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NASA NTRS1988

Investigation of stress concentration factor - Stress intensity factor interaction for flaws in filleted rods

To predict the fatigue life of machine parts which contain flaws in regions of stress concentration, the engineer needs to treat a series of crack sizes and/or shapes quickly and economically. In this paper the stress intensity factor distributions for circular surface flaws in the roots of fillets in rods loaded by remote tension are presented and examined. The examination reveals insight into the interaction of cracks with other stress concentrating discontinuities, and based on this it is suggested that weight function methods used in conjunction with known crack solutions may provide needed, efficient stress intensity factor prediction methods for such three-dimensional geometries.

Springfield, C. W., Jr.↗
NASA NTRS1978

A review and assessment of the stress-intensity factors for surface cracks

The stress-intensity factor solutions proposed for a surface crack in a finite plate subjected to uniform tension are reviewed. Fourteen different solutions for the stress-intensity factors are compared. These solutions were obtained over the past 16 years using approximate analytical methods, experimental methods, and engineering estimates. The accuracy is assessed of the various solutions by correlating fracture data on surface-cracked tension specimens made of a brittle epoxy material. Fracture of the epoxy material was characterized by a constant value of stress-intensity factor at failure. Thus, the correctness of the various solutions is judged by the variations in the stress-intensity factors at failure. The solutions were ranked in order of minimum standard deviation. The highest ranking solutions correlated 95 percent of data analyzed within + or - 10 percent, whereas the lowest ranking solutions correlated 95 percent of data analyzed within + or - 20 percent. However, some solutions could be applied to all data considered, whereas others are limited with respect to crack shapes and crack sizes that could be analyzed.

Newman, J. C., Jr.↗
NASA NTRS1988

A re-evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method.

Tan, P. W.↗
NASA NTRS1985

Parametric study of stress-intensity factors in bonded composite stringer panels

Stress-intensity factors are determined for an infinite cracked orthotropic sheet adhesively bonded to an orthotropic stringer. Since the stringer is modeled as a semi-infinite sheet, the solution is most appropriate for a crack tip located near a stringer edge. Both adherends are treated as homogeneous, orthotropic media which are representative of many fiber-reinforced composite materials. The complex variable theory of elasticity was used to obtain a set of integral equations describing the problem. The integral equations are replaced by an equivalent sheet of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer. From these adhesive stresses, the stress-intensity factors are found. A parametric study is conducted to determine the sensitivity of the system to material properties and specimen configuration. Unless the crack tip is very close to or under the stringer, the stress-intensity factor is approximately that of the unstiffened sheet. However, as the crack propagates beneath the stringer, the stress-intensity factor decreases significantly. Increasing the stringer stiffness or the adhesive stiffness also decreases the stress-intensity factor.

Bigelow, C. A.↗
NASA NTRS1988

Effect of adhesive debond on stress-intensity factors in bonded composite panels

Stress-intensity factors are calculated for a cracked infinite sheet adhesively bonded to a stringer, and debonding of the adhesive layer is predicted. The stringer is modeled as a semiinfinite sheet. Adhesive nonlinearity is also included. Both the sheet and stringer are treated as homogeneous, orthotropic materials, a set of integral equations is formulated and solved to obtain the adhesive shear stresses and crack-tip stress-intensity factors. Adhesive debonding is predicted using a rupture criterion based on the combined adhesive stresses. A through-the-thickness crack is located in the infinite sheet perpendicular to the edge of the stringer. When the crack is not under the stringer, the debond extends along the edge of the stringer. When the crack tip is beneath the stringer, the debond extends to the crack tip, then along the edge of the stringer. Stress levels required for debond initiation decrease as the crack tip is moved beneath the stringer. With a nonlinear adhesive, the debond initiates at higher applied stress levels than in linear adhesive cases. Compared with the linear adhesive solution, modeling a nonlinear adhesive causes the stress-intensity factor to decrease when debonding is included.

Bigelow, C. A.↗
NASA NTRS1979

A review and assessment of the stress-intensity factors for surface cracks

The stress-intensity factor solutions proposed for a surface crack in a finite plate subjected to uniform tension are reviewed. Fourteen different solutions obtained over the past 16 years using approximate analytical methods, experimental methods, and engineering estimates are compared. The accuracy of the various solutions is assessed by correlating fracture data on surface-cracked tension specimens made of a brittle epoxy material. Fracture of the epoxy material was characterized by a constant value of stress-intensity factor as failure. Thus, the correctness of various solutions is judged by the variations in the stress-intensity factors at failure. The solutions were ranked in order of minimum standard deviation. The highest ranking solutions correlated 95% of data analyzed within + or - 10% whereas the lowest ranking solutions correlated 95% of data analyzed within + or - 20%. Some solutions could be applied to all data considered, whereas others were limited with respect to crack shapes and crack sizes that could be analyzed.

Newman, J. C., Jr.↗
NASA NTRS1972

Collocated interfacial stress intensity factors for finite bi-material plates.

This paper deals with elastic stress intensity factors associated with stress fields near partially debonded interfaces in finite, bi-material plates. Bi-material stress intensity factors K1 and K2 are not associated, respectively, with symmetric and skew-symmetric loading and are functions of an arbitrary length parameter. Any fracture condition involving bi-material stress intensity factors must be independent of the arbitrary length parameter and must be consistent with experiment. We define a new parameter called the interfacial stress intensity factor which satisfies the former condition. A truncated Williams power series stress function for stresses in a cracked bi-material plate, as modified by Sih and Rice, is used with a modified boundary collocation procedure to generate interfacial stress intensity factors for finite bi-material plates.

Sawyer, S. G.↗
NASA NTRS1990

Evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models.

Tan, P. W.↗
NASA NTRS1988

Stress-intensity factors for corner cracks in rectangular bars

Stress intensity factors are presented for a wide range of quarter-elliptical corner cracks in a rectangular bar. The bars were subjected to remote tension, out-of-plane bending, or in-plane bending loading, and the stress intensity factors were calculated from a three-dimensional finite element analysis using the nodal-force method. For all loadings considered, smaller width bars produce higher normalized stress intensity factors than the larger width bars. For tensile loading, quarter-circular corner cracks give higher stress intensity factors near the free surfaces and lower values in the interior. The results are compared with data in the literature for remote tensile loading.

Raju, I. S.↗
NASA NTRS2009

Calculation of Stress Intensity Factors for Interfacial Cracks in Fiber Metal Laminates

Stress intensity factors for interfacial cracks in Fiber Metal Laminates (FML) are computed by using the displacement ratio method recently developed by Sun and Qian (1997, Int. J. Solids. Struct. 34, 2595-2609). Various FML configurations with single and multiple delaminations subjected to different loading conditions are investigated. The displacement ratio method requires the total energy release rate, bimaterial parameters, and relative crack surface displacements as input. Details of generating the energy release rates, defining bimaterial parameters with anisotropic elasticity, and selecting proper crack surface locations for obtaining relative crack surface displacements are discussed in the paper. Even though the individual energy release rates are nonconvergent, mesh-size-independent stress intensity factors can be obtained. This study also finds that the selection of reference length can affect the magnitudes and the mode mixity angles of the stress intensity factors; thus, it is important to report the reference length used with the calculated stress intensity factors.

Wang, John T.↗
NASA NTRS1974

Shear-stress intensity factors for elastic sheets with cover plates

Shear stress intensity factors are calculated for three problems concerning inextensible cover plates either bonded to or embedded in an elastic sheet which is under uniaxial tension. The stress intensity factors are small when the ratio of sheet thickness to cover plate length is small and, as the ratio increase, rapidly approach their asymptotic values for infinite sheet thickness. In the problem of the embedded cover plate, the stress intensity factor also depends on the Poisson's ratio of the sheet material. The dependence on Poisson's ratio, however, is significant only when the ratio of sheet thickness to cover plate length is small. Some possible implications of the present results for debonding of reinforced sheets under cyclic loading are briefly discussed.

Fichter, W. B.↗
NASA NTRS1979

Stress-intensity factors for internal surface cracks in cylindrical pressure vessels

The stress intensity factors were calculated by a three dimensional finite element method. The finite element models employed singularity elements along the crack front and linear strain elements elsewhere. The models had about 6500 degrees of freedom. The stress intensity factors were evaluated from a nodal force method. An equation for the stress intensity factors was obtained form the results of the present analysis. The equation applies over a wide range of configuration parameters and was within about 5 percent of the present results. A comparison was made between the present results and other analyses of internal surface cracks in cylinders. The results from a boundary integral equation method were in agreement (+ or - 2 percent) and those from another finite element were in fair agreement (+ or - 8 percent) with the present results.

Newman, J. C., Jr.↗
NASA NTRS1986

Effect of debond growth on stress-intensity factors in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

Stress-intensity factors are determined for a cracked infinite sheet adhesively bonded to a stringer, and debonding of the adhesive layer is predicted. The stringer is modeled as a semi-infinite sheet. Adhesive nonlinearity is also included. Both the sheet and stringer are treated as homogeneous, orthotropic materials. A set of integral equations is formulated and solved to obtain the adhesive shear stresses and crack-tip stress-intensity factors. Adhesive debonding is predicted using a rupture criterion based on the combined adhesive stresses. When the crack is not under the stringer, the debond extends along the edge of the stringer. When the crack tip is beneath the stringer, the debond grows to the end of the crack, then along the edge of the stringer. Stress levels required for debond initiation decrease as the crack tip is moved beneath the stringer. With a nonlinear adhesive, the debond initiates at higher applied stress levels than in linear adhesive cases. Compared with the linear adhesive solution, modeling a nonlinear adhesive causes the stress-intensity factor to increase when the bond is assumed to remain intact but causes the stress-intensity factor to decrease when debonding is included.

Bigelow, C. A.↗
NASA NTRS1981

Stress-intensity factor equations for cracks in three-dimensional finite bodies

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Newman, J. C., Jr.↗
NASA NTRS1974

Mixed mode stress intensity factors for semielliptical surface cracks

The three-dimensional equations of elasticity are solved for a flat elliptical crack which has nonuniform shear stresses applied to its surfaces. An alternating method is used to determine the mode two and mode three stress intensity factors for a semielliptical surface crack in the surface of a finite thickness solid. These stress intensity factors are presented as a function of position along the crack border for a number of crack shapes and crack depths. This same technique is followed to determine the mode one stress intensity factors for the semielliptical surface crack which has normal loading applied to its surface. Mode one stress intensity factors are presented and compared with the results obtained from previous work.

Smith, F. W.↗
NASA NTRS1977

Mode I stress intensity factors for round compact specimens

Mode I stress intensity factors were computed for round compact specimens by the boundary collocation method. Results are presented for ratios At/R0 in the range 0.3 to 0.8, where At is the distance from the specimen center to the crack tip for a specimen of diameter 2R0.

Gross, B.↗