Dynamic Fracture Mechanics Problems Research Articles

Influence of Dynamic Loading on Fracture Behaviour of DCB Sandwich Specimen

Numerical simulations of dynamic fracture behaviour of a double cantilever sandwich beam subjected to uneven bending moments in plane conditions are carried out using the dynamic finite element analyses with the ABAQUSTM code. The strain energy release rate was evaluated by means of the finite element model developed within the two-dimensional (2-D) linear elastodynamic theory. This demonstrates the capability and the reliability of the finite element modelling as an extremely useful numerical tool for solving dynamic fracture mechanics problems. Also, the dynamic behaviour of fracture parameters and interface crack progression is discussed.

Elastodynamic problems by meshless local integral method: Analytical formulation

Abstract In this paper, analytical forms of integrals in the meshless local integral equation method in the Laplace space are derived and implemented for elastodynamic problems. The meshless approximation based on the radial basis function (RBF) is employed for implementation of displacements. A weak form of governing equations with a unit test function is transformed into local integral equations. A completed set of the local boundary integrals are obtained in closed form. As the closed form of the local boundary integrals are obtained, there are no domain or boundary integrals to be calculated numerically. Several examples including dynamic fracture mechanics problems are presented to demonstrate the accuracy of the proposed method in comparison with analytical solutions and the boundary element method.

Three-Dimensional Problems in the Dynamic Fracture Mechanics of Materials with Interface Cracks (Review)

Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks are considered as nonclassical problems of fracture mechanics. Physically correct results in fracture mechanics in the case where the interaction of the crack edges must be taken into account are analyzed. The linear (classical) and nonlinear (nonclassical) problems of dynamic fracture mechanics for materials with interface cracks are formulated using the above approaches. A method for solving three-dimensional linear dynamic problems based on boundary integral equations for piecewise-homogeneous materials and the boundary-element method is outlined. This method can be used for incremental solution of nonlinear problems. The method involves the regularization of hypersingular integrals. New classes of three-dimensional linear dynamic problems for circular and elliptic interface cracks are solved. Numerical values of stress intensity factors obtained with the linear problem formulation are the first step toward calculating them in the nonlinear formulation. The first results obtained in solving nonlinear dynamic problems for interface cracks with interacting faces are briefly analyzed

General BE approach for three-dimensional dynamic fracture analysis

A general mixed boundary element approach for three-dimensional dynamic fracture mechanics problems is presented in this paper. A mixed traction-displacement integral equation formulation in the frequency domain is used. The hypersingular and strongly singular kernels are regularized by analytical transformations yielding an easy to implement BE approach. Nine-node quadrilateral and six-node triangular continuous quadratic elements are used for external boundaries and crack surfaces. The crack front elements have their mid node at one quarter of the element length allowing for a proper representation of the crack surface displacement. The present approach is intended for the frequency domain analysis of fracture mechanics problems of any general 3D geometry; i.e. boundless or bounded regions, single or multiple, surface or internal cracks. Transient dynamic problems are studied using the FFT algorithm. The numerical results presented show the robustness and accuracy of the approach which requires a reasonable number of elements and degrees of freedom.

Hierarchical, adaptive, material point method for dynamic energy release rate calculations

A crack-closure method was developed for use in material point method (MPM) calculations. The method can be used for calculation of the dynamic energy release rate in a variety of dynamic fracture mechanics problems. Most previous MPM analyses have used regular grids and a “lumped” mass matrix. For the most accurate energy release rate calculations, the regular grid had to be replaced by an adaptive grid that automatically refined the mesh around the crack tip and the lumped mass matrix had to be replaced by a full mass matrix. Using an adaptive mesh was more important to accuracy than was switching to a full mass matrix. Some sample calculations are given for energy release rate in a double cantilever beam specimen carried out by several different MPM methods.

Dynamic crack problems in three-dimensional transversely isotropic solids

In this paper, a general boundary element approach for three-dimensional dynamic crack problems in transversely isotropic bodies is presented for the first time. Quarter-point and singular quarter-point elements are implemented in a quadratic isoparametric element context. The procedure is based on the subdomain technique, the displacement integral representation for elastodynamic problems and the expressions of the time-harmonic point load fundamental solution for transversely isotropic media. Numerical results corresponding to cracks under the effects of impinging waves are presented. The accuracy of the present approach for the analysis of dynamic fracture mechanics problems in transversely isotropic solids is shown by comparison of the obtained results with existing solutions.

On the Dynamic Growth of a Spherical Inclusion With Dilatational Transformation Strain in Infinite Elastic Domain

In this paper, the dynamic effect was incorporated into the initiation and propagation process of a transformation inclusion. Based on the time-varying propagation equation of a spherical transformation inclusion with pure dilatational eigenstrain, the dynamic elastic fields both inside and outside the inclusion were derived explicitly, and it is found that when the transformation region expands at a constant speed, the strain field inside the inclusion is time-independent and uniform for uniform eigenstrain. Following the basic ideas of crack propagation problems in dynamic fracture mechanics, the reduction rate of the mechanical part of the free energy accompanying the growth of the transformation inclusion was derived as the driving force for the move of the interface. Then the equation to determine the propagation speed was established. It is found that there exists a steady speed for the growth of the transformation inclusion when time is approaching infinity. Finally the relation between the steady speed and the applied hydrostatic stress was derived explicitly.

Formulation of problems in dynamic fracture mechanics

This note presents an analysis of the standard formulation of dynamic fracture mechanics problems. It is shown that this formulation does not correspond to the physics of such problems.

Derivation of In-plane Mixed-Mode Asymptotic Solutions for an Unsteadily Fast-Propagating Crack Tip Using a Symbolic Manipulation System.

Explicit expressions for in-plane mixed-mode asymptotic solutions of an unsteadily fast-propagating crack tip had not been derived so far, due to seemingly insurmountable mathematical and algebraic difficulties To overcome these difficulties, a symbolic manipulation system was used in the present study. The explicit expressions for the mixed-mode transient stress and displacement fields up to the first five terms (n=0∼4) in asymptotic series were successfully derived. It was found that the transient effects do not appear in the first three terms (rigid body (n=O), singular (n=1) and constant-stress (n=2) terms), but appear only in the higher-order terms greater than or equal to the third order (ng3). The transient effects in the near-tip stress distributions were also visualized using the symbolic manipulation system. It was found that both effects of the crack acceleration and of the changes in the asymptotic coefficients increase the stress distribution ahead of the propagating crack tip. These stress-increases in the unsteady part may clarify the problem of the crack-acceleration effects in the dynamic fracture toughness versus crack velocity curves, which is one of important unsolved problems in dynamic fracture mechanics.

Problems of dynamic fracture mechanics with allowance for contact of the crack edges

This article - the second part of a survey of dynamic problems of fracture mechanics - looks at questions related to the solution of dynamic problems of the theory of elasticity for cracked bodies in which the crack edges can come into contact with one another during deformation.

Problems of dynamic fracture mechanics without contact of the crack faces

In this, the first part of the survey we have discussed only certain aspects of dynamic fracture mechanics. The surveyed material has been selected with a preference for the most highly developed parts of the theory, specifically those elements which have direct bearing on the second part of the survey. We have also included information on the dynamic fracture mechanics of initially stressed materials, in the development of which one of the authors has been a major contributor.

Theory of Mixed-Mode Caustics for Stationary Cracks in Optically Anisotropic Materials

The optical method of caustics is one of the most powerful techniques for evaluating stress intensity factors in static as well as dynamic fracture mechanics problems. In the method of transmitted caustics, optically anisotropic (birefringent) materials such as Araldite B and polycarbonate are often used. Double caustic curves appear for the tip of a crack in an optically anisotropic plate due to the birefringence. In this paper, a theory of caustics was developed for stationary cracks in birefringent materials under in-plane mixed-mode conditions. Completely analytical expressions were derived for the double caustic curves as well as for the double initial curves. The combined effects of optical anisotropy and mixed-mode state on the caustic curves and initial curves were investigated. A new procedure was also developed for the evaluation of mixed-mode stress intensity factors using the characteristic dimensions of the double caustic patterns.

A method of caustics for the direct experimental measurement of the [formula omitted] in nonlinear and dynamic fracture mechanics problems

This paper presents a methodology for the direct experimental measurement of the T ∗- integral . The method of caustics (the shadow pattern method) has proven to be a powerful optical method with which to measure stress intensity factors in static and dynamic fracture mechanics problems. An attempt has been made to extend the method of caustics to problems in nonlinear and dynamic fracture mechanics. The formation process of the caustic pattern for an elastoplastic crack tip in a compact-tension specimen was simulated by a finite-element analysis. The stimulated and actual caustic patterns agreed with each other very well. The relations between the T ∗- integral and the size of the caustic pattern were obtained for various optical set-ups. The experimental measurement of the caustic pattern in the dynamic tear test specimen of a nuclear pressure vessel steel was also carried out. High-speed photographs of the caustic patterns were taken using a laser caustic method, which can be quickly synchronized to the initiation of impact loading by a hammer that was dropped on the specimen. The time variation of the T ∗- integral during impact loading was evaluated by using the relation between the T ∗- integral and the size of the caustic pattern that was obtained by the numerical simulation. The hybrid numerical-experimental method developed here, in conjunction with laser caustic high-speed photography, has made it possible to measure the T ∗- integral for an elastoplastic material under impact loading conditions.

Theory of Mixed-Mode Caustics for Stationary Cracks in Optically Anisotropic Materials.

The optical method of caustics is one of the most powerful techniques for evaluating stress intensity factors in static as well as dynamic fracture mechanics problems. In the method of transmitted caustics, optically anisotropic (birefringent) materials such as Araldite B and polycarbonate were often used. Double caustic curves appear for a tip of the crack in an anisotropic (birefringent) plate, due to the birefringence. In this paper, a caustic theory was developed for stationary cracks in birefrigent materials under in-plane mixed-mode conditions. Completely analytical expressions were derived for the double caustic curves as well as for the double initial curves. The combined effects of optical anisotropy and mixed-mode state on the caustic curves and the initial curves were investigated. New procedures were also developed for the evaluation of mixed-mode stress intensity factors using the characteristic dimensions of the double caustic patterns.

Dynamic fracture mechanics studies by time-domain BEM

Transient dynamic fracture mechanics problems are studied using an advanced two-dimensional formulation of the time-domain boundary element method. This formulation employs a set of well-behaved kernel functions, which have been used recently for the solution of general problems of transient elastodynamics. These kernels produce very stable results with respect to both time step and element size variations and consequently, are ideally suited for fracture mechanics studies. In the present implementation, both ordinary quarter-point and traction-singular quarter-point elements are developed. The dynamic stress intensity factors (DSIF) are then obtained from the crack opening displacements (COD) as well as from the crack-tip nodal tractions of the traction-singular elements. A number of example problems are investigated in detail. Included are convergence studies, comparisons with previously published results, and an evaluation of the various methods available for computing DSIF.

A theory of caustics for mixed-mode fast running cracks

The method of caustics (shadow spot method) has proven to be a powerful optical method to measure stress intensity factors in static and dynamic fracture mechanics problems. In this paper, a theory of caustics was developed for elastodynamically propagating cracks under inplane mixed-mode conditions. Complex potentials for the general solutions of a near-tip field which have been previously derived by the authors were used in this theoretical development. Completely analytical expressions were derived for the caustic curves as well as for the initial curves for fast running cracks under inplane mixed-mode conditions. The effects of crack velocity and mixed-mode condition on the caustic pattern and the initial curve were investigated. New procedures were also proposed for the evaluation of the dynamic stress intensity factors K I and K II using the overall dimensions of the caustic pattern. The method of caustics developed here enables one to study quantitatively various mixed-mode dynamic fracture phenomena such as crack branching, crack curving, and crack kinking.

Measurement of stress intensity factors during dynamic crack propagation and arrest using a laser caustic method.

The method of caustics (shadow spot method) has proven to be a powerful optical method to measure stress intensity factors in static and dynamic fracture-mechanics problems. In this paper, high-speed photographs of the caustic patterns for dynamically propagating cracks were taken by a laser caustic method which can be rapidly synchronized to the initiation of the brittle fracture event. The dynamic stress intensity factors were evaluated on the basis of a theory of caustics for mixed-mode fast-running cracks, which was developed by the present authors. Influences of the length of the double cantilever beam (DCB) specimen were thoroughly investigated. It was found that the crack arrest toughness values, KIA, in shorter specimens were larger than those in longer specimens.

A theory of caustics for mixed-mode fast running cracks. 1st Report. Inplane mixed-mode theory.

The method of caustics (shadow spot method) has proven to be a powerful optical method to measure stress intensity factors in static and dynamic fracture mechanics problems. In this paper, a theory of caustics was developed for elastodynamically propagating cracks under inplane mixed-mode conditions. Complex potentials for the general solutions of a near-tip field which have been previously derived by the authors were used in this theoretical development. The effects of crack velocity and the mixed-mode condition on the caustic pattern and intial curve were investigated. A new procedure was also proposed for the evaluation of the dynamic stress intensity factors KI and KII using appropriate dimensions of the caustic pattern. The method of caustics developed here enables one to study quantitatively various mixed-mode dynamic fracture phenomena such as crack branching, crack curving, and crack kinking.

動的破壊力学問題の有限要素法シミュレーション

動的破壊力学問題の有限要素法シミュレーション