Tag Archives: metal

Publication: Experimental Assessment of Unvalidated Assumptions in Classical Plasticity Theory

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R. Brannon, J.A. Burghardt, D. Bronowski, and S. Bauer

Common isotropic yield surfaces. Von Mises and Drucker-Prager models are often used for metals. Gurson’s function, and others like it, are used for porous media. Tresca and Mohr-Coulomb models approximate the yield threshold for brittle media. Fossum’s model, and others like it, combine these features to model realistic geological media.

This report investigates the validity of several key assumptions in classical plasticity theory regarding material response to changes in the loading direction. Three metals, two rock types, and one ceramic were subjected to non-standard loading directions, and the resulting strain response increments were displayed in Gudehus diagrams to illustrate the approximation error of classical plasticity theories. A rigorous mathematical framework for fitting classical theories to the data,thus quantifying the error, is provided. Further data analysis techniques are presented that allow testing for the effect of changes in loading direction without having to use a new sample and for inferring the yield normal and flow directions without having to measure the yield surface. Though the data are inconclusive, there is indication that classical, incrementally linear, plasticity theory may be inadequate over a certain range of loading directions. This range of loading directions also coincides with loading directions that are known to produce a physically inadmissible instability for any nonassociative plasticity model.

Available Online:

http://www.mech.utah.edu/~brannon/pubs/7-BrannonBurghardtSAND-Report2009-0351.pdf

http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=948711

Publication: On the thermodynamic requirement of elastic stiffness anisotropy in isotropic materials

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Measure of anisotropy for Zircon, Quartz, Uranium, Titanium, Hornblende, and Copper.

T. Fuller and R.M. Brannon

In general, thermodynamic admissibility requires isotropic materials develop reversible deformation induced anisotropy (RDIA) in their elastic stiffnesses. Taking the elastic potential for an isotropic material to be a function of the strain invariants, isotropy of the elastic stiffness is possible under distortional loading if and only if the bulk modulus is independent of the strain deviator and the shear modulus is constant. Previous investigations of RDIA have been limited to applications in geomechanics where material non-linearityand large deformations are commonly observed. In the current paper, the degree of RDIA in other materials is investigated. It is found that the resultant anisotropy in materials whose strength does not vary appreciably with pressure, such as metals, is negligible, but in materials whose strength does vary with pressure, the degree of RDIA can be significant. Algorithms for incorporating RDIA in a classical elastic–plastic model are provided.

Available Online:

http://www.mech.utah.edu/~brannon/pubs/7-2011FullerBrannonInducedElasticAnisotropy.pdf

http://www.sciencedirect.com/science/article/pii/S0020722511000024

Publication: KAYENTA: Theory and User’s Guide

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R.M. Brannon, A.F. Fossum, and O.E. Strack

Kayenta continuous yield surface. (a) three-dimensional view in principal stress space, (b) the meridional “side” view (thick line), and (c) the octahedral view

The physical foundations and domain of applicability of the Kayenta constitutive model are presented along with descriptions of the source code and user instructions. Kayenta, which is an outgrowth of the Sandia GeoModel, includes features and fitting functions appropriate to a broad class of materials including rocks, rock-like engineered materials (such as concretes and ceramics),and metals. Fundamentally, Kayenta is a computational framework for generalized plasticity models. As such, it includes a yield surface, but the term“yield” is generalized to include any form of inelastic material response including microcrack growth and pore collapse. Kayenta supports optional anisotropic elasticity associated with ubiquitous joint sets. Kayenta support optional deformation-induced anisotropy through kinematic hardening (inwhich the initially isotropic yield surface is permitted to translate in deviatoric stress space to model Bauschinger effects). The governing equations are otherwise isotropic. Because Kayenta is a unification and generalization of simple models, it can be run using as few as 2 parameters (for linear elasticity) to as many as 40 material and control parameters in the exceptionally rare case when all features are used. For high-strain-rate applications, Kayenta support rate dependence through an overstress model. Isotropic damage is model through loss of stiffness and strength.

Available Online:
http://www.mech.utah.edu/~brannon/pubs/7-2009Kayenta_Users_Guide.pdf
http://dx.doi.org/10.1111/j.1744-7402.2010.02487.x

Publication: Advances in X-ray Computed Tomography Diagnostics of Ballistic Impact Damage

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J.M. Wells and R.M. Brannon

Dynamic indentation of SiC-N ceramic by a tungsten carbide sphere. Left: experimentally observed impact crater and radial cracking (both highlighted for clarity). Middle: BFS model prediction of externally visible damage. Right: prediction of internal damage (suitable for validation against XCT data).

With the relatively recent introduction of quantitative and volumetric X-ray computedtomography (XCT) applied to ballistic impact damage diagnostics, significant inroads have beenmade in expanding our knowledge base of the morphological variants of physical impactdamage. Yet, the current state of the art in computational and simulation modeling of terminalballistic performance remains predominantly focused on the penetration phenomenon, withoutdetailed consideration of the physical characteristics of actual impact damage. Similarly, armorceramic material improvements appear more focused on penetration resistance than on improved intrinsic damage tolerance and damage resistance. Basically, these approaches minimizeour understanding of the potential influence that impact damage may play in the mitigation orprevention of ballistic penetration. Examples of current capabilities of XCT characterization,quantification, and visualization of complex impact damage variants are demonstrated anddiscussed for impacted ceramic and metallic terminal ballistic target materials. Potential benefitsof incorporating such impact damage diagnostics in future ballistic computational modeling arealso briefly discussed.

Available Online:

http://dx.doi.org/10.1007/s11661-007-9304-5
http://www.mech.utah.edu/~brannon/pubs/7-2007WellsBrannonAdvancesInXrayComputedTomographyDiagnosticsOfBallisticDamage.pdf

Powder metal jet penetration into stressed rock

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The Uintah computational framework (UCF) has been adopted for simulation of shaped charge jet penetration and subsequent damage to geological formations.  The Kayenta geomechanics model, as well as a simplified model for shakedown simulations has been  incorporated within the UCF and is undergoing extensive development to enhance it to account for fluid in pore space.

A generic penetration simulation using Uintah

The host code (Uintah) itself has been enhanced to accommodate  material variability and scale effects. Simulations have been performed that import flash X-ray data for the velocity and geometry of a particulated metallic jet so that uncertainty about the jet can be reduced to develop predictive models for target response.  Uintah’s analytical polar decomposition has been replaced with an iterative algorithm to dramatically improve accuracy under large deformations. Continue reading →

Computational approaches for dynamically loaded low-ductility metals

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A generic Charpy simulation showing fracture at locations not observed in the lab

Eulerian simulations of un-notched Charpy impact specimens, provide unsatisfactory results in that experimentally observed bend angle, absorbed energy, and fracture mode are not reproduced. The Utah CSM group is independently confirming poor simulation fidelity using conventional constitutive models. From there, we aim to identify the cause, and investigate solutions using capabilities in the Kayenta material framework.

UofU Contributors/collaborators:
Krishna Kamojjala (PhD student, Mech. Engr., UofU)
Scot Swan (MS student, Mech. Engr., UofU)

Publication: Experimental Assessment of Unvalidated Assumptions in Classical Plasticity Theory

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Abstract: This report investigates the validity of several key assumptions in classical plasticity theory regarding material response to changes in the loading direction. Three metals, two rock types, and one ceramic were subjected to non-standard loading directions, and the resulting strain response increments were displayed in Gudehus diagrams to illustrate the approximation error of classical plasticity theories. A rigorous mathematical framework for fitting classical theories to the data, thus quantifying the error, is provided. Further data analysis techniques are presented that allow testing for the effect of changes in loading direction without having to use a new sample and for inferring the yield normal and flow directions without having to measure the yield surface. Though the data are inconclusive, there is indication that classical, incrementally linear, plasticity theory may be inadequate over a certain range of loading directions. This range of loading directions also coincides with loading directions that are known to produce a physically inadmissible instability for any nonassociative plasticity model.

You may download the full report here.