Leslie Banks-Sills

Update: Application of the Finite Element Method to Linear Elastic Fracture Mechanics

Use of the finite element method to treat two and three-dimensional linear elastic fracture mechanics problems is becoming common place. In general, the behavior of the displacement field in ordinary elements is at most quadratic or cubic, so that the stress field is at most linear or quadratic. On the other hand, the stresses in the neighborhood of a crack tip in a linear elastic material have been shown to be square root singular. Hence, the problem begins by properly modeling the stresses in the region adjacent to the crack tip with finite elements. To this end, quarter-point, singular, isoparametric elements may be employed; these will be discussed in detail. After that difficulty has been overcome, the stress intensity factor must be extracted from either the stress or displacement field or by an energy based method. Three methods are described here: displacement extrapolation, the stiffness derivative and the area and volume J-integrals. Special attention will be given to the virtual crack extension which is employed by the latter two methods. A methodology for calculating stress intensity factors in two and three-dimensional bodies will be recommended.

The effect of adhesive thickness on interlaminar fracture toughness of interleaved cfrp specimens

Abstract The investigation concentrated on the adhesive size effect on interlaminar fracture toughness ( ift ) of interleaved cfrp specimens. In tests an artificial interlaminar edge crack was forced to propagate under two modes: separation (Mode I) and shear (Mode II). Two types of adhesive were used and adhesive thickness ranged from 0.04 mm–1.1 mm. Results indicated that ift increased with adhesive thickness up to 10-fold in the case of Mode I and up to 7-fold in the case of Mode II compared with the ift of non-interleaved counterparts. The toughening effect was more pronounced at the low range of thickness and tended to decrease in the case of thick layers. In Mode II ( enf test), ift was found to decrease above an adhesive thickness of 0.7 mm. It was concluded that optimum adhesive thickness for improved ift is in the range of 0.1 - 0.7 mm.

A note on fracture criteria for interface fracture

Several criteria for interface fracture are examined and compared to test results obtained from glass/epoxy specimens. These include two energy release rate criteria, a critical hoop stress criterion and a critical shear stress criterion. In addition, approximate plastic zone size and shape within the epoxy are determined for these tests.

A mixed mode fracture specimen for mode II dominant deformation

Abstract Several theories have been proposed for the failure of metals, as well as for the angle of crack propagation in mixed mode loading. In order to demonstrate the validity of these theories, the majority of tests have been carried out with an oblique crack placed in a uniaxial stress field. Better testing conditions may be achieved by placing a crack in a uniform bidimensional stress field. A specimen which was recently developed for K IIC measurement may be readily adapted to achieve a bidimensional stress field and be used for mixed mode testing for the case in which shear deformation is dominant. The main aims of this study are to examine both the cracked and uncracked specimen by means of photoelasticity and finite elements in order to analyze the capabilities and limitations of this specimen for mixed mode testing. It will be demonstrated that there exists a nearly uniform biaxial field in the uncracked specimen. Moreover, calibration formulas will be presented for K I and K II .

Modeling of functionally graded materials in dynamic analyses

Abstract In this investigation, functionally graded material is modeled in several different ways. Five models are presented, two of which simulate fiber phases and three simulate particle phases. For fibers, there is a model in which the detailed micro-structure is simulated and one in which the material is represented by layers such that the volume fraction of the fibers in each layer changes. For the particles, a model with layers is employed and two models with continuously changing material parameters are presented. Four different dynamic input loads are applied to the detailed micro-structure to examine its effect. The finite element method is employed to determine the effective stress. Then one of the dynamic loads which simulates a step function is applied to all models. It is observed that there are no significant differences in the effective stresses at particular points within the time domain. The amplitude of the wave for each model is quite similar. The phase of the wave shifts as time increases. Thus, in the space domain, differences are observed in the effective stress at a particular time. As may be expected, the stresses are rather high within the fibers in the detailed micro-structural model. It is concluded that a continuously changing material model is a good candidate for carrying out dynamic analyses of functionally graded material.

Numerical assessment of T-stress computation using a p-version finite element method

Two path independent integrals for T-stress computations, one based on the Betti-Rayleigh reciprocal theorem and the other based on Eshelbys energy momentum tensor are studied. Analytical as well as numerical equivalence between the two integrals is found. To quantify and assess the accuracy of computed values, error analysis for the proposed numerical computation of the T-stress is presented. Specifically, it is found that the error of the computed T-stress is proportional to the ratio of the stress intensity factor divided by the square root of the characteristic dimension of the integration domain where the path independent integral is evaluated. Using a highly accurate hierarchical p-version finite element method, the convergence and accuracy of computed values are easily monitored, and it is shown for numerical examples that the error of the computed T-stress complies with the described error analysis. We conclude that path independent integrals, in conjunction with hierarchical p-version finite element methods, provide a powerful and robust tool to obtain highly accurate numerical results for the T-stress.

A conservative integral for determining stress intensity factors of a bimaterial strip

Both conservative line and area integrals are derived from the Betti reciprocal principle to determine the stress intensity factor for a bimaterial strip. Numerical results are presented to demonstrate the accuracy of the methods. Several mesh types have been exploited to examine the effect of meshing on the results. Stress intensity factors obtained by means of the line integral vary somewhat between paths. Those found by means of the area integral have the same value on different paths.

On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods

Two methods are examined for accurately calculating stress intensity factors in two and three dimensions: the stiffness derivative technique and the J-integral method. In two dimensions the J-integral is expressed as an area integral, whereas in three dimensions it is a volume integral. With both techniques, a virtual crack extension is introduced. Although the expressions employed for each method are quite different, it is proven that when written analytically for finite element calculation, they reduce to identical expressions.Numerical calculations are carried out in both two and three dimensions. As a result of the equivalence of the two methods, close numerical agreement is expected. For two-dimensional geometries and a penny shaped crack in a finite height cylinder, there is at least five significant figure agreement between solutions determined by both methods. For an elliptical crack embedded in a plate, the agreement is generally to four significant figures.

Stress and strain distribution in the intact canine femur: finite element analysis

Information regarding the stresses and strains in the canine femur during various activities is important for veterinary orthopaedic surgeons, engineers designing implants for dogs, and researchers of human orthopaedics who use dogs as models. Nevertheless, such information is currently unavailable. The objective of this study is to determine the stress and strain distribution in the canine femur during mid-stance, for two loading scenarios. Three-dimensional finite element models of the canine femur were created. Two loading cases were considered: the hip joint reaction force alone, and the hip joint reaction force with all muscle forces acting on the femur. Force directions and magnitudes were obtained from the literature. Analyses were performed with NASTRAN for Windows software. When all muscle forces were considered, stresses and strains were significantly reduced, peak compressive stresses were found to occur in the medial diaphysis, and peak tensile stresses occurred in the lateral diaphysis. While the canine femur seems to be loaded primarily in bending when only the hip joint reaction force is considered, the bending moment is significantly decreased when all muscle forces are considered as well. Further in vivo and in vitro experiments are needed to validate the results of the calculations described in this paper. It is expected that future studies will be carried out, in which the stress and strain distributions in femora with different types of implants and stems will be compared to those in the normal femur.

On the effect of particle shape and orientation on elastic properties of metal matrix composites

Abstract In this investigation, an aluminum alloy, A1 2124-T6, matrix composite containing alumina particles is examined. Both a standard mechanical approach and the homogenization method are employed to calculate effective elastic material constants. A periodic cubic array of particles is assumed leading to three-dimensional finite element analyses. Effective elastic properties are determined. The ceramic particles are assumed to be of four shapes: spherical, cylindrical, cubic and rectangular parallelepiped. For the latter two particles, the effect of particle orientation is examined. These lead to a lack of symmetry which produce effective elastic constants which are not usually observed. Rectangular parallelepiped particles appear to produce some benefits for effective axial elastic moduli.