why Even after the formation of large cracks on the surface of the deformed ingot due to excessive strain the inner of the ingot still suffering insufficient deformation strain to achieve the desired

There could be several reasons why the inner part of the ingot may still suffer from insufficient deformation strain, even after the formation of large cracks on the surface. Some possible explanations include:

1. Strain localization: During deformation, the material may undergo strain localization, where the deformation concentrates in specific areas, such as near the surface or along grain boundaries. This can result in limited strain reaching the inner regions of the ingot, leading to insufficient deformation.

2. Crack propagation: The formation of large cracks on the surface can act as stress concentrators, allowing cracks to propagate deeper into the ingot. As cracks propagate, they may hinder the uniform distribution of deformation strain throughout the ingot, limiting the extent of deformation in the inner regions.

3. Strain relaxation: The material may experience strain relaxation, where the internal stresses within the ingot redistribute or decrease over time. This can occur due to factors like thermal effects or the presence of impurities. As a result, the strain required for achieving the desired microstructure and properties may not be sustained in the inner regions.

It is important to note that without specific information about the type of material, ingot shape, and processing conditions, it is difficult to provide a definitive answer. The reasons mentioned above are general possibilities that can contribute to insufficient deformation strain in the inner part of an ingot.

As for a specific source of reference, given that the question pertains to a specific scenario, it would be best to consult relevant research papers, textbooks, or technical reports that discuss the deformation behavior of the specific material or ingot shape under consideration