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Forming limits and retained austenite (RA) transformation in Q&P 1180 steel are quantified as a function of plastic strain levels for three different strain paths. In-plane uniaxial tension testing was performed in a standard test frame, while limiting dome height tooling was employed for out-of-plane biaxial and plane strain tension experiments. Sheet specimens were tested incrementally for each strain path, and the RA content at each level of strain was measured using electron backscatter diffraction (EBSD). The biaxial tension strain path resulted in the greatest effective strain prior to necking at 0.355, compared to 0.123 for plane strain and 0.142 for uniaxial tension. EBSD measurements for various levels of plastic strain reveal a clear dependence of RA rate of transformation on strain path for the three linear strain paths that were employed in this work. Thinning strains appear to provide a slightly better correlation to RA transformation than effective strain levels, where biaxial tension achieved the greatest level just prior to necking, followed by plane-strain tension, and then uniaxial tension.

A “bottom-up” representative volume element (RVE) for a dual phase steel was constructed based on measured microstructural properties (“microproperties”). This differs from the common procedure of inferring hypothetical microproperties by fitting to macroscopic behavior using an assumed micro-to-macrolaw. The bottom-up approach allows the assessment of the law itself by comparing RVE-predicted mechanical behavior with independent macroscopic measurements, thus revealing the nature of the controlling micromechanisms. An RVE for DP980 steel was constructed using actual microproperties. Finite element (FE) simulations of elastic-plastic transitions were compared with independent loading-unloading-loading and compression-tension experiments. Constitutive models of three types were utilized: 1) a standard continuum model, 2) a standard Crystal Plasticity (CP) model, and 3) a SuperDislocation (SD) model similar to CP but including the elastic interactions of discrete dislocations. These comparisons led to following conclusions: 1) While a constitutive model that ignores elastic interaction of defects can be fit to macroscopic or microscopic behavior, it cannot represent both accurately, 2) Elastic interactions among dislocations are the predominant source of nonlinearity in the nominally-elastic region (i.e. at stresses below the standard yield stress), and 3) Continuum stress inhomogeneity arising from the hard martensite / soft ferrite microstructure has a minor role in the observed transitional nonlinearity in the absence of discrete dislocation interactions.

This study explores the evolution of GNDs and their effects on back stress through experimental and computational methods. Four large-grained tantalum tensile specimens were strained in uniaxial tension, electron backscatter diffraction (EBSD) data were collected, and geometrically necessary dislocation (GND) maps of the four specimens in the unloaded state were produced. EBSD-based GND maps revealed several types of features with high GND content which caused back stress in the specimens. Correlations between five geometrically-based grain boundary (GB) transmission factors and the GB GND content were evaluated, and statistically significant correlations were found for transmission factors based on Livingston and Chalmer's N factor, Werner and Prantl's slip transfer number, and GB misorientation. The sign of individual components of the Nye tensor were used to visually and quantitatively identify clustering of GNDs of the same sign, thus giving additional evidence of increasing back stress due to deformation. Deformation of one of the specimens was simulated using multiple CPFEM based modeling approaches and predicted stress-strain responses are compared. The super dislocation model (SD model) — a crystal plasticity finite element method (CPFEM) which incorporates elastic dislocation interactions — was able to isolate impact of back stress on the overall flow stress. The SD model predicted correct stresses when compared with experimental data; however, when the elastic interactions in the SD model were turned off, stress predictions were 25% too low. Thus, demonstrating the importance of incorporating back stress into the model.