Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.

Initiation and early crack growth in VHCF of stainless steels : Experimental and theoretical analysis

Mechanical fatigue is a failure phenomenon that occurs due to repeated application of mechanical loads. Very High Cycle Fatigue (VHCF) is considered as the domain of fatigue life greater than 10 million load cycles. Increasing numbers of structural components have service life in the VHCF regime, for instance in automotive and high speed train transportation, gas turbine disks, and components of paper production machinery. Safe and reliable operation of these components depends on the knowledge of their VHCF properties. In this thesis both experimental tools and theoretical modelling were utilized to develop better understanding of the VHCF phenomena. In the experimental part, ultrasonic fatigue testing at 20 kHz of cold rolled and hot rolled stainless steel grades was conducted and fatigue strengths in the VHCF regime were obtained. The mechanisms for fatigue crack initiation and short crack growth were investigated using electron microscopes. For the cold rolled stainless steels crack initiation and early growth occurred through the formation of the Fine Granular Area (FGA) observed on the fracture surface and in TEM observations of cross-sections. The crack growth in the FGA seems to control more than 90% of the total fatigue life. For the hot rolled duplex stainless steels fatigue crack initiation occurred due to accumulation of plastic fatigue damage at the external surface, and early crack growth proceeded through a crystallographic growth mechanism. Theoretical modelling of complex cracks involving kinks and branches in an elastic half-plane under static loading was carried out by using the Distributed Dislocation Dipole Technique (DDDT). The technique was implemented for 2D crack problems. Both fully open and partially closed crack cases were analyzed. The main aim of the development of the DDDT was to compute the stress intensity factors. Accuracy of 2% in the computations was attainable compared to the solutions obtained by the Finite Element Method.

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.

IDED Strategic Plan For State Economic Growth, March 2004

Strategic Plan for Iowa Department of Economic Development

Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

Fatigue crack growth of Al 7475 T761 under constant and variable amplitude loading

Experimental programs in constant and variable amplitude loading were performed to obtain a x N curves and to study retardation in fatigue crack growth due to overloads. The main aim of this research program was to analyse the effect of overload ratio and number of overload peaks. The effect of underloads, before and after the overload blocks was also studied. The generalised equation of Paris-Erdogan type was used for modelling of obtained data on crack propagation under constant amplitude load.

Mechanical strength and subcritical crack growth under wet cyclic loading of glass-infiltrated dental ceramics

Objectives. Evaluate the flexural strength (sigma) and subcritical crack growth (SCG) under cyclic loading of glass-infiltrated alumina-based (IA, In-Ceram Alumina) and zirconia-reinforced (IZ, In-Ceram Zirconia) ceramics, testing the hypothesis that wet environment influences the SCG of both ceramics when submitted to cyclic loading.Methods. Bar-shaped specimens of IA (n = 45) and IZ ( n = 45) were fabricated and loaded in three-point bending (3P) in 37 degrees C artificial saliva (IA(3P) and IZ(3P)) and cyclic fatigued (F) in dry (D) and wet (W) conditions (IA(FD), IA(FW), IZ(FD), IZ(FW)). The initial sigma and the number of cycles to fracture were obtained from 3P and F tests, respectively. Data was examined using Weibull statistics. The SCG behavior was described in terms of crack velocity as a function of maximum stress intensity factor (K(Imax)).Results. The Weibull moduli (m = 8) were similar for both ceramics. The characteristic strength (sigma(0)) of IA and IZ was and 466 MPa 550 MPa, respectively. The wet environment significantly increased the SCG of IZ, whereas a less evident effect was observed for IA. In general, both ceramics were prone to SCG, with crack propagation occurring at K(I) as low as 43-48% of their critical K(I). The highest sigma of IZ should lead to longer lifetimes for similar loading conditions.Significance. Water combined with cyclic loading causes pronounced SCG in IZ and IA materials. The lifetime of dental restorations based on these ceramics is expected to increase by reducing their direct exposure to wet conditions and/or by using high content zirconia ceramics with higher strength. (C) 2010 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.