Strain-based Approach Research Articles

Modelling the scatter of E–N curves using a serial hybrid neural network

If structural reliability is estimated by following a strain-based approach, a material’s strength should be represented by the scatter of the e–N (E–N) curves that link the strain amplitude with the corresponding statistical distribution of the number of cycles-to-failure. The basic shape of the e–N curve is usually modelled by the Coffin–Manson relationship. If a loading mean level also needs to be considered, the original Coffin–Manson relationship is modified to account for the non-zero mean level of the loading, which can be achieved by using a Smith–Watson–Topper modification of the original Coffin–Manson relationship. In this paper, a methodology for estimating the dependence of the statistical distribution of the number of cycles-to-failure on the Smith–Watson–Topper modification is presented. The statistical distribution of the number of cycles-to-failure was modelled with a two-parametric Weibull probability density function. The core of the presented methodology is represented by a multilayer perceptron neural network combined with the Weibull probability density function using a size parameter that follows the Smith–Watson–Topper analytical model. The article presents the theoretical background of the methodology and its application in the case of experimental fatigue data. The results show that it is possible to model e–N curves and their scatter for different influential parameters, such as the specimen’s diameter and the testing temperature.

Fatigue life prediction of friction stir spot welds based on cyclic strain range with hardness distribution and finite element analysis

The main aim of the present study is to investigate the fatigue behavior of single friction stir spot welds (FSSW) using strain-based modified Morrow’s damage equation. The correlation between microhardness, cyclic material constants, and mechanical strength of different zones around the FSSW are assumed to be proportional to the base material hardness. Experimental fatigue tests of friction stir spot welded specimens have been carried out using a constant amplitude load control servo-hydraulic fatigue testing machine. ANSYS finite element code has been used to simulate a single tensile shear friction stir spot welded joint, and non-linear elastic-plastic finite element analysis has been employed to obtain the values of local equivalent stress and strain near the notch roots of the joints. The results based on the numerical predictions have been compared with the experimental fatigue test data. It has been shown that the strain-based approach does a very good job for estimating the fatigue life of friction stir spot welded joints.

Strain and Damage-Based Analytical Methods to Determine the Kachanov–Rabotnov Tertiary Creep-Damage Constants

In the power generation industry, the goal of increased gas turbine efficiency has led to increased operating temperatures and pressures necessitating nickel-base superalloy components. Under these conditions, the tertiary creep regime can become the dominant form of creep deformation. In response, the classical Kachanov–Rabotnov coupled creep-damage constitutive model is often used to predict the creep deformation and damage of Ni-base superalloys. In this model, the secondary creep behavior can be determined through analytical methods while the tertiary creep behavior is often found using trial and error or numerical optimization. Trial and error may produce no constants. Numerical optimization can be computationally expensive. In this study, a strain-based and damage-based approach to determine the tertiary creep behavior of nickel-base superalloys has been developed. Analytically determined constants are found for a given nickel-base superalloy. Creep deformation and damage evolution curves are compared. Methods to deal with stress dependence are introduced and studied.

The Effect of Pressure Induced Hoop Stress on Bi-Axially Loaded through Wall Cracked Cylindrical Structures – A Strain Based Method

This paper presents a simplified strain-based fracture mechanics approach to study the effect of pressure induced hoop stress on bi-axially loaded through walled cracked (TWC) pipes subjected to an external bending load in combination with internal pressure. Elastic-plastic finite element analyses are conducted to establish the relation between global strain and Crack tip opening displacement (CTOD). In the finite element model X65 pipeline steel is considered using power-law idealization of stress-strain, and the inelastic deformations, including ductile tearing effects, are accounted for by use of the Gurson–Tvergaard–Needleman model. Several parameters are taken into account, such as crack length, internal pressure and material hardening. Strain based crack driving force equation is used and maximum load criterion is adopted to determine the critical strain from ductile tearing in the cracked pipeline. The results suggest that presence of pressure-induced hoop stresses increases the fracture response in high-hardening materials and their effects are significant due to large plastic-zone size.

The shape of a strain-based failure assessment diagram

There have been a number of recent developments of strain-based fracture assessment approaches, including proposals by Budden [Engng Frac Mech 2006;73:537–52] for a strain-based failure assessment diagram (FAD) related to the conventional stress-based FAD. However, recent comparisons with finite element (FE) data have shown that this proposed strain-based FAD can be non-conservative in some cases, particularly for deeper cracks and materials with little strain-hardening capacity. Therefore, this paper re-examines the shape of the strain-based FAD, guided by these FE analyses and some theoretical analysis. On this basis, modified proposals for the shape of the strain-based FAD are given, including simplified and more detailed options in line with the options available for stress-based FADs in existing fitness-for-service procedures. The proposals are then illustrated by a worked example and by comparison with FE data, which demonstrate that the new proposals are generally conservative.

Finite element analysis of blister formation in laser-induced forward transfer

Abstract

A broadband vibro-impacting power harvester with symmetrical piezoelectricbimorph-stops

The certification of retrofitted structural health monitoring (SHM) systems for use onaircraft raises a number of challenges. One critical issue is determining the optimal meansof supplying power to these systems, given that access to the existing aircraft power systemis often problematic. Previously, the Australian Defence Science and TechnologyOrganisation has shown that a structural strain-based energy harvesting approach can beused to power a device for SHM of aircraft structure. Acceleration-based powerharvesting from airframes can be more demanding than a strain-based approachbecause the vibration spectrum of an aircraft structure can vary dynamicallywith flight conditions. A vibration spectrum with varying frequency may severelylimit the energy harvested by a single-degree-of-freedom resonance-based device,and hence a frequency agile or (relatively) broadband device is often requiredto maximize the energy harvested. This paper reports on an investigation intothe use of a vibro-impact approach to construct a piezoelectric-based kineticpower harvester that can operate in the approximate frequency range of 29–63 Hz.

Creep-fatigue behavior of various alloys used in power industry and their predictability

Material behavior under creep-fatigue interaction has been receiving wide attention in association with the development of fast reactor plants. A considerable effort has been undertaken for developing methods which can predict failure life with reasonable accuracy. However, no established consensus seems to have been reached yet, for creep-fatigue liofe prediction due to its more complex nature compared to failures under pure creep or pure fatigue conditions. This paper summarizes the results of creep-fatigue tests performed on several alloys used in the power generation industry and clarifies common characteristics and differences concerning their behavior. Then the representative failure prediction methods are applied to tension-hold creep-fatigue tests of these materials to study their performances for various types of alloy. Inter-relations existing between the stress-based and strain-based approaches for creep damage calculation and their consequence on life predictability are also discussed.

Load Ratio Effect on the Fatigue Behaviour of Adhesively Bonded Joints: An Enhanced Damage Model

Structural adhesives are used widely in aerospace and automotive applications. However, fatigue damage in these adhesives is an important factor to be considered in the design of adhesively bonded structural members that are subjected to cyclic loading conditions during their service life. Fatigue life of adhesively bonded joints depends mainly on the fatigue load and the load ratio. A fatigue damage model is presented in this paper to include the effect of fatigue mean stresses on the failure behaviour of adhesively bonded joints. The fatigue damage model is developed using an effective strain-based approach. The model is implemented on a tapered single lap joint configuration and is validated by experimental test results. The adhesive layer in the tapered single lap joint is modelled by using a cohesive zone with a bi-linear traction-separation response. The adverse effect of increasing fatigue mean stresses on the failure behaviour of adhesively bonded joints is successfully predicted.

Automated Versus Visual Segmental Scoring

Echocardiography is the most widely used noninvasive test for assessing the structure and function of the heart, accounting for 14% of overall Medicare expenditures for imaging in 2007.1 Despite the availability of a variety of validated quantitative methods for assessing chamber size and cardiac function, many elements of echocardiographic interpretation remain qualitative rather than quantitative. This is particularly true of the assessment of regional wall motion. Notwithstanding progress in the field of myocardial perfusion echocardiography2 and earlier efforts to quantitate regional function with acoustic quantitation3 and Doppler tissue imaging-based methods,4 echocardiographic assessment of regional wall motion remains the principal method by which echocardiographers make the diagnosis of coronary disease. Moreover, the ability to visually identify stress-induced regional wall motion abnormalities is the foundation for stress echocardiography. Article see p 47 The ability to reproducibly and reliably detect regional wall motion abnormalities is an essential skill for any physician interpreting echocardiograms and conceded to be one of the most difficult skills to acquire.5 Consequently, an automated quantitative approach to assessing regional function would be invaluable as a tool for the interpretation of echocardiograms for teaching and research and could prove useful in training echocardiographers. The study of Liel Cohen6 in this issue of Circulation: Cardiovascular Imaging proposes just such a tool. In their article, the authors report their evaluation of a semiautomated method of measuring regional longitudinal strain to develop segmental scores, classifying segments as normal, hypokinetic, or akinetic/dyskinetic/aneurysmal. As the authors note, strain analysis based on speckle tracking as opposed to angle-dependent Doppler tissue imaging methods is appealing because it avoids translation artifact and angle dependence. Twelve expert echocardiographers of the Israeli Echocardiography Research Group at 9 major Israeli cardiology centers used this approach as well as qualitative visual segmental scoring in 15 patients …

Interfaces in ferroelastics: Fringing fields, microstructure, and size and shape effects

We develop a strain-based approach to study the transformation of a finite martensite domain within an austenite host matrix. Analytical and numerical solutions are obtained for the fringing fields in the austenite and in the martensite and we test how well the stress and strain matching conditions are obeyed at the habit planes. We investigate the scaling of the energy of the fringing fields and show how simulations on relaxed microstructures corroborate the $1/|{k}_{y}|$ behavior for the energy in Fourier space. Our results show that the functional form $F={F}_{0}+a{L}_{1}\ensuremath{\xi}+bL{L}_{1}/\ensuremath{\xi}$ for the total elastic energy provides an excellent fit to the numerical simulations, thus demonstrating that $\ensuremath{\xi}\ensuremath{\sim}\sqrt{L}$, where $\ensuremath{\xi}$ is the twin width for a martensite region $L\ifmmode\times\else\texttimes\fi{}{L}_{1}$ with length of the habit plane ${L}_{1}$ and where $a{L}_{1}\ensuremath{\xi}$, $bL{L}_{1}/\ensuremath{\xi}$, and ${F}_{0}$ are the energies of the decaying strain field at the habit plane, twin-boundary energy, and energy of a single martensite variant, respectively. However, the result is only true for sufficiently large $L$ and we provide insight into the breakdown of the $\ensuremath{\xi}\ensuremath{\sim}\sqrt{L}$ scaling at the nanoscale. Our approach allows us to investigate the effect of varying the finite distance between habit planes, $L$, and our key finding is that there is a minimum length, ${L}^{\text{min}}$, for the nucleation of the twinned martensite structure which depends on temperature. As the temperature is lowered, ${L}^{\text{min}}$ decreases, and at temperatures close to the stability limit of the austenite phase a lattice martensite structure in which the parent and product phases spatially alternate in a checker-board pattern is stable in a narrow region of the temperature versus $L$ phase diagram. Such patterns have been seen at the nanoscale in lithium-based perovskites and inorganic spinels, as well as in coherent decomposition of precipitates in Co-Pt alloys. Finally, we show how the nature of the fringing fields due to an inclusion within an austenite matrix sensitively depends on its shape, size, and orientation and determines whether twinning or lattice martensite are the stable structures.

Remarks on axially and centrally symmetric elasticity problems

The solutions to axially and centrally symmetric Lamé problems are derived within the displacement, stress and strain-based approach by the specification of the general boundary conditions which encompass all possible combinations of kinematic and kinetic conditions at the inner and outer boundaries. It is shown that the mathematical structure of the governing differential equations in the strain-based approach is identical to that in the stress-based approach. A reduction of the compatibility conditions from general two and three-dimensional elasticity to their form applicable to axially and centrally symmetric problems is also discussed.

Towards a practical structural health monitoring technology for patched cracks in aircraft structure

Although bonded composite patches often offer a far more effective repair than conventional mechanically fastened patches, full credit can not be given for their effectiveness in reducing crack growth when used to repair flight safety structure. This is because of the lack of non-destructive techniques to detect bonds with poor long-term integrity and ability to predict the likelihood and rate of patch disbonding. Structural health monitoring (SHM) may overcome this limitation, since patch health can be monitored on a continuous basis. After discussing some of the requirements and options for structural health monitoring of bonded repair patches, a case history is presented on the application of a simple strain-based SHM approach for monitoring the boron/epoxy patch repair of a critical fatigue crack in an F-111C wing. The effectiveness of the strain-based SHM approach is demonstrated, and improvements which would reduce its limitations and raise its practicality to the level (TRL8) where it could be used for in- flight application are discussed. Conventional strain gauges were used in the SHM system which, although found effective, have several limitations. A study on the option of using Bragg grating optical fibres as strain sensors is briefly described. Finally brief details are provided on an alternative longer-term approach and study to use acousto-ultrasonics as the basis of the SHM system.

Neural Networks and Principal Components Analysis for Strain-Based Vehicle Classification

A large database has been acquired and compiled of vehicles crossing over a simply supported bridge deck system. Over the course of 1.5 years, deck strains caused by traffic, along with time-synchronized video images have been archived (400,000 records). Herein, this dataset is presented and used to develop a strain-based vehicle classification approach, as a machine learning application. To achieve this goal, the principal components analysis technique is applied to extract essential features from the strain time histories. Using these features as input, a two-layered back-propagation neural network is built and trained to sort vehicles into five classes. In this regard, availability of the video images provides essential information for developing the needed labeled datasets. The trained network is tested, and satisfactory results are achieved, showing viability of the classification approach for this bridge deck system.

Formulation and numerical implementation of a constitutive law for concrete with strain-based damage and plasticity

A triaxial constitutive law for concrete within the framework of isotropic damage combined with plasticity is proposed in this paper. It covers typical characteristics of concrete like non-linear uniaxial compression and tension, bi- and triaxial failure criteria and dilatancy with a unified strain-based approach. Thus, this model is quite simple and especially suitable for strain-driven methods like common finite elements. It is complemented with a regularization method based on the crack band approach. A further issue is discussed with procedures for the model parameter determination for a wide range of concrete grades. The application of the model is demonstrated with typical benchmark tests for plain concrete.

Confinement Model of Concrete with Externally Bonded FRP Jackets or Posttensioned FRP Shells

A design-oriented confinement model for square and rectangular columns confined with bonded fiber-reinforced polymer (FRP) jackets, and shape-modified square and rectangular sections confined with posttensioned FRP shells is developed. The proposed design model for FRP-confined concrete columns is based on the bilinear four-parameter formulation by Richard and Abbott. The axial compressive strength of FRP-confined concrete is obtained using concrete plasticity theory based on the five parameter Willam and Warnke model. The ultimate axial strain of FRP-confined concrete is obtained from a strain-based approach depending on either passive or active confinement; the ultimate axial strain is based on the concepts of secant concrete modulus and strain dependent stiffness established by Pantazopoulou and Mills. Comparisons of the proposed stress-strain model with uniaxial compression experiments for columns with bonded FRP jackets or posttensioned FRP shells, performed by the writers and other researchers, show satisfactory agreement for the entire stress-strain curve.

Piezoresistance in liquid suspensions: graphite in silicone elastomer

Piezoresistance is defined as a change in the conductivity or resistivity of a solid material with deformations. Phenomenological formulation of this effect involves either stresses or strains to describe the deformations. Each description introduces two piezoresistance coefficients, characterizing the response of an isotropic material. This study extends the concept of piezoresistance to liquid suspensions. Deformations are limited to small changes in the material microstructure and, therefore, induce small variations in specific resistance. As a working hypothesis, it is assumed the piezoresistance effect is determined by fluctuations in the local electric field caused by displacement of the inclusions. An experimental study is conducted with graphite micro-particles dispersed in silicone rubber. Small amplitude oscillatory shear deformations are produced by a rheometer in cone-and-plate configuration. A specially designed sensor rosette, attached to the fixed plate of a rheometer, extracts two piezoresistance coefficients. Both the stress and strain descriptions are verified against experimental data. Typically, the stress description shows better linearity of the piezoresistance response in liquid systems; the strain-based approach seems more suitable for rigorously defining experimental conditions and microscopic modelling.

Optimal Management Strategies for Patients With Complex Congenital Heart Disease

The combination of critical pulmonary outflow obstruction with a large ventricular septal defect is symbolized by the diagnosis of tetralogy of Fallot, the most common form of cyanotic congenital heart disease. In many ways, the history of management for patients with tetralogy is representative of the evolution of management for all children with complex congenital cardiac diagnoses. Tetralogy was the first complex lesion addressed surgically with the palliative Blalock-Taussig shunt in 1945 and the first repaired completely with patients’ mothers serving as the bypass machine in 1954.1,2 The introduction of valved conduits in 1964 allowed repair of lesions not previously considered amenable to correction.3 The next 3 decades were marked by improved survival at open heart repair, recognition of the progressive deterioration of valved conduits necessitating early and repeated reoperation, and a progressive decrease in the age of primary repair to now the first few months of life.4,5 In the late 1970s, reports of arrhythmia and late sudden death among tetralogy survivors led to evaluation of tetralogy cohorts with residual right ventricular (RV) volume and/or pressure overload identified as predictors of late complications.6,7 Recognition of this problem heightened appreciation of the importance of arrhythmias in postoperative congenital heart disease patients and identified the need for informed long-term care and attention to residua of earlier procedures for all patients with congenital heart disease.8 Finally, the last 20 years have witnessed the dramatic rise in interventional procedures to address both correction of simple lesions and palliation/management of complex diagnoses.9 Article p 2598 The remarkable progress in care of children with tetralogy exemplifies the collaboration between pediatric cardiologists and congenital cardiac surgeons, the development of new techniques to address problems as they emerge, and the continuous evolution of management that have characterized care of all patients with …

Modelling of Damage in Stress Concentration Zones under Low Cycle Fatigue*

Abstract The primary objective of this investigation was to develop a method for low cycle fatigue lifetime prediction in stress concentration zones of components. It was assumed that crack appearance takes place when a critical amount of normalized global damage is reached. Modelling was performed of damage accumulation in stress concentration zones using a plastic strain-based approach. The total damage under low cycle loading at room temperature, consisting of cyclic damage and low cycle fatigue induced creep damage or ratcheting, was calculated employing a finite element method together with additional procedures. This paper presents calculated fields of cyclically accumulated plastic strain; calculated lifetime compared with experimental results; and accumulated plastic strain results calculated at the notch root together with experimental data.

Probabilistic fracture assessment of surface cracked pipes using strain-based approach

Simplified strain-based fracture mechanics equations, established for external surface cracked pipelines subjected to an external bending load, are presented and used in probabilistic assessment of a pipeline girth weld. The model takes into account several parameters, such as variation in crack depth, crack length, internal pressure and material hardening. The critical strain from ductile tearing in the cracked pipeline is found by using the tangency criterion. The reliability problem is solved using first and second order reliability methods for different pipe dimensions and load levels.