Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Fracture Mechanics Investigation of Structures with Defects

Fracture mechanics plays an important role in the material science, structure design and industrial production due to the failure of materials and structures are paid high attention in human activities. This dissertation, concentrates on some of the fractural aspects of shaft and composite which have being increasingly used in modern structures, consists four chapters within two parts. Chapters 1 to 4 are included in part 1. In the first chapter, the basic knowledge about the stress and displacement fields in the vicinity of a crack tip is introduced. A review involves the general methods of calculating stress intensity factors are presented. In Chapter 2, two simple engineering methods for a fast and close approximation of stress intensity factors of cracked or notched beams under tension, bending moment, shear force, as well as torque are presented. New formulae for calculating the stress intensity factors are proposed. One of the methods named Section Method is improved and applied to the three dimensional analysis of cracked circular section for calculating stress intensity factors. The comparisons between the present results and the solutions calculated by ABAQUS for single mode and mixed mode are studied. In chapter 3, fracture criteria for a crack subjected to mixed mode loading of two-dimension and three-dimension are reviewed. The crack extension angle for single mode and mixed mode, and the critical loading domain obtained by SEDF and MTS are compared. The effects of the crack depth and the applied force ratio on the crack propagation angle and the critical loading are investigated. Three different methods calculating the crack initiation angle for three-dimension analysis of various crack depth and crack position are compared. It should be noted that the stress intensity factors used in the criteria are calculated in section 2.1.

On the Disintegration of Ice Shelves: The Role of Fracture

Crevasses can be ignored in studying the dynamics of most glaciers because they are only about 20 m deep, a small fraction of ice thickness. In ice shelves, however, s urface crevasses 20 m deep often reach sealevel and bottom crevasses can move upward to sea-level (Clough, 1974; Weertman, 1980). The ice shelf is fractured completely through if surface and basal crevasses meet (Barrett, 1975; Hughes, 1979). This is especially likely if surface melt water fills surface crevasses (Weertman, 1973; Pfeffer, 1982; Fastook and Schmidt, 1982). Fracture may therefore play an important role i n the disintegration of ice shelves. Two fracture criteria which can be evaluated experimentally and applied to ice shelves, are presented. Fracture is then examined for the general strain field of an ice shelf and for local strain fields caused by shear rupture alongside ice streams entering the ice shelf, fatigue rupture along ice shelf grounding lines, and buckling up-stream from ice rises. The effect of these fracture patterns on the stability of Antarctic ice shelves and the West Antarctic ice sheet is then discussed.

Cleavage initiation in the intercritically reheated coarse-grained heat affected zone:Part II. Failure criteria and statistical effects

In part 1 of this article, cleavage initiation in the intercritically reheated coarse-grained heat affected zone (IC CG HAZ) of high-strength low-alloy (HSLA) steels was determined to occur between two closely spaced blocky MA particles. Blunt notch, crack tip opening displacement (CTOD), and precracked Charpy testing were used in this investigation to determine the failure criteria required for cleavage initiation to occur by this mechanism in the IC CG HAZ. It was found that the attainment of a critical level of strain was required in addition to a critical level of stress. This does not occur in the case of high strain rate testing, for example, during precracked Charpy testing. A different cleavage initiation mechanism is then found to operate. The precise fracture criteria and microstructural requirements (described in part I of this article) result in competition between potential cleavage initiation mechanisms in the IC CG HAZ.

Influence of the cohesive law parameters on the strength prediction of adhesively-bonded joints

Adhesive joints are largely employed nowadays as a fast and effective joining process. The respective techniques for strength prediction have also improved over the years. Cohesive Zone Models (CZM’s) coupled to Finite Element Method (FEM) analyses surpass the limitations of stress and fracture criteria and allow modelling damage. CZM’s require the energy release rates in tension (Gn) and shear (Gs) and respective fracture energies in tension (Gnc) and shear (Gsc). Additionally, the cohesive strengths (tn0 for tension and ts0 for shear) must also be defined. In this work, the influence of the CZM parameters of a triangular CZM used to model a thin adhesive layer is studied, to estimate their effect on the predictions. Some conclusions were drawn for the accuracy of the simulation results by variations of each one of these parameters.

A crack on the interface of piezo-electric bodies

Singularities of elastic and electric fields are investigated at the tip of a crack on the interface of two anisotropic piezo-electric media under various boundary conditions on the crack surfaces. The Griffith formulae are obtained for increments of energy functionals due to growth of the crack and the notion of the energy release matrix is introduced. Normalization conditions for bases of singular solution are proposed to adapt them to the energy, stress, and deformation fracture criteria. Connections between these bases are determined and additional properties of the deformation basis related to the notion of electric surface enthalpy are established.

Postoperative renal function evaluation, through RIFLE criteria, of elderly patients who underwent femur fracture surgery under spinal anesthesia

Introduction. The postoperative acute renal failure (ARF) incidence in different kinds of surgery has rarely been studied. Age, cardiac dysfunction, previous renal dysfunction, intraoperative hypoperfusion, and use of nephrotoxic medications are mentioned as risk factors for ARF at the postoperative period. The postoperative ARF definition was based on the creatinine increase by the RIFLE classification (R = risk, I = injury, F = failure, L = loss, E = end stage), which corresponds to a 1.5 creatinine increase, two to three times, respectively, above the basal value. This study aimed to evaluate the postoperative ARF incidence in elderly patients who underwent femur fracture surgery under subarachnoid anesthesia and stratify it by the RIFLE criteria. Methods. Ninety patients older than 65 years under spinal anesthesia with fixed dosage of 15 mg of 0.5% isobaric bupivacaine associated with morphine 50 g were studied. Immediate postoperative creatinine was considered basal and compared with maximal creatinine evaluated at 24, 48, and 72 postoperative hours. Results. The mean age of the patients was 80.27 years. ARF incidence was 24.44% and stratified this way: R = 21.11% and I = 3.33%. Conclusions. In conclusion, the postoperative ARF incidence after femur fracture surgery in patients over 65 years was 24.44%. By analyzing the stratification based on the RIFLE classification, the incidence was categorized as Risk (R) = 21.11% and Injury (I) = 3.33%.

Tomographic index as auxiliary criteria for surgery indication in fracture dislocation of acetabulum posterior wall

There are situations which the tomographic exam is done on the affected hip or situations where the contralateral hip presents abnormalities that make it impossible to compare. In this study we aimed to evaluate a tomographic index that does not require comparison between the both hips. Twenty two patients with unilateral acetabular fracture dislocation with fracture of posterior wall were studied. We established the relationship between the remaining posterior wall and the femoral head diameter (head/wall index-H/W index). We evaluated 45 two-dimensional computed tomography scan in normal hips and established the H/W index. In 45 normal hips we simulated a posterior wall fracture with involvement of 25% and 30% of the posterior wall and calculated the H/W index. We divided into five groups with five different H/W index (fractured group with non surgical treatment; fractured group; normal group; normal group with simulated fracture of 25% and; 30% of the posterior wall). 2.4 was the lowest limit of confidence interval of the group with 25% of the posterior wall fracture. When we analyzed the confidence interval of the 30% fracture group the upper limit of the confidence interval was 2.7, close to the lower limit of the surgical group that was 2.9. Thus, we suggest the 2.4 the H/W index limit as an auxiliary criteria to indicate whether or not to operate. H/W index is helpful to decide whether or not surgery indication in the fracture dislocation of the posterior wall of the acetabulum. © 2012 Fujiki et al.; licensee BioMed Central Ltd.

Orthodontic extrusion as treatment option for crown-root fracture: literature review with systematic criteria

To review the literature searching for a consensus for the choice of orthodontic extrusion as treatment for crown-root fracture. An electronic search was performed in the databases PubMed, Cochrane Central Register of Controlled Trials and Scopus and a manual search of the Journal Dental Traumatology. Forty articles were found in PubMed and 38 in Scopus and after removal of duplicate sample 51 contained articles. Of these, 48 were excluded for not having orthodontic treatment, no follow-up or follow-up less than 6 months, or not report the presence of crown-root fracture. In manual search in Dental Traumatology 20 articles were found, but none of them met the prerequisites established. So, three articles formed the basis of the study. The choice of how to treat orthodontic extrusion of crown-root fracture was effective and stable, without root and periodontal changes. Factors, such as root formation and presence of pulp vitality were decisive for determining the stages of treatment, however, there is no consensus based on scientific evidence about these protocols.

Preliminary criteria for the fracture control of space shuttle structures.

"Compiling, integrating, and editing of the document were performed by the Design Criteria Program Office of the McDonnell Douglas Astronautics Company under the direction of the Langley Research Center's Structural Systems Office (SSO)."

Failure assessments of corroded pipelines with axial defects using stress-based criteria: Numerical studies and verification analyses

Conventional procedures used to assess the integrity of corroded piping systems with axial defects generally employ simplified failure criteria based upon a plastic collapse failure mechanism incorporating the tensile properties of the pipe material. These methods establish acceptance criteria for defects based on limited experimental data for low strength structural steels which do not necessarily address specific requirements for the high grade steels currently used. For these cases, failure assessments may be overly conservative or provide significant scatter in their predictions, which lead to unnecessary repair or replacement of in-service pipelines. Motivated by these observations, this study examines the applicability of a stress-based criterion based upon plastic instability analysis to predict the failure pressure of corroded pipelines with axial defects. A central focus is to gain additional insight into effects of defect geometry and material properties on the attainment of a local limit load to support the development of stress-based burst strength criteria. The work provides an extensive body of results which lend further support to adopt failure criteria for corroded pipelines based upon ligament instability analyses. A verification study conducted on burst testing of large-diameter pipe specimens with different defect length shows the effectiveness of a stress-based criterion using local ligament instability in burst pressure predictions, even though the adopted burst criterion exhibits a potential dependence on defect geometry and possibly on material`s strain hardening capacity. Overall, the results presented here suggests that use of stress-based criteria based upon plastic instability analysis of the defect ligament is a valid engineering tool for integrity assessments of pipelines with axial corroded defects. (C) 2008 Elsevier Ltd. All rights reserved.

Prevention of recurrent hip fracture.

Our objective was to describe the interventions aimed at preventing a recurrent hip fracture, and other injurious falls, which were provided during hospitalization for a first hip fracture and during the two following years. A secondary objective was to study some potential determinants of these preventive interventions. The design of the study was an observational, two-year follow-up of patients hospitalized for a first hip fracture at the University Hospital of Lausanne, Switzerland. The participants were 163 patients (median age 82 years, 83% women) hospitalized in 1991 for a first hip fracture, among 263 consecutively admitted patients (84 did not meet inclusion criteria, e.g., age>50, no cancer, no high energy trauma, and 16 refused to participate). Preventive interventions included: medical investigations performed during the first hospitalization and aimed at revealing modifiable pathologies that raise the risk of injurious falls; use of medications acting on the risk of falls and fractures; preventive recommendations given by medical staff; suppression of environmental hazards; and use of home assistance services. The information was obtained from a baseline questionnaire, the medical record filled during the index hospitalization, and an interview conducted 2 years after the fracture. Potential predictors of the use of preventive interventions were: age; gender; destination after discharge from hospital; comorbidity; cognitive functioning; and activities of daily living. Bi- and multivariate associations between the preventive interventions and the potential predictors were measured. In hospital investigations to rule out medical pathologies raising the risk of fracture were performed in only 20 patients (12%). Drugs raising the risk of falls were reduced in only 17 patients (16%). Preventive procedures not requiring active collaboration by the patient (e.g., modifications of the environment) were applied in 68 patients (42%), and home assistance was provided to 67 patients (85% of the patients living at home). Bivariate analyses indicated that prevention was less often provided to patients in poor general conditions, but no ascertainment of this association was found in multivariate analyses. In conclusion, this study indicates that, in the study setting, measures aimed at preventing recurrent falls and injuries were rarely provided to patients hospitalized for a first hip fracture at the time of the study. Tertiary prevention could be improved if a comprehensive geriatric assessment were systematically provided to the elderly patient hospitalized for a first hip fracture, and passive preventive measures implemented.

Vertebral microarchitecture and fragility fracture in men: a TBS study.

INTRODUCTION: Although osteoporosis is considered a disease of women, 25% of the individuals with osteoporosis are men. BMD measurement by DXA is the gold standard used to diagnose osteoporosis and assess fracture risk. Nevertheless, BMD does not take into account alterations of microarchitecture. TBS is an index of bone microarchitecture extracted from the spine DXA. Previous studies have reported the ability of the spine TBS to predict osteoporotic fractures in women. This is the first case-controlled study in men to evaluate the potential diagnostic value of TBS as a complement to bone mineral density (BMD), by comparing men with and without fractures. METHODS: To be eligible for this study, subjects had to be non-Hispanic US white men aged 40 and older. Furthermore, subjects were excluded if they have or have had previously any treatment or illness that may influence bone metabolism. Fractured subjects were included if the presence of at least one fracture was confirmed. Cases were matched for age (±3 years) and BMD (±0.04 g/cm(2)) with three controls. BMD and TBS were first retrospectively evaluated at AP spine (L1-L4) with a Prodigy densitometer (GE-Lunar, Madison, USA) and TBS iNsight® (Med-Imaps, France) in Lausanne University Hospital blinded from clinical outcome. Inter-group comparisons were undertaken using Student's t-tests or Wilcoxon signed rank tests. Odds ratios were calculated per one standard deviation decrease as well as areas under the receiver operating curve (AUC). RESULTS: After applying inclusion/exclusion criteria, a group of 180 male subjects was obtained. This group consists of 45 fractured subjects (age=63.3±12.6 years, BMI=27.1±4.2 kg/m(2)) and 135 control subjects (age=62.9±11.9 years, BMI=26.7±3.9 kg/m(2)) matched for age (p=0.86) and BMD (p=0.20). A weak correlation was obtained between TBS and BMD and between TBS and BMI (r=0.27 and r=-0.28, respectively, p<0.01). Subjects with fracture have a significant lower TBS compared to control subjects (p=0.013), whereas no differences were obtained for BMI, height and weight (p>0.10). TBS OR per standard deviation is 1.55 [1.09-2.20] for all fracture type. When considering vertebral fracture only TBS OR reached 2.07 [1.14-3.74]. CONCLUSION: This study showed the potential use of TBS in men. TBS revealed a significant difference between fractured and age- and spine BMD-matched nonfractured subjects. These results are consistent with those previously reported on for men of other nationalities.

Defining risk thresholds for a 10-year probability of hip fracture model that combines clinical risk factors and quantitative ultrasound: results using the EPISEM cohort.

Using a large prospective cohort of over 12,000 women, we determined 2 thresholds (high risk and low risk of hip fracture) to use in a 10-yr hip fracture probability model that we had previously described, a model combining the heel stiffness index measured by quantitative ultrasound (QUS) and a set of easily determined clinical risk factors (CRFs). The model identified a higher percentage of women with fractures as high risk than a previously reported risk score that combined QUS and CRF. In addition, it categorized women in a way that was quite consistent with the categorization that occurred using dual X-ray absorptiometry (DXA) and the World Health Organization (WHO) classification system; the 2 methods identified similar percentages of women with and without fractures in each of their 3 categories, but the 2 identified only in part the same women. Nevertheless, combining our composite probability model with DXA in a case findings strategy will likely further improve the detection of women at high risk of fragility hip fracture. We conclude that the currently proposed model may be of some use as an alternative to the WHO classification criteria for osteoporosis, at least when access to DXA is limited.

A Practical Micro Mechanical Model Based Local Approach Methodology for the Analysis of Ductile Fracture of Welded T-Joints

This thesis concentrates on developing a practical local approach methodology based on micro mechanical models for the analysis of ductile fracture of welded joints. Two major problems involved in the local approach, namely the dilational constitutive relation reflecting the softening behaviour of material, and the failure criterion associated with the constitutive equation, have been studied in detail. Firstly, considerable efforts were made on the numerical integration and computer implementation for the non trivial dilational Gurson Tvergaard model. Considering the weaknesses of the widely used Euler forward integration algorithms, a family of generalized mid point algorithms is proposed for the Gurson Tvergaard model. Correspondingly, based on the decomposition of stresses into hydrostatic and deviatoric parts, an explicit seven parameter expression for the consistent tangent moduli of the algorithms is presented. This explicit formula avoids any matrix inversion during numerical iteration and thus greatly facilitates the computer implementation of the algorithms and increase the efficiency of the code. The accuracy of the proposed algorithms and other conventional algorithms has been assessed in a systematic manner in order to highlight the best algorithm for this study. The accurate and efficient performance of present finite element implementation of the proposed algorithms has been demonstrated by various numerical examples. It has been found that the true mid point algorithm (a = 0.5) is the most accurate one when the deviatoric strain increment is radial to the yield surface and it is very important to use the consistent tangent moduli in the Newton iteration procedure. Secondly, an assessment of the consistency of current local failure criteria for ductile fracture, the critical void growth criterion, the constant critical void volume fraction criterion and Thomason's plastic limit load failure criterion, has been made. Significant differences in the predictions of ductility by the three criteria were found. By assuming the void grows spherically and using the void volume fraction from the Gurson Tvergaard model to calculate the current void matrix geometry, Thomason's failure criterion has been modified and a new failure criterion for the Gurson Tvergaard model is presented. Comparison with Koplik and Needleman's finite element results shows that the new failure criterion is fairly accurate indeed. A novel feature of the new failure criterion is that a mechanism for void coalescence is incorporated into the constitutive model. Hence the material failure is a natural result of the development of macroscopic plastic flow and the microscopic internal necking mechanism. By the new failure criterion, the critical void volume fraction is not a material constant and the initial void volume fraction and/or void nucleation parameters essentially control the material failure. This feature is very desirable and makes the numerical calibration of void nucleation parameters(s) possible and physically sound. Thirdly, a local approach methodology based on the above two major contributions has been built up in ABAQUS via the user material subroutine UMAT and applied to welded T joints. By using the void nucleation parameters calibrated from simple smooth and notched specimens, it was found that the fracture behaviour of the welded T joints can be well predicted using present methodology. This application has shown how the damage parameters of both base material and heat affected zone (HAZ) material can be obtained in a step by step manner and how useful and capable the local approach methodology is in the analysis of fracture behaviour and crack development as well as structural integrity assessment of practical problems where non homogeneous materials are involved. Finally, a procedure for the possible engineering application of the present methodology is suggested and discussed.