# The Influence of Grain Size on the Abrasive Wear Resistance of Hardox 500 Steel
## 1 Introduction
In larger grains, dislocations tend to accumulate at boundaries, creating stresses that can surpass the energy barrier, allowing for further atomic diffusion. The Hall-Petch relationship is described by Equations (1) and (2) [17]:  
\[\sigma_{y}=\sigma_{0}+\frac{k_{y}}{\sqrt{d}} \tag{1}\]  
where:  
\(\sigma_{y}\) is the yield strength,  
\(\sigma_{0}\) is the friction stress of the network, yield strength of the single crystal,  
\(k_{y}\) is the strengthening coefficient, a constant value for each material, and  
\(d\) is the average grain size. \[k_{y}\sim 3\left[\frac{2 Gb\tau_{b}}{q\pi}\right]^{1/2} \tag{2}\]  
where:  
\(G\) is the shear modulus,  
\(b\) is Burgers vector,  
\(q\) is a geometric factor (dependent on the type of lattice), and  
\(\tau_{b}\) is critical stress required for passing the slide through the grain boundary. A similar correlation can also be formulated for the brittle decohesion of high-strength steels, as seen in (3) and (4) [17; 18]:  
\[\sigma_{f}=\sigma_{0f}\frac{k_{f}}{\sqrt{d}} \tag{3}\]  
where:  
\(\sigma_{f}\) is the material strength, and  
\(\sigma_{0f}\) and \(k_{f}\) are constants determined experimentally, for \(k_{f}>k_{y}\). \[k_{f}\geq\left(\frac{6\pi\gamma G}{1-v}\right)^{2} \tag{4}\]  
where:  
\(\gamma\) is the surface fracture energy, and  
\(\
u\) is Poisson's ratio. In martensitic and bainitic steels, this relationship extends to hierarchical substructures such as packets, blocks, and laths. The refinement of prior austenite grains (PAGs) leads to a higher density of these substructures, particularly high-angle grain boundaries (HAGBs), which effectively impede crack propagation and enhance the toughness of the steel. Studies [19; 20; 21; 22] have shown that uniform refinement of prior austenite grains significantly improves the mechanical performance of bainitic and martensitic steels. For example, finer prior austenite grains increase the density of high-angle grain boundaries, creating a microstructure that is more resistant to brittle fracture, while low-angle grain boundaries (LAGBs) are less effective at arresting cracks. Crack propagation in steel extends along the boundary of a block within a packet but bends when it encounters the packet boundary [22]. The presence of these boundaries increases energy dissipation during fracture events by deflecting and arresting cracks, which is particularly evident in Charpy impact tests. For instance, steels with refined prior austenite grains exhibit smaller cleavage facets and delayed brittle fracture tendencies, indicating superior performance under high-stress conditions. This microstructural refinement also has implications for tribological applications. Smaller grains contribute to increased surface hardness and resistance to abrasive wear, while maintaining sufficient ductility to absorb energy during wear processes. Plastic deformation also plays a role in abrasive wear mechanisms, such as grooving, scratching, and fatigue wear. In steels exhibiting plasticity, a single pass of an abrasive particle may not result in material detachment. Instead, a grow forms at the grain's leading edge, with material displacing to the sides and forming ridges along the groove. However, volume loss may still occur due to repeated abrasive actions or ongoing impact by individual grains, eventually leading to material detachment through low-cycle fatigue or micro-fatigue [16]. Notably, plastic deformation within the surface layer can positively influence abrasion resistance [3; 23]. At the same time, a decrease in yield strength associated with grain growth can negatively impact materials subjected to micro-cutting and brittle fracture wear mechanisms. Additionally, materials with smaller grain sizes display higher fracture resistance, as energy dissipates during directional changes in crack propagation; larger grain boundary areas introduce more obstacles for progressing structural discontinuities. Grain size can also indirectly affect tribological resistance by modifying strength and plastic properties.