**1. Introduction**

Machining of brittle materials such as ceramics, rocks, composites, and bones is common in aerospace/automotive industries and the medical field [1]. Although efforts [2–6] have been made to model machining of fiber-reinforced composite materials for predicting brittle failure, there is not a generalized method that can successfully and efficiently emulate the physics behind brittle cutting—the rapid and randomized crack initiation and propagation upon tool-workpiece contact. Unlike ductile material cutting, which is dominated by shear deformation across the shear plane, brittle material cutting is driven by fractures. Finite element method (FEM) has been widely used to simulate ductile material machining (e.g., metals) using the Johnson–Cook plasticity model for cutting forces and chip formation [7–9]. However, FEM has not yet been successfully applied to brittle materials because of the difficulty of capturing numerous and unpredictable cracks at the same time. Technically, FEM needs an extremely fine mesh to simulate stress concentration and consequent element failure at each time increment, which is not practical due to a high computational cost.

Researchers have tried to apply mesh-free methods such as smooth particle hydrodynamics (SPH) to cutting simulation because they do not require a gridded domain and can handle large deformation [10]. However, there are discrepancies among the published works, especially on damage definition. Takabi et al. [11] investigated SPH in orthogonal cutting and showed the uncertainty of damage due to particles losing connection to each other (i.e., the natural separation), which can drastically change the outcome. Also, particle separation is not determined by the fracture toughness

but the material strength. Therefore, mesh-free methods are not considered an ideal approach for brittle materials cutting.

To deal with fracture problems, the cohesive element has been developed for FEM, which forms the cohesive zone (CZ) in the model. The cohesive zone concept links the microstructural failure mechanism to the continuum fields [12]. A CZ element can begin to separate based on the strain energy release rate, which is often defined by a traction–displacement relationship. The cohesive zone–finite element method (CZ–FEM) has been a useful tool for investigation of interfacial fracture problems, such as crack tip propagation, the adhesive strength between two materials, and modeling of composite delamination. CZ–FEM has been used to solve machining problems of composites and ceramics, though not many. Rao et al. [2] simulated the orthogonal cutting of unidirectional carbon fiber-reinforced polymer and glass fiber-reinforced polymer composites using CZ between the fibers and matrix. They used a 2D plane strain model and zero-thickness cohesive elements to enable fiber detachment when the interfacial energy exceeds the threshold defined by an exponential traction–displacement relationship. Umer et al. [3] used CZ–FEM to simulate metal matrix composite machining. They modeled the orthogonal machining of SiC particle-reinforced aluminum-based metal matrix composites by placing CZ elements between the particles and the matrix. A bilinear traction–displacement profile was used for CZ elements with zero thickness. Dong and Shin [13] developed a multi-scale model for simulating the machining of alumina ceramics in laser-assisted machining. Zero-thickness CZ was assigned around the ceramic grain boundaries, and the traction–displacement profile was determined based on a separate molecular dynamics (MD) simulation. Note that CZ is often modeled as zero thickness because it is an imaginary interface inside the material in these cases, unlike physical adhesives.

In the above-mentioned CZ–FEM works, the CZ elements are placed either at known interfaces or paths as a pre-determined condition where cracks will initiate and propagate [14]. Therefore, CZ–FEM does not seem possible for a homogenous, flaw-free brittle material in which potential cracking path cannot be defined. To address this issue, the current study proposes using a CZ mesh together with a regular element mesh to enable a network of potential cracks. A zero-thickness CZ element is embedded between regular elements. In other words, this CZ mesh will force the material to fail between elements instead of within an element. This modified CZ–FEM is named embedded cohesive zone–finite element method (ECZ–FEM). The ECZ–FEM for brittle machining is developed and validated in this paper using the commercial FEM software ABAQUS.

#### **2. Finite Element Model Setup**

This section presents the overall configuration of ECZ–FEM, step-by-step procedures to construct the model, and the required modification for material properties. The model introduced here is built based on the corresponding orthogonal cutting experiment.
