## 3 A Proposed Transferable DT for the Grinding Industry
### Layer 2: Advanced Testing for Mechanical Characterization of Alumina Grinding Wheels  
As previously mentioned, one of the drawbacks for mechanical characterization of grinding wheels is their composition. The wheels are composed of abrasive grains, bonding agents and pores, and each of these elements have different mechanical properties. Moreover, during grinding wheel manufacturing, high temperatures are reached, which also modifies the mechanical properties of the body. Whilst there are studies in the literature that have conducted in-depth analyses to determine the mechanical properties of abrasive grains, there is no consensus regarding the values of such properties. Moreover, the most recent trend has been to manufacture customized grinding wheels depending on the particular needs of each case. Thus, for each application, there are differences in abrasive and bonding materials and grain shape and wheel porosity, which hinders establishing a common  
Figure 2: The discrete element method DEM model of a high-performance alumina grinding wheel.  
characterization of grinding wheels. Therefore, following a review of the literature regarding the mechanical properties and behavior of grinding wheels and composites, it is concluded that the best option is to characterize the mechanical behavior of these grinding wheels as a concrete, and thus, quasi-brittle material.  
Quasi-brittle materials show a nonlinear response, combining a moderate strain hardening (which is a characteristic of metallic materials) with sharp softening responses representative of brittle materials. With regard to the behavior of the wheel binder during grinding, among the various mechanical properties, particular attention is paid to the ultimate principal tensile strength \(\sigma_{max}\) which will be used as an input parameter in the DEM model proposed in Layer 1. Likewise, [PERSON]'s modulus E and the Poisson coefficient \(\
u\) are the two other input mechanical properties in the DEM model. The development of precise experimental methods for determining these variables also becomes a primary objective when developing the DT of the process. The behavior laws of the grinding wheel material, assumed to be a quasi-brittle material, must be determined by mechanical tests such as the Brazilian test, which is described in the following paragraphs.  
In the reviewed literature, the Brazilian tests are carried out using a disk, as shown in Figure 3a. However, this specimen configuration does not take into account the shape of the grinding wheel, which has a central hole. Moreover, the shape of the specimen determines the beginning of crack propagation. Therefore, new specimens are designed and manufactured as shown in Figure 3b. The specimen presents a central hole and flat surfaces to secure the specimen and to impose the load.  
The modified Brazilian tests need to include digital image correlation (DIC) analysis and fractography in order to thoroughly analyze crack propagation together with the quantification of ultimate principal tensile strength \(\sigma_{max}\). The values of ultimate tensile strengths varied between 60 and 85 MPa for the different specimens that were tested. The values were archived, as this information is critical for feeding the DEM simulation model presented in Layer 1. The ultimate tensile strength determines the fracture of the bonding agent and thus the wear of the grinding wheel.