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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

Finite element solutions for crack-tip behavior in small-scale yielding

The subject considered is the stress and deformation fields in a cracked elastic-plastic power law hardening material under plane strain tensile loading. An incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region. The formulation has general applicability and was used to solve the small scale yielding problem for a set of material hardening exponents. Distributions of stress, strain, and crack opening displacement at the crack tip and through the elastic-plastic zone are presented as a function of the elastic stress intensity factor and material properties.

Tracey, D. M.↗

NASA NTRS1976

Symmetric stiffness matrix for incompressible hyperelastic materials

Symmetric structure matrices are derived for solving plane strain and axisymmetric problems involving incompressible hyperelastic materials. An infinite hollow cylinder subjected to internal pressure is considered as an example. Displacement and hydrostatic pressure profiles are calculated using the Newton-Raphson iteration technique. The results are in good agreement with the exact curves.

Takamatsu, T.↗

NASA NTRS1977

Investigation of the fracture mechanism in Ti-5Al-2.5Sn at cryogenic temperatures

The influence of microstructure on the fracture mechanism and plane-strain fracture toughness of Ti-5Al-2.5Sn was studied through the use of fractography and metallographic sectioning techniques. One-inch thick plates of extra low interstitial (ELI) and normal interstitial Ti-5Al-2.5Sn were mill annealed at 815 C followed by either air or furnace cooling. These variations in composition and cooling rate resulted in differences in the volume fraction and internal structure of the iron-stabilized phase, and in the crystallographic texture and ordering of the alpha matrix. The tensile properties of these plates were determined at 20 K, 77 K, and 295 K. The air-cooled ELI plate was the toughest material evaluated.

Vanstone, R. H.↗

NASA NTRS1977

Investigation of some problems in developing standards for precracked Charpy slow bend tests

The reported investigation was undertaken in connection with an attempt to develop procedures which would be useful in standardizing a test method for the precracked Charpy slow bend specimen. A number of alloys was studied for which valid plane-strain fracture toughness values have been established. The investigation shows that useful relations between precracked Charpy slow bend results and crack size factors can be obtained under some circumstances. However, it is not yet known what factors control these circumstances.

Succop, G.↗

NASA NTRS1977

Estimation of K/Ic/ from slow bend precracked Charpy specimen strength ratios

Data are presented concerning strength ratios which have been derived from slow bend tests on 0.25-in.-thick precracked Charpy specimens of steels, aluminum alloys, and a titanium alloy for which valid K(Ic) values have been established. The K(Ic) values considered are plane strain fracture toughness values as defined in the ASTM Method E 399-74. The strength ratios are used to develop calibration curves which could be useful in estimating K(Ic) for the purposes of alloy development or quality control.

Succop, G.↗

NASA NTRS1977

The influence of composition, annealing treatment, and texture on the fracture toughness of Ti-5Al-2.5Sn plate at cryogenic temperatures

The plane strain fracture toughness K sub Ic and conventional tensile properties of two commercially produced one-inch thick Ti-5Al-2.5Sn plates were determined at cryogenic temperatures. One plate was extra-low interstitial (ELI) grade, the other normal interstitial. Portions of each plate were mill annealed at 1088 K (1500 F) followed by either air cooling or furnace cooling. The tensile properties, flow curves, and K sub Ic of these plates were determined at 295 K (room temperature), 77 K (liquid nitrogen temperature), and 20 K (liquid hydrogen temperature).

Vanstone, R. H.↗

NASA NTRS1978

Microstructure and mechanical properties of quenched and tempered 300M steel

Type 300M steel, which is being used for the landing gear on the space shuttle orbiter, was subjected to a wide range of quenched and tempered heat treatments. The plane-strain fracture toughness and the tensile ultimate and yield strengths were evaluated. Cryogenic mechanical properties were obtained for conventionally heat-treated steel. The microstructure of all heat-treated test coupons was studied both optically and by transmission electron microscopy. Fracture surfaces were studied by means of scanning electron microscopy. Results indicate that substantial improvement in toughness with no loss in strength can be accomplished in quenched and tempered steel by austenitizing at 1255 K or higher. Low fracture toughness in conventionally austenitized 300M steel (1144 K) appears to be caused by undissolved precipitates, seen both in the submicrostructure and on the fracture surface, which promote failure by quasi-cleavage. The precipitates appeared to dissolve in the range 1200 to 1255 K.

Youngblood, J. L.↗

NASA NTRS1977

An orthotropic laminate composite containing a layer with a crack

A laminate composite containing an orthotropic layer with a crack situated normal to the interfaces, and bonded to two orthotropic half-planes of dissimilar materials, is considered. The solutions for two different classes of orthotropic materials are presented separately. In each case, the problem is first reduced to a system of dual integral equations, then to a singular integral equation which is subsequently solved numerically for the stress intensity factors at the tip of the crack. The effect of the material properties on the stress intensity factor is investigated. Two cases, the generalized plane stress and the plane strain, are treated simultaneously.

Arin, K.↗

NASA NTRS1977

Stress-free end problem in layered materials

In this paper the plane elastostatic problem for a medium which consists of periodically arranged two sets of bonded dissimilar layers or strips is considered. First it is assumed that one set of strips contains a crack which crosses the bimaterial interfaces. Then, by letting the collinear cracks join, the stress-free end problem is formulated. The singular behavior of the solutions at the point on intersection of the stress-free boundary and the interfaces is examined and appropriate stress intensity factors are defined. The results of some numerical examples are then presented which include the cases of both plane stress and plane strain.

Erdogan, F.↗

NASA NTRS1977

Alloy design with oxide dispersoids and precipitates

The mechanical behavior of particle-strengthened alloys is reviewed. On the basis of this knowledge, it is concluded that second-phase particles, coherent or incoherent, can enhance the flow strength, creep resistance, and stress-rupture life of alloys. Unfortunately, particles are usually not beneficial alloy-design elements if enhanced uniaxial ductility, plane-strain ductility, stress-rupture ductility, and toughness are called for. Such properties as fatigue-crack propagation resistance appear to require, for example, both high strength and high ductility, a situation which can come to pass only when the perennial conflict between strength and ductility is resolved in particle-strengthened systems in particular and in any other material system in general. Wherever possible, the role of coherent and incoherent particles in alloy design is distinguished.

Tien, J. K.↗

NASA NTRS1977

Development of a moderately sized finite element program for nonlinear structural analysis

AGGIE 1 is a computer program for predicting the linear and nonlinear, static and dynamic structural response of two- and three-dimensional continuum solids. The program is based on isoparametric finite elements and allows for 2-D plane stress, plane strain, and axisymmetric analyses and general 3-D analyses. Large strain kinematics is based on the total Lagrangian formulation. Materially nonlinear models include several elastic-plastic work-hardening models as well as an incompressible Mooney-Rivlin model. Included in this report is a brief description of the theoretical bases of the program, the material models used, the element library and the overall program organization. Instructions for data input preparation are given in detail. Several sample problems are given along with the required program input and program generated solutions.

Haisler, W. E.↗

NASA NTRS1979

Energy absorption mechanisms during crack propagation in metal matrix composites

The stress distributions around individual fibers in a unidirectional boron/aluminum composite material subjected to axial and transverse loadings are being studied utilizing a generalized plane strain finite element analysis. This micromechanics analysis was modified to permit the analysis of longitudinal sections, and also to incorporate crack initiation and propagation. The analysis fully models the elastoplastic response of the aluminum matrix, as well as temperature dependent material properties and thermal stress effects. The micromechanics analysis modifications are described, and numerical results are given for both longitudinal and transverse models loaded into the inelastic range, to first failure. Included are initially cracked fiber models.

Murphy, D. P.↗

NASA NTRS1980

Progress in turbulence modeling for complex flow fields including effects of compressibility

Two second-order-closure turbulence models were devised that are suitable for predicting properties of complex turbulent flow fields in both incompressible and compressible fluids. One model is of the "two-equation" variety in which closure is accomplished by introducing an eddy viscosity which depends on both a turbulent mixing energy and a dissipation rate per unit energy, that is, a specific dissipation rate. The other model is a "Reynolds stress equation" (RSE) formulation in which all components of the Reynolds stress tensor and turbulent heat-flux vector are computed directly and are scaled by the specific dissipation rate. Computations based on these models are compared with measurements for the following flow fields: (a) low speed, high Reynolds number channel flows with plane strain or uniform shear; (b) equilibrium turbulent boundary layers with and without pressure gradients or effects of compressibility; and (c) flow over a convex surface with and without a pressure gradient.

Wilcox, D. C.↗

NASA NTRS1980

Implementation of a trapezoidal ring element in NASTRAN for elastic-plastic analysis

The explicit expressions for an elastic-plastic trapezoidal ring element are presented and implemented in NASTRAN computer program. The material is assumed to obey the von Mises' yield criterion, isotropic hardening rule and the Prandtl-Reuss flow relations. For the purpose of demonstration, two elastic-plastic problems are solved and compared with previous results. The first is a plane-strain tube under uniform internal pressure and the second, a finite-length tube loaded over part of its inner surface. A very good agreement was found in both test problems.

Chen, P. C. T.↗

NASA NTRS1980

Sudden bending of cracked laminates

A dynamic approximate laminated plate theory is developed with emphasis placed on obtaining effective solution for the crack configuration where the 1/square root of r stress singularity and the condition of plane strain are preserved. The radial distance r is measured from the crack edge. The results obtained show that the crack moment intensity tends to decrease as the crack length to laminate plate thickness is increased. Hence, a laminated plate has the desirable feature of stabilizing a through crack as it increases its length at constant load. Also, the level of the average load intensity transmitted to a through crack can be reduced by making the inner layers to be stiffer than the outer layers. The present theory, although approximate, is useful for analyzing laminate failure to crack propagation under dynamic load conditions.

Sih, G. C.↗

NASA NTRS1980

Fracture toughness of brittle materials determined with chevron notch specimens

The use of chevron-notch specimens for determining the plane strain fracture toughness (K sub Ic) of brittle materials is discussed. Three chevron-notch specimens were investigated: short bar, short rod, and four-point-bend. The dimensionless stress intensity coefficient used in computing K sub Ic is derived for the short bar specimen from the superposition of ligament-dependent and ligament-independent solutions for the straight through crack, and also from experimental compliance calibrations. Coefficients for the four-point-bend specimen were developed by the same superposition procedure, and with additional refinement using the slice model of Bluhm. Short rod specimen stress intensity coefficients were determined only by experimental compliance calibration. Performance of the three chevron-notch specimens and their stress intensity factor relations were evaluated by tests on hot-pressed silicon nitride and sintered aluminum oxide. Results obtained with the short bar and the four-point-bend specimens on silicon nitride are in good agreement and relatively free of specimen geometry and size effects within the range investigated. Results on aluminum oxide were affected by specimen size and chevron-notch geometry, believed due to a rising crack growth resistance curve for the material. Only the results for the short bar specimen are presented in detail.

Shannon, J. L., Jr.↗

NASA NTRS1980

Elastic-plastic analysis using a triangular ring element in NASTRAN

An elastic plastic triangular ring element is implemented in NASTRAN computer program. The plane strain problem of partially plastic thick walled cylinder under internal pressure is solved and compared with the earlier finite difference solution. A very good agreement has been reached. In order to demonstrate its application to more general problems, an overloaded thread problem for the British Standard Buttress is examined. The maximum axial and principal stresses are located and their values are determined as functions of loadings.

Chen, P. C. T.↗