Fatigue behaviour of friction stir welded AA2024-T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024-T3 aluminium alloy have been studied under constant load amplitude (increasing-Delta K), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka`s method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold Delta K values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K-C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non-conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non-conservative crack growth rate predictions next to K-C instability. At threshold Delta K values non-conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.

On the finite element modeling of fatigue crack growth in pressurized cylindrical shells

A methodology for the computational modeling of the fatigue crack growth in pressurized shell structures, based on the finite element method and concepts of Linear Elastic Fracture Mechanics, is presented. This methodology is based on that developed by Potyondy [Potyondy D, Wawrzynek PA, Ingraffea, AR. Discrete crack growth analysis methodology for through crack in pressurized fuselage structures. Int J Numer Methods Eng 1995;38:1633-1644], which consists of using four stress intensity factors, computed from the modified crack integral method, to predict the fatigue propagation life as well as the crack trajectory, which is computed as part of the numerical simulation. Some issues not presented in the study of Potyondy are investigated herein such as the influence of the crack increment size and the number of nodes per element (4 or 9 nodes) on the simulation results by means of a fatigue crack propagation simulation of a Boeing 737 airplane fuselage. The results of this simulation are compared with experimental results and those obtained by Potyondy [1]. (C) 2008 Elsevier Ltd. All rights reserved.

Slow crack growth and reliability of dental ceramics

Objective. To determine the slow crack growth (SCG) and Weibull parameters of five dental ceramics: a vitreous porcelain (V), a leucite-based porcelain (D), a leucite-based glass-ceramic (E1), a lithium disilicate glass-ceramic (E2) and a glass-infiltrated alumina composite (IC). Methods. Eighty disks (empty set 12mm x 1.1mm thick) of each material were constructed according to manufacturers` recommendations and polished. The stress corrosion susceptibility coefficient (n) was obtained by dynamic fatigue test, and specimens were tested in biaxial flexure at five stress rates immersed in artificial saliva at 37 degrees C. Weibull parameters were calculated for the 30 specimens tested at 1MPa/s in artificial saliva at 37 degrees C. The 80 specimens were distributed as follows: 10 for each stress rate (10(-2), 10(-1), 10(1), 10(2) MPa/s), 10 for inert strength (10(2) MPa/s, silicon oil) and 30 for 10(0) MPa/s. Fractographic analysis was also performed to investigate the fracture origin. Results. E2 showed the lowest slow crack growth susceptibility coefficient (17.2), followed by D (20.4) and V (26.3). E1 and IC presented the highest n values (30.1 and 31.1, respectively). Porcelain V presented the lowest Weibull modulus (5.2). All other materials showed similar Weibull modulus values, ranging from 9.4 to 11.7. Fractographic analysis indicated that for porcelain D, glass-ceramics E1 and E2, and composite IC crack deflection was the main toughening mechanism. Significance. This study provides a detailed microstructural and slow crack growth characterization of widely used dental ceramics. This is important from a clinical standpoint to assist the clinician in choosing the best ceramic material for each situation as well as predicting its clinical longevity. It also can be helpful in developing new materials for dental prostheses. (c) 2010 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Effect of ion exchange on strength and slow crack growth of a dental porcelain

Objectives. To determine the effect of ion exchange on slow crack growth (SCG) parameters (n, stress corrosion susceptibility coefficient, and sigma(f0), scaling parameter) and Weibull parameters (m, Weibull modulus, and sigma(0), characteristic strength) of a dental porcelain. Methods. 160 porcelain discs were fabricated according to manufacturer`s instructions, polished through 1 mu m and divided into two groups: GC (control) and GI (submitted to an ion exchange procedure using a KNO(3) paste at 470 degrees C for 15 min). SCG parameters were determined by biaxial flexural strength test in artificial saliva at 37 degrees C using five constant stress rates (n =10). 20 specimens of each group were tested at 1 MPa/s to determine Weibull parameters. The SPT diagram was constructed using the least-squares fit of the strength data versus probability of failure. Results. Mean values of m and sigma(0) (95% confidence interval), n and sigma(f0) (standard deviation) were, respectively: 13.8 (10.1-18.8) and 60.4 (58.5 - 62.2), 24.1 (2.5) and 58.1 (0.01) for GC and 7.4 (5.3 -10.0) and 136.8 (129.1-144.7), 36.7 (7.3) and 127.9 (0.01) for GI. Fracture stresses (MPa) calculated using the SPT diagram for lifetimes of 1 day, 1 year and 10 years (at a 5% failure probability) were, respectively, 31.8, 24.9 and 22.7 for GC and 71.2, 60.6 and 56.9 for GI. Significance. For the porcelain tested, the ion exchange process improved strength and resistance to SCG, however, the material`s reliability decreased. The predicted fracture stress at 5% failure probability for a lifetime of 10 years was also higher for the ion treated group. (C) 009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Subcritical crack growth in porcelains, glass-ceramics, and glass-infiltrated alumina composite for dental restorations

The objective was to compare fracture toughness (K(Ic)), stress corrosion susceptibility coefficient (n), and stress intensity factor threshold for crack propagation (K(I0)) of two porcelains [VM7/Vita (V) and d.Sign/Ivoclar (D)], two glass-ceramics [Empress/Ivolcar (E1) and Empress2/Ivlocar (E2)] and a glass-infiltrated alumina composite [In-Ceram Alumina/Vita (IC)]. Disks were constructed according to each manufacturer`s processing method, and polished before induction of cracks by a Vickers indenter. Crack lengths were measured under optical microscopy at times between 0.1 and 100 h. Specimens were stored in artificial saliva at 37A degrees C during the whole experiment. K(Ic) and n were determined using indentation fracture method. K(I0) was determined by plotting log crack velocity versus log K(I). Microstructure characterization was carried out under SEM, EDS, X-ray diffraction and X-ray fluorescence. IC and E2 presented higher K(Ic) and K(I0) compared to E1, V, and D. IC presented the highest n value, followed by E2, D, E1, and V in a decreasing order. V and D presented similar K(Ic), but porcelain V showed higher K(I0) and lower n compared to D. Microstructure features (volume fraction, size, aspect ratio of crystalline phases and chemical composition of glassy matrix) determined K(Ic). The increase of K(Ic) value favored the increases of n and K(I0).

Influence of leucite content on slow crack growth of dental porcelains

Objectives. To determine the stress corrosion susceptibility coefficient, n, of seven dental porcelains (A: Ceramco I; B: Ceramco-II; C: Ceramco-III; D: d.Sign; E: Cerabien; F: Vitadur-Alpha; and G: Ultropaline) after aging in air or artificial saliva, and correlate results with leucite content (LC). Methods. Bars were fired according to manufacturers` instructions and polished before induction of cracks by a Vickers indenter (19.6 N, 20 s). Four specimens were stored in air/room temperature, and three in saliva/37 degrees C. Five indentations were made per specimen and crack lengths measured at the following times: similar to 0; 1; 3; 10; 30; 100; 300; 1000 and 3000 h. The stress corrosion coefficient n was calculated by linear regression analysis after plotting crack length as a function of time, considering that the slope of the curve was (2/(3n + 2)]. Microstructural analysis was performed to determine LC. Results. LC of the porcelains were 22% (A and B); 6% (C); 15% (D); 0% (E and F); and 13% (G). Except for porcelains A and D, all materials showed a decrease in their n values when stored in artificial saliva. However, the decrease was more pronounced for porcelains B, F, and G. Ranking of materials varied according to storage media (in air, porcelain G showed higher n compared to A, while in saliva both showed similar coefficients). No correlation was found between n values and LC in air or saliva. Significance. Storage media influenced the n value obtained for most of the materials. LC did not affect resistance to slow crack growth regardless of the test environment. (c) 2008 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Influence of pH on slow crack growth of dental porcelains

Objectives. To evaluate the effect of pH of storage medium on slow crack growth (SCG) parameters of dental porcelains. Methods. Two porcelains were selected: with (UD) and without (VM7) leucite particles, in order to assess if the microstructure would affect the response of the material to the pH variation. Disc specimens were produced following manufacturers` instructions. Specimens were stored in artificial saliva in pHs 3.5, 7.0 or 10.0 for 10 days and after that the fatigue parameters (n: SCG susceptibility coefficient and sigma(0): scaling parameter) were obtained by the dynamic fatigue test using the same pH of storage. Microstructural analysis of the materials was also performed. Results. For VM7, the values of n obtained in the different pHs were similar and varied from 29.9 to 31.2. The sigma(0) value obtained in pH 7.0 for VM7 was higher than that obtained in the other pHs, which were similar. For porcelain UD, n values obtained in pHs 7.0 and 10.0 were similar (40.8 and 39.6, respectively), and higher than that obtained in pH 3.5 (26.5). With respect to sigma(0), the value obtained for porcelain UD in pH 10.0 was lower than those obtained in pHs 3.5 and 7.0, which were similar. Significance. The effect of pH on the stress corrosion susceptibility (n) depended on the porcelain studied. While the n value of VM7 was not affected by the pH, UD presented lower n value in acid pH. For both porcelains, storage in acid or basic pH resulted in strength degradation. (C) 2007 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation

Fatigue and crack propagation are phenomena affected by high uncertainties, where deterministic methods fail to predict accurately the structural life. The present work aims at coupling reliability analysis with boundary element method. The latter has been recognized as an accurate and efficient numerical technique to deal with mixed mode propagation, which is very interesting for reliability analysis. The coupled procedure allows us to consider uncertainties during the crack growth process. In addition, it computes the probability of fatigue failure for complex structural geometry and loading. Two coupling procedures are considered: direct coupling of reliability and mechanical solvers and indirect coupling by the response surface method. Numerical applications show the performance of the proposed models in lifetime assessment under uncertainties, where the direct method has shown faster convergence than response surface method. (C) 2010 Elsevier Ltd. All rights reserved.

Non-linear boundary element formulation with tangent operator to analyse crack propagation in quasi-brittle materials

This work deals with analysis of cracked structures using BEM. Two formulations to analyse the crack growth process in quasi-brittle materials are discussed. They are based on the dual formulation of BEM where two different integral equations are employed along the opposite sides of the crack surface. The first presented formulation uses the concept of constant operator, in which the corrections of the nonlinear process are made only by applying appropriate tractions along the crack surfaces. The second presented BEM formulation to analyse crack growth problems is an implicit technique based on the use of a consistent tangent operator. This formulation is accurate, stable and always requires much less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Comparison examples of classical problem of crack growth are shown to illustrate the performance of the two formulations. (C) 2009 Elsevier Ltd. All rights reserved.

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris` law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena. (C) 2010 Elsevier Ltd. All rights reserved.

Numerical modeling of ductile crack extension in high pressure pipelines with longitudinal flaws

This study examines the applicability of a micromechanics approach based upon the computational cell methodology incorporating the Gurson-Tvergaard (GT) model and the CTOA criterion to describe ductile crack extension of longitudinal crack-like defects in high pressure pipeline steels. A central focus is to gain additional insight into the effectiveness and limitations of both approaches to describe crack growth response and to predict the burst pressure for the tested cracked pipes. A verification study conducted on burst testing of large-diameter, precracked pipe specimens with varying crack depth to thickness ratio (a/t) shows the potential predictive capability of the cell approach even though both the CT model and the CTOA criterion appear to depend on defect geometry. Overall, the results presented here lend additional support for further developments in the cell methodology as a valid engineering tool for integrity assessments of pipelines with axial defects. (C) 2011 Elsevier Ltd. All rights reserved,

Load Ratio Estimation Through Striation Height and Spacing Analysis of an Aerospace Al Alloy 7475-T7351

It is well known that striation spacing may be related to the crack growth rate, da/dN, through Paris equation, as well as the maximum and minimum loads under service loading conditions. These loads define the load ratio, R, and are considered impossible to be evaluated from the inter-spacing striations analysis. In this way, this study discusses the methodology proposed by Furukawa to evaluate the maximum and minimum loads based on the experimental fact that the relative height of a striation, H, and the striation spacing, s, are strongly influenced by the load ratio, R. Fatigue tests in C(T) specimens were conducted on SAE 7475-T7351 Al alloy plates at room temperature and the results showed a straightforward correlation between the parameters H, s, and R. Measurements of striation height, H, were performed using scanning electron microscopy and field emission gun (FEG) after sectioning the specimen at a large inclined angle to amplify the height of the striations. The results showed that for increasing R the values of H/s tend to increase. Striation height, striation spacing, and load ratio correlations were obtained, which allows one to estimate service loadings from fatigue fracture surface survey.

Dual boundary element formulation applied to analysis of multi-fractured domains

This paper deals with analysis of multiple random crack propagation in two-dimensional domains using the boundary element method (BEM). BEM is known to be a robust and accurate numerical technique for analysing this type of problem. The formulation adopted in this work is based on the dual BEM, for which singular and hyper-singular integral equations are used. We propose an iterative scheme to predict the crack growth path and the crack length increment at each time step. The proposed scheme able us to simulate localisation and coalescence phenomena, which is the main contribution of this paper. Considering the fracture mechanics analysis, the displacement correlation technique is applied to evaluate the stress intensity factors. The propagation angle and the equivalent stress intensity factor are calculated using the theory of maximum circumferential stress. Examples of simple and multi-fractured domains, loaded up to the rupture, are considered to illustrate the applicability of the proposed scheme. (C) 2010 Elsevier Ltd. All rights reserved.

A BEM model applied to failure analysis of multi-fractured structures

Due to manufacturing or damage process, brittle materials present a large number of micro-cracks which are randomly distributed. The lifetime of these materials is governed by crack propagation under the applied mechanical and thermal loadings. In order to deal with these kinds of materials, the present work develops a boundary element method (BEM) model allowing for the analysis of multiple random crack propagation in plane structures. The adopted formulation is based on the dual BEM, for which singular and hyper-singular integral equations are used. An iterative scheme to predict the crack growth path and crack length increment is proposed. This scheme enables us to simulate the localization and coalescence phenomena, which are the main contribution of this paper. Considering the fracture mechanics approach, the displacement correlation technique is applied to evaluate the stress intensity factors. The propagation angle and the equivalent stress intensity factor are calculated using the theory of maximum circumferential stress. Examples of multi-fractured domains, loaded up to rupture, are considered to illustrate the applicability of the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.