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NASA NTRS1983

Crack arrest in structural ceramics

The non-unique, dynamic stress intensity factor versus crack-velocity relation as well as the lack of a dynamic arrest stress intensity factor in reaction bonded silicon nitride are contrasted with the gamma-shaped, dynamic stress intensity factor versus crack velocity relation and the dynamic arrest stress intensity factor of structural steel. These differences in dynamic fracture responses resulted in fracture of a hypothetical reaction bonded silicon nitride disk during a simulated start up condition of a gas turbine engine. A larger initial crack in a similar steel disk was arrested after propagating into a decreasing stress field generated by a steady state thermal gradient.

Kobayashi, A. S.↗

NASA NTRS2006

The Effect of the Laboratory Specimen on Fatigue Crack Growth Rate

Over the past thirty years, laboratory experiments have been devised to develop fatigue crack growth rate data that is representative of the material response. The crack growth rate data generated in the laboratory is then used to predict the safe operating envelope of a structure. The ability to interrelate laboratory data and structural response is called similitude. In essence, a nondimensional term, called the stress intensity factor, was developed that includes the applied stresses, crack size and geometric configuration. The stress intensity factor is then directly related to the rate at which cracks propagate in a material, resulting in the material property of fatigue crack growth response. Standardized specimen configurations and experimental procedures have been developed for laboratory testing to generate crack growth rate data that supports similitude of the stress intensity factor solution. In this paper, the authors present laboratory fatigue crack growth rate test data and finite element analyses that show similitude between standard specimen configurations tested using the constant stress ratio test method is unobtainable.

Forth, S. C.↗

NASA NTRS1975

Finite element techniques applied to cracks interacting with selected singularities

The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.

Conway, J. C.↗

NASA NTRS1973

Some effects of experimental error in fracture testing.

The purpose of this paper is to show the effects of experimental imprecision on the stress intensity factors calculated for various practical specimen types. A general form equation for the stress intensity factor is presented, and a general error equation is derived. The expected error in the stress intensity factor is given in terms of the precision levels of the basic experimental measurements and derivatives of the stress intensity calibration factor. Nine common fracture specimen types are considered, and the sensitivity of the various types to experimental error is illustrated. Some implications for fracture toughness testing and crack growth rate testing are discussed, and methods of analysis are proposed to compensate for the effects of experimental error.

Orange, T. W.↗

NASA NTRS2000

Determination of the Fracture Parameters in a Stiffened Composite Panel

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Lin, Chung-Yi↗

NASA NTRS1973

Some effects of experimental error in fracture testing

Effects of experimental imprecision on the stress intensity factors calculated for various practical specimen types are shown. A general form equation for the stress intensity factor is presented and a general error equation is derived. The expected error in the stress intensity factor is given in terms of the precision levels of the basic experimental measurements and derivatives of the stress intensity calibration factor. Nine common fracture specimen types are considered, and the sensitivity of the various types to experimental error is illustrated. Some implications for fracture toughness testing and crack growth rate testing are discussed and methods of analysis are proposed to compensate for the effects of experimental error.

Orange, T. W.↗

NASA NTRS1987

Plates and shells containing a surface crack under general loading conditions

Various through and part-through crack problems in plates and shells are considered. The line-spring model of Rice and Levy is generalized to the skew-symmetric case to solve surface crack problems involving mixed-mode, coplanar crack growth. Compliance functions are introduced which are valid for crack depth to thickness ratios at least up to .95. This includes expressions for tension and bending as well as expressions for in-plane shear, out-of-plane shear, and twisting. Transverse shear deformation is taken into account in the plate and shell theories and this effect is shown to be important in comparing stress intensity factors obtained from the plate theory with three-dimensional solutions. Stress intensity factors for cylinders obtained by the line-spring model also compare well with three-dimensional solution. By using the line-spring approach, stress intensity factors can be obtained for the through crack and for part-through crack of any crack front shape, without recalculation integrals that take up the bulk of the computer time. Therefore, parameter studies involving crack length, crack depth, shell type, and shell curvature are made in some detail. The results will be useful in brittle fracture and in fatigue crack propagation studies. All problems considered are of the mixed boundary value type and are reducted to strongly singular integral equations which make use of the finite-part integrals of Hadamard. The equations are solved numerically in a manner that is very efficient.

Joseph, Paul F.↗

NASA NTRS1985

Nonlinear adhesive behavior effects in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

The stress-intensity factors are determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer where the adhesive layer is modeled with a nonlinear stress-strain curve. By the use of Green's functions and the complex variable theory of orthotropic elasticity, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer, with which the crack-tip stress-intensity factors are found. When the adhesive was modeled with a nonlinear stress-strain curve, the peak shear stresses in the adhesive were considerably reduced in comparison to the solution for the linear elastic adhesive. This resulted in increases in the stress-intensity factors for the nonlinear adhesive solution compared to the linear adhesive solution. The nonlinear adhesive has no significant effect on the stress-intensity factor unless the near crack tip is beneath the stringer. It is assumed that the adhesive bond remains intact and it is predicted that onset of adhesive failure occurs at decreasing levels of applied stress as the crack propagates beneath the stringer.

Bigelow, C. A.↗

NASA NTRS1986

Nonlinear adhesive behavior effects in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

Bigelow, C. A.↗

NASA NTRS1985

A cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

The stress intensity factor is determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer. Since the stringer is modeled as a semiinfinite sheet, the solution is most appropriate for a crack tip located near a stringer edge. Both adherends are treated as homogeneous, orthotropic media. It is assumed they are in plane stress and the adhesive is in pure shear. From Green's functions and the complex variable theory of orthotropic elasticity developed by Lekhnitskiy, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations which is solved to obtain the shear stress distribution in the adhesive layer. With these stresses, equations for the stress intensity factors at both crack tips 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 an unstiffened sheet. However, as the crack propagates beneath the stringer, the stress intensity factor decreases significantly. Increasing the stiffness of the stringer or the adhesive also results in a decrease in the stress intensity factor.

Bigelow, C. A.↗

NASA NTRS1988

Methods for analysis of cracks in three-dimensional solids

Various methods used for determining stress-intensity factors for cracked three-dimensional bodies are reviewed. The review is limited to the determination of mode-I stress-intensity factors. Some exact solutions for cracks in infinite solids are presented, and various approximate methods that have been used for the solution of the boundary-value problem of finite solids with cracks are addressed. The techniques used to extract the stress-intensity factors from these solutions are considered, and various methods used to calculate the stress-intensity factors for through-the-thickness cracks, semielliptical surface cracks, and quarter-elliptical corner cracks at holes are compared for the case of remote tensile loading.

Raju, I. S.↗

NASA NTRS2016

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

A high-cycle fatigue (HCF) knockdown factor was estimated for Inconel 718, manufactured with the selective laser melt (SLM) process. This factor is the reduction at a common fatigue life from the maximum stress in fatigue for low-stress ground (LSG) specimens to the maximum stress of those left with the original surface condition. Various vendors provided specimens. To reduce the number of degrees-of-freedom, only one heat treat condition was evaluated. Testing temperatures included room temperature, 800F, 1000F, and 1200F. The two surface conditions were compared at constant lives, where data was available. The recommended knockdown factor of the as-built surface condition (average roughness of approximately 245 micro-inches/inch) versus low-stress ground condition (roughness <= 4 micro-inches/inch) is 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 the same life in the as built surface condition. As an alternative method, the surface finish was incorporated into a new parameter with the maximum stress. The new parameter was formulated to be similar to the fracture mechanics stress intensity factor, and it was named the pseudo stress intensity factor, Kp. Using Kp, the variance seemed acceptable across all sources, and the knockdown factor was estimated over the range of data identified by Kp 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 is greater than the knockdown observed above about one million cycles, where it stabilizes. One data point at room temperature was clearly different, and the sparsity of data in the higher life region reduces the value of these results. The method does appear to provide useful results, and further characterization of the method is suggested.

Lambert, Dennis M.↗

NASA NTRS1972

Some remarks on elastic crack-tip stress fields.

It is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factor for any other symmetrical load system whatsoever on the same body may be directly determined. The result is closely related to Bueckner's (1970) weight function, through which the stress intensity factor is expressed as a sum of work-like products between applied forces and values of the weight function at their points of application. An example of the method is given wherein the solution for a crack in a remotely uniform stress field is used to generate the expression for the stress intensity factor due to an arbitrary traction distribution on the faces of a crack. A corresponding theory is developed in an appendix for three-dimensional crack problems, although this appears to be directly useful chiefly for problems in which there is axial symmetry.

Rice, J. R.↗

NASA NTRS1995

Working toward a three-dimensional fatigue closure model for surface cracks

The first reliable elastic fracture mechanics solutions for a surface crack in a plate were obtained by Newman and Raju. The authors, both from the Mechanics of Materials Branch at NASA-Langley, used a highly detailed finite element solution requiring substantial computational resources. Computers have since become more powerful and available; however, many important related problems remain computationally expensive. The problem of three-dimensional fatigue crack growth taking into account plasticity-induced crack closure is one such problem. It is the goal of this research to provide an efficient method to account for three-dimensional crack closure in fatigue. Newman developed a two-dimensional plasticity-induced crack closure model for center cracked specimens. This model requires iterations to determine both the contact solution at each growth step and the extent of the plastic zone at the crack tip. A three-dimensional version of this model would require obtaining these nonlinear variables all along the crack front. This model must be efficient so that repeated calculations can be performed during crack growth simulations. The highly versatile line spring model (LSM) with contact, fatigue, and plasticity will form the basis of the closure model. There are several required additions to past work to address the three-dimensional crack closure problem. Initially, these additions will include (1) an improved LSM to more accurately obtain the crack opening displacement, stress intensity factors, and elastic T-stress near the ends of the surface crack; (2) a method to determine the extent of the plastic zone all along the crack front; (3) a method to determine the contact zone given a perfectly plastic layer of material on the crack surfaces; (4) a method to determine the magnitude of the compressive contact stress; and (5) a way to implement the degree of constraint along the curved crack front. During the summer ASEE program an enhanced LSM was developed. A method similar to that of 'strip synthesis' first introduced by Fujimoto was used. Briefly, the crack opening displacements of 'slices' of the surface crack in a direction parallel to the plate surface are considered in addition to the standard LSM approach that makes use of springs obtained from slices perpendicular to the plate surface. This enhancement is necessary so that an accurate three-dimensional representation of quantities such as contact zone size, plastic zone size, stress intensity factors, T-stress, and crack opening displacement can be determined. By combining results of previous investigations with the LSM, the problem of three-dimensional crack closure will be addressed. In addition to a closure model, the enhanced LSM can be used for many other problems including interacting surface cracks and fatigue crack growth of a through crack with a curved crack front.

Joseph, Paul F.↗

NASA NTRS1974

Stress analysis of the compact specimen including the effects of pin loading

An improved method of boundary collocation was applied to the two-dimensional stress analysis of the compact specimen. The effects of the pin-loaded holes on stress-intensity factors and crack-opening displacements were investigated for various crack-length-to-specimen-width ratios, hole locations, and internal loadings. The stress-intensity factors for the 'standard' compact specimen under plane-stress or plane-strain conditions were found to be within 1 percent of the stress-intensity factors reported in the ASTM Test for Plane-Strain Fracture Toughness of Metallic Materials (E 399-72) over a range of crack-length-to-specimen-width ratios of 0.4 to 0.7. However, for crack-length-to-specimen-width ratios less than 0.4, the pin-load holes (which were not previously accounted for) had a significant effect on stress intensity and crack-opening displacements.

Newman, J. C., Jr.↗

NASA NTRS1984

A review of chevron-notched fracture specimens

The historical development of chevron notched fracture specimens is reviewed. Stress intensity factors and load line displacement solutions proposed for some of these specimens are compared. The original bend bar configurations up to the present day short rod and bar specimens are reviewed. The results of an analytical round robin that was conducted on chevron-notched specimens are presented. In the round robin, stress-intensity factors for either the chevron notched round rod or square bar specimens were calculated. The consensus stress intensity factor (compliance) solution for these specimens is assessed. The stress intensity factor solutions proposed for three and four point bend chevron notched specimens are reviewed.

Newman, J. C., Jr.↗

NASA NTRS1991

The surface and through crack problems in layered orthotropic plates

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Erdogan, Fazil↗

NASA NTRS1987

Fracture study of windshield glass panes

The major stresses which cause crack propagation in windshield glass panes are induced by bending moments which result from the pressure differentials across the panes. Hence the stress intensity factors for the finite plate with the semi-elliptical surface flaw and edge crack under the bending moments are examined. The results show that the crack growth will be upperbound if it is computed by using the stress intensity factor for the finite plate with the edge crack subjected to pure bending moments. Furthermore, if the ratio of crack depth to plate thickness, a/t, is within 0.3, the stress intensity factor can be conservatively assumed to be constant at the value of a/t equal to zero. A simplified equation to predict the structural life of glass panes is derived based on constant stress intensity factor. The accuracy of structural life is mainly dependent on how close the empirical parameter, m, can be estimated.

Yeh, H. Y.↗