An integrated approach to model strain localization bands in magnesium alloys

Abstract

Strain localization bands (SLBs) that appear at early stages of deformation of magnesium alloys have been recently associated with heterogeneous activation of deformation twinning. Experimental evidence has demonstrated that such “Lüders-type” band formations dominate the overall mechanical behavior of these alloys resulting in sigmoidal type stress–strain curves with a distinct plateau followed by pronounced anisotropic hardening. To evaluate the role of SLB formation on the local and global mechanical behavior of magnesium alloys, an integrated experimental/computational approach is presented. The computational part is developed based on custom subroutines implemented in a finite element method that combine a plasticity model with a stiffness degradation approach. Specific inputs from the characterization and testing measurements to the computational approach are discussed while the numerical results are validated against such available experimental information, confirming the existence of load drops and the intensification of strain accumulation at the time of SLB initiation.

Appendix

Material

Two sets of samples were machined from two different commercial magnesium AZ31 alloy (3 wt.% Al and 1 wt.% Zn) plates. The notched specimens were prepared from a 25.4 mm thick plate in the soft annealed condition (O temper). Two cubes were extruded from the plate and then compressed to 5% load in either the normal to rolling (ND) or transverse to rolling (TD) direction. The cubes were later held at 500${^{\circ }}$C for 50 h to increase their grain size. Texture and grain size were measured in samples cut from the normal direction. The straight specimens were prepared from a 50.8 mm thick plate in H24 condition. Cubes were cut from the plate and heat treated to O temper at 350${^{\circ }}$C for 1 h. Both tensile specimens were machined from the cubes using Electrical Discharged Machining (EDM) according to ASTM E606.

Samples were mechanically ground using 800, 1200, and 2400 SiC papers. Subsequent polishing was carried out using an alcohol based diamond solution through a sequence of 6, 3, and 1 $\mu$m Buehler’s TriDent and Struers’ Nap polishing cloths. Polishing was completed using a mixed solution comprising of 25% MasterPrepTM Polishing Suspension (0.05 $\mu$m), 5% LiquinoxTM critical-cleaning liquid detergent, and 70% water. In each polishing step, ultrasonic cleansing was used to completely eliminate adhered particles from previous polishing courses. Specimens were then immersed in a chemical polishing solution comprised of 5% nitric acid, 15% acetic acid, 20% distilled water, and 60% ethanol for 3 s.

All EBSD data was collected with a Scanning Electron Microscope (SEM) FEI XL30 equipped with an EBSD detector, controlled by the TSL software. Grain information, including lattice orientations and grain size, were measured at intervals of 2 $\mu$m on a hexagonal grid by automated acquisition and processing of backscatter diffraction patterns. The accelerating voltage and working distance were set at 30 kV and 15 mm, respectively. EBSD data was post processed using MTEX algorithm in MATLAB platform [37].

Mechanical Testing

A speckle pattern was applied on the surface of samples before testing for DIC measurements. A white paint coating was sprayed using at aerosol canister, while black dots were scattered on top using an airbrush. The notched samples were tested using a MTS 858 table top system with a load cell of 3 kips (13.35 kN). The testing was carried out using displacement control, at a rate of 5.315 $\times$ 10$^{-4}$ in/s (1.35 $\times$ 10$^{-2}$ mm/s). Experiments of the ND and TD specimens both to failure and to a pre-determined value of engineering strain are reported in this article. DIC was carried out by an optical microscope with dual (2) cameras in concurrence with the commercial software VIC-3D (commercially available by Correlated Solutions, Inc.) monitored deformation in a Field of View (FOV) of 5 mm $\times$ 6 mm size during two tension tests (Fig. 1). Along with the selected FOV, a narrower diagonal area marked in Fig. 1 was used to quantify the deformation of the shear band region only.

The straight specimens were tested with a screw-driven Gatan MTEST stage with a 2000 N load cell. The tests were conducted using displacement control with a rate of 0.1 mm/min. The Gatan stage has pre-tilted grips providing the capability for in-situ EBSD measurement testing inside of SEM. DIC measurements were attained using a GOM (Trillion) 5M dual cameras setup and the ARAMIS software.