**Published:** Jan 2004

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**Source: **STP1429-EB

Measurements of multiaxial properties of materials, such as yield surfaces, damage surfaces and fracture limit surfaces, are a time and resource intensive problem. For three-dimensional (3D) multiaxial yield of a complex microstructure, hundreds of points are required at different 3D strain states to define a full yield surface to the resolution required for constitutive model implementation. Experimental determination of the effects generated by a specific microstructure on a multiaxial yield surface is hindered by the inability to produce multiple specimens with the exact same microstructure or the inability to subject the same specimen to multiple stress or strain states without changing its response. Full nonlinear analysis of a specific microstructure for such a large set of points is also prohibitive, due to the time constraints of solving large, 3D nonlinear problems. A technique has been developed that uses high resolution 3D tomographic images and finite element simulations to track the development of microplastic connectivity for actual material microstructures in an 1100 aluminum/TiB^{2} particle composite. This information is then used to estimate the 3D multiaxial yield surface of the material in strain space for the imaged microstructures. The multiaxial yield surface is estimated using linear superposition and load scaling of three orthogonal displacement basis loads. Macroscopic yielding is defined as the percolation of microplastic elements across the model. Interval halving is used to solve for the scaling parameter, iterating to the value at which plastic flow percolation occurs and defining a point on the yield surface. Percolation can occur across one or more of the three directions defined by the model, but it need not occur simultaneously. A small selected set of nonlinear analyses is used as calibration for the estimated yield surface. The aim of this approach is to accelerate the process of building 3D multiaxial yield surfaces from microstructures and to gain insight into the material microstructure performance.

**Keywords:**

Multiaxial yield surfaces, material properties, X-ray computed microtomography, image-based modeling, percolation analysis

**Author Information:**

Geltmacher, AB *Materials Scientist, Section Head, and Branch Head, Naval Research Laboratory, Washington, DC,*

Everett, RK *Materials Scientist, Section Head, and Branch Head, Naval Research Laboratory, Washington, DC,*

Matic, P *Materials Scientist, Section Head, and Branch Head, Naval Research Laboratory, Washington, DC,*

Dyka, CT *Mechanical Engineer, GEO-Centers, Inc., Fort Washington, MD*

**Committee/Subcommittee:** E08.04

**DOI:** 10.1520/STP10665S