Plastic Work Partitioning During Slip- and Twinning-Dominated Deformation in AZ31B Magnesium Alloy

1. Problem Statement

The hexagonal close-packed (HCP) AZ31B magnesium alloy exhibits strong elastic-plastic anisotropy depending on the loading direction relative to its crystallographic texture.

• Mechanism Competition: Loading parallel to the extrusion direction (ED) primarily activates dislocation slip, while loading perpendicular to the ED activates mechanical twinning (specifically $\{10\bar{1}2\}$ extension twinning).
• Knowledge Gap: While the mechanical behavior (stress-strain response) of AZ31B is well-characterized, the thermodynamic partitioning of plastic work (how much energy is stored vs. dissipated as heat) remains insufficiently resolved.
• Experimental Challenges: Previous studies on energy dissipation in Mg alloys face significant hurdles:
  • High Thermal Diffusivity: AZ31B has a thermal diffusivity ($\alpha \approx 55 \text{ mm}^2/\text{s}$) roughly 16 times higher than austenitic steel, making transient temperature measurements difficult.
  • Dynamic Loading Limitations: Many prior studies used dynamic loading (e.g., Split-Hopkinson bars) where heat transfer effects are neglected, or relied on infrared thermography (IRT) with spatial mismatches between the measurement window and the moving specimen, leading to potential overestimation of temperature rises.
  • Lack of Validation: Existing conclusions (e.g., that slip dissipates more energy than twinning) often lack rigorous experimental support due to these measurement limitations.

2. Methodology

The study employs a rigorous, quasi-static experimental approach combining full-field mechanical and thermal measurements to quantify energy partitioning.

• Specimen Preparation:
  • Extruded AZ31B rods were cut into cubic specimens.
  • Two orientations were tested: Parallel to ED (slip-dominated) and Perpendicular to ED (twinning-dominated).
  • Surfaces were prepared for Digital Image Correlation (DIC) and Infrared Thermography (IRT).
• Thermal Characterization:
  • Prior to deformation, the anisotropic thermal conductivity tensor ($k$) was determined experimentally using a semi-infinite body heat conduction model with Neumann boundary conditions.
  • Results: $k_{\parallel} = 95.35 \text{ W m}^{-1}\text{K}^{-1}$ and $k_{\perp} \approx 87 \text{ W m}^{-1}\text{K}^{-1}$.
• Experimental Setup:
  • Loading: Displacement-controlled tension at a strain rate of $\dot{\varepsilon} \approx 0.67 \text{ s}^{-1}$ (quasi-static).
  • Synchronization: Simultaneous acquisition of:
    • Mechanical Data: MTS 858 hydraulic testing machine.
    • Strain Fields: PCO Edge 5.5 visible camera with DIC (25 px subsets, ~32,000 points/frame).
    • Temperature Fields: ThermaCam Phoenix IR camera (346 Hz initially, 100 Hz during test; 20 mK sensitivity).
• Data Analysis:
  • Heat Source Calculation: The surface power density of heat sources ($\dot{q}_v$) was derived by solving the transient heat conduction equation (Eq. 2), explicitly accounting for anisotropic thermal conductivity ($k_x, k_y$).
  • Energy Partitioning:
    • Plastic Work ($w_p$): Calculated from the area under the stress-strain curve.
    • Dissipated Heat ($q_d$): Time-integrated heat source density.
    • Stored Energy ($e_s$): Calculated as $e_s = w_p - q_d$.
    • Taylor-Quinney Coefficients: Both integral ($\beta_{int}$) and differential ($\beta_{diff}$) coefficients were calculated to quantify the fraction of work converted to heat.

3. Key Results

A. Mechanical Response

• Slip-Dominated (Parallel to ED): Exhibits higher yield stress and stable plastic flow. Strain hardening is gradual, leading to diffuse necking and ductile failure.
• Twinning-Dominated (Perpendicular to ED): Shows lower yield stress but significantly higher initial strain hardening. Deformation localizes rapidly into narrow bands, leading to abrupt, brittle-like fracture without significant load drop.
• Hardening Behavior: The twinning-dominated specimen exhibits a "dynamic Hall-Petch" effect due to twin boundaries acting as barriers to dislocation motion, causing rapid hardening.

B. Thermal and Energy Partitioning

• Temperature Rise: The slip-dominated specimen reached a mean temperature rise ($\Delta T_{mean}$) of >4 K (max 5.38 K), whereas the twinning-dominated specimen only reached ~2.5 K (max 3.62 K).
• Heat Dissipation ($q_d$):
  • Slip: Heat dissipation increases nearly linearly with plastic strain. At $\varepsilon_p \approx 0.23$, $q_d \approx 17.5 \text{ J/g}$ (approx. 50% of total work).
  • Twinning: Heat dissipation is delayed. Up to $\varepsilon_p \approx 0.07$, dissipation is minimal, indicating most work is stored. At failure ($\varepsilon_p \approx 0.18$), $q_d \approx 8 \text{ J/g}$.
• Stored Energy ($e_s$):
  • Slip: Stored energy accumulates gradually as low-energy dislocation structures (LEDS) form.
  • Twinning: A large fraction of plastic work is stored initially (likely as interfacial energy of twin boundaries). This storage drives rapid hardening but promotes mechanical instability.
• Taylor-Quinney Coefficients ($\beta$):
  • Slip: $\beta_{diff}$ is stable (0.5–0.7); $\beta_{int}$ rises from ~0.33 to ~0.52.
  • Twinning: $\beta_{diff}$ varies widely (near 0 to ~0.7), reflecting the complex interplay of twin nucleation and slip. $\beta_{int}$ rises from near 0 to ~0.4.

C. Microstructural Evolution

• Slip-Dominated: EBSD maps show extensive intragranular orientation gradients and fragmented grains, consistent with distributed defect accumulation and gradual energy dissipation.
• Twinning-Dominated: Characterized by thick $\{10\bar{1}2\}$ twin lamellae causing massive lattice reorientation (misorientation $\approx 86^\circ$). Limited intragranular refinement occurs before failure, supporting the observation that energy is stored in twin interfaces rather than dissipated as heat.

4. Key Contributions

1. Quantitative Partitioning: Provides the first robust, quantitative comparison of plastic work partitioning between slip- and twinning-dominated deformation in AZ31B, overcoming previous limitations of thermal diffusivity and measurement accuracy.
2. Anisotropic Thermal Modeling: Successfully adapted the transient heat conduction approach to account for the anisotropic thermal conductivity of extruded Mg alloys, improving the accuracy of heat source calculation.
3. Mechanism-Dependent Energy Storage: Demonstrates that the Taylor-Quinney coefficient is not a material constant but is strictly dependent on the active deformation mechanism. Twinning acts as an energy storage mechanism (high $\beta_{diff}$ variability, low initial dissipation), while slip acts as a dissipation mechanism.
4. Link to Instability: Establishes a direct causal link between delayed heat dissipation (high energy storage in twin boundaries) and early strain localization/brittle fracture in twinning-dominated regimes.

5. Significance

This study fundamentally alters the understanding of thermomechanical behavior in HCP magnesium alloys. It reveals that deformation mechanism dictates energy balance:

• Slip promotes stable, ductile deformation by efficiently converting plastic work into heat.
• Twinning promotes rapid strain hardening and early failure by storing energy in the microstructure (twin boundaries) rather than dissipating it.

These findings are critical for:

• Predictive Modeling: Improving constitutive models for Mg alloys by incorporating mechanism-dependent energy partitioning rather than assuming a constant Taylor-Quinney coefficient.
• Forming Processes: Optimizing processing routes (e.g., temperature, strain rate, texture control) to favor slip over twinning for improved formability and ductility in automotive and aviation applications.
• Failure Analysis: Understanding why twinning-dominated loading leads to premature, brittle-like failure despite high strain hardening rates.