NCAL: Multiaxial Material Performance

Summary

The performance of sheet metals is of fundamental interest to a wide range of manufacturing sectors including automotive, aerospace, construction, home appliances, and medical devices. Conventional single axis (uniaxial) testing methods are usually unable to provide sufficient characterization of these materials to develop manufacturing process models needed by industry to reduce manufacturing costs, improve efficiency, predict in-service performance and incorporate new, advanced lightweight materials. 

This project develops unique multiaxial test machines, experimental methods, analysis methods, and documentary standards to supply critical data and standard test methods for U.S. industry and materials suppliers.

Description

NIST Center for Automotive Lightweighting (NCAL) Cruciform Test Machine 

Credit: Mark Iadicola

Modern metal forming methods are designed and optimized using digital models of specific manufacturing operations. These models rely on a precise understanding of the mechanical behavior of sheet materials as they undergo multiaxial loading out to large plastic strains without failure (necking or tearing). Conventional uniaxial test methods alone are insufficient to inform models for multiaxial deformation, in large part because sheet materials are produced by progressively rolling thick cast billets into thin (~1 mm thick) sheets. The resulting sheets exhibit pronounced anisotropic mechanical behavior because the rolling process elongates and thins the microstructure (grains) of the billet material, such that the strength in the rolling direction differs markedly from the other two orthogonal directions. Although performing uniaxial tests in each direction can reveal the level of anisotropy present, these tests cannot be used to predict sheet metal behavior as it undergoes multiaxial loading during forming processes unless an anisotropic constitutive law is assumed for the material. Worse yet, because plastic deformation is path-dependent,a series of uniaxial tests performed in different directions also fail to mimic real hardening behavior during forming operations.

The overarching impetus for this project is to develop standard tests that produce clean multiaxial yield and forming limit data for sheet metals that can help industry develop more efficient manufacturing processes and incorporate advanced lightweight materials. To this end, the methods we are developing must work with industrially relevant sheet materials in the as-received condition (no thinning of the gauge area, for example), and that the tests work for as wide a range of materials as possible.

Several different methods and instruments for measuring the behavior of sheet metals subject to multiaxial deformation are used in this project.  These include a Forming Limit Press, a Cruciform Test Machine, and an Octostrain Test Machine.  Details of the capabilities of each test machine can be found by following the listed links. Current research focus areas are described below, and the methods used are compared and contrasted.

 

Forming Limit Measurements

Strain-based Forming Limit

A conventional method for measuring multiaxial material performance is a set of tests to characterize the strain behavior and creation of a forming limit diagram (FLD) or forming limit curve (FLC).  This technique determines the strain at which a manufactured part would be considered unusable, and this strain limit is used to guide part design and manufacture.  During the test a sheet metal specimen is deformed using a punch press, and the strain distribution is measured as the sheet is deformed. Different punch geometries (e.g. Marciniak flat punch and Nakajima hemispherical punch) are used in industry to mimic the manufacturing process and assess the FLD.

Limitations

It is well known that strain-based forming limits are dependent on the in-plane strain-ratio paths used.  In the documentary standard tests a monotonic linear path is used. This path dependence is a major shortcoming since forming processes often follow non-linear and non-monotonic paths. 

The use of digital image correlation (DIC) is limited in current documentary standards in that it either is an expensive replacement for legacy less accurate circle/grid measurement techniques or lacks a consensus method to determine a forming limit based on the more accurate DIC measurement results.

Active Work

• Consensus incorporation and interpretation of DIC in international documentary standards.

Multiaxial Stress and Strain Measurements

An improved approach (vs. uniaxial testing) for measuring yield surfaces is to measure both strain and stress simultaneously during multiaxial deformation simultaneously.  In our work, we have combined X-ray diffraction stress measurement, DIC strain measurement, and various multiaxial testing methods.

Marciniak Measurements

NIST pioneered the use of X-ray diffraction to measure the stresses during a forming limit style test. The current testing system is based on a modified Marciniak specimen geometry, where a sheet specimen is stretched multiaxially over a circular punch with a recessed center backed by a driver sheet. In this manner, the center of the specimen is forced into the plastic strain regime without frictional contact with the die or punch. The strain state (in-plane strain-ratio) can be varied by changing the width of the sheet specimen from uniaxial through plane strain to equal biaxial tension. In this way, the tensile quadrant of the planar principal stress space can be fully explored.  Bi-linear strain paths can be tested sequentially by first forming a large specimen in one direction (the first strain path), then cutting out a thinner specimen from the larger, already-strained specimen, and then performing a test along a second strain path.

X-ray stress measurements are performed (at the surface of the sheet) after advancing the punch to stretch the sheet incrementally. Stresses are computed from the change in the atomic lattice spacings due to the applied load on the sheet and from calibrated elastic constants (“X-ray elastic constants”) for the material under test. The full X-ray scan takes 2 minutes to 20 minutes depending on the accuracy and number of stress axes desired, more details are available at the NCAL: Diffraction Stress Measurement Systems page . Along with strains measured using DIC, the yield locus in the tensile principal stress quadrant can be mapped from initial yield through ultimate failure.

Limitations

Obtaining accurate stress measurements with X-ray diffraction requires significant calibration and verification of the X-ray elastic constants which vary by material and strain path. Current practice in NCAL is to calibrate for each material and strain path for more accurate stress measurements. The strain path is set by the specimen geometry, so changes in strain path can only be obtained by unloading and sectioning the specimen.

Cruciform Measurements

A cruciform mechanical test is a versatile method to measure the multiaxial deformation behavior of materials. In this test, load is applied to a cross-shaped specimen via four independent loading arms. Multiaxial stresses are achieved in the test section at the center of the cross. The cruciform test method allows arbitrary strain paths to be explored while under continuous load using an integrated real-time optical biaxial extensometer based on Digital Image Correlation (DIC) measurements to control the loading arms. Stresses in the test section are usually inferred from the forces measured on the arms and either assuming an equal force distribution in the gage area or by simulating the test using finite element analysis. However, the real force distribution is generally unequal due to specimen geometry and material anisotropy effects, and modeling the test requires an a priori selection of a material model, which can introduce a significant level of uncertainty. Instead, we use an X-ray system to measure stresses directly, similar to our Marciniak Measurements.

 Limitations

While the Cruciform Test method is much more versatile than the Forming Limit Press test method, most cruciform specimen geometries are only able to reach a maximum of 5 % plastic strain in the test section, and only for the more ductile materials of industrial interest. At this point, most specimens fail at the intersection of adjacent loading arms where there is a high stress concentration. While this strain level can help inform how strain path changes the yield surface at low strain levels, strains near the forming limit cannot be achieved for most sheet materials of industrial interest. 

Active Work

• Comparison and optimization of different cruciform specimen geometries and analysis methods.
• Development of specimen geometries and fabrication methods to achieve deformation on 'as received' sheets instead of thinning the sheet.
• Validation of cruciform specimen geometries and analysis methods for future documentary standards.

Octostrain Measurements

To increase the range of strains that can be applied to sheet metals using the multiple loading arm methods, an ‘octostrain’ device was developed at the NCNR having eight loading arms rather than four as in the cruciform system. The additional arms help achieve higher strains in the central test section by reducing the magnitude of the inter-arm stress concentrations compared to the cruciform specimen geometry.  This type of device is solely available at NIST.  We utilize the same methods of X-ray diffraction to measure gauge section stresses under load. We are currently evaluating and exploring capabilities of the octostrain test system. Two versions of the device have been created, the initial test frame with lower capacity that currently resides in NCAL and a more recent higher capacity test frame developed at NCNR. Both frames can be used on the BT-8 NCNR beamline. Stress measurements using the NCNR beamline have the advantage of sampling the entire thickness of the sheet material being tested, which contrasts with our X-ray reflection mode measurements that specimen a relatively shallow portion on one side of the sheet.

Limitations

The octostrain device is unique to NIST, so availability of the instrument is limited. The system is also being improved upon as we learn more about the testing and control systems.  

Active Work

• Continued development, testing, and evaluation of the test method and test equipment.
• Comparison to other methods of multiaxial deformation.

 

 

Major Accomplishments

• Jinjae Kim et al., “Multi-Interpolation Method to Linearize Stress Path in Cruciform Specimen for In-Plane Biaxial Test,” JOM 75, no. 12 (December 2023): 5505–14, https://doi.org/10.1007/s11837-023-06158-x
• Elizabeth M. Mamros et al., “Plastic Anisotropy Evolution of SS316L and Modeling for Novel Cruciform Specimen,” INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 234 (November 15, 2022), https://doi.org/10.1016/j.ijmecsci.2022.107663
• Adam Creuziger, Whitney Poling, and Thomas Gnaeupel-Herold, “Assessment of Martensitic Transformation Paths Based on Transformation Potential Calculations,” Steel Research International 90 (January 2019), https://doi.org/10.1002/srin.201800370
• Adam Creuziger, Whitney A. Poling, and Thomas Gnaeupel-Herold, “Supporting Information: Assessment of Martensitic Transformation Paths Based on Transformation Potential Calculations,” Steel Research International, January 2019, https://doi.org/10.1002/srin.201800370
• Adam Creuziger, Whitney Poling, and Thomas Gnäupel-Herold, “DataSet: Assessment of Martensitic Transformation Paths Based on Transformation Potential Calculations” (National Institute of Standards and Technology, October 23, 2018), https://doi.org/10.18434/T4/1503156
• A. Creuziger et al., “Insights into Cruciform Sample Design,” JOM 69, no. 5 (May 2017): 902–6, https://doi.org/10.1007/s11837-017-2261-6
• M.S. Pham et al., “Roles of Texture and Latent Hardening on Plastic Anisotropy of Face-Centered-Cubic Materials during Multi-Axial Loading,” Journal of the Mechanics and Physics of Solids 99 (February 2017): 50–69, https://doi.org/10.1016/j.jmps.2016.08.011
• Y. Jeong et al., “Uncertainty in Flow Stress Measurements Using X-Ray Diffraction for Sheet Metals Subjected to Large Plastic Deformations,” Journal of Applied Crystallography 49, no. 6 (December 1, 2016): 1991–2004, https://doi.org/10.1107/S1600576716013662
• Y. Jeong et al., “Multiaxial Constitutive Behavior of an Interstitial-Free Steel: Measurements through X-Ray and Digital Image Correlation,” Acta Materialia 112 (June 15, 2016): 84–93, https://doi.org/10.1016/j.actamat.2016.04.013
• Youngung Jeong et al., “Forming Limit Prediction Using a Self-Consistent Crystal Plasticity Framework: A Case Study for Body-Centered Cubic Materials,” Modelling and Simulation in Materials Science and Engineering 24, no. 5 (May 10, 2016): 055005, https://doi.org/10.1088/0965-0393/24/5/055005
• Minh-Son Pham et al., “Thermally-Activated Constitutive Model Including Dislocation Interactions, Aging and Recovery for Strain Path Dependence of Solid Solution Strengthened Alloys: Application to AA5754-O,” International Journal of Plasticity 75 (December 2015): 226–43, https://doi.org/10.1016/j.ijplas.2014.09.010
• Youngung Jeong et al., “Evaluation of Biaxial Flow Stress Based on Elasto-Viscoplastic Self-Consistent Analysis of X-Ray Diffraction Measurements,” International Journal of Plasticity 66 (March 2015): 103–18, https://doi.org/10.1016/j.ijplas.2014.06.009
• Adam Creuziger et al., “Crystallographic Texture Evolution in 1008 Steel Sheet during Multi-Axial Tensile Strain Paths,” Integrating Materials and Manufacturing Innovation 3, no. 1 (January 7, 2014): 1–19, https://doi.org/10.1186/2193-9772-3-1
• Adam Creuziger et al., “Data Citation: Crystallographic Texture Evolution in 1008 Steel Sheet During Multi-Axial Tensile Strain Paths,” MatDL, December 30, 2013, https://materialsdata.nist.gov/handle/11115/231
• M.A. Iadicola et al., “Crystal Plasticity Analysis of Constitutive Behavior of 5754 Aluminum Sheet Deformed along Bi-Linear Strain Paths,” International Journal of Solids and Structures 49, no. 25 (December 2012): 3507–16, https://doi.org/10.1016/j.ijsolstr.2012.03.015
• Mark A. Iadicola and Thomas H. Gnaeupel-Herold, “Effective X-Ray Elastic Constant Measurement for in Situ Stress Measurement of Biaxially Strained AA5754-O,” MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 545 (May 30, 2012): 168–75, https://doi.org/10.1016/j.msea.2012.02.100
• L. Hu et al., “Constitutive Relations for AA 5754 Based on Crystal Plasticity,” Metallurgical and Materials Transactions A 43, no. 3 (March 2012): 854–69, https://doi.org/10.1007/s11661-011-0927-1
• T. Gnäupel-Herold and A. Creuziger, “Diffraction Study of the Retained Austenite Content in TRIP Steels,” Materials Science and Engineering: A 528, no. 10–11 (April 2011): 3594–3600, https://doi.org/10.1016/j.msea.2011.01.030
• Creuziger, Adam, and T. Foecke. “Transformation Potential Predictions for the Stress-Induced Austenite to Martensite Transformation in Steel.” Acta Materialia 58, no. 1 (January 2010): 85–91. https://doi.org/10.1016/j.actamat.2009.08.059
• M.A. Iadicola, T. Foecke, and S.W. Banovic, “Experimental Observations of Evolving Yield Loci in Biaxially Strained AA5754-O,” International Journal of Plasticity 24, no. 11 (November 2008): 2084–2101, https://doi.org/10.1016/j.ijplas.2008.03.003
• S.W. Banovic, M.A. Iadicola, and T. Foecke, “Textural Development of AA 5754 Sheet Deformed under In-Plane Biaxial Tension,” Metallurgical and Materials Transactions A 39, no. 9 (September 2008): 2246–58, https://doi.org/10.1007/s11661-008-9547-9
• T. Foecke et al., “A Method for Direct Measurement of Multiaxial Stress-Strain Curves in Sheet Metal,” Metallurgical and Materials Transactions A 38, no. 2 (March 30, 2007): 306–13, https://doi.org/10.1007/s11661-006-9044-y
• T. Foecke and T. Gnaeupel-Herold, “Robustness of the Sheet Metal Springback Cup Test,” METALLURGICAL AND MATERIALS TRANSACTIONS A-PHYSICAL METALLURGY AND MATERIALS SCIENCE 37A, no. 12 (December 2006): 3503–10, https://doi.org/10.1007/s11661-006-1045-3
• T Gnaeupel-Herold et al., “An Investigation of Springback Stresses in AISI-1010 Deep Drawn Cups,” MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 399, no. 1–2 (June 15, 2005): 26–32, https://doi.org/10.1016/j.msea.2005.02.017
• SW Banovic et al., “Studies of Deformation-Induced Texture Development in Sheet Materials Using Diffraction Techniques,” MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 380, no. 1–2 (August 25, 2004): 155–70, https://doi.org/10.1016/j.msea.2004.03.084
• T Gnaeupel-Herold et al., “A Synchrotron Study of Residual Stresses in a Al6022 Deep Drawn Cup,” MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 366, no. 1 (February 5, 2004): 104–13, https://doi.org/10.1016/j.msea.2003.08.059
• SW Banovic and T Foecke, “Evolution of Strain-Induced Microstructure and Texture in Commercial Aluminum Sheet under Balanced Biaxial Stretching,” METALLURGICAL AND MATERIALS TRANSACTIONS A-PHYSICAL METALLURGY AND MATERIALS SCIENCE 34, no. 3 (March 2003): 657–71, https://doi.org/10.1007/s11661-003-0100-6
• T Foecke, SW Banovic, and RJ Fields, “Sheet Metal Formability Studies at the National Institute of Standards and Technology,” JOM-JOURNAL OF THE MINERALS METALS & MATERIALS SOCIETY 53, no. 2 (February 2001): 27–30, https://doi.org/10.1007/s11837-001-0116-6