A Planar Biaxial Experiment Platform for In Situ High-Energy Diffraction Studies


An experimental platform for multiscale studies of materials subjected to plane stress loads is presented. Coupling with far-field high-energy diffraction microscopy for grain-by-grain measurements of elastic strains and rotations provides an additional benefit; it enables the direct assessment of elastic vs. inelastic deformation of the gauge sections of cruciform specimens subjected to plane stress loadings, without any a priori assumptions of the form of constitutive relationships, resolving a long-outstanding challenge of multiaxial mechanical testing. Specifically, a planar biaxial mechanical load frame with four independent hydraulic actuators capable of applying arbitrary loading paths and ratios of tension and compression was designed and built for in situ diffraction experimentation. The load frame is integrated for use at the Argonne National Laboratory Advanced Photon Source (APS) synchrotron, Sector 1, 1-ID-E endstation and the Los Alamos Neutron Science Center (LANSCE) spallation neutron source, Spectrometer for Materials Research at Temperature and Stress (SMARTS) instrument. Cruciform specimen geometries were designed to experience loading ratios in the gauges commensurate with those applied at the grips, and to minimize interference with diffracted X-rays and neutrons. The finite element models used to design the cruciform specimen geometries were experimentally validated using stereo digital image correlation measurements. This complete planar biaxial in situ diffraction platform provides a new capability for studying multiaxial micromechanics of crystalline materials (e.g., elastic, slip, twinning, phase transformation) and their dependencies on grain size, location, texture, and neighborhood characteristics.

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\( {\upvarepsilon}_{11}^{\mathrm{ts}} \) :

11 component of the applied total specimen strain

\( {\upvarepsilon}_{22}^{\mathrm{ts}} \) :

22 component of the applied total specimen strain


\( {\upvarepsilon}_{11}^{\mathrm{ts}}/{\upvarepsilon}_{22}^{\mathrm{ts}} \)

\( {\upvarepsilon}_{11}^{\mathrm{s}} \) :

11 component of gauge strain from finite element analysis

\( {\upvarepsilon}_{22}^{\mathrm{s}} \) :

22 component of gauge strain from finite element analysis

λs :

\( {\upvarepsilon}_{11}^{\mathrm{s}}/{\upvarepsilon}_{22}^{\mathrm{s}} \)

\( {\upvarepsilon}_{11}^{\mathrm{a}} \) :

11 component of gauge strain from analytic solution

\( {\upvarepsilon}_{22}^{\mathrm{a}} \) :

22 component of gauge strain from analytic solution

λa :

\( {\upvarepsilon}_{11}^{\mathrm{a}}/{\upvarepsilon}_{22}^{\mathrm{a}} \)

\( {\upvarepsilon}_{11}^e \) :

11 component of gauge strain from experimental measurement

\( {\upvarepsilon}_{22}^e \) :

22 component of gauge strain from experimental measurement

λe :

\( {\upvarepsilon}_{11}^e/{\upvarepsilon}_{22}^e \)


Poisson’s ratio


Young’s modulus

ε11 :

11 component of strain

ε22 :

22 component of strain

σ11 :

11 component of stress

σ22 :

22 component of stress


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This work was conducted within the National Science Foundation (NSF) I/UCRC Center for Advanced Non-Ferrous Structural Alloys (CANFSA) which is a joint industry-university center between the Colorado School of Mines and Iowa State University. G.M. Hommer, Z.D. Brunson, J. Dahal, and A.P. Stebner acknowledge the support of NSF CAREER Award CMMI-1454668. G.M. Hommer, Z.D. Brunson, and A.P. Stebner acknowledge the support of Dr. Adam L. Pilchak at Air Force Research Laboratory (AFRL), Wright-Patterson AFB and the University of Dayton Research Institute (UDRI) Subcontract RSC16008, Account L46S32, Prime Contract FA8650-14-D-5205. G.M. Hommer acknowledges Dr. Branden Kappes at Colorado School of Mines for his data visualization contributions. This research used resources of the Advanced Photon Source (APS), a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory (ANL) under Contract No. DE-AC02-06CH11357.

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Appendix 1

Fig. 15

Fully dimensioned drawing of the 400 MPa X-ray specimen geometry

Fig. 16

Fully dimensioned drawing of the 800 MPa X-ray specimen geometry

Fig. 17

Fully dimensioned drawing of the 1100 MPa X-ray specimen geometry

Fig. 18

Fully dimensioned drawing of the 1700 MPa X-ray specimen geometry

Fig. 19

Fully dimensioned drawing of the 1000 MPa neutron specimen geometry

Appendix 2

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Hommer, G.M., Park, JS., Brunson, Z.D. et al. A Planar Biaxial Experiment Platform for In Situ High-Energy Diffraction Studies. Exp Mech 59, 749–774 (2019). https://doi.org/10.1007/s11340-019-00509-z

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  • Cruciform specimen
  • Multiaxial mechanics
  • Micromechanics
  • 3D X-ray diffraction (3DXRD)
  • High-energy diffraction microscopy (HEDM)