The use of pre-hardened mold steels has increased appreciably over the years; more than 80% of the plastic mold steels are used in pre-hardened condition. These steels are delivered to the customer in finished state i.e. there is no need of any post treatment. With hardness around ~40HRC, they have properties such as good polishability, good weldability, corrosion resistance and thermal conductivity. Machinability is a very important parameter in pre-hardened mold steels as it has a direct impact on the cost of the mold. In normal machining operations involving intricate or near net shapes, machining constitutes around 60% of the total mold cost. Efforts are underway to explore every possible way to reduce costs associated with machining and to make production more economical. All the possible parameters which are considered to affect the machinability are being investigated by the researchers. This thesis work focuses on the effect of prior austenite grain size on the machinability of pre-hardened mold steel (Uddeholm Nimax).  Austenitizing temperatures and holding times were varied to obtain varying grain sized microstructures in different samples of the same material. As it was difficult to delineate prior-austenite grain boundaries, experimental and empirical methods were employed to obtain reference values. These different grain sized samples were thereafter subjected to machining tests, using two sets of cutting parameters. Maximum flank wear depth=0.2mm was defined for one series of test which were more akin to rough machining, and machining length of 43200mm or maximum wear depth=0.2mm were defined for second series of tests which were similar to finishing machining. The results were obtained after careful quantative and qualitative analysis of cutting tools. The results obtained for Uddeholm Nimax seemed to indicate that larger grain sized material was easier to machine. However, factors such as retained austenite content and work hardening on machined surface, which lead to degradation of machining operations were also taken into consideration. Uddeholm Nimax showed better machinability in large grained samples as retained austenite(less than 2%) content was minimal in the large grained sample. Small grained sample in Uddeholm Nimax had a higher retained austenite (7+2%) which resulted in degradation of machining operation and a lesser cutting tool life.

This thesis concerns the mathematical modelling of phase transformations with a special emphasis on martensitic phase transformations and their application to the modelling of steels. In Chapter 1, we develop a framework that determines the optimal transformation strain between any two Bravais lattices and use it to give a rigorous proof of a conjecture by E.C. Bain in 1924 on the optimality of the so-called Bain strain. In Chapter 2, we review the Ball-James model and related concepts. We present some simplification of existing results. In Chapter 3, we pose a conjecture for the explicit form of the quasiconvex hull of the three tetragonal wells, known as the three-well problem. We present a new approach to finding inner and outer bounds. In Chapter 4, we focus on highly compatible, so called self-accommodating, martensitic structures and present new results on their fine properties such as estimates on their minimum complexity and bounds on the relative proportion of each martensitic variant in them. In Chapter 5, we investigate the contrary situation when self-accommodating microstructures do not exist. We determine, whether in this situation, it is still energetically favourable to nucleate martensite within austenite. By constructing different types of inclusions, we find that the optimal shape of an inclusion is flat and thin which is in agreement with experimental observation. In Chapter 6, we introduce a mechanism that identifies transformation strains with orientation relationships. This mechanism allows us to develop a simpler, strain-based approach to phase transformation models in steels. One novelty of this approach is the derivation of an explicit dependence of the orientation relationships on the ratio of tetragonality of the product phase. In Chapter 7, we establish a correspondence between common phenomenological models for steels and the Ball-James model. This correspondence is then used to develop a new theory for the (5 5 7) lath transformation in low-carbon steels. Compared to existing theories, this new approach requires a significantly smaller number of input parameters. Furthermore, it predicts a microstructure morphology which differs from what is conventionally believed.