ALBERT

Notes: Abstract Previous work in modeling dynamic fracture has assumed the crack will propagate along predefined mesh lines (usually a straight line). In this paper we present a finite element model of mixed-mode dynamic crack propagation in which this constraint is removed. Applying linear elasto-dynamic fracture mechanics concepts, discrete cracks are allowed to propagate through the mesh in arbitrary directions. The fracture criteria used for propagation and the algorithms used for remeshing are described in detail. Important features of the implementation are the use of triangular elements with quadratic shape functions, explicit time integration, and interactive computer graphics. These combine to make the approach robust and applicable to a broad range of problems. Example analyses of straight and curving crack problems are presented. Verification problems include a stationary crack under dynamic loading and a propagating crack in an infinite body. Comparisons with experimental data are made for curving propagation in a cracked plate under biaxial loading.

Notes: Abstract The FRANC3D/STAGS software system has been developed to model curvilinear crack growth in aircraft fuselages. Simulations of fatigue crack growth have been reported previously (Potyondy et al. 1995). This paper presents two enhancements to this system. One is the generalization of the representation of cracks that allows the system to represent realistic damaged structures more accurately. With this capability, parameters that may affect the trajectory of a fatigue crack are studied. Results are compared with measurements from a full-scale test. The second enhancement is to model stable tearing for residual strength prediction. A stable tearing simulation along a crack path that captures the material nonlinearities inherent at the crack tip is performed. The CTOA (Crack Tip Opening Angle) is used as a crack growth criterion to characterize the fracture process under conditions of general yielding. Residual strength of cracked structures is predicted.

Notes: Abstract The short rod is a simple, inexpensive configuration for fracture toughness testing. Since no rigorous analytical stress-intensity factor calibration of this geometry has yet appeared, a three-dimensional finite element study was undertaken. Successively finer meshes were employed to investigate convergence in compliance versus crack length, and the dimensionless calibration constant, A, in the expression% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-Teada% WgaaWcbaacbaGaa4xmaiaa-ngaaeqaaOGaeyypa0Jaa8NramaaBaaa% leaacaWFJbaabeaakiaa-feacaGFVaGaa43waiaa-jeadaahaaqcba% uabeaalmaalyaajeaqbaGaaG4maaqaaiaaikdaaaaaaOGaaiikaiaa% igdacqGHsislcaWF2bWaaWbaaSqabKqaafaacaWFYaaaaOGaaiykam% aaCaaaleqajeaqbaWaaSGbaeaacaaIXaaabaGaaGOmaaaaaaGccaGG% Dbaaaa!4A74!\[K_{1c} = F_c A/[B^{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} (1 - v^2 )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} ]\] Quarter-point singular elements were used along the crack front, and a range of crack lengths 0.65 〈- a/B 〈- 1.1 was investigated. Distributed and point loading cases were considered. Polynomials were least-squares fit through the compliance data and were differentiated to yield expressions for average stress-intensity factor along the crack front% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-Teada% WgaaWcbaacbaGaa4xmaaqabaGccqGH9aqpdaWadaqaamaalaaabaGa% a8NramaaCaaaleqajeaybaGaa8Nmaaaakiaa-veacaWFNaaabaGaaG% Omaiaa-jgacaWFGaaaamaalaaabaGaa4hzaiaa-neaaeaacaqGKbGa% a8xyaaaaaiaawUfacaGLDbaadaahaaWcbeqcbauaamaalyaabaGaaG% ymaaqaaiaaikdaaaaaaaaa!477B!\[K_1 = \left[ {\frac{{F^2 E'}}{{2b }}\frac{{dC}}{{{\text{d}}a}}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \] Minima of this expression were obtained corresponding to critical average stress-intensity factors and crack lengths. The above expressions were then equated to solve for calibration constant values of, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-feacq% GH9aqpcaaIYaGaaGynaiaac6cacaaI5aGaaeiiaiabgglaXkaabcca% caqGXaGaaeOlaiaabkdacaqG1aaaaa!4227!\[A = 25.9{\text{ }} \pm {\text{ 1}}{\text{.25}}\] at a c/B=0.86 for the distributed load case and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-feacq% GH9aqpcaaIYaGaaGimaiaac6cacaaI5aGaaeiiaiabgglaXkaabcca% caqGXaaaaa!4004!\[A = 20.9{\text{ }} \pm {\text{ 1}}\] at a c/B=.69 for the point load case. The distributed load case value of A is in very good agreement with previously reported values of 24.4 ± 1.3 and 25.0, and is about 11 percent higher than the currently recommended value obtained through K Ic correlation. Preliminary results of a study of stress-intensity factor variation along the crack front are also presented. They show that maximum stress-intensity factor occurs at the edges of the crack front. This observation is consistent with the reverse tunneling phenomenon sometimes observed in short rod testing. Recommendations for further numerical study of the short rod configuration are suggested.

Notes: Abstract A method is developed for estimating (i) confidence intervals on the initial direction of crack extension and (ii) the probability of crack initiation in plane stress and plane strain problems. The method accounts for the uncertainty in applied stresses, fracture toughness, and crack geometry. It is based on classical theories of linear fracture mechanics for homogeneous isotropic materials, a computer code for deterministic fracture mechanics analysis (FRANC) and first and second order structural reliability algorithms (FORM/SORM). Several examples are presented to demonstrate the use and generality of the proposed method for probabilistic fracture mechanics analysis.

Notes: A simple, efficient method for propagating cracks through a finite element mesh is presented: nodes, borrowed from other points in the mesh, are ‘grafted’ along the advancing crack front. The method requires neither an increase in bandwidth nor a mesh regeneration. It can be easily implemented in any existing program using iso(sub)parametric elements of at least quadratic order.

Notes: An efficient hypersingular boundary integral equation method for three-dimensional fracture mechanics was presented in a previous paper. The details of the numerical implementation of this method are further discussed herein. In particular, an algorithm for achieving the required differentiability of the crack surface displacement function is discussed. To illustrate the utility of the method, computational results for several strongly interacting multiple-crack geometries are presented. The calculated stress intensity factors are in excellent agreement with those obtained by an approximate analytical method due to Kachanov and Laures.

Notes: A new general purpose boundary element method for domains with cracks has been recently developed. This technique avoids the use of a multi-domain decomposition by including an additional integral equation expressing the boundary condition on the crack. The principal requirement of this technique is the analytic determination of certain hypersingular integrals of the Green's function which arise from this equation. In order to establish the applicability of this method for fracture, these integrals are evaluated herein for the Kelvin solution of the three-dimensional Navier equations of linear elasticity. Numerical results for fracture problems using the single-domain boundary element analysis are also presented.

Notes: Analytical studies of the stresses on and within ultra high molecular weight polyethylene joint components suggest that damage modes associated with polyethylene fatigue failure are caused by a combination of surface and subsurface crack propagation. Fatigue crack propagation tests under mixed mode loading conditions were conducted on center-cracked tension specimens machined from extruded blocks of sterilized polyethylene in an attempt to determine how fatigue cracks change direction in this material. Cyclic testing was performed using a sinusoidal wave form at a frequency of 5 Hz and an R-ratio (minimum load/ maximum load) of 0.15. Specimens had the notch oriented perpendicular to the direction of applied load and at angles of 60° and 45° to the loading direction. Numerical analyses were used to interpret the experimental test and to predict the fatigue behavior of polyethylene under mixed mode conditions. It was found that all cracks eventually propagated horizontally, regardless of the initial angle of inclination of the notch to the direction of applied cyclic load. In fact, the extent of the curvilinear crack growth was quite limited. An effective range of cyclic stress intensity factor was calculated for correlation with the rate of crack growth. The results followed a Paris relation, with crack growth rate linearly related to a power of the range of stress intensity, for all three crack orientations. The numerical analyses adequately modeled the experimental fatigue crack growth results. © 1994 John Wiley & Sons, Inc.