Intersonic Crack Propagation—Part I: The Fundamental Solution

2000 ◽  
Vol 68 (2) ◽  
pp. 169-175 ◽  
Author(s):  
Y. Huang ◽  
H. Gao
Keyword(s):  
Fundamental Solution ◽  
Crack Propagation ◽  
Cohesive Zone Model ◽  
Shear Crack ◽  
Crack Tip ◽  
Zone Model ◽  
Shear Wave Speed ◽  
Numerical Studies ◽  
Intersonic Crack Propagation ◽  
Tip Velocity

Recent experiments of Rosakis et al. have clearly shown that the crack-tip velocity can exceed the shear wave speed for a crack tip propagating between two weakly bonded, identical and isotropic solids under shear-dominated loading. This has motivated recent theoretical and numerical studies on intersonic crack propagation. We have obtained analytically the fundamental solution for mode-II intersonic crack propagation in this paper. This fundamental solution can provide the general solutions for intersonic crack propagation under arbitrarily initial equilibrium fields. We have also developed a cohesive zone model to determine the crack-tip energy release for an intersonic shear crack.

scholarly journals Numerical Simulation of Fatigue Crack Growth Rate and Crack Retardation due to an Overload Using a Cohesive Zone Model

2014 ◽  
Vol 891-892 ◽  
pp. 777-783 ◽  
Author(s):  
Sarmediran Silitonga ◽  
Johan Maljaars ◽  
Frans Soetens ◽  
Hubertus H. Snijder
Keyword(s):  
Finite Element ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Propagation ◽  
Crack Growth ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Zone Model ◽  
Cohesive Elements

In this work, a numerical method is pursued based on a cohesive zone model (CZM). The method is aimed at simulating fatigue crack growth as well as crack growth retardation due to an overload. In this cohesive zone model, the degradation of the material strength is represented by a variation of the cohesive traction with respect to separation of the cohesive surfaces. Simulation of crack propagation under cyclic loads is implemented by introducing a damage mechanism into the cohesive zone. Crack propagation is represented in the process zone (cohesive zone in front of crack-tip) by deterioration of the cohesive strength due to damage development in the cohesive element. Damage accumulation during loading is based on the displacements in the cohesive zone. A finite element model of a compact tension (CT) specimen subjected to a constant amplitude loading with an overload is developed. The cohesive elements are placed in front of the crack-tip along a pre-defined crack path. The simulation is performed in the finite element code Abaqus. The cohesive elements behavior is described using the user element subroutine UEL. The new damage evolution function used in this work provides a good agreement between simulation results and experimental data.

Intersonic Crack Propagation—Part II: Suddenly Stopping Crack

2001 ◽  
Vol 69 (1) ◽  
pp. 76-80 ◽  
Author(s):  
Y. Huang ◽  
H. Gao
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fundamental Solution ◽  
Crack Propagation ◽  
Auxiliary Problem ◽  
Crack Tip ◽  
Mode Ii ◽  
Static Crack ◽  
Intersonic Crack Propagation

In Part I of this series, we have obtained the fundamental solution for a mode II intersonic crack which involves a crack moving uniformly at a velocity between the shear and longitudinal wave speeds while subjected to a pair of concentrated forces suddenly appearing at the crack tip and subsequently acting on the crack faces. The fundamental solution can be used to generate solutions for intersonic crack propagation under arbitrary initial equilibrium fields. In this paper, Part II of this series, we study a mode II crack suddenly stopping after propagating intersonically for a short time. The solution is obtained by superposing the fundamental solution and the auxiliary problem of a static crack emitting dynamic dislocations such that the relative crack face displacement in the fundamental solution is negated ahead of where the crack tip has stopped. We find that, after the crack stops moving, the stress intensity factor rapidly rises to a finite value and then starts to change gradually toward the equilibrium value for a static crack. A most interesting feature is that the static value of stress intensity is reached neither instantaneously like a suddenly stopping subsonic crack nor asymptotically like a suddenly stopping edge dislocation. Rather, the dynamic stress intensity factor changes continuously as the shear and Rayleigh waves catch up with the stopped crack tip from behind, approaches negative infinity when the Rayleigh wave arrives, and then suddenly assumes the equilibrium static value when all the waves have passed by. This study is an important step toward the study of intersonic crack propagation with arbitrary, nonuniform velocities.

scholarly journals Two-Dimensional Mode I Crack Propagation in Saturated Ionized Porous Media Using Partition of Unity Finite Elements

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
F. Kraaijeveld ◽  
J. M. Huyghe ◽  
J. J. C. Remmers ◽  
R. de Borst
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Crack Propagation ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Partition Of Unity ◽  
Failure Behavior ◽  
Zone Model ◽  
Intervertebral Disks ◽  
The Relationship

Shales, clays, hydrogels, and tissues swell and shrink under changing osmotic conditions, which may lead to failure. The relationship between the presence of cracks and fluid flow has had little attention. The relationship between failure and osmotic conditions has had even less attention. The aim of this research is to study the effect of osmotic conditions on propagating discontinuities under different types of loads for saturated ionized porous media using the finite element method (FEM). Discontinuous functions are introduced in the shape functions of the FEM by partition of unity method, independently of the underlying mesh. Damage ahead of the crack-tip is introduced by a cohesive zone model. Tensile loading of a crack in an osmoelastic medium results in opening of the crack and high pressure gradients between the crack and the formation. The fluid flow in the crack is approximated by Couette flow. Results show that failure behavior depends highly on the load, permeability, (osmotic) prestress and the stiffness of the material. In some cases it is seen that when the crack propagation initiates, fluid is attracted to the crack-tip from the crack rather than from the surrounding medium causing the crack to close. The results show reasonable mesh-independent crack propagation for materials with a high stiffness. Stepwise crack propagation through the medium is seen due to consolidation, i.e., crack propagation alternates with pauses in which the fluid redistributes. This physical phenomenon challenges the numerical scheme. Furthermore, propagation is shown to depend on the osmotic prestressing of the medium. This mechanism may explain the tears observed in intervertebral disks as degeneration progresses.

Dynamic Fracture Criteria for Crack Growth Along Bimaterial Interfaces

1998 ◽  
Vol 65 (2) ◽  
pp. 293-299 ◽  
Author(s):  
M. Kavaturu ◽  
A. Shukla
Keyword(s):  
Crack Propagation ◽  
Crack Growth ◽  
Shear Wave ◽  
Wave Speed ◽  
Crack Tip ◽  
Fracture Criteria ◽  
Shear Wave Speed ◽  
Bimaterial Interfaces ◽  
Opening Mode ◽  
Tip Velocity

Dynamic fracture criteria based on experimental observations are proposed for subsonic crack growth along bimaterial interfaces. These criteria are based on the premise that the crack-face displacements at a point behind the crack tip increase exponentially with the instantaneous crack-tip velocity. This assumption establishes a generalized relationship between the dynamic energy release rate and the instanta-neous crack-tip velocity. Experiments are performed on PSM-1/aluminum bimaterial systems for both shear dominated and opening-mode dominated crack growth to verify the proposed criteria. Two different bimaterial specimen geometries are employed to obtain the complete range of crack-tip speeds in the subsonic regime. The dynamic loading is achieved either by detonating two explosive charges on the specimen or by impacting the specimen in one-point bend configuration. Dynamic photoelasticity in conjunction with high-speed photography is used to analyze the fracture event. Explosive loading of the interface crack results in crack propagation speeds on the order of 65 percent of the shear wave speed of PSM-1 and the crack growth is observed to be stable and opening-mode dominated. In contrast, the impact loading results in very high crack propagation speeds on the order of shear wave speed of PSM-1 and the crack growth is observed to be shear dominated.

Subsonic and Intersonic Failure of Composites: High-Speed Optical and Thermographic Measurements and Numerical Simulations

2000 ◽  
Author(s):  
A. J. Rosakis ◽  
D. Coker ◽  
C. Yu ◽  
M. Ortiz
Keyword(s):  
Crack Growth ◽  
High Speed ◽  
Large Scale ◽  
Wave Speed ◽  
Epoxy Composite ◽  
Shear Crack ◽  
Crack Tip ◽  
Composite Plates ◽  
Crack Face ◽  
Shear Wave Speed

Abstract In this paper dynamic fracture behavior of unidirectional graphite-epoxy composite plates is investigated experimentally and numerically. Crack propagation experiments are conducted on thick unidirectional graphite-epoxy composite plates subjected to in-plane, symmetric and asymmetric, impact loading. The coherent gradient sensing technique (CGS) is used in conjunction with high-speed photography to visualize the crack growth events. Cracks are found to propagate at subsonic speeds in the Mode-I case, whereas in both mixed mode and Mode-II the crack tip speed clearly exceeds the shear wave speed of the laminate. In the case of symmetric loading (Mode-I), the crack tip speeds approach the Rayleigh wave speed of the composite (1500 m/s), however it never exceeds it as predicted by asymptotic analysis. The situation is found to be entirely different for growing shear (Mode-II) cracks. A shock wave emanating from the crack tip is observed in the optical patterns. This provides direct evidence that the crack propagates faster than the shear wave speed of the composite. The crack tip speed is then observed to jump to a level close to the axial longitudinal wave speed along the fibers (7500 m/s) and then to stabilize to a lower level of approximately 6500 m/s. This speed corresponds to the speed at which the energy release rate required for shear crack growth is non-zero as determined from asymptotic analysis. The CGS interferograms also reveal the existence of large-scale frictional contact of the crack faces behind the moving shear cracks. In addition high speed thermographic measurements are conducted that show concentrated hot spots behind the crack tip indicating crack face frictional contact. Finally, these experiments are modeled by a detailed dynamic finite element calculation involving cohesive elements, newly developed adaptive remeshing using subdivision and edge collapse, composites element, and penalty contact. The numerical calculations are calibrated on the basis of fundamental material properties measured in the laboratory. The numerical methodology is subsequently validated by direct comparison to optical experimental measurements (crack speed record and near tip deformation field structure). For shear crack growth the numerics also reveal the experimentally observed shock wave structure and confirm the optical observation of large-scale crack face contact.

scholarly journals Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150571 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Critical Value ◽  
Zone Model ◽  
Cohesive Stress ◽  
Generalized Stress Intensity Factor

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters ( α and β ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

A Crack Close to and Perpendicular to an Interface: Resolution of Anomalous Behavior With a Cohesive Zone

2019 ◽  
Vol 86 (3) ◽  
Author(s):  
George G. Adams
Keyword(s):  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Applied Pressure ◽  
Stress Singularity ◽  
Crack Tip ◽  
Anomalous Behavior ◽  
Work Of Adhesion ◽  
Bimaterial Interface ◽  
Zone Model ◽  
Finite Distance

In this investigation, we consider a crack close to and perpendicular to a bimaterial interface. If the crack tip is at the interface then, depending on material properties, the order of the stress singularity will be equal to, less than, or greater than one-half. However, if the crack tip is located any finite distance away from the interface the stress field is square-root singular. Thus, as the crack tip approaches the interface, the stress intensity factor approaches zero (for cases corresponding to a singularity of order less than one-half) or infinity (for a singularity of order greater than one-half). The implication of this behavior is that for a finite applied pressure the crack will either never reach the interface or will reach the interface with vanishing small applied pressure. In this investigation, a cohesive zone model is used in order to model the crack behavior. It is found that the aforementioned anomalous behavior for the crack without a cohesive zone disappears and that the critical value of the applied pressure for the crack to reach the interface is finite and depends on the maximum stress of the cohesive zone model, as well as on the work of adhesion and the Dundurs' parameters.

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