# Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity
## 1 Introduction  
Polymeric biomaterials are generally categorized, as many other families of materials, into three different groups, depending on their fracture behavior: brittle, quasi-brittle, and ductile. Fracture in brittle biomaterials usually takes place suddenly, with no plastic deformation from the pre-existing defect (crack or notch) tip. The fracture process in quasi-brittle biomaterials is still abrupt, but a small plastic zone is developed around the crack/notch tip at the fracture onset. Finally, ductile biomaterials usually exhibit elastic-plastic stress-strain behavior, and fracture normally occurs with an intermediate or large plastic zone in the vicinity of the crack/notch tip. Bone cement is a well-known type of biomaterial. Bone cements are used in clinical applications for fixing joint prostheses in the hip and knee joints. Depending on the implant shape, notches ofvarious shapes (e.g., U-shaped notches) can form in the bone cement. Due to the stress concentration around the notch tip and the corresponding reduction of the load-carrying capacity of the notched bone cement, prostheses may fail prematurely. Thus, the fracture behavior of notched biomaterials, particularly bone cements, should be carefully analyzed. Polymer-based bone cement is the oldest and most well-known type of bone cement. Polymeric bone cements generally consist of two main components: the solid component, which is usually a Polymethyl-methacrylate powder, and the liquid component, frequently made of a methyl-methacrylate monomer [1]. Additionally, bone cements include additives to increase biocompatibility. In 1970, [PERSON] used bone cement material for orthopedic applications, with subsequent extensive research on this material [2]. In 1984, [PERSON] et al. [3] widely investigated the mechanical properties of bone cement, including tensile strength, compression strength, viscoelastic behavior, fatigue response, impact strength, and fracture toughness [3]. Other works analyzing the properties of bone cements may be found in [4; 5; 6; 7]. Low compatibility with body tissues and high heat generation during polymerization are the main issues of bone cement materials [8]. [PERSON] et al. [9] investigated the fracture behavior of bone cement. They found that by adding nano-hydroxyapatite particles, the heat problem during the polymerization reaction could be reduced and the mechanical properties of the material could be increased [9]. Furthermore, [PERSON] et al. [10] studied the fracture resistance, elastic modulus, and Poisson's ratio of PMMA containing micro and nano MgO particles. They revealed that by adding nanoparticles to PMMA, the resulting mechanical properties could be improved considerably [10]. [PERSON] et al. [11] and [PERSON] et al. [12] studied the fracture properties of bone cement materials by adding vancomycin. They measured the four-point bending strength, compressive strength, and fracture toughness of these materials [11; 12]. Likewise, [PERSON] et al. [13] investigated the effect of adding the CS/Go optimized nanocomposite with different weight percentages to bone cement on mechanical properties of this material. They found that the addition of this nanocomposite (25 wt.%) could improve the mechanical, physical, and biological properties [13]. Concerning some of the latest advances in stress-based fracture criteria, [PERSON] et al. [14] have recently investigated the fracture properties of three different dental biomaterials under mixed mode loading. They concluded that the use of T-stress in the generalized maximum tangential strain (GMTSN) criterion could improve the agreement between the theoretical predictions and the experimental results [14]. Previously, [PERSON] et al. [15] successfully predicted the fracture load of bone cement in presence of U-shaped notches under mode I loading by using the theory of critical distances (TCD).