Dynamic Energy Release Rate Research Articles

Elastic-plastic analysis of a dynamically loaded circumferentially notched round bar

Dynamic elastic-plastic finite-element analyses of a circumferentially notched round bar subject to loading by a tensile stress pulse are presented. The finite-element study is motivated by the dynamic fracture initiation experiment introduced by Costin, Duffy and Freund and therefore provides a critique of this experiment. Static elastic-plastic analyses are carried out for externally notched round bars of various relative crack depths. The J integral is calculated at each load increment using an invariant finite-domain integral representation for the energy release rate. These values of J, obtained by integrating the computed field quantities over arbitrary contours and areas enclosed by the contours, are taken as the reference values. Through comparison with these results, we evaluate the accuracy of a deep crack formula based on the load-displacement behavior. Similar formulas are frequently employed for fracture toughness measurements using standardized test configurations. In the dynamic elastic-plastic analysis, the circumferentially notched round bar subject to a tensile pulse is examined. A uniform rate of loading is applied at one end of the bar to simulate the long pulse loading in the experiment. An invariant finite-domain integral expression, which is particularly suited for finite-element analyses, is employed to calculate the dynamic energy release rate. Our analyses provide some insight concerning the accuracy of these invariant domain integral expressions and their usefulness in computational studies. We also calculate the value of the J integral from the load-displacement behavior, using a formula proposed by Costin, Duffy and Freund. The present study clarifies the applicability of such a formula for the determination of the dynamic fracture toughness and provides information concerning the effect of relative crack depth and the extent of plasticity on its accuracy.

Dynamic energy release rate and fracture heat in polymethylmethacrylate (PMMA) and a high-strength steel

The energy release rate G is a measure of the elastic energy causing crack propagation whereas the fracture heat Q indicates the amount of energy dissipated in the fracture zone. As long as any change in structure and energy losts by elastic waves can be neglected, the fracture heat represents the energy consumption of the crack and should be equivalent with G. If this can be proven one could use Q- measurements as an alternative method for investigating running cracks and dynamic fracture criteria, which in some cases may be a more appropriate measurement of the dynamic energy release rate G dyn or the dynamic stress intensity factor K dyn .

On the crack propagation in micropolar elastic solids

This paper is concerned with the dynamic energy release rate for a sharp, straight crack in a micropolar elastic body.

Comparison of static and dynamic energy release rates for different fracture specimens

Static and dynamic energy release rates were utilised to study energy losses away from the crack tip in three different fracture specimens during a dynamic fracture event. The method of analysis utilizes an energy balance in the system. The results show that a substantial amount of energy is lost away from the crack tip. Moreover the energy loss is found to be dependent on the specimen geometry and material.

Rapid crack propagation and arrest in the dcb specimen—an improved numerical analysis

AbstractA two‐dimensional linear elastodynamic analysis of crack initiation, fast crack propagation and crack arrest in the DCB specimen is presented. The analysis is performed using the previously developed SMF2D code in its generation mode. The experimentally measured crack tip motion, as well as the specimen's geometry and its material characteristics, serve as input to the simulation. The dynamic stress intensity factor, the dynamic energy release rate and the various distributions of energies are subsequently evaluated. The numerical results are found to be in very good agreement with analytical and experimental findings.

Dynamic fracture of unidirectional graphite fiber composite strips

An approximate equation of motion is derived and is used in the analysis of a dynamically propagating crack in a highly orthotropic fiber composite infinite strip subjected to constant displacement Mode I loading. With the use of Fourier transforms, the problem is reduced to an equation which is solved by the Wiener-Hopf technique. The dynamic stress intensity factor is derived and is expressed as the product of a velocity correction factor and a static stress intensity factor. The corresponding dynamic energy release rate is derived also and it is found not to be explicitly dependent upon the crack-tip velocity. It is found experimentally that the long strip configuration subjected to constant extensional displacement can simulate constant crack propagation velocities. Accordingly, the model's dynamic energy release rate is used to determine the dynamic fracture energy (toughness) of 90° Hercules AS/3501-6 graphite epoxy composites.

Approximate Mode II velocity correction factors for 90° unidirectional fiber composites

A static Mode III isotropic/Mode II orthotropic analogy is developed for 90° highly orthotropic fiber composites. This static analogy is extended to the dynamic regime and the velocity correction factors for the dynamic energy release rate and the dynamic stress intensity factor are obtained for the Mode II case. The complete dynamic analogies are given. The approximate Mode II 90° velocity correction factors W II(90°) and S II((90°) are of the same general form as the approximate Mode I velocity correction factors, W I(0°) , W I(90°) , S I(0°) and S I(90°) Whereas the four Mode I velocity correction factors approach zero as the crack-tip velocity approaches the composite shear wave speed, w II(90°) and s II(90°) approach zero as the crack-tip velocity approaches the larger extensional wave speed.

動的エネルギ解放率に関する基礎的考察

This paper presents theoretical considerations on the expressions for the dynamic energy release rate in elastic crack propagation.The validity of the expressions, which have been proposed by Erdogan, by Achenbach and by Freund, is discussed on the basis of the fundamental expression defined by an overall energy rate balance.The energy release rate is divided into the usual quasi-static energy release rate plus a non-positive dynamic contribution; they are discussed as the strain energy release rate for the former and as the kinetic energy generating rate for the latter. They will be useful as new parameters related to the dynamical behavior of crack propagation.The mathematical derivations given here are not in detail, but rather the background of the assumptions and physical considerations of the results are emphasized.

Approximate mode I velocity correction factors for 90° unidirectional fibre composites

A static Mode III isotropic/Mode I orthotropic analogy is developed for 90° highly orthotropic fibre composites. This static analogy is extended to the dynamic regime and velocity correction factors are obtained for the dynamic energy release rate and the dynamic stress intensity factor. The complete dynamic analogies are given. The approximate 90° orthotropic velocity correction factors are compared with various isotropic velocity correction factors and are shown to be equal to the approximate 0° orthotropic velocity correction factors which were derived via a similar analogy. The Mode I velocity correction factors for orthotropic composites which do not satisfy the ‘highly orthotropic’ requirement are discussed also.

Computer simulation of fast crack propagation in brittle material

A method is presented to simulate the behavior of a rapidly running crack by employing the finite element method with a singular element. The crack-tip is assumed to move so as to satisfy a dynamic fracture criterion that the dynamic energy release rate be equal to a specific fracture energy during failure. Simulation is carried out for a crack in a rectangular plate subjected to a suddenly applied load, and it has indicated that the dynamic behavior of a crack, such as onset of crack propagation, bifurcation, or stopping, is deeply influenced by the magnitude and the time duration of the applied load.

Crack bifurcation under hydrostatic pressure

Glass tubes were fractured by internal pressure under atmospheric or superimposed hydrostatic pressure. It is found that the crack length at bifurcation is significantly increased by superimposed hydrostatic pressures. The dynamic energy release rate for a crack propagating with superimposed hydrostatic pressure is calculated. It is shown that the pressure effect on crack length at bifurcation may be explained by combining the energy balance condition and the Yoffe's concept for crack bifurcation.

Dynamic problem of expanding crack under concentrated load

An analysis is presented on a dynamic problem of two-dimensional crack which is subjected to a time-increasing concentrated load on the surface and expands at both ends at a constant velocity. The dynamic stress intensity factor and the dynamic energy release rate are calculated for a linear elastic solid. A further extension of elastic analysis with simulated plasticity is made by the strip yield model, the Dugdale's model. It is shown that the plastic zone length, the COD and the energy release rate are expressed by functions decreasing with the crack velocity.

Influence of Rotatory Inertia on Steady-State Crack Propagation in a Finite Plate Subjected to Out-of-Plane Bending

A dynamic stress-intensity factor and energy release rate are obtained for a running semi-infinite crack traversing a strip of elastic material subjected to out-of-plane bending. It is shown that the maximum ratio of crack tip velocity to shear wave velocity is identical to the maximum ratio of flexural wave velocity to shear wave velocity in the limit of vanishingly small wavelength. The dynamic stress-intensity factor is written as the product of a static stress-intensity factor multiplied by a function of Poisson’s ratio and crack tip velocity the function decreasing monotonically with increasing crock tip velocity. The energy release rate is shown to be independent of crack tip velocity for this type of problem.

Dynamic Problem of Expanding Crack under Concentrated Load

Abstract An analysis is presented on a dynamic problem of two-dimensional crack which is subjected to a time-increasing concentrated load on the surface and expands at both ends at a constant velocity. The dynamic stress intensity factor and the dynamic energy release rate are calculated for a linear elastic solid. A further extension of elastic analysis with simulated plasticity is made by the strip yield model, the Dugdale's model. It is shown that the plastic zone length, the COD and the energy release rate are expressed by functions decreasing with the crack velocity.

An approximate expression relating dynamic and static strain energy release rates for finite specimens

An approximate expression relating dynamic and static strain energy release rates for finite specimens

Application of an energy balance and an energy method to dynamic crack propagation

The speeds of fast running cracks in a range of quasi-brittle materials are measured as a function of the dynamic strain energy release rate. From the results, the heat output associated with the plastic work at the crack tip is calculated as a function of crack speed using an energy balance, and compared with the heat outputs determined experimentally using an energy method. A generally good agreement is found between the calculated and the experimentally measured variation of heat output with crack speed.

Steady-State Crack Propagation in Pressurized Pipelines Without Backfill

In a previous paper, a simplified dynamic-shell theory representation was formulated for steady-state motion in a pipeline without backfill. The present work extends this model by (1) incorporating a gas dynamics treatment to determine the axial variation in the pressure exerted by the gas on the pipe walls, and (2) incorporating a plastic yield hinge behind the crack tip. Solutions to the governing dynamic equations are obtained for these conditions and used to calculate the steady-state dynamic energy release rate as a function of crack speed. In the single full-scale experiment in which an independent estimate of the dynamic fracture energy is available for a pipe without backfill, the model predicts a steady-state speed of 780 fps. This can be compared with measured speeds which ranged from 725 to 830 fps in the test. Because the calculated steady-state dynamic energy release rate exhibits a maximum, it is suggested that this approach may offer a basis for crack arrest design of pipelines.