Revealing the gradient strain forming mechanism: The semi-analytical modeling of chamfer extrusion machining

In extrusion machining (EM), when the chip compression ratio is below a certain value (0.5–1.5), the interior microstructure of the formed chip can be transformed into the gradient structure. However, the low chip compression ratios (<1) induce fragmentation in the tool-tip region. To address this limitation, the chamfer extrusion machining (CEM) process is proposed, enabling the production of the gradient structure chips while mitigating tool damage. This study develops a semi-analytical model to evaluate the strain gradient along the chip thickness direction in CEM. The core innovation of the model lies in the incorporation of non-constant material deviating angles in the calculations. This approach offers a more accurate representation of dynamic material flow and a reduction in prediction errors within variable shear zones. Additionally, the model incorporates the actual chip compression ratio $\lambda$ as a critical variable, further enhancing the precision of the analysis. The results demonstrate that the predicted strain closely matches both experimental data and finite element values. As a result, a novel methodology is established for strain gradient calculation. This approach provides a universal framework that can be applied to a wide range of machining contexts, ensuring its versatility and reliability across different conditions.