints are extremely sensitive to fatigue failure and making accurate lifetime predictions is still challenging when Variable Amplitude (VA) loading conditions are involved. Among all design criteria available in the literature, the present investigation focuses on the Peak Stress Method (PSM), an engineering finite element (FE)-based approach to rapidly assess the fatigue strength of welded joints. In more detail, the PSM suggests modelling both weld toe and weld root as sharp V-notches having null tip radius and correlates their fatigue strength using the intensity of the local linear elastic asymptotic stress distributions described by the Notch Stress Intensity Factors (NSIFs). The theoretical formulation of the PSM for the fatigue strength assessment of welded joints subjected to VA loadings has been recently proposed by combining its Constant Amplitude (CA) formulation with the Palmgren-Miner's cumulative linear damage rule. Such VA formulation has been successfully validated against a large bulk of experimental fatigue results generated by testing welded joints made of structural steels under uniaxial as well as multiaxial loadings. In the present investigation, the VA formulation of the PSM has been further validated against experimental data relevant to welded joints made of aluminium alloy under VA loadings.

Probabilistic finite element analysis of failures in concrete dams with large asperities in the rock–concrete interface

Common analytical assessment methods for concrete dams are unlikely to predict material fracture in the dam body because of the assumption of rigid body behavior and uniform- or linear stress distribution along a predetermined failure surface. Hence, probabilistic non-linear finite element analysis, calibrated from scale model tests, was implemented in this study to investigate the impact of concrete material parameters (modulus of elasticity, tensile strength, compressive strength, fracture energy) on the ultimate capacity of scaled model dams. The investigated dam section has two types of large asperities, located near the downstream and/or upstream end of the rock–concrete interface. These large-scale asperities significantly increased the interface roughness. Post-processing of the numerical simulations showed interlocking between the buttress and the downstream asperity leading to fracture of the buttress with the capacity being determined mainly by the tensile strength of the buttress material. The capacity of a model with an asperity near the upstream side, with lower inclination, was less dependent on the material parameters of the buttress as failure occurred by sliding along the interface, even with inferior material parameters. Results of this study show that material parameters of the concrete in a dam body can govern the load capacity of the dam granted that significant geometrical variations in the rock–concrete interface exists. The material parameters of the dam body and their impact on the capacity with respect to the failure mechanism that developed for some of the studied models are not commonly considered to be decisive for the load capacity. Also, no analytical assessment method for this type of failure exists. This implies that common assessment methods may misjudge the capacity and important parameters for certain failure types that may develop in dams.

Solution of a Multiple Crack Problem under the Influence of a Linear Stress Distribution and Coalesced Yield Zones

Solution of a Multiple Crack Problem under the Influence of a Linear Stress Distribution and Coalesced Yield Zones

A three-phase anisotropic elastic elliptical inhomogeneity with internal linear stress and strain distributions

A three-phase anisotropic elastic elliptical inhomogeneity with internal linear stress and strain distributions

Numerical and analytical solutions for describing the mechanical response of segment joints for tunnels

In literature there are several analytical models for describing the mechanical behavior of non-bolted segment joints (longitudinal joints) of shield driven tunnels. These joints modify the structural response of the segmental lining and therefore they affect the global response of this kind of tunnels. The rotational stiffness of these joints is divided into linear and multi-linear models being two typical moment-rotation constitutive equations those exposed by Janssen and Gladwell. The first one considers a linear stress distribution in the longitudinal joint. However, this is not correct according to elasticity theory due to at the edge of the contact area stresses reach infinite values and non-linear stress distributions are produced at the joint. The second typical moment-rotation equation is based on elasticity theory. The analytical results obtained from these moment-rotation equations were compared to numerical results of a 3D model based on Finite Element Method (FEM) using isoparametric solid elements for modeling the concrete segments, whilst for simulating the joint were incorporated contact elements; achieving to confirm that the constitutive equation proposed by Gladwell provides results more precise of the mechanical response of these joints achieving a difference of 0.07% in the maximum capacity of bending moment between the analytical model proposed by Gladwell and 3D numerical model carried out in this study.

Improved Shear-Lag Analytical Model for Mixed Adhesive Double Lap Joint

In the present work, the improved shear-lag model based on a linear shear stress distribution in the substrates' thickness of a mixed-adhesive double-lap joint (MADLJ) has been developed to establish the shear stress profile along the joint length. A closed-form solution has been obtained and numerically validated by a 2D finite element simulation carried out on ABAQUS CAE commercial software. The analytical model has been then employed to conduct a parametric study where the influences of the stiff and soft adhesives Young moduli, their lengths as well as the joint's thickness on the maximum shear stress in the joint have been examined, and this for seven different substrate's thicknesses. Many key values of those parameters defining the transition of maximum shear stress from stiff to a soft region or defining an optimum stress or a limit value where the pure joint becomes advantageous along with their evolution with the adherents' thicknesses have been determined.

Flexural Resistance Factors for Structural Ultra Lightweight Engineered Cementitious Composite Slabs

Many problems associated with the use of normal weight concrete have been solved with the development of structural ultra-lightweight engineered cementitious composite (SULWECC) that has the capability to exhibit strain-hardening behavior prior to failure. However, the feasibility and standards that address the design of such engineered cementitious composites (ECC) in flexural slab systems are not available. In this study, reliability analysis and calibration process are carried out on three different SULWECC slab systems with the intention of estimating the potential flexural resistance factors. Although the high volume of randomly dispersed synthetic short fiber is considered the main reinforcement, SULWECC slab systems internally reinforced with carbon FRP mesh are also considered. The reinforcement ratio is selected so that the section is under-reinforced. Relevant load and resistance random variables are used, and appropriate statistical parameters are selected. The target reliability indices are chosen to be consistent with those used to develop current design code specifications. The nominal moment capacity is calculated based on a new model that consists of: elastic linear stress distribution in the compression zone and elastic-perfectly-plastic uniform stress distribution in the tension zone. The determined flexural resistance factors ranged from 0.59 to 0.69, although higher values are justifiable in special circumstances. The average slab thickness needed to satisfy the strength requirements ranged from 1/37 to 1/22 times the slab length. Flexural toughness to measure ductility is evaluated using load-deflection curves of experimentally tested SULWECC specimens.

Determination of complex stress intensity factors for interface cracks in bi-material specimens subjected to ununiform stresses

This paper presents the calculation of complex stress intensity factors (K) for interface cracks in commonly used bi-material specimens subjected to arbitrary ununiform stress fields. First, detailed finite element analyses were carried out for cracks in centre-cracked plate (CCP) and single edge-cracked plate (SECP) bi-material specimens of different material combinations under non-uniform stress distributions. The complex SIFs were determined for the loading cases of uniform, linear, parabolic or cubic stress distributions applied to the crack faces in both normal and shear directions. Then, general mathematical forms of the two complex crack face weight functions for interface cracks, one for normal loading, and one for shear loading, have been formulated by taking advantages of the knowledge of specific analytical complex weight functions available in the literature, and certain properties of the complex weight functions in general. The existence of the general functional forms simplifies the determination of these weight functions for specific crack geometrical configurations and bi-material combinations. The determination of a specific weight function is thus reduced to the determination of the unknown parameters of the generalized weight function functional forms. It was demonstrated these unknown parameters can be determined from reference stress intensity factors. This method was used to derive the complex weight functions for interface cracks in bi-material CCP and SECP specimens. The derived closed-form weight functions were then validated against complex stress intensity factors solutions for several non-linear normal and shear stress distributions.

Method of calculating the electric strength of oil channels of the main insulation of power transformers

The most damage-sensitive unit of power transformers is the main insulation of the oil barrier type. The breakdown of such insulation occurs as a result of the breakdown of the oil channel near the high voltage winding. In accordance with traditional methods of calculating the dielectric strength of insulation, the value of the breakdown strength is determined by empirical formulas depending on the selected width of the oil channel. The existing methods do not consider the influence of the oil channel volume, of the electric strength the statistical characteristics of the oil, the design features of the insulation of power transformers, and do not contain recommendations for creating design models. Thus, to improve the calculation accuracy, it is relevant to develop the evaluation method of dielectric strength of the main insulation of power transformers taking into account the volume and parameters of the breakdown voltage distribution of transformer oil, design features. The research results of the breakdown tension in oil channels with different volumes of transformer oil were used. To improve the accuracy of the calculation and taking into account the design features, the model of the main insulation of power transformers was made in the ANSYS program. Boundary data and assumption of linear stress distribution of transformer coils were considered. A method for calculating the dielectric strength of oil channels of the main insulation of power transformers, considering the volume and parameters of the breakdown voltage distribution of transformer oil was proposed. Unlike the existing methods, when calculating the minimum breakdown strength in the model of the main insulation, the design features of power transformers are taken into account and assumptions are justified to improve the accuracy of the calculation. In accordance with the methodology, the parameters of the dielectric strength of the transformer oil in the oil channel of the high voltage winding of the transformer were calculated. It was concluded that with increase of relative value of breakdown tension, dielectric strength of oil channel is decreasing, and it corresponds to physical sense of breakdown. The method for calculating the dielectric strength of transformer oil can be used when choosing the main insulation of power transformers in design.

2D weight functions of stress intensity factors for high aspect ratio semi-elliptical surface cracks in finite thickness plate

This paper presents the application of the weight function method for calculating the stress intensity factors for high aspect ratio semi-elliptical surface cracks in finite thickness plate subjected to arbitrary two-dimensional stress fields. Based on the formulation initially proposed by Wang and Glinka (2009), an extended 2D weight function for surface cracks with aspect ratio 1.0 ≤ a/c ≤ 8.0 is developed. The unknown coefficients in the formulation can be determined from reference stress intensity factors which are obtained by finite element analysis with the J-integral method. The effectiveness of the proposed weight functions have been verified by comparing the stress intensity factors available in the literatures and those obtained from FEM for several linear and nonlinear two-dimensional stress distributions, indicating a good accuracy. The present results complement the application range of 2D weight functions for low-aspect-ratio cracks, 0.0 < a/c ≤ 1.0, developed by the previous researchers.

Size effect on double-K fracture parameters of concrete based on fracture extreme theory

Based on fracture extreme theory (FET), the size effect on initial fracture toughness $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and unstable fracture toughness $$K_{\mathrm{I}}^{\mathrm{un}}$$ of concrete for three-point bending beam was investigated. Nine groups of geometrically similar specimen were simulated to obtain peak load and critical crack mouth opening displacement, of which specimen depth was from 200 to 1000 mm and initial crack length-to-depth ratios were from 0.1 to 0.6. The $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ were calculated by FET and double-K method, in which FET adopted the linear, bilinear, and trilinear cohesive stress distribution assumptions and double-K method only used the linear cohesive stress distribution assumption. With linear cohesive stress distribution assumption, $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ determined by FET and double- K method were compared. Then, the influence of specimen depth on $$K_{\mathrm{I}}^{\mathrm{ini}}$$ and $$K_{\mathrm{I}}^{\mathrm{un}}$$ was discussed. In addition, $$K_{\mathrm{I}}^{\mathrm{ini}}/K_{\mathrm{I}}^{\mathrm{un}}$$ calculated via FET using different cohesive stress distribution assumptions were analyzed.

Buckling of a clamped strip‐like beam with a linear pre‐stress distribution

AbstractA thin linear elastic strip is clamped at both ends and subjected to a linear stress distribution across its width. We use Kirchhoff beam theory to study this problem. If displacements out of the strips own plane are prohibited, the straight configuration remains stable as long as the compression is not too high. With the three‐dimensional spatial description of the rod theory, we find possible buckling modes even in the case of average tensile stresses in the beam. Comparison with shell and beam finite elements shows excellent agreement with the analytical investigation, also with respect to the supercritical behavior.

Behaviour of 690 MPa high strength steel built-up H-section columns under eccentric load scenarios

A numerical investigation on built-up columns fabricated from high strength steel (HSS) plates with nominal yield stress of 690 MPa is described in this paper. The benchmark models are initially created and validated against the test data and after that a full-scale parametric study (432 models) is organized. The effect of the ratio of flange width to thickness (α), the ratio of web height to thickness (β), initial lateral imperfection (D), residual stress distribution pattern (R) and eccentricities along strong and weak axes (ex and ey) on strength and behaviour of the built-up HSS columns is investigated and analysed. It is found that the normalized bearing capacity of the columns (χ) positively relates with α. Higher α value would produce higher χ. With given β and flange thickness tf, higher α would enhance restriction effect of the flange on the web and delay occurrence of local buckling of the web. However, χ increases with rise of α at different growth rates. β could produce smooth negative effect on χ and the column load bearing capacity decreases smoothly with the increase of β. Two residual stress distribution patterns (linear and quadratic distribution) are compared. It is found that linear residual stress distribution model would produce more conservative column strength. The eccentricity along the strong axis direction has more significant impact on column load bearing capacity than along the weak axis direction. The envelope diagram analysis for normalized axial load and normalized bending moment is organized and analysed.

Topology Optimisation of Engine Cross Members for Lightweight Structure in Light Commercial Vehicles

Topology and topography optimisations of engine cross members that were produced from sheet metal are presented. The Hyper Mesh, Opti-Struct, and Hyper-View tools in the Hyper Works software package, which is programmed by the Altair Company, were utilised in the analyses. For this purpose, two designs, software-based design optimisation (SBDOP) and expert-based design optimisation (EBDOP), were created using the trial-and-error method. The methods were compared and contrasted to the baseline in terms of the equivalent static and dynamic stiffness under both translational and rotational conditions and in terms of the linear stress distribution. In the final stage, the production design was created to conduct manufacturability analyses. Consequently, it was observed that with the use of optimisation software and tools, SBDOP can provide significant improvements in terms of time and functionality. Without violating the performance targets, such as the static and dynamic stiffness and stress distribution expected by the related OEM, the mass was reduced, and 12% improvements in weight were obtained.

Fatigue strength capacity of load-carrying fillet welds on ultra-high-strength steel plates subjected to out-of-plane bending

Weld root fatigue strength capacity is an important design criterion in load-carrying (LC) fillet welded joints subjected to cyclic loads. This paper elaborates on the weld root fatigue strength capacity of fillet welded LC joints made of ultra-high-strength steel (UHSS) and subjected to out-of-plane bending. Experimental fatigue tests are carried out using constant amplitude loading with an applied stress ratio of R = 0.1 with both pure axial, i.e. DOB = 0 (degree of bending, bending stress divided by total stress) and bending, i.e. DOB = 1.0, load conditions. The applicability of different approaches – nominal weld stress, effective notch stress concepts, and 2D linear elastic fracture mechanics (LEFM) – for the fatigue strength assessment of weld root capacity is evaluated. Furthermore, a parametric LEFM analysis is used to evaluate the effect of weld penetration on the root fatigue strength capacity in axial and bending loading. The results indicate that in the case of bending, nominal weld stress can be calculated using the linear stress distribution over the joint section and FAT36 as a reference curve. In the bending loading, for the joints failing from the weld toe, a mean fatigue strength of up to 185 MPa in the nominal stress system was achieved, indicating that the reference curve FAT63 is overly conservative. The ENS concept with FAT225 seemed to be slightly unconservative for assessing the root fatigue strength capacity. LEFM analyses revealed that in the case of increasing weld penetration and bending loading, weld root fatigue strength capacity seemed to correlate with the nominal weld stress calculated using effective weld throat thickness, while in axial loading, weld stress should be calculated using external throat thickness summed with penetration length.

Numerical test for the Neumann problem of interior BVP of plane elasticity

Following the concept of the patch test in FEM (finite element method), several numerical tests are suggested for the Neumann problem of interior BVP (boundary value problem) of plane elasticity by using different techniques. We choose the elliptic plate as an object in the test. Along the boundary of the plate, two groups of boundary traction are assumed. The first group is derived from the constant stress solution (or constant strain solution), and the second group is derived from the linear stress distribution. From displacement solution, we can evaluate the normal peripheral stress along the boundary, which is compared with the result from an exact solution. In addition, several error estimation factors are defined to evaluate the achieved accuracy. Extensive numerical examples and computed results are provided.

Investigation on the Resonant Oscillations in an 11 kV Distribution Transformer under Standard and Chopped Lightning Impulse Overvoltages with Different Shield Placement Configurations

This paper presents an investigation on the resonant oscillations of an 11 kV layer-type winding transformer under standard and chopped lightning impulse overvoltage conditions based on calculated parameters. The resistances, inductances and capacitances were calculated in order to develop the transformer winding equivalent circuit. The impulse overvoltages were applied to the high voltage (HV) winding and the resonant oscillations were simulated for each of the layers based on different electrostatic shield placement configurations. It is found that the placement of grounded shields between layer 13 and layer 14 results in the highest resonant oscillation and non-linear initial voltage distribution. The oscillation and linear stress distributions are at the lowest for shield placement between the HV and low voltage (LV) windings.

Numerical and experimental investigation on thermal expansion of UO2-5 vol% Mo microcell pellet for qualitative comparison to UO2 pellet

Thermally conductive microcell UO2 pellets in which metallic networks enclose UO2 granules have been highlighted due to their enhanced thermal performance for a potential candidate of accident-tolerant fuels. However, studies on thermal expansion effects of microcell UO2 pellets are still lacking. Here, stress and strain distributions of the fabricated UO2-5 vol% Mo microcell pellet under thermal expansion were investigated. After we confirmed that the numerical results agreed well with experimental measurement in terms of linear thermal expansion, stress and strain distributions of the microcell pellets were calculated under maximum stress and maximum strain conditions. As a result, formation of Mo network decreases the maximum hoop stress and the maximum radial strain of UO2 pellets by 50.9% and by 29.4%, respectively under a linear heat generation rate of 200 W/cm. Finally, the UO2-5 vol% Mo microcell pellet can decrease the maximum cladding stresses by 36.7%.

On the link between fracture toughness, tensile strength, and fracture process zone in anisotropic rocks

This paper presents experimental results on the anisotropy of the fracture toughness, Brazilian tensile strength, and the fracture process zone (FPZ) in granodiorite samples. The fracture toughness is measured using semi-circular bending tests, while Brazilian disk tests were conducted to measure the tensile strength indirectly. Digital image correlation (DIC) was employed to obtain full-field surface deformation associated with the fracture propagation and identify the FPZ. An averaging scheme is proposed to determine the length and width of the FPZ from the strain field. The DIC results confirm a semi-elliptical FPZ developing ahead of the crack tip, with an average length-to-width ratio of approximately two. The results also indicate that the theoretical models such as Irwin and strip-yield with uniform traction, which are based on plastic deformation near the crack tip, underestimate the extent of the inelastic zone, while the strip-yield model with a linear cohesion stress distribution overestimate the length of the process zone. The anisotropy ratio of the FPZ length obtained from the models, however, agrees very well with the ratio obtained from the DIC measurements. This evidence supports the basis of the theoretical models that predict the FPZ length to be proportional to the square of fracture toughness over tensile strength.

A novel pseudo-grain approach for the estimation of the elastic stress distributions within the matrix of short fiber-reinforced polymers

Abstract The aim of the work is to provide a new methodology for the calculation of the linear elastic stress distributions within the matrix of a short fiber-reinforced Representative Volume Element (RVE) with misaligned fibers, without relying on complex algorithms for the generation and solution of the microstructure. For this purpose, a Pseudo-Grain approach is adopted, the novelty of which lies in the computation of local stress distributions through the analytical combination of numerical solutions from unidirectional (UD) grains that can be easily and quickly solved through commercial codes. The new approach consists in two steps: i) the application of Voigt boundary conditions to Finite Element (FE) models (grains) with fully aligned fibers and ii) the mathematical combination of the computed Stress Cumulative Distribution Functions (S-CDF) on the basis of the second-order Fiber Orientation Tensor (FOT) of the microstructure of interest. The latter can be generally derived from process simulations or experimental analyses. The method is validated by comparing the resulting stress fields with those calculated from actual RVEs with different fiber volume fractions, fiber aspect ratios and Fiber Orientation Tensors, showing a very good agreement.