Numerical investigation of die thickness and height effects on temperature distribution and energy consumption during spark plasma sintering of TiB2

Abstract

Precise temperature control during spark plasma sintering is critically important because it directly affects densification kinetics, microstructural evolution, and the final mechanical properties of the sintered component. However, direct temperature measurement inside the tooling remains experimentally inaccessible, and the complex interactions among electro-thermal coupling, contact resistances, and tooling geometry make process optimization particularly challenging. Numerical and experimental studies specifically addressing conductive TiB2 ceramics remain limited. This work establishes a coupled electro‑thermal finite element model, validated against experimental pyrometer data, to evaluate the effects of die wall thickness (7 mm, 14 mm, and 28 mm) and die height (11 mm, 22 mm, and 35 mm) on current and temperature distribution, thermal uniformity, heating rates, and energy consumption while fully incorporating electrical and thermal contact resistances and graphite sheet interlayers. Results demonstrate that die height dominates thermal performance. Increasing height from 11 mm to 35 mm reduces the sample center temperature from 1932 °C to 1754 °C, while increasing the die surface radiative loss from 1675 W to 3592 W. The heating rate at the sample center decreases from 140 °C/min to 116 °C/min as height increases to 35 mm, while the die surface heating rate drops more sharply from 130 °C/min to 80 °C/min, widening the difference from 10 °C/min to 36 °C/min. In contrast, increasing wall thickness from 7 mm to 28 mm raises radiative loss more modestly from 2351 W to 2792 W, while the sample center temperature declines from 1992 °C to 1878 °C. The heating rate at the sample center decreases from 150 °C/min to 116 °C/min, and the die surface heating rate drops from 120 °C/min to 76 °C/min. The required input power to maintain 1900 °C at the sample center is lowest for the 7 mm thick die (9596 W). For die height, the 22 mm configuration minimizes power consumption (10103 W) by surrounding the punch and reducing heat accumulation inside it, whereas increasing the height to 35 mm yields no additional energy savings due to increased die surface losses. These findings quantitatively establish die height as the primary lever for controlling current focusing and thermal efficiency.