# Cracking and Toughening Mechanisms in Nanoscale Metallic Multilayer Films: A Brief Review
## 5 Conclusions and Future Developments
\begin{tabular}{l l} \(H_{\text{rom}}\) & Rule-of-mixtures hardness (GPa) \\ \(\overline{H}_{m}\) & Mean values of the melting enthalpy (kJ/mol) \\ \(h\) & Individual layer thickness (nm) \\ \(h_{c}\) & The critical thickness to form perfect coherent interfaces (nm) \\ \(h_{f}\) & The film thickness (nm) \\ \(h_{0}\) & The penetration depth (nm) \\ \(h_{\varphi}\) & The layer thickness measured parallel to the glide plane (nm) \\ \(K_{app}\) & The far field mode I stress intensity (MPa-m\({}^{1/2}\)) \\ \(K_{IC}\) & The fracture toughness (MPa-m\({}^{1/2}\)) \\ \(k_{B}\) & The Boltzmann constant \\ \(L\) & The distance between source and obstacle (nm) \\ \(L_{0}\) & Half initial height of the pillar (nm) \\ \(L_{p}\) & The final height of the pillar (nm) \\ \(L_{Su}\) & The total length of the substrate pillar (nm) \\ \(l\) & Half of the buckle width (nm) \\ M & The Taylor factor \\ \(N_{d}\) & The defects density across the radiation damage region \\ \(n\) & The equilibrium number of dislocations \\ \(p\) & The load in compression test (mN) \\ \(P_{\text{max}}\) & Peak load in nanoindentation (mN) \\ \(Q\) & The activation energy (J) \\ \(R\) & The ideal gas constant (J/(mol\cdot\)K) \\ \(r\) & Crack length (nm) \\ \(r_{0}\) & The effective core radius, the radius at the top of the pillar (nm) \\ \(r_{d}\) & The radius of the defect cluster (nm) \\ \(S\) & Contact stiffness (N/m) \\ \(s\) & The equilibrium spacing of misfit dislocations (nm) \\ \(\overline{S}_{\text{zib}}\) & Mean values of the vibration part of the overall melting entropy (kJ/mol) \\ \(T\) & The absolute temperature (K) \\ \(t\) & Time (s) \\ \(U_{e}\) & The elastic energy (J) \\ \(V\) & The plastic volume displaced by the indenter (nm\({}^{3}\)) \\ \(\overline{V}_{m}\) & Mean values of the molar volumes of corresponding substances consisting of interfaces \\ \(\alpha\) & The [PERSON]'s constant \\ \(\alpha_{1},\alpha_{2}\) & Two Dundurs' parameters \\ \(\beta\) & A constant which depends on the geometry of the indenter \\ \(\gamma\) & Surface or interface energy (J\(\cdot\)m\({}^{-2}\)) \\ \(\gamma_{c}\) & The coherent interface energy (J\(\cdot\)m\({}^{-2}\)) \\ \(\gamma_{in}\) & The incoherent interface energy (J\(\cdot\)m\({}^{-2}\)) \\ \(\gamma_{s}\) & Stacking fault energy (J\(\cdot\)m\({}^{-2}\)) \\ \(\Delta\gamma\) & Change in interfacial free energy (J\(\cdot\)m\({}^{-2}\)) \\ \(\Gamma\) & Interfacial adhesion energy \\ \(\Gamma_{AB}\) & Surface energy mismatch \\ \(\varepsilon\) & The misfit strain \\ \(\varepsilon_{c}\) & Macroscopic strain \\ \(\varepsilon_{0}\) & The in-plane plastic strain \\ \(\varepsilon_{T}\) & The true strain in flat punch compression \\ \(\sigma_{T}\) & The true stress in flat punch compression (GPa) \\ \(\lambda\) & The bilayer thickness (nm) \\ \(\mu\) & Shear modulus (GPa) \\ \(u_{tot}\) & The total displacement in pillar compression (nm) \\ \(\mu^{*}\) & The mean shear modulus (GPa) \\ \(\varphi\) & The Poisson ratio \\ \(\xi\) & Steady-state energy release rate (J\(\cdot\)m\({}^{-2}\)) \\ \(\xi_{c}\) & The critical energy release rate (J\(\cdot\)m\({}^{-2}\)) \\ \(\delta\) & Lattice mismatch \\ \end{tabular}