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NASA NTRS1993

surf3d: A 3-D finite-element program for the analysis of surface and corner cracks in solids subjected to mode-1 loadings

A computer program, surf3d, that uses the 3D finite-element method to calculate the stress-intensity factors for surface, corner, and embedded cracks in finite-thickness plates with and without circular holes, was developed. The cracks are assumed to be either elliptic or part eliptic in shape. The computer program uses eight-noded hexahedral elements to model the solid. The program uses a skyline storage and solver. The stress-intensity factors are evaluated using the force method, the crack-opening displacement method, and the 3-D virtual crack closure methods. In the manual the input to and the output of the surf3d program are described. This manual also demonstrates the use of the program and describes the calculation of the stress-intensity factors. Several examples with sample data files are included with the manual. To facilitate modeling of the user's crack configuration and loading, a companion program (a preprocessor program) that generates the data for the surf3d called gensurf was also developed. The gensurf program is a three dimensional mesh generator program that requires minimal input and that builds a complete data file for surf3d. The program surf3d is operational on Unix machines such as CRAY Y-MP, CRAY-2, and Convex C-220.

Raju, I. S.↗

NASA NTRS1991

The characterization of a crack-tip field

The stress intensity factor, K, has been successfully used as a measure of fracture toughness, and stress intensity factor range, Delta K, correlates well with the fatigue crack growth rate. This paper gives a deductive logic to demonstrate rigorously that, in the case of small-scale yielding, K and Delta K are capable of characterizing the elastic-plastic crack-tip field both under a monotonic loading and cyclic fatigue loading. This capability to characterize the entire crack-tip field is the underlying reason for the successful application of K and Delta K to linear fracture mechanics.

Liu, H. W.↗

NASA NTRS1974

A note on the effect of bending stiffness of stringers attached to a plate with a crack

An infinite stringer partially bonded to a plate through a layer of adhesive is considered. The stringer had bending as well as longitudinal stiffness. The effect of the stringer's bending rigidity on the stress intensity factor at the tip of the crack is illustrated. Shear stress distribution between the plate and the stringer and the stress intensity factors are obtained from the solution of a system of Fredholm integral equations. The continuity of displacements along the line of bond is represented by the equations.

Arin, K.↗

NASA NTRS1975

A note on the effect of lateral bending stiffness of stringers attached to a plate with a crack

An infinite stringer which is assumed to be partially bonded to a plate through a layer of adhesive is considered. The stringer is assumed to have bending as well as longitudinal stiffness. The effect of the stringer's bending rigidity on the stress intensity factor at the tip of the crack is illustrated. Shear stress distribution between the plate and the stringer and the stress intensity factors will be obtained from the solution of a system of Fredholm integral equations which represent the continuity of displacements along the line of bond.

Arin, K.↗

NASA NTRS2015

Fracture Growth Testing of Titanium 6AL-4V in AF-M315E

The Green Propellant Infusion Mission (GPIM) will demonstrate the performance of AF-M315E monopropellant in orbit. Flight certification requires a safe-life analysis of the titanium alloy fuel tank to ensure inherent flaws will not cause failure during the design life. Material property inputs for this analysis require testing to determine the stress intensity factor for environmentally-assisted cracking (K (sub EAC)) of Ti 6Al-4V in combination with the AF-M315E monopropellant. Testing of single-edge notched specimens SE(B) representing the bulk tank membrane and weld material were performed in accordance with ASTM E1681. Specimens with fatigue pre-cracks were loaded into test fixtures so that the crack tips were exposed to the monopropellant at 50 degrees Centigrade for a duration of 1,000 hours. Specimens that did not fail during exposure were opened to inspect the crack surfaces for evidence of crack growth. The threshold stress intensity value, KEAC, is the highest applied stress intensity that produced neither a failure of the specimen during the exposure nor showed evidence of crack growth. The threshold stress intensity factor of the Ti 6Al-4V forged tank material when exposed to AF-M315E monopropellant was found to be at least 22.0 kilopounds per square inch. The stress intensity factor of the weld material was at least 31.3 kilopounds per square inch.

AF-M315E↗

NASA NTRS1976

The semi-elliptical surface crack - A solution by the alternating method

A numerical solution to the three-dimensional equations of elasticity is presented for the problem of a semi-elliptical surface crack in the surface of a finite thickness solid. The alternating method is used to develop the numerical results which incorporate the effects on the stress intensity factor due to the presence of both the front and the back surfaces. The stress intensity factor is presented as a function of position along the crack border for a variety of crack shapes and crack depths. A comparison of the results of this study is made with previous theoretical and experimental work.

Smith, F. W.↗

NASA NTRS2001

Crack Turning Mechanics of Composite Wing Skin Panels

The safety of future composite wing skin integral stiffener panels requires a full understanding of failure mechanisms of these damage tolerance critical structures under both in-plane and bending loads. Of primary interest is to derive mathematical models using fracture mechanics in anisotropic cracked plate structures, to assess the crack turning mechanisms, and thereby to enhance the residual strength in the integral stiffener composite structures. The use of fracture mechanics to assess the failure behavior in a cracked structure requires the identification of critical fracture parameters which govern the severity of stress and deformation field ahead of the flaw, and which can be evaluated using information obtained from the flaw tip. In the three-year grant, the crack-tip fields under plane deformation, crack-tip fields for anisotropic plates and anisotropic shells have been obtained. In addition, methods for determining the stress intensity factors, energy release rate, and the T-stresses have been proposed and verified. The research accomplishments can be summarized as follows: (1) Under plane deformation in anisotropic solids, the asymptotic crack-tip fields have been obtained using Stroh formalism; (2) The T-stress and the coefficient of the second term for sigma(sub y), g(sub 32), have been obtained using path-independent integral, the J-integral and Betti's reciprocal theorem together with auxiliary fields; (3) With experimental data performed by NASA, analyses indicated that the mode-I critical stress intensity factor K(sub Q) provides a satisfactory characterization of fracture initiation for a given laminate thickness, provided the failure is fiber-dominated and crack extends in a self-similar manner; (4) The high constraint specimens, especially for CT specimens, due to large T-stress and large magnitude of negative g(sub 32) term may be expected to inhibit the crack extension in the same plane and promote crack turning; (5) Crack turning out of crack plane in generally anisotropic solids under plane deformation has been studied; (6) The role of T-stress and the higher-order term of sigma(sub y) on the crack turning and stability of the kinked crack has been quantified; (7) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner plate theory) in an anisotropic plate under bending, twisting moments, and transverse shear loads has been presented; (8) The expression of the path-independent J-integral in terms of the generalized stress and strain has been derived; (9) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner shallow shell theory) in a general anisotropic shell has been developed; (10) The Stroh formalism was used to characterize the crack tip fields in shells up to the second term and the energy release rate was expressed in a very compact form.

Yuan, F. G.↗

NASA NTRS1982

The crack problem in a specially orthotropic shell with double curvature

The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip.

Delale, F.↗

NASA NTRS1983

The crack problem in a specially orthotropic shell with double curvature

Delale, F.↗

NASA NTRS2016

Evaluation of the Effect of Surface Finish on High-Cycle Fatigue of SLM-IN718

The surface finish of parts produced by additive manufacturing processes is much rougher than the surface finish generated by machining processes, and a rougher surface can reduce the fatigue strength of a part. This paper discusses an effort to quantify that reduction of strength in high-cycle fatigue for selective laser melt (SLM) coupons. A high-cycle fatigue (HCF) knockdown factor was estimated for Inconel 718, manufactured with the SLM process. This factor is the percentage reduction from the maximum stress in fatigue for low-stress ground (LSG) specimens to the maximum stress of those left with the original surface condition at the same fatigue life. Specimens were provided by a number of vendors, free to use their "best practice"; only one heat treat condition was considered; and several test temperatures were characterized, including room temperature, 800F, 1000F, and 1200F. The 1000F data had a large variance, and was omitted from consideration in this document. A first method used linear approximations extracted from the graphs, and only where data was available for both. A recommended knockdown factor of the as-built surface condition (average roughness of approximately 245 micro-inches/inch) versus low-stress ground condition (roughness no more than 4 micro-inches/inch) was established at approximately 1/3 or 33%. This is to say that for the as-built surface condition, a maximum stress of 2/3 of the stress for LSG can be expected to produce a similar life in the as-built surface condition. In this first evaluation, the knockdown factor did not appear to be a function of temperature. A second approach, the "KP method", incorporated the surface finish measure into a new parameter termed the pseudo-stress intensity factor, Kp, which was formulated to be similar to the fracture mechanics stress intensity factor. Using Kp, the variance seemed to be reduced across all sources, and knockdown factors were estimated using Kp over the range where data occurred. A plot of the results suggests that the knockdown factor is a function of temperature, and that for low lives the knockdown might be lower than the knockdown observed above about one million cycles, where it tended to stabilize. This was not universal for all temperatures tested. The higher temperature tests are thought to be influenced by the test temperature, which perhaps continued the aging process. Further evaluation of the method is suggested.

Lambert, D. M.↗

NASA NTRS1992

Analysis and prediction of Multiple-Site Damage (MSD) fatigue crack growth

A technique was developed to calculate the stress intensity factor for multiple interacting cracks. The analysis was verified through comparison with accepted methods of calculating stress intensity factors. The technique was incorporated into a fatigue crack growth prediction model and used to predict the fatigue crack growth life for multiple-site damage (MSD). The analysis was verified through comparison with experiments conducted on uniaxially loaded flat panels with multiple cracks. Configuration with nearly equal and unequal crack distribution were examined. The fatigue crack growth predictions agreed within 20 percent of the experimental lives for all crack configurations considered.

Dawicke, D. S.↗

NASA NTRS1976

Interaction between an elastic circular inclusion and two symmetrically placed collinear cracks

The paper investigates the fracture toughness of a flat large elastic cracked plate containing an elastic circular inclusion, using the plane stress crack-tip stress intensity factor as a criterion for fracture. In this plane stress geometry, each of the two collinear finite cracks is located on either side of the elastic circular inclusion and the geometry is subjected to uniform stresses at infinity. The analysis is based on the two-dimensional theory of elasticity by using the Muskhelishvili complex variable approach. Numerical calculations are reported for the case of simple tension normal to the crack direction and show the variation of the stress intensity factor with the configuration and elastic properties of the plate and the inclusion.

Hsu, Y. C.↗

NASA NTRS1981

Line-spring model for surface cracks in a Reissner plate

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.

Delale, F.↗

NASA NTRS1979

An analysis of interface crack in adhesively bonded lap shear joints

This paper presents an analytical study of interface crack problems in adhesively bonded lap shear joints. A convenient and accurate method of analysis is developed on the basis of conservation laws in elasticity and of the fundamental relationships in fracture mechanics of interface crack problems. The problem is eventually reduced to a system of linear algebraic equations of mixed-mode stress intensity factor solutions. One of the salient features of the present approach is that the interface crack-tip stress intensity solutions can be determined accurately and directly by the information extracted from the far field. Solutions of the interface crack problems in lap shear joints have been obtained for the cases of various adhesive/adherend material systems and geometric configurations of the crack and the joint. Of particular interest is the evaluation of the mixed-mode stress intensity factors and the associated energy release rates. They are determined explicitly to illustrate the fundamental nature of the joint fracture problem.

Wang, S. S.↗

NASA NTRS1976

Several intact or broken stringers attached to an orthotropic sheet with a crack

Several intact or broken stringers which are continuously attached to a cracked orthotropic sheet through an adhesive are considered. The effect of orthotropy on the stress intensity factors is investigated. The stringers are assumed to be partially debonded due to high stress concentrations. The shear stress distribution between the stringers and the plate and the stress intensity factors are obtained from an integral equation which represents the continuity of displacements along the bond lines.

Arin, K.↗

NASA NTRS1981

Interlaminar crack growth in fiber reinforced composites during fatigue, part 3

Interlaminar crack growth behavior in fiber-reinforced composites subjected to fatigue loading was investigated experimentally and theoretically. In the experimental phase, inter-laminar crack propagation rates and mechanisms were determined for the cases of various geometries, laminate parameters and cyclic stress levels. A singular hybrid-stress finite element method was used in conjuction with the experimental results to examine the local crack-tip behavior and to characterize the crack propagation during fatigue. Results elucidate the basic nature of the cyclic delamination damage, and relate the interlaminar crack growth rate to the range of mixed-mode crack-tip stress intensity factors. The results show that crack growth rates are directly related to the range of the mixed-mode cyclic stress intensity factors by a power law relationship.

Wang, S. S.↗

NASA NTRS1984

The crack-inclusion interaction problem

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Xue-Hui, L.↗

NASA NTRS1986

The crack-inclusion interaction problem

Liu, X.-H.↗