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Instability of rectangular solid in plane strain subjected axially to constant pressure and laterally to constant hydrostatic pressure
Multiple element continuity gage measures plane stress crack growth plus surface crack growth under plane strain conditions. The gage measures flat and curved surfaces and operates at cryogenic temperatures.
Double-cantilever displacement gauge for use in plane-strain crack-toughness tests of through- cracked plate specimens
The plane strain threshold stress intensity and sustained stress flaw growth rates were experimentally determined for 6AI-4V S.T.A. titanium forging and weldments in environments of Freon TF at room temperature. Sustained load tests of surface flawed specimens were conducted with the experimental approach based on linear elastic fracture mechanics. It was concluded that sustained stress flaw growth rates, in conjunction with threshold stress intensities, can be used in assessing the service life of pressure vessels.
Elastic displacements for edge cracked plate specimens used as crack extension indicator in plane strain fracture toughness measurements
Al alloys sheet, plate and weldments crack behavior and fracture toughness at cryogenic temperatures, using notched and surface flawed plane strain specimens
Specimen size and mechanical factors in plane strain fracture toughness testing of metallic materials
The correlation between fatigue crack propagation and stress intensity factor is analyzed. When determining fatigue crack propagation rate, a crack increment, delta a, and its corresponding increment in load cycles, delta N, are measured. Fatigue crack propagation must be caused by a shear and/or a normal separation mode. Both of these two processes are discrete if one looks at the atomic level. If the average deformation and fracture properties over the crack increments, delta a, can be considered as homogeneous, if the characteristic discrete lengths of sigma a, if the plastic zone size is small, and if a plate is thick enough to insure a plane strain case, da/dN is proportional to delta K squared. Any deviation of empirical data from this relation must be caused by the fact that one or more of these conditions are not satisfied. The effects of plate thickness and material inhomogeneity are discussed in detail. A shear separation mode of fatigue crack propagation is described and is used to illustrate the effects of material inhomogeneity.
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.
The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.
Discussion of adhesive fracture of single lap shear joints in terms of a maximum stress criterion and an energy balance. The Goland and Reissner (1944) analysis is used to determine the stress distribution in the adhesive assembly, and the results obtained are introduced into an energy balance to determine the initiation of adhesive fracture. In the stress analysis the loads at the edges of the joint are first determined. This is a problem in which the deformation of the joint sheets must be taken into account and is solved by using the finite-deflection theory of cylindrically bent plates. Then the stress in the joint due to applied loads is determined. This problem is formulated as one in plane strain consisting of two rectangular sheets of equal thickness and unit width. With the aid of this stress analysis and the stresses obtained from the conditions of equilibrium the contributions to the energy change with crack length are calculated. The analysis performed is then compared with a maximum stress criterion for a lap joint.
A model is discussed for the analysis of long part-through surface cracks in the walls of plate or shell structures. Such problems are formulated within the context of two dimensional plate and shell theory with the part-cracked section represented as a line-spring in the middle surface. The spring allows relative separations and rotations of the middle surface, and constitutive laws relating these discontinuities to the prevailing force and moment per unit length at any point are taken from the plane strain solution for a strip in combined tension and bending, which contains an edge crack of a corresponding depth. Prior work is reviewed and further line spring constitutive laws are discussed as appropriate to elastic analysis with thermal or residual stresses and to elastic-plastic analysis, with yielding in the ligament between the crack front and far wall in the latter case.
This experimental program was undertaken to determine the effects of combined cyclic/sustained loads, stress level, and crack shape on the fatigue crack growth rate behavior of cracks subjected to plane strain conditions. Material/environment combinations tested included: 2219-T87 aluminum plate in gaseous helium, room air, and 3.5% NaCl solution at room temperature, liquid nitrogen, and liquid hydrogen; 5Al-2.5 Sn (ELI) titanium plate in liquid nitrogen and liquid hydrogen and 6AL-4V (ELI) STA titanium plate in gaseous helium and methanol at room temperature. Most testing was accomplished using surface flawed specimens instrumented with a clip gage to continuously monitor crack opening displacements at the specimen surface. Tapered double cantilever beam specimens were also tested. Static fracture and ten hour sustained load tests were conducted to determine fracture toughness and apparent threshold stress intensity values. Cyclic tests were performed using sinusoidal loading profiles at 333 MHz (20 cpm) and trapezoidal loading profiles at both 8.3 MHz (0.5 cpm) and 3.3 MHz (0.2 cpm). Data were evaluated using modified linear elastic fracture mechanics parameters.
The plane strain problem of a multi-layered 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.
A special plasticity theory for soils in a triaxial compression drained condition which was extracted from a general theory of soil plasticity presented by Aguirre-Ramirez is generalized for three-dimensional complex stress fields. A theory for plane-strain is then constructed from the generalized three-dimensional theory. Both theories are then compared and found to be in agreement with the corresponding theories presented by Roscoe and Burland at Cambridge.
Measurement of subcritical crack growth during static loading of precracked titanium alloys in salt water using samples too thin for plane strain loading to predominate was examined as a method for determining the critical stress intensity for crack propagation in salt water. Significant internal crack growth followed by arrest was found at quite low stress intensities, but crack growth rates were relatively low. Assuming these techniques provided a reliable measurement of the critical stress intensity, the value for annealed Ti-4Al-1.5Mo-0.5V alloy was apparently about 35 ksi-in. to the 1/2 power, while that for annealed Ti-4Al-3Mo-1V was below 45 ksi-in. to the 1/2 power. Crack growth was also observed in tests conducted in both alloys in an air environment. At 65 ksi-in. to the 1/2 power, the extent of crack growth was greater in air than in salt water. Ti-4Al-3Mo-1V showed arrested crack growth in air at a stress intensity of 45 ksi-in. to the 1/2 power.
Stress corrosion cracking (SSC) tests were performed on 13 aluminum alloys, 13 precipitation hardening stainless steels, and two titanium 6Al-4V alloy forgings to compare fracture mechanics techniques with the conventional smooth specimen procedures. Commercially fabricated plate and rolled or forged bars 2 to 2.5-in. thick were tested. Exposures were conducted outdoors in a seacoast atmosphere and in an inland industrial atmosphere to relate the accelerated tests with service type environments. With the fracture mechanics technique tests were made chiefly on bolt loaded fatigue precracked compact tension specimens of the type used for plane-strain fracture toughness tests. Additional tests of the aluminum alloy were performed on ring loaded compact tension specimens and on bolt loaded double cantilever beams. For the smooth specimen procedure 0.125-in. dia. tensile specimens were loaded axially in constant deformation type frames. For both aluminum and steel alloys comparative SCC growth rates obtained from tests of precracked specimens provide an additional useful characterization of the SCC behavior of an alloy.
A brief review is given of the application of the notched cylinder as a screening specimen for use in sorting materials in respect to their relative levels of plane strain fracture toughness and a discussion of fracture mechanics applications including Irwin's important contributions in this area. In addition, practical problems encountered in application of this specimen will be presented.