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The plane strain problem of a millilayered composite with parallel cracks is considered. The main objective is to study the interaction between parallel and collinear cracks. The problem is formulated in terms of a set of simultaneous singular integral equations which are solved numerically. The effect of material properties on the interaction between cracks is also demonstrated.
The present work reviews the use of the notched cylinder as a screening specimen for use in sorting materials with respect to their relative levels of plane strain fracture toughness. Irwin's work in developing an estimate of stress intensity factors for the circumferentially cracked cylinder is reviewed. Some discrepancies between stress intensity factors determined with fatigue cracked notched cylinders and those determined with plate specimens are discussed. Problems in the technical realization of fatigue cracking a specimen are briefly discussed, and the problem of ensuring low eccentricity of loading when testing notch cylindrical specimens is considered. Finally, specimen size requirements for testing are examined.
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 was considered. The solutions for two different classes of orthotropic materials are presented. In each case, the problem was first reduced to a system of dual integral equations, then to a singular integral equation which was 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 was investigated. The generalized plane stress and the plane strain were treated simultaneously.
Theory is stated in terms of increments of displacement and stress, and of instantaneous or accumulated values of stress. The equilibrium equations, in the absence of body forces, are written, along with constitutive relations for plane strain.
The microstructure of the alpha titanium alloy Ti-5Al-2.5Sn and the metastable beta titanium alloy Beta 3 was examined. The material was from normal and extra low interstitial grade plates which were either air-cooled or furnace-cooled from an annealing treatment. Beta 3 was studied in alpha-aged and omega-aged plates which were heat treated to similar strength levels. Tensile and plane strain fracture toughness tests were conducted at room temperature on the alpha-aged material. The microstructure and fracture mechanisms of alloys were studied using optical metallography, electron microscopy, microprobe analyses, and texture pole figures. Future experiments are described.
The effect of load interactions on the crack growth velocity of D6AC steel under stress corrosion cracking conditions was determined. The environment was a 3.5 percent salt solution. The modified-wedge opening load specimens were fatigue precracked and subjected to a deadweight loading in creep machines. The effects of load shedding on incubation times and crack growth rates were measured using high-sensitivity compliance measurement techniques. Load shedding results in an incubation time, the length of which depends on the amount of load shed and the baseline stress intensity. The sequence of unloading the specimen also controls the subsequent incubation period. The incubation period is shorter when load shedding passes through zero load than when it does not if the specimen initially had the same baseline stress intensity. The crack growth rates following the incubation period are also different from the steady-state crack growth rate at the operating stress intensity. These data show that the susceptibility of this alloy system to stress corrosion cracking depends on the plane-strain fracture toughness and on the yield strength of the material.
Five methods are used to calculate plane strain fracture toughness (K sub Q) values for bend-specimens of various sizes from two high-strength steels. None of the methods appeared to satisfactorily predict valid stress intensity factor (K sub IC) values from specimens of sizes well below that required by E399 standard tests.
A preliminary study was conducted to assess the feasibility of ultrasonically ranking material fracture toughness. Specimens of two grades of maraging steel for which fracture toughness values were measured were subjected to ultrasonic probing. The slope of the attenuation coefficient versus frequency curve was empirically correlated with the plane strain fracture toughness value for each grade of steel.
Tension, notched tension, compression, density, thermal conductivity, and thermal expansion tests were conducted on Incoloy 903 over the temperature range 20 K (-423 F) through 1033 K (1400 F). Fracture toughness tests were performed at room temperature (RT). Creep and rupture tests were conducted at 811 K (1000 F), 922 K (1200 F), and 1033 K (1400 F) for this alloy. Transverse unnotched and notched fatigue tests at R = 0.1 were performed at RT and 922 K (1200 F). For CTX-1 alloy, tension, Charpy V-notch impact, density, thermal conductivity, and thermal expansion tests were conducted over the temperature range 20 K (-423 F) through 1033 K (1400 F). Poisson's ratio was determined at RT, 811 K (1000 F), 922 K (1200 F), and 1033 K (1400 F). Notched tension and compression tests were performed at 20 K (-423 F), RT, and 922 K (1200 F); plane strain fracture toughness tests were conducted at RT, 77 K (-320 F), and 20 K (-423 F). Creep and rupture tests were performed at 811 K (1000 F), 922 K (1200 F), and 1033 K (1400 F); longitudinal unnotched and notched fatigue tests at R = 0.1 were conducted at RT and 922 K (1200 F). Results are presented and discussed.
The three-dimensional, primitive equations of motion are solved numerically for the case of isotropic box turbulence and the distortion of homogeneous turbulence by irrotational plane strain at large Reynolds numbers. A Gaussian filter is applied to governing equations to define the large scale field. This gives rise to additional second order computed scale stresses (Leonard stresses). The residual stresses are simulated through an eddy viscosity. Uniform grids are used, with a fourth order differencing scheme in space and a second order Adams-Bashforth predictor for explicit time stepping. The results are compared to the experiments and statistical information extracted from the computer generated data.
A 300 grade maraging steel was chosen as a vehicle by which to understand the inverse relationship between strength and toughness in high strength alloys such as the 18 Ni maraging steels. The 18 Ni, 300 grade maraging material was a commercial grade consumable-electrode, vacuum arc remelted heat obtained in the form of forged and annealed plate. The matrix contained a population of second-phase impurity inclusions which was a product of the casting and hot working processes. These inclusions did not change with subsequent precipitation hardening. Changes in microstructure resulting in strength increases were brought about by variations in aging temperature and time. Maximum strength was attained in the 300 grade maraging steel by aging at 427 C (800 F) for 100 hours. Tensile, fatigue precracked Charpy impact, and plane-strain fracture toughness tests were performed at room temperature, 20 C (68 F). With increasing strength the fracture toughness decreases as smaller and smaller inclusions act as sites for void initiation.
A formulation is presented for the development of a finite element program for the elastic analysis of two-dimensional bodies using the eight-node isoparametric quadrilateral. The program solves for both plane stress and plane strain problems. The finite element formulation based on the isoparametric displacement functions is presented. The program structure is given in the form of flow diagrams with descriptions of the numerical procedure used to obtain the element stiffness matrix, and the solution method employed to solve for nodal displacements. Three numerical examples (a plate under uniaxial tension, a plate under pure shear, and a beam under pure bending) are presented to illustrate the capability and limitations of the element implementation. The first problem is solved exactly by the element, as predicted by the form of its displacement functions. In the other two problems the accuracy of the solution is highly dependent upon the slenderness of the element, the number of elements in the map, and the numerical integration scheme used to build the element stiffness matrix.
The plane strain fracture toughness and tensile strength response of 300M Steel to a wide variety of austenitizing and tempering temperatures were investigated. The results make it possible for one to select heat treatments which provide an optimum combination of strength and toughness for a variety of structural applications. In particular, improvements in toughness on the order of 20% were found possible with no loss in tensile properties by increasing the austenitizing temperature from the currently employed 1144 K to 1255 K or higher, and this change in heat treatment therefore appears worthy of general implementation.
A boundary collocation procedure has been applied to the Williams stress function to determine the elastic stress distribution for the crack tip region of a finite, edge-cracked plate subjected to mode II loading at the crack tips. The asymmetric specimen selected was particularly suitable for the determination of plane strain fracture toughness for mode II loading. Numerical solutions for stress intensity factors for the edge-sliding mode obtained by the boundary collocation method were in close agreement with values obtained from photoelastic experiments. Fracture tests of several compact shear specimens of 2024-T4 aluminum were conducted in order to experimentally investigate the behavior of the edge-sliding mode. In each case a brittle shear failure was observed and mode II fracture toughness values were obtained. The average value for K-IIc obtained from two tests was 39.5 ksi radical (in). No K-Ic data for 2024-T4 were available for comparison purposes; however, K-Ic values for a similar alloy, 2024-T351, have been reported as 34 ksi radical (in) which is only about 15 per cent below the corresponding K-IIc value.
A preliminary study was conducted to assess the feasibility of ultrasonically ranking material fracture toughness. Specimens of two grades of maraging steel for which fracture toughness values were measured were subjected to ultrasonic probing. The slope of the attenuation coefficient vs frequency curve was empirically correlated with the plane strain fracture toughness value for each grade of steel.
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.
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.
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.