Application of incubation time approach to simulate dynamic crack propagation

The incubation time criterion for dynamic fracture is applied to simulate dynamic crack propagation. Being incorporated into ANSYS finite element package, this criterion is used to simulate the classical dynamic fracture experiments of Ravi-Chandar and Knauss on dynamic crack propagation in Homalite-100. In these experiments a plate with a cut simulating the crack was loaded by an intense pressure pulse applied on the faces of the cut. The load consisted of two consequent trapezoidal pulses. This, in the experimental conditions used by Ravi-Chandar and Knauss, resulted in a crack initiation, propagation, arrest and reinitiation. Dependence of the crack length on time was measured in those experiments. The results for crack propagation obtained by FEM modelling are in agreement with experimental measurements of crack length histories. This result shows the applicability of the incubation time approach to describe the initiation, propagation and arrest of dynamically loaded cracks.     

Energy balance anlaysis on mode-III dynamic crack propagation in fixed sided strip

Mode-III crack propagating in a fixed sided strip is studied by the global energy balance method. First the kinetic energy and the strain energy of the crack system are obtained in analytic forms based on the displacement field of dynamic elastic analysis. Using the energy equilibrium concept, the motion equation of the crack is derived. The acceleration or deceleration of the crack is explained by the derived equation. The phenomena of crack velocity oscillation and unstable propagation are interpreted by the particular characteristics of the fracture toughness and a simulation of the oscillations is demonstrated.     

An XFEM/Spectral element method for dynamic crack propagation

A high-order extended finite element method based on the spectral element method for the simulation of dynamic fracture is developed. The partition of unity for the discontinuous displacement is constructed by employing p order spectral element. This method shows great advantages in the simulations of moving crack and mixed mode crack. The numerical oscillations are effectively suppressed and the accuracy of computed stress intensity factors and crack path are improved markedly. Furthermore the simulation results show that p-refinement is more effective in improving the stress contour near the crack tip than h-refinement. The well known form of the explicit central difference method is used and the critical time step for this method is investigated. We find that by using lumped mass matrix the critical time step Δt _c for this high-order extended finite element is almost independent of the crack position.     

Analysis of the optical method of caustics for dynamic crack propagation

In the interpretation of experimental data on dynamic crack propagation in solids obtained by means of the optical method of caustics, it has been customary to neglect the effect of material inertia on the stress distribution in the vicinity of the crack tip. In this paper, the elastodynamic crack tip stress field is used to establish the exact equations of the caustic envelope formed by the reflection of light rays from the surface of a planar solid near the tip of a propagating crack. These equations involve the instantaneous crack tip speed, the material parameters and the instantaneous dynamic stress intensity factor, and they can be used to determine the stress intensity factor for given material parameters and crack tip speed. The influence of inertial effects on stress intensity factor measurements for system parameters typical of experiments with PMMA specimens is considered. It is found that the stress intensity factor values inferred through a dynamic analysis may differ by as much as 30–40% from values based on a quasi-static analysis.     

A method of measuring energy dissipation during crack propagation in polymers with an instrumented ultramicrotome

In order to characterize very local energy dissipation during crack propagation in polymers, an ultramicrotome was instrumented to measure the energy dissipated during sectioning. The work to section per unit area, W _s, was measured for five different amorphous polymers [polymethyl methacrylate (PMMA), polystyerene (PS), polycarbonate (PC) and two epoxy resins] in the glassy state. When the section thickness was varied between 60 and 250 nm, W _s varied between 15 and 100 Jm^–2, depending on the material and section thickness. The method and the results are compared with other methods used for determining the energy dissipation at a local level as well as at a macroscopic level in polymers. The differences between different polymers were found to be contradictory to macroscopic fracture toughness, G _lc, measurements. The material that showed the highest W _s had the lowest G _lc values reported. Possible mechanisms for energy dissipation during sectioning are also discussed.     

Multiscale modeling of dynamic crack propagation

A multiscale approach is employed to investigate a center-cracked specimen with the purpose to redefine fracture toughness from the atomistic perspective and to simulate different modes of crack propagation. The specimen is divided into three regions: (1) far field, modeled by classical fracture mechanics, (2) near field, modeled by a multiscale field theory and analyzed by a generalized finite element method, and (3) crack tip atomic region, modeled by molecular dynamics (MD). The exact and analytical solution of the far field is utilized to specify boundary conditions at the interface between the far field and the near field. The interaction between the near field and the crack tip region is described by full-blown interatomic forces. In this work, crystals of perovskite (Barium Titanate) and rocksalt (Magnesia) have been studied. Fracture toughness is defined as a material property associated with instability of the MD simulation. Mode I, Mode II, and mixed mode fracture have been investigated and numerical results will be presented and discussed.     

Analysis of stable crack propagation in filled rubber based on a global energy balance

Stable crack propagation in filled rubber is investigated by means of experimental and finite element analyses. Based on an experimental evaluation of multiple specimens under different loading states, dissipation rates are computed by applying a global energy balance. The dissipation rates calculated analogously from results of a numerical simulation of the multiple specimen method are in good accordance with the experimental findings. A further comparison of simulation results evaluated on basis of the material force method with energy release rates computed by means of an energy balance of two crack states under fixed loading conditions shows that the measured fracture sensitivity values are mainly related to the development and increase of a dissipative zone.     

Studies of dynamic crack propagation and crack branching with peridynamics

In this paper we discuss the peridynamic analysis of dynamic crack branching in brittle materials and show results of convergence studies under uniform grid refinement (m-convergence) and under decreasing the peridynamic horizon (δ-convergence). Comparisons with experimentally obtained values are made for the crack-tip propagation speed with three different peridynamic horizons. We also analyze the influence of the particular shape of the micro-modulus function and of different materials (Duran 50 glass and soda-lime glass) on the crack propagation behavior. We show that the peridynamic solution for this problem captures all the main features, observed experimentally, of dynamic crack propagation and branching, as well as it obtains crack propagation speeds that compare well, qualitatively and quantitatively, with experimental results published in the literature. The branching patterns also correlate remarkably well with tests published in the literature that show several branching levels at higher stress levels reached when the initial notch starts propagating. We notice the strong influence reflecting stress waves from the boundaries have on the shape and structure of the crack paths in dynamic fracture. All these computational solutions are obtained by using the minimum amount of input information: density, elastic stiffness, and constant fracture energy. No special criteria for crack propagation, crack curving, or crack branching are used: dynamic crack propagation is obtained here as part of the solution. We conclude that peridynamics is a reliable formulation for modeling dynamic crack propagation.     

A method for dynamic crack and shear band propagation with phantom nodes

A new method for modelling of arbitrary dynamic crack and shear band propagation is presented. We show that by a rearrangement of the extended finite element basis and the nodal degrees of freedom, the discontinuity can be described by superposed elements and phantom nodes. Cracks are treated by adding phantom nodes and superposing elements on the original mesh. Shear bands are treated by adding phantom degrees of freedom. The proposed method simplifies the treatment of element‐by‐element crack and shear band propagation in explicit methods. A quadrature method for 4‐node quadrilaterals is proposed based on a single quadrature point and hourglass control. The proposed method provides consistent history variables because it does not use a subdomain integration scheme for the discontinuous integrand. Numerical examples for dynamic crack and shear band propagation are provided to demonstrate the effectiveness and robustness of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling dynamic crack propagation using the scaled boundary finite element method

This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi‐analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack‐tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode‐I and mix‐mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. Copyright © 2011 John Wiley & Sons, Ltd.     

Time dependent crack tip enrichment for dynamic crack propagation

We study several enrichment strategies for dynamic crack propagation in the context of the extended finite element method and the effect of different directional criteria on the crack path. A new enrichment method with a time dependent enrichment function is proposed. In contrast to previous approaches, it entails only one crack tip enrichment function. Results for stress intensity factors and crack paths for different enrichments and direction criteria are given.     

Influence of dynamic fracture toughness on dynamic crack propagation

A dynamic finite element code was used in its “propagation mode” to assess the differences in dynamic crack propagation in a wedge-loaded (WL) single-edged notch (SEN) specimen, a tapered double cantilever beam (TDCB) specimen and a rectangular double cantilever beam (RDCB) specimen. The dynamic fracture toughness, K_ID, vs the crack velocity, a, relations determined experimentally for WL-SEN, WL-TDCB and WL-RDCB specimens machined from Araldite B were used as dynamic fracture criteria and the resultant k_id variations with crack propagations in the three specimens were compared with the corresponding experimental results. While the specific K_ID vs /.a relations established for each specimen obviously yielded calculated k_ID which were in best agreement with the experimental K_ID for the respective specimen, the K_ID vs /.a relation for the large WL-SEN specimen provided the best overall fit between the calculated and measured K_ID variations with crack propagation in all three specimens.     

Acoustic energy during pop-in crack propagation

The acoustic energy emitted during a brittle multiple pop-in fracture process in DCB specimens has been measured and its values have been correlated with the mechanical parameters. An approximate formulation has also been developed in order to explain the behaviour of the emitted acoustic energy to the temperature.     

An experimental investigation of dynamic crack propagation

The dynamic fracture behavior of polymethylmethacrylate (bdPMMA) has been investigated. The specimens were in the form of rectangular sheets with sharp notches. The elastodynamic crack tip stress field and the crack velocity were determined by the use of resistance strain gauges. An analytic expression for the dynamic crack tip stress field was used to evaluate the dynamic stress intensity factors, and the dynamic arrest toughness was also determined.The dynamic response of the stresses at the notch tip at varying loading rates was considered and some “hysteresis” fracture phenomena were observed.     

A coupled molecular dynamics and extended finite element method for dynamic crack propagation

A multiscale method is presented which couples a molecular dynamics approach for describing fracture at the crack tip with an extended finite element method for discretizing the remainder of the domain. After recalling the basic equations of molecular dynamics and continuum mechanics, the discretization is discussed for the continuum subdomain where the partition‐of‐unity property of finite element shape functions is used, since in this fashion the crack in the wake of its tip is naturally modelled as a traction‐free discontinuity. Next, the zonal coupling method between the atomistic and continuum models is recapitulated. Finally, it is discussed how the stress has been computed in the atomic subdomain, and a two‐dimensional computation is presented of dynamic fracture using the coupled model. The result shows multiple branching, which is reminiscent of recent results from simulations on dynamic fracture using cohesive‐zone models. Copyright © 2009 John Wiley & Sons, Ltd.     

裂纹止裂技术及裂纹动态扩展规律研究

为了对动态荷载作用下水泥粉煤灰砂浆的裂缝动态扩展行为进行研究,提出了一种大尺寸带V型底边的半圆边裂纹(SECVB)试件,其V形底部具有止裂功能。SECVB试件的V形底部设计为180°,150°和120°三个角度。采用落锤冲击装置进行了冲击试验,并使用裂纹扩展计(CPG)用于测量裂纹扩展的相关参数。利用有限差分程序AUTODYN对裂纹扩展行为进行了数值模拟,并用有限元程序ABAQUS计算了裂纹的动态应力强度因子(DSIF);根据CPG测量的裂纹萌生时间和扩展时间来确定临界应力强度因子。试验和数值模拟结果表明,SECVB试件适合于研究动态荷载作用下水泥粉煤灰砂浆的裂纹扩展行为和止裂行为。在裂纹扩展过程中,裂纹可能在一段时间内止裂,并且裂纹在起始时刻的断裂韧度高于裂纹扩展时的断裂韧度。     

Effect of crack layer on dynamic crack propagation behaviour in polystyrene

Dynamic crack propagation in thin, edge-notched polystyrene specimens was studied by the method of dynamic caustics. During crack propagation, an intensive zone of crazing surrounds and precedes the propagating crack. Therefore, an active zone ahead of the crack tip is developed. This active zone is related to the velocity of crack propagation and the strain rate of loading. The velocity of the crack and the stress intensity factor, K_I, or the energy release rate, G_I, were strongly influenced by the development of the active zone at the crack tip.