# Cracking and Toughening Mechanisms in Nanoscale Metallic Multilayer Films: A Brief Review
## 4 Other Fracture Properties
### Fracture Toughness
#### 4.1.2 Phase Transformation Enhanced Toughening  
A contradictory to the length scale dependent deformation and fracture mode in Cu/Nb NMMFs have been experimental observed in Cu/Ru multilayers, which indicated that the deformation mode changed from brittle cracking to ductile shearing with decreasing \(h\)[15]. With a relatively strong interface and small lattice mismatch in fcc/hcp Cu/Ru, the degree of coherency, texture, and epitaxy of multilayers increase with decreasing \(h\), then the transmissibility for dislocation is much higher as the slip system between the layers was continuous across the interface. Then continuous dislocation emission process controls the crack blunting and growth processes (see in Figure 16). As the dislocations will not be constrained by the interface, the propagation of dislocations emitted from a crack can loosely move both in-plane and out-of-plane. In this condition, when the crack tip reaches interface with crack length equals to the thickness of Ru layers, the fracture toughness is obtained as [15]:  
Figure 14: (**a**) Sketch of the micromechanical fracture model in NMMFs; (**b**) Model predicted \(n_{\text{max}}\) at different normalized cohesive strengths (\(\sigma_{c}\) ) as a function of \(h\)[8]. Figure 15: FIB cross-sectional images of microcracks of Cu/Nb NMMFs with (**a**) \(h_{\text{Cu}}=125\) nm and (**b**) \(h_{\text{Cu}}=5\) nm [8]. \[K_{IC}=mh^{-1/2} \tag{20}\]  
where \(m\) is a constant of the NMMFs dependent on material systems. Equation (20) suggested that a small \(h\) is in favor of suppressing microcrack growth and increasing the fracture toughness. Furthermore, when \(h\) is decreasing, the slip continuity across interface increases, which provides more chances for dislocation transmission, thereby encouraging homogeneous deformation. Additionally, the strong bonding interface is more resistant to atomic decohesion compared to incoherent interface and, therefore, can store a larger amount of deformation-induced incompatibility before fracture occurs. On the other hand, the length scale dependent the fracture toughness of fcc/hcp NMMFS is also influenced by the transformation of lattice structures [15]. Due to the dimension induced phase transformation in Ru layer, the fcc/fcc Cu/Ru should possess a great deal of slip systems to accommodate plastic deformation; while, hcp Ru are difficult to deform due to few slip systems are available [21; 115; 116]. Accordingly, the difference in fracture toughness between fcc/hcp multilayers whether has structure transformation are summarized, as shown in Figure 17. Clearly, both the multilayers exhibit fracture toughness improvement with decreasing \(h\) first, which is account for the effective interface shielding effect on crack propagation. In contrast, at a relatively large \(h\) the fcc/bcc without structure transformation display a decrease trend in fracture toughness compared with the fcc/hcp multilayers with structure transformation. This decrease can be reasonably explained on the basis of the slip discontinuity of dislocations crossing the layer interface and thus broke down the interface shielding effect. While with further reducing \(h\) in fcc/hcp multilayers, the coherent trend accompanied with structure transformation makes the dislocations crossing interface process possible and elevate the fracture toughness. The complex cracking behaviors in a series of multilayers are functions of length scales and interface structures. This approach is potentially able to effectively explain 'preparation-structure-properties' relationships that are pointing to promising route for the optimized combination of toughness and strength. The experimental results and theoretical analyses are helpful to control the dimension configurations or constituent phases to achieve target toughening properties in NMMFs. Figure 16: Dependence of \(K_{IC}\) on \(h\) (dots and left y-axis) for the Cu/Ru multilayers. Calculated normalized \(K_{IC}\) (lines and right y-axis) based on Equation (20) fits well with experimental results.