Numerical modeling of crack growth under dynamic loading conditions

Needleman, A.

doi:10.1007/s004660050194

Cited by 49 publications

(23 citation statements)

References 21 publications

(25 reference statements)

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“…Similar equations are given in References [3,21,22]; see References [23] or [18] for a detailed explanation of (8).…”

Section: Unassembled Finite Element Equationsmentioning

confidence: 73%

“…In this case, a new active interface is initiated. Focus on a particular quadrature point, and let the values of the tractions at the time of incipient softening (computed by inversion of Gaussian quadrature just described) be denoted T (22) Consider that some time has passed since activation, and let ( n ; s ) be values of the normal and shear relative displacements, so n ¡0 indicates interpenetration. Let max n , max s be the maximum normal and maximum absolute shear values occurring so far.…”

Section: A Possible Remedymentioning

confidence: 99%

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Time continuity in cohesive finite element modeling

Papoulia

Sam

Vavasis

2003

Numerical Meth Engineering

110

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SUMMARYWe introduce the notion of time continuity for the analysis of cohesive zone interface ÿnite element models. We focus on 'initially rigid' models in which an interface is inactive until the traction across it reaches a critical level. We argue that methods in this class are time discontinuous, unless special provision is made for the opposite. Time discontinuity leads to pitfalls in numerical implementations: oscillatory behavior, non-convergence in time and dependence on nonphysical regularization parameters. These problems arise at least partly from the attempt to extend uniaxial traction-displacement relationships to multiaxial loading. We also argue that any formulation of a time-continuous functional traction-displacement cohesive model entails encoding the value of the traction components at incipient softening into the model. We exhibit an example of such a model. Most of our numerical experiments concern explicit dynamics. Copyright COHESIVE ZONE MODELINGCohesive zone modeling is one of the most widely used techniques for modeling fracture. It is predicated on the fact that a process zone forms ahead of the crack front, in which material softening takes place. In the spirit of Dugdale [1] and Barenblatt [2] cohesive zone modeling idealizes the process zone with a weak interface of thickness zero. A material point on this interface is initially undamaged, but when the traction across the interface reaches some critical level it starts losing cohesion and gradually softens until a stress-free surface is created. In one dimension, softening is manifested as a gradual drop in traction with increasing relative displacement. Decohesion is usually modeled by a pointwise relationship between the traction across the interface and the relative displacement between the two faces of the interface.We formulate the problem in the following setting. Let the initial conÿguration of the body be denoted B 0 , and let M(X; t) : B 0 × [0; T ] → R 3 be its deformation map. The ÿrst argument to M is a coordinate X in the undeformed body, and the second argument is time. This map is * Correspondence to:

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“…Similar equations are given in References [3,21,22]; see References [23] or [18] for a detailed explanation of (8).…”

Section: Unassembled Finite Element Equationsmentioning

confidence: 73%

Section: A Possible Remedymentioning

confidence: 99%

Time continuity in cohesive finite element modeling

Papoulia

Sam

Vavasis

2003

Numerical Meth Engineering

110

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“…With the element sizes considered in the present models, mesh density is not very important, especially for the global energy absorption predicted. It should be noted that although cohesive zone models are theoretically mesh independent, the mesh must not be so coarse that the calculation of local plastic strain field is imprecise or mesh dependent [48].…”

Section: Crack Growth Simulations and Resultsmentioning

confidence: 99%

Simulation of dynamic ductile crack growth using strain-rate and triaxiality-dependent cohesive elements

Anvari

Scheider

Thaulow

2006

Engineering Fracture Mechanics

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Rate-sensitive and triaxiality-dependent cohesive elements are used to simulate crack growth under quasi-static and dynamic loading conditions. The simulations are performed for a middle-cracked tension M(T) specimen made of an aluminum alloy (6XXX-series). To consider the effect of stress triaxiality and strain rate on the cohesive properties, a single plane strain element obeying the constitutive equations of a rate-dependent Gurson type model has been used. The single element is loaded under various stress biaxiality ratios and strain rates and the obtained stress-displacement curves are considered as traction separation law for the cohesive elements. These curves are used for analyzing the aluminum M(T) specimen. The qualitative effects of constraint, strain rate, inertia and stress waves on the energy absorption of the specimen and crack growth are discussed.

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“…One consideration in the finite element modeling of interface debonding, and crack propagation in general, is modeling the generation of free surfaces. Previous finite element studies have used cohesive zone approaches (Dugdale, 1960;Barenblatt, 1962) to model, for example, fracture in rocks (Boone et al, 1986), inclusion debonding in ductile materials Xu and Needleman, 1993) dynamic crack propagation in brittle materials (Camacho and Ortiz, 1996), failure of adhesive joints Hutchinson 1994, 1996), and various other interfacial crack growth problems (Needleman, 1990-a, b;Suo et al, 1992;Tvergaard and Hutchinson 1992;Needleman, 1992;Xu and Needleman, 1993, 1995Needleman, 1997;Bigoni et al, 1997;Siegmund et al, 1997;Xu et al, 1997). The mathematical forms for cohesive zone equations are motivated (Needleman, 1990-a) from metallic atomic binding energy relationships (Rose et al, 1981;Ferrante and Smith, 1985).…”

Section: -2mentioning

confidence: 99%

From Atoms to Autos - A new Design Paradigm Using Microstructure-Property Modeling Part 1: Monotonic Loading Conditions

Horstemeyer¹

2001

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A multiscale analysis was performed to develop a macroscale microstructure-mechanical property model that includes several types of microstructural inclusions found in an A356-T6 cast aluminum alloy for use in automotive chassis component design. This microstructureproperty model can be used for finite element analysis in which the deformation history, temperature dependence, and strain rate dependence vary. To capture the history effects from the boundary conditions and load histories, the microstructural defects and progression of damage from these defects and microstructural features such as casting porosity, silicon particles, and intermetallics must be reflected in the model. Internal state variables are used in the material model to reflect void/crack nucleation, void growth, and void coalescence from the casting microstructural features under different temperatures, strain rates, and deformation paths. Furthermore, internal state variables are used to reflect the dislocation density evolution that affects the work hardening rate and thus stress state under different temperatures and strain rates. In order to determine the pertinent effects of the microstructural features, several different length scale analyses were performed. Once the pertinent microstructural features were determined and included in the microstructure-mechanical property model, tests were performed on a control arm to validate its precision. Very encouraging results were demonstrated when using the model for optimizing structural components in a predictive fashion. EXECUTIVE SUMMARYIn designing a structural component, a failure analysis will typically include a finite element analysis and microstructural evalutation. Sometimes the microstructural evalution will quantify the inclusion content (source of damage in a component) in a prioritized fashion differently than the finite element analysis. Let us consider the hypothetical situation exemplified in Figure 1.Here we have an automotive control arm that shows that has undergone certain boundary conditions in a finite element analysis. The finite element analysis revealed that the highest Mises stress occurred at point D. For the different regions of interest, microstructural analysis using optical imaging revealed the largest defect occurred at point B. Both camps would argue about the location of final failure. However, in our hypothetical example, both are wrong, because the final failure state is both a function of the initial inclusion state and boundary conditions. As such, point A failed first. The key is the development of the microstructureproperty model that can be included in a finite element analysis, which includes the inclusion content (or the sources of damage progression). IIIn order to accomplish such a task, a multiscale analysis was performed with a focus on a macroscale microstructure-mechanical property model that includes several types of microstructural inclusions found in an A356-T6 cast aluminum alloy for use in automotive chassis component design. This...

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Numerical modeling of crack growth under dynamic loading conditions

Cited by 49 publications

References 21 publications

Time continuity in cohesive finite element modeling

Time continuity in cohesive finite element modeling

Simulation of dynamic ductile crack growth using strain-rate and triaxiality-dependent cohesive elements

From Atoms to Autos - A new Design Paradigm Using Microstructure-Property Modeling Part 1: Monotonic Loading Conditions

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