Theory of spall damage accumulation in ductile metals

Davison, Lee; Stevens, A.L.; Kipp, M.E.

doi:10.1016/0022-5096(77)90017-5

Cited by 143 publications

(36 citation statements)

References 10 publications

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“…Using the results of Budiansky (1970), and following Davison et al (1977) and Rabier (1989), a model can be found, in which the bulk modulus K and the shear modulus G depend on the damage. For a composite with two constituents, one of which is the collection of voids, the voids being associated both with a zero shear modulus and a zero bulk modulus, it follows that…”

Section: Specific Constitutive Modelmentioning

confidence: 99%

Modeling of the Degradation of Elastic Properties due to the Evolution of Ductile Damage

Wallin

Olsson

Ristinmaa

2007

International Journal of Damage Mechanics

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An elasto-plastic constitutive model for porous materials is formulated within the thermodynamic framework. The formulation facilitates a natural modeling of damage as well as growth and the shrinkage of voids. Metal plasticity is used for demonstrating the possibilities of the formulation. The yield function employed is assumed to depend upon the void-volume fraction, whereas the free energy is dependent on a scalar damage field. To show the capabilities of the model the algorithmic constitutive equations are derived and implemented into a finite element program. It is shown that an extremely simple system involving only two scalar equations needs to be solved in the constitutive driver. Two numerical examples are considered: the necking of an axi-symmetric bar and localization in a notched specimen.

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Section: Specific Constitutive Modelmentioning

confidence: 99%

Modeling of the Degradation of Elastic Properties due to the Evolution of Ductile Damage

Wallin

Olsson

Ristinmaa

2007

International Journal of Damage Mechanics

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“…The formulation of the kinematics development follows closely that of Davison et al (1977) and Bammann and Aifantis (1989). The kinematics of motion combine elastic straining, inelastic flow, and formation and growth of damage and is illustrated by the multiplicative decomposition of the deformation gradient shown in Figure 2 = + assuming that the volume in State 0 equals that in State 1 because of inelastic incompressibility.…”

Section: Kinematics Of the Macroscale Modelmentioning

confidence: 99%

“…This formulation for damage was employed by Davison et al (1977). If the number of voids per unit volume is defined in the intermediate configuration, we can write…”

Section: Kinematics Of the Macroscale Modelmentioning

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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“…Equations (38), (47), (49), (50), and (55) form a set of relationships that has to be solved numerically to describe the stress-strain response of a void contained aggregate material. We developed the corresponding numerical algorithm to describe chese equations in the STEALTH finite difference code.…”

Section: Y Mmentioning

confidence: 99%

Plastic Flow and Failure Modeling under High Strain Rate Loading

Rajendran¹,

Bless²

1988

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Theory of spall damage accumulation in ductile metals

Cited by 143 publications

References 10 publications

Modeling of the Degradation of Elastic Properties due to the Evolution of Ductile Damage

Modeling of the Degradation of Elastic Properties due to the Evolution of Ductile Damage

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

Plastic Flow and Failure Modeling under High Strain Rate Loading

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