A pinboard by
Manas Upadhyay

Post Doctoral Researcher, Paul Scherrer Institute


Combining multi-scale modeling and in-situ experiments to study mechanical behavior of materials

Metals and alloys used for engineering applications often undergo multi-axial strain path changes during their fabrication (e.g. forming processes) or under service conditions (e.g. pressure vessels). These strain path changes significantly affect their subsequent mechanical behavior such as the yield strength (Bauschinger effect), extended transient regime, different work hardening rates, among others. The origin of these macroscale mechanical phenomena can be found at the microstructural level through the material anisotropy, texture evolution, dislocation activity, internal stresses, etc. Most of our understanding of the multi-scale material behavior is largely derived from uniaxial monotonic loading or load reversal studies. However, understanding the mutli-axial response of materials requires performing multi-axial tests and developing tools to characterize material behavior.

As a post-doc, working on a European Research Council funded project (MULTIAX), I am studying the biaxial strain path change behavior of materials. My research approach is to develop state-of-the-art multi-scale models that work in synergy with in-situ neutron and synchrotron x-ray diffraction measurements during biaxial strain path changes. Recently, I developed a computationally efficient multi-scale finite element and fast Fourier transform approach that models the complex part geometry at the macroscale while simulating its microstructural response. Together with in-situ neutron diffraction, this technique was applied to study biaxial strain path change behavior of 316L stainless steel. This research has been published in 3 peer-reviewed journals [1-3] and I have been invited to give talks at two international conferences.

This method can be applied to characterize the multi-scale behavior of a wide range of different metal and alloy systems. This makes it particularly interesting for the sheet metal forming, automotive and aerospace industries.


[1] Upadhyay et al., Study of lattice strain evolution during biaxial deformation of stainless steel using a finite element and fast Fourier transform based multi-scale approach, Acta Materialia 118 (2016) 28-43

[2] Upadhyay et al., Intergranular Strain Evolution During Biaxial Loading: A Multiscale FE-FFT Approach, The Journal of The Minerals, Metals & Materials Society (TMS) 69 (2017) 839-847

[3] Upadhyay et al., Stresses and Strains in Cruciform Samples Deformed in Tension, Experimental Mechanics 57 (2017) 905-920


Multiaxial constitutive behavior of an interstitial-free steel: Measurements through X-ray and digital image correlation.

Abstract: Constitutive behaviors of an interstitial-free steel sample were measured using an augmented Marciniak experiment. In these tests, multiaxial strain field data of the flat specimens were measured by the digital image correlation technique. In addition, the flow stress was measured using an X-ray diffractometer. The flat specimens in three different geometries were tested in order to achieve 1) balanced biaxial strain, and plane strain tests with zero strain in either 2) rolling direction or 3) transverse direction. The multiaxial stress and strain data were processed to obtain plastic work contours with reference to a uniaxial tension test along the rolling direction. The experimental results show that the mechanical behavior of the subjected specimen deviates significantly from isotropic behavior predicted by the von Mises yield criterion. The initial yield loci measured by a Marciniak tester is in good agreement with what is predicted by Hill's yield criterion. However, as deformation increases beyond the vonMises strain of 0.05, the shape of the work contour significantly deviates from that of Hill's yield locus. A prediction made by a viscoplastic self-consistent model is in better agreement with the experimental observation than the Hill yield locus with the isotropic work-hardening rule. However, none of the studied models matched the initial or evolving anisotropic behaviors of the interstitial-free steel measured by the augmented Marciniak experiment.

Pub.: 12 Jul '17, Pinned: 24 Aug '17

A synchrotron X-ray diffraction study of non-proportional strain-path effects

Abstract: Publication date: 1 February 2017 Source:Acta Materialia, Volume 124 Author(s): D.M. Collins, T. Erinosho, F.P.E. Dunne, R.I. Todd, T. Connolley, M. Mostafavi, H. Kupfer, A.J. Wilkinson Common alloys used in sheet form can display a significant ductility benefit when they are subjected to certain multiaxial strain paths. This effect has been studied here for a polycrystalline ferritic steel using a combination of Nakajima bulge testing, X-ray diffraction during biaxial testing of cruciform samples and crystal plasticity finite element (CPFE) modelling. Greatest gains in strain to failure were found when subjecting sheets to uniaxial loading followed by balanced biaxial deformation, resulting in a total deformation close to plane-strain. A combined strain of approximately double that of proportional loading was achieved. The evolution of macrostrain, microstrain and texture during non-proportional loading were evaluated by in-situ high energy synchrotron diffraction. The results have demonstrated that the inhomogeneous strain accumulation from non-proportional deformation is strongly dependent on texture and the applied strain-ratio of the first deformation pass. Experimental diffraction evidence is supported by results produced by a novel method of CPFE-derived diffraction simulation. Using constitutive laws selected on the basis of good agreement with measured lattice strain development, the CPFE model demonstrated the capability to replicate ductility gains measured experimentally. Graphical abstract

Pub.: 19 Nov '16, Pinned: 24 Aug '17

A higher order elasto-viscoplastic model using fast Fourier transforms: effects of lattice curvatures on mechanical response of nanocrystalline metals

Abstract: In this work a couple stress continuum based elasto-viscoplastic fast Fourier transform model is developed with the intent to study the role of curvatures - gradient of rotation - on the local meso scale and effective macroscale mechanical response of nanocrystalline materials. Development of this model has led to the formulation of an extended periodic Lippmann Schwinger equation that accounts for couple stress equilibrium. In addition to the standard boundary conditions on strain rate and Cauchy stresses, the model allows imposing non-standard couple stress and curvature rate boundary conditions. Application to representative nanocrystalline microstructures reveals that elastic and plastic curvatures accommodate a part of the local and macroscopic Cauchy stresses. Next, grain boundary interfaces are characterized using curvatures that are representative of their structure and defect content. Depending on the magnitude and distribution of these curvatures, local stresses in the grain boundary neighborhood are generated that activate slip systems besides those fulfilling the Schmid criterion. Generation of both polar dislocations and disclinations as a possible plasticity mechanism in nanocrystalline materials is explored. At the macro scale, this results in a strain rate dependent ”softening” or the inverse Hall-Petch effect. The modeling framework naturally captures this grain size effect without any ad hoc assumptions.

Pub.: 23 Apr '16, Pinned: 24 Aug '17