Abstract
A multi-scale elastic-plastic finite element and fast Fourier transform based approach is proposed to study lattice strain evolution during uniaxial and biaxial loading of stainless steel cruciform shaped samples. At the macroscale, finite element simulations capture the complex coupling between applied forces in the arms and gauge stresses induced by the cruciform geometry. The predicted gauge stresses are used as macroscopic boundary conditions to drive a mesoscale elasto-viscoplastic fast Fourier transform model, from which lattice strains are calculated for particular grain families. The calculated lattice strain evolution matches well with experimental values from in-situ neutron diffraction measurements and demonstrates that the spread in lattice strain evolution between different grain families decreases with increasing biaxial stress ratio. During equibiaxial loading, the model reveals that the lattice strain evolution in all grain families, and not just the 311 grain family, is representative of the polycrystalline response. A detailed quantitative analysis of the 200 and 220 grain family reveals that the contribution of elastic and plastic anisotropy to the lattice strain evolution significantly depends on the applied stress ratio.
Highlights
Metals and alloys used for engineering applications often experience biaxial stress states during their fabrication or under service conditions
Minor differences between them may be due to the tolerances associated with manufacturing the cruciform samples
The cruciform geometry results in a coupling between the applied forces in the arms and the gauge stresses: S11 1⁄4 aF1ÀbF2 and S22 1⁄4 ÀbF1þaF2 [11e13]; where a and b are constant in the elastic regime and vary in the plastic regime
Summary
Metals and alloys used for engineering applications often experience biaxial stress states during their fabrication or under service conditions Their macroscopic yield and subsequent plastic behavior significantly depends on this applied biaxial stress state. Relying solely on uniaxial tests may result in an erroneous description of biaxial mechanical behavior for these materials. Biaxial testing on cruciform shaped samples has proven to be useful in characterizing the macroscopic behavior of materials [2e7]. FE simulations of Bonnand et al [12] and Claudio et al [13] showed that for a cruciform geometry similar to the one used in this study a uniaxial load in the arm results in biaxial gauge stresses with a compressive component normal to the loading direction. Foecke and co-workers proposed to use an x-ray diffractometer to measure multiaxial stresses and corresponding yield loci [17e19]
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