C. Levy

Dynamic fracture of a beam or plate under tensile loading

Abstract The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. In a parallel analysis to [t] the crack length and applied loading at the fracture face are determined as functions of time measured from fracture initiation. The results of the analysis are shown in graphs of crack length, crack tip speed and fracturing section tensile loading vs time. As found in [1], the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then decelerates rapidly in the final stage of the process. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate under pure tensile loading.

Effect of shear and rotary inertia on dynamic fracture of a beam or plate in tensile loading

Abstract The dynamic fracture response of a long beam of brittle material subjected to tensile loading is studied. If the magnitude of the applied tensile loading is increased to a critical value, a crack will propagate from one of the longitudinal surfaces of the beam. As an extension of previous work, the effect of shear and of rotary inertia on the tensile loading and the induced bending moment at the fracturing section is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment and axial force at the fracture section are determined as functions of time after crack initiation. It is found that the rotary effect diminishes the bending moment effect and retards total fracture time whereas the shear has an opposite effect. Thus by combining the two effects (to simulate to first order the Timoshenko beam) overall fracture is retarded. The results also apply for plane strain fracture of a plate in tensile loading provided the value of the elastic modulus is appropriately modified.

The Influence of Autofrettage With Bauschinger Effect on the SIFS of Multiple Longitudinal Coplanar Cracks in Pressurized Cylinders

The influence of the Bauschinger Effect (BE) on the three dimensional, Mode I, Stress Intensity Factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The generation and comparison of the SIFs for a “realistic” - Bauschinger Effect Dependent Autofrettage (BEDA) and those for an “ideal” - Bauschinger Effect Independent Autofrettage (BEIA), which until now did not exist, is undertaken. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. More than 250 different crack configurations are analyzed. SIFs for various crack densities (2c/d = 0.25–0.75), a wide range of crack depth to wall thickness ratios (a/t = 0.01–0.25), various ellipticities (a/c = 0.5–1.5), and different levels of autofrettage (e = 30%–100%) are evaluated. The Bauschinger Effect (BE) is found to significantly lower the beneficial stress intensity factor due to autofrettage, KIA , by up to 52%, as compared to the case of “ideal” autofrettage. The reduction in KIA varies along the crack front with the maximum determined by the crack ellipticity, crack depth and crack separation distance. In some cases the maximum occurs at the deepest point of the crack and in others the maximum is at the point of intersection between the crack plane and the inner surface of the cylinder. In certain situations, the maximum transitions from one to the other as crack density increases. The detrimental influence of the BE increases as the crack density decreases and as crack depth decreases. For a partially autofrettaged cylinder, as the level of overstrain becomes smaller the influence of the BE is considerably reduced. As a result, the SIFs due to 100% BEDA differ by less than 15–17% when compared to 60% BEDA, and on the average the difference is only about 6%. Furthermore, the results indicate that crack density, and, in some cases, crack depth and crack ellipticity have opposing effects on the SIF of longitudinally coplanar crack arrays.Copyright

The Influence of the Bauschinger Effect on the Combined Stress Intensity Factors of Multiple Longitudinally Coplanar Cracks in Autofrettaged Pressurized Cylinders

The influence of the Bauschinger Effect (BE) on the three dimensional, Mode I, Combined Stress Intensity Factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The combined SIFs, KIN , that depend on both the “realistic” - Bauschinger Effect Dependent Autofrettage (BEDA) and “ideal” - Bauschinger Effect Independent Autofrettage (BEIA) are obtained and compared for crack to wall thickness, a/t = 0.01–0.25; crack ellipticity, a/c = 0.5–1.5; crack spacing ratio, 2c/d = 0.25–0.75; and autofrettage level, e = 30, 60 and 100%. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. The KIN is found to vary along the crack front with the maximum determined by the crack ellipticity, crack depth and crack spacing ratio. For a partially autofrettaged cylinder, the influence of the BE on the combined SIF, KIN , is considerably reduced as the level of overstrain becomes smaller. For some cases, when comparing like crack distributions, the KIN values obtained from the BEDA model are found to be as much as 100% higher than the KIN values that are computed using the BEIA model. A pressurized thick-walled cylinder with BEDA can be most dangerous when small cracks have small spacing ratio, i.e., when the cracks are farther apart. As crack length increases, or, for increased spacing ratio when the spacing between cracks is smaller, the SIFs increase. Though the differences in the BEDA SIF, KIA , between e = 100% and 60% are small (7–15%, in most cases), the increased level of autofrettage produces a 23–30% decrease in the combined SIF values, KIN . In certain cases, the BEIA model implies an infinite fatigue life, whereas the BEDA model for the same parameters implies a finite life. Therefore, it is important to perform a full 3-D analysis to determine the real life cycle of the pressurized cylinder for materials that exhibit the Bauschinger effect.Copyright

Controlled fracture in a finite geometry body as a stone shaping tool

Abstract A stone cutting technique capable of manufacturing curved shell sections from rectangular stone slabs has been recently proposed. Initially the rectangular slap of stone is prestressed by means of metal stamp pads which are rubber lined to prevent damage to the stone. Knife edges are then applied to the prestressed system at some fixed distance from the pads. As the load on the knives reaches a critical value, the stone fractures underneath the knife edges. The resulting crack propagation is curved and symmetric. Experiments with a limited number of different stones have shown that the initial angle of crack propagation is practically independent of the type of stone being cut. The purpose of this paper is to perform a preliminary analysis of this fracture process and to quantify such values as the initial angle of crack propagation and the critical knife-to-stamp load ratios producing fracture. Assuming the stone to be homogeneous, isotropic, linearly elastic and brittle, a two-dimensional plane model with an appropriate fracture condition is employed. The analysis shows that the conditions under which fracture occurs are material dependent in a small region about the knife location, but are independent of material properties outside this region. Further, the initial angles of crack propagation predicted by the analytical model are found to be in very good agreement with the experimental data.

Effect of bending moment on the dynamic fracture of a beam or plate under tensile loading

Abstract The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. As an extension of previous work, an induced bending moment generated during fracture is incorporated into the analysis and this improved formulation is presented. The crack length, crack tip speed, axial force and bending moment on the fracturing section are determined as functions of time after crack initiation. It is found that the bending moment has a significant effect on the fracture process in that it tends to retard fracture and causes a drastic change in the slope of the loading curve for large crack depths. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate in pure tensile loading.

On the symmetric dynamic fracture of a beam under tensile loading

Abstract The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied by means of two different one-dimensional models. If the magnitude of the applied loading is increased quasi-statically to a critical value, two coplanar edge cracks are assumed to propagate across the beams cross section. The first model parallels that of [6] with the crack length, crack speed and the loading on the fracturing section being determined as functions of time after fracture initiation. The second model is derived by means of energy considerations in the vicinity of the fracturing section. The results obtained from both models are similar except during the final phase of the fracture process.