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NASA NTRS1992

Calculation of stress intensity factors in an isotropic multicracked plate: Part 2: Symbolic/numeric implementation

Analytical derivations of stress intensity factors (SIF's) of a multicracked plate can be complex and tedious. Recent advances, however, in intelligent application of symbolic computation can overcome these difficulties and provide the means to rigorously and efficiently analyze this class of problems. Here, the symbolic algorithm required to implement the methodology described in Part 1 is presented. The special problem-oriented symbolic functions to derive the fundamental kernels are described, and the associated automatically generated FORTRAN subroutines are given. As a result, a symbolic/FORTRAN package named SYMFRAC, capable of providing accurate SIF's at each crack tip, was developed and validated. Simple illustrative examples using SYMFRAC show the potential of the present approach for predicting the macrocrack propagation path due to existing microcracks in the vicinity of a macrocrack tip, when the influence of the microcrack's location, orientation, size, and interaction are taken into account.

Arnold, S. M.↗
NASA NTRS2019

Stress Intensity Factors for Layered Pressure Vessel Inner Layer Through Cracks

A difficulty encountered when performing Fitness-for- Service assessments for layered pressure vessels (LPVs) is the lack of stress intensity factor solution in literature that produce accurate results for inner layer longitudinal through cracks. Using surrogate solutions such as a through crack in a plate or cylinder produce results that can be overly conservative especially for longer cracks. This is largely due to the ability of a layered pressure vessel to redistribute hoop load to other layers, the restricted radial movement of the cracked layer, and the friction forces applied in the cracked region. To understand this problem, a parametric finite element model (FEM) generator was developed that is capable of producing layered pressure vessel models with inner layer through cracks. The results from the FEMs were used to create a dataset of inner layer through crack stress intensity factors (KI) for layered pressure vessels corresponding to variations of internal pressure, radius, layer thicknesses, friction factor, and crack length. The elastic modulus of the material also has an effect on KI but, for this dataset, the elastic modulus was fixed at the typical value for steel - 29,500 ksi (203 GPa). Finally, a non-dimensional model was developed and calibrated using the dataset. This allows KI to be calculated without the need of a FEM using a closed-form equation. The results of the closed-form solution were then compared to FEM results showing accuracy was generally within 10%.

Hobbs, Joel R.↗
NASA NTRS1979

Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates

Surface cracks are among the more common flaws in aircraft and pressure vessel components. Several calculations of stress-intensity factors for semi-elliptical surface cracks subjected to tension have appeared in the literature. However, some of these solutions are in disagreement by 50-100%. In this paper, stress-intensity factors for shallow and deep semi-elliptical surface cracks in plates subjected to tension are presented. To verify the accuracy of the three-dimensional finite-element models employed, convergence was studied by varying the number of degrees of freedom in the models from 1500 to 6900. The 6900 degrees of freedom used here were more than twice the number used in previously reported solutions. Also, the stress-intensity variations in the boundary-layer region at the intersection of the crack with the free surface were investigated.

Raju, I. S.↗
NASA NTRS1985

Stress intensity factor in a tapered specimen

The general problem of a tapered specimen containing an edge crack is formulated in terms of a system of singular integral equations. The equations are solved and the stress intensity factor is calculated for a compact and for a slender tapered specimen, the latter simulating the double cantilever beam. The results are obtained primarily for a pair of concentrated forces and for crack surface wedge forces. The stress intensity factors are also obtained for a long strip under uniform tension which contains inclined edge cracks.

Xue-Hui, L.↗
NASA NTRS1974

Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface

A technique consisting of freezing photo-elasticity and a numerical method was used to obtain stress intensity factors for natural cracks emanating from the corner at which a hole intersects a plate surface. Geometries studied were: (1) crack depth to thickness ratios of approximately 0.2, (2) 0.5 and 0.75; (3) crack depth to crack length ratios of approximately 1.0 to 2.0; and (4) crack length to hole radius ratios of about 0.5 to 2.0. All final crack geometries were grown under monotonic loading and growth was not self similar, with most of the growth occuring through the thickness under remote extension. Stress intensity factors were determined at the intersection of the flaw border.

Mcgowan, J. J.↗
NASA NTRS1977

Transverse shear effects on the stress-intensity factor for a circumferentially cracked, specially orthotropic cylindrical shell

The problem of a cylindrical shell containing a circumferential through crack is considered by taking into account the effect of transverse shear deformations. The formulation is given for a specially orthotropic material within the confines of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions regarding moment and stress resultants on the crack surface. Consequently, aside from multiplicative constants representing the stress intensity factors, the membrane and bending components of the asymptotic stress fields near the crack tip are found to be identical. The stress intensity factors are calculated separately for a cylinder under a uniform membrane load, and that under a uniform bending moment. Sample results showing the nature of the out-of-plane crack surface displacement and the effect of the Poisson's ratio are presented.

Delale, F.↗
NASA NTRS1976

Wide range stress intensity factor expressions for ASTM E 399 standard fracture toughness specimens

For each of the two types of specimens, bend and compact, described previously for plane strain fracture toughness of materials, E 399, a polynominal expression is given for calculation of the stress intensity factor, K, from the applied force, P, and the specimen dimensions. It is explicitly stated, however, that these expressions should not be used outside the range of relative crack length, a/W, from 0.45 to 0.55. While this range is sufficient for the purpose of E 399, the same specimen types are often used for other purposes over a much wider range of a/W; for example, in the study of fatigue crack growth. Expressions are presented which are at least as accurate as those in E 399-74, and which cover much wider ranges of a/W: for the three-point bend specimen from 0 to 1; and for the compact specimen from 0.2 to 1. The range has to be restricted for the compact specimen because of the proximity of the loading pin holes to the crackline, which causes the stress intensity factor to be sensitive to small variations in dimensions when a/W is small. This is a penalty inherently associated with the compactness of the specimen.

Srawley, J. E.↗
NASA NTRS1976

Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface

The stress intensity factors (SIFs) at the end points of flaws emanating from the corner formed by the intersection of a plate with a hole were determined using stress freezing photoelasticity and a numerical technique known as the Taylor series correction method to extract the SIF values from the photoelastic data. The geometries studied were crack depth to thickness ratios of about 0.2, 0.5, and 0.75; crack depth to crack length ratios of about 1.0 to 2.0; and crack length to hole radius ratios of about 0.5 to 2.0. The SIFs were determined at the intersection of the flaw border with the plate surface (KS) and with the edge of the hole (KH). It is shown that extension of a crack emanating from a corner of intersection of a hole with a plate under monotonically increasing load is not self-similar and that as the flaw depth increases, KH decreases and KS increases. Existing theories and design criteria significantly overestimate the SIF at both the hole and the surface except for shallow flaws at the hole and deep flaws at the surface.

Mcgowan, J. J.↗
NASA NTRS1992

Mixed mode stress-intensity-factors in mode-3 loaded middle crack tension specimen

A three dimensional stress analysis of a middle-crack tension specimen subjected to mode-3 type loading was performed using fracture mechanics based finite element code FRAC3D. Three-dimensional stress intensity factors were calculated for a range of specimen thicknesses that represent the structures used in aerospace and nuclear industries. Calculated SIF for very thick specimen (thickness-to-crack length b/a greater than or equal to 30) agreed very well with the antiplane solution in the literature. The K(sub II) stress field exists near the intersection of the crack front and free surface in a boundary-layer region covers the complete thickness of the plate and K(sub II) dominates all through the thickness. For very thin plates (b/a is less than .1), the average K(sub II) is larger than K(sub III) (about 25% for b/a = 0.1).

Shivakumar, Kunigal N.↗
NASA NTRS2024

On the Validity of the Tada Stress Intensity Factor Solution for the Single Edge Notch Tension Specimen With Pinned Ends

The validity of the Tada stress intensity factor (K Tada ) for pinned-ends single edge notch tension [SEN(T)] specimens is assessed via a combined experimental-modeling approach. Analysis of fatigue crack growth rate reductions during constant-∆K Tada loading demonstrates that specific combinations of alloy stiffness, geometry, and loading result in the true K deviating below K Tada . Geometrically non-linear, 3-dimensional finite element calculations confirm mild-to-strong influences of these parameters, which are not captured by K Tada . Most existing pinned SEN(T) data are found to use parameters where KTada is not significantly reduced, but the present results underscore the need for a more broadly applicable K solution.

Non-linear FEA↗
NASA NTRS1985

Strain energy release rate determination of stress intensity factors by finite element methods

The stiffness derivative finite element technique is used to determine the Mode I stress intensity factors for three-crack configurations. The geometries examined include the double edge notch, single edge notch, and the center crack. The results indicate that when the specified guidelines of the Stiffness Derivative Method are used, a high degree of accuracy can be achieved with an optimized, relatively coarse finite element mesh composed of standard, four-node, plane strain, quadrilateral elements. The numerically generated solutions, when compared with analytical ones, yield results within 0.001 percent of each other for the double edge crack, 0.858 percent for the single edge crack, and 2.021 percent for the center crack.

Walsh, R. M., Jr.↗
NASA NTRS1992

Determination of stress intensity factors for interface cracks under mixed-mode loading

A simple technique was developed using conventional finite element analysis to determine stress intensity factors, K1 and K2, for interface cracks under mixed-mode loading. This technique involves the calculation of crack tip stresses using non-singular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating three different bimaterial combinations. For the normal loading case, the K's were within 2.6 percent of an exact solution. The normalized K's under shear loading were shown to be related to the normalized K's under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from knowledge of the K's under normal loading. The equation was verified by computing the K's for a mixed-mode case with equal and normal shear loading. The correlation between exact and finite element solutions is within 3.7 percent. This study provides a simple procedure to compute K2/K1 ratio which has been used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/K1 ratios could be used to fully characterize interface fracture toughness.

Naik, Rajiv A.↗
NASA NTRS1974

Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface

A technique consisting of a marriage between stress freezing photoelasticity and a numerical method was used to obtain stress intensity factors for natural cracks emanating from the corner at which a hole intersects a plate surface. Geometrics studied were: crack depth to thickness ratios of approximately 0.2, 0.5, and 0.75; crack depth to crack length ratios of approximately 1.0 to 2.0. All final crack geometries were grown under monotonic loading and growth was not self similar with most of the growth occurring through the thickness under remote extension. Stress intensity plate surface K sub s factors were determined at the intersection of the flaw border with the plate surface K sub s and with the edge of the hole K sub h. Results showed that for the relatively shallow flaws K sub h approximately equal to 1.5 K sub s, for the moderately deep flaws K sub h approximately equal to K sub s, and for the deep flaws K sub h approximately equal to 0.5 K sub s, revealing a severe sensitivity of K to flaw geometry.

Mcgowan, J. J.↗