Sibo YUAN PhD

Experimental study and numerical modeling of length scale effects in nickel sheets - Shear, uniaxial tensile and large tensile tests at various temperatures

The main objective of this thesis is to study the influence on the mechanical behavior of variations of the ratio between part dimensions and the material microstructure, as well as the influence of various interfaces. Such features are generally labelled as ‘size effects’. At small length scale (typically in micro/meso range), the relative size between mechanical part and the grains of the polycrystal plays an important role on the overall mechanical behavior. Indeed, the sample size becomes comparable to the grain size at such length scale and the influence of individual grains cannot be neglected. The literature review demonstrates that such dependence between the mechanical behavior and the length scale is widely observed in the experimental tests on various materials. The Hall-Petch (HP) relation, in which the flow stress is expressed by a function of the grain size, is used to compute the effects of the mechanisms underlying such size dependent mechanical behavior.

In this work, the size effects, triggered by varying the number of grains across the sample thickness, are investigated for high purity nickel polycrystal sheets. The influences of the stress path and the temperature on the size effects are also considered by performing shear, simple (uniaxial) tensile and large tensile experimental tests at room temperature and 573 K. As expected, the modifications of the mechanical behavior with different numbers of grains across the thickness, are affected by the test conditions (different types of loading and temperatures). The reduced stress level with an increase in grain size (or a decrease in number of grains across the thickness) depends not only on the stress path but also on the temperature. A moderate increase in temperature can promote the emergence of quasi-single crystal behavior.

For the numerical modeling, a Strain Gradient Crystal Plasticity (SGCP) model was implemented into a Finite Element (FE) framework using Lagamine software. A specific 3D displacement based brick shape element with 20 nodes, 8 integration points and 21 nodal degrees of freedom was developed. Among the 21 degrees of freedom, 18 are dedicated to the Geometrically Necessary Dislocation (GND) densities, including 12 edge types and 6 screw types in a Face-Centered Cubic (FCC) crystalline structure. To improve the modeling of interfaces, an original flexible boundary condition for GND densities was proposed. With a tunable length scale parameter, the interfacial behavior of GND can be modeled as any intermediate state between the fully permeable and the impermeable states.

The FE simulations with a microscopic approach were carried out by employing a small Representative Volume Element (RVE) with constant dimensions. The number of grains inside the RVE was modified by varying the grain size in agreement with the values measured on the experimental samples. The reduced stress level with an increase in grain size can be correctly predicted in the form of a HP relation by the microscopic simulations. The mechanisms behind the modification of mechanical behavior with the grain size were analyzed through various microstructural properties (e.g. resistance to lattice slip, mean free path for the motion of dislocations etc.) thanks to the microscopic approach with the SGCP model. Furthermore, the free surface effects, stemmed from the escape of dislocations at free surfaces, can be characterized by the gradient of mechanical behavior and microstructural properties between surface grains and core grains.

[1]       S. Yuan, L. Duchêne, C. Keller, E. Hug, A. Habraken, Tunable surface boundary conditions in strain gradient crystal plasticity model, Mech. Mater. 145 (2020) 103393. https://doi.org/10.1016/j.mechmat.2020.103393.

[2]       S. Yuan, L. Duchêne, C. Keller, E. Hug, C. Folton, E. Betaieb, O. Milis, A. Habraken, Mechanical response of nickel multicrystals for shear and tensile conditions at room temperature and 573 K, Mater. Sci. Eng. A. 809 (2021). https://doi.org/10.1016/j.msea.2021.140987.