Materials informatics

Abstract

Materials informatics employs techniques, tools, and theories drawn from the emerging fields of data science, internet, computer science and engineering, and digital technologies to the materials science and engineering to accelerate materials, products and manufacturing innovations. Manufacturing is transforming into shorter design cycles, mass customization, on-demand production, and sustainable products. Additive manufacturing or 3D printing is a popular example of such a trend. However, the success of this manufacturing transformation is critically dependent on the availability of suitable materials and of data on invertible processing–structure–property–performance life cycle linkages of materials. Experience suggests that the material development cycle, i.e. the time to develop and deploy new material, generally exceeds the product design and development cycle. Hence, there is a need to accelerate materials innovation in order to keep up with product and manufacturing innovations. This is a major challenge considering the hundreds of thousands of materials and processes, and the huge amount of data on microstructure, composition, properties, and functional, environmental, and economic performance of materials. Moreover, the data sharing culture among the materials community is sparse. Materials informatics is key to the necessary transformation in product design and manufacturing. Through the association of material and information sciences, the emerging field of materials informatics proposes to computationally mine and analyze large ensembles of experimental and modeling datasets efficiently and cost effectively and to deliver core materials knowledge in user-friendly ways to the designers of materials and products, and to the manufacturers. This paper reviews the various developments in materials informatics and how it facilitates materials innovation by way of specific examples.

Appendices

Appendixes

Appendix 1: Mean squared error (MSE) and $\hbox {R}^{2}$ statistics

The predictability of a trained machine learning model is usually measured by RMSE (or MSE) and coefficient of determination ($R^{2}$). Their definitions are given by

$$\begin{aligned} RMSE= & {} \sqrt{\frac{\mathop {\sum }\nolimits _{i=1}^n \left( {p_i -e_i } \right) ^{2}}{n}}\\ MSE= & {} \frac{\mathop {\sum }\nolimits _{i=1}^n \left( {p_i -e_i } \right) ^{2}}{n}\\ R^{2}= & {} 1-\frac{\mathop {\sum }\nolimits _{i=1}^n {(e_i -p_i )^{2}} }{\mathop {\sum }\nolimits _{i=1}^n {(e_i -\bar{{e}})^{2}} } \end{aligned}$$

where $e_i$ and $p_i$ are respectively the measured and predicted values of a property in interest for test i, n is the number of total tests, and $\bar{e}=\frac{1}{n}\sum _{i=1}^n e_i$.

Appendix 2: Voigt–Reuss–Hill (VRH) average

In linear elasticity, stress is linearly proportional to strain and vice versa. This linear relationship is called Hooke’s law. For anisotropic materials, Hooke’s law takes the forms of ${\varvec{\sigma }}_{\mathrm{ij}}=\hbox {c}_{\mathrm{ijkl}}{\varvec{\varepsilon }}_{\mathrm{kl}}$ and ${\varvec{\varepsilon }}_{\mathrm{ij}}=\hbox {s}_{\mathrm{ijkl}}{\varvec{\sigma }}_{\mathrm{kl}}$, i, j, k, $\hbox {l}= 1$, 2, 3, where $\sigma$ and $\varepsilon$ denote the stress and strain tensors, respectively, c is the elastic constant tensor, and s is the elastic compliance tensor. For isotropic materials, there are only two independent elastic constants, although five elastic constants are widely used. The five elastic constants are Young’s modulus Y, shear modulus G, bulk modulus K, Poisson ratio $\nu$, and Lame constant $\lambda$, and their relations are given by $\hbox {Y}=2\hbox {G}({1+\nu }),\hbox {K}=({3\lambda +2\nu })/3,\hbox {v}=\lambda /[{2({G+\lambda })}].$ Based on the uniform stress assumption, the Voigt averaged shear modulus and Lame constant are respectively given by $G_{{ Voigt}} =\frac{1}{30}( {3c_{{ ijij}} -c_{{ iijj}}})$ and $\lambda _{{ Voigt}} =\frac{1}{15}( {2c_{{ iijj}} -c_{{ ijij}}})$, where the repeated i and j mean the summation over i and j for i, $\hbox {j}=1$ 2, 3. Then, $K_{{ Voigt}}$ is calculated from $G_{{ Voigt}}$ and $\lambda _{{ Voigt}}$. The Voigt averaged elastic moduli are the upper bounds of the elastic moduli. Based on the uniform stress assumption, the Reuss averaged shear modulus and Young’s modulus are respectively given by $\frac{1}{G_{{ Reuss}} }=\frac{2}{15}( {3s_{{ ijij}} -s_{{ iijj}}})$ and $Y_{{ Reuss}} =\frac{1}{15}( {2s_{{ ijij}} +s_{{ iijj}}})$, where the repeated i and j mean the summation over i and j for i, $\hbox {j}=1$ 2, 3. Then, $K_{Reuss}$ is calculated from $G_{{ Ruess}}$ and $Y_{{ Reuss}}$. The Reuss averaged elastic moduli are the lower bounds of the elastic moduli. Voigt–Reuss–Hill average takes the mean of Voigt average and Reuss average, meaning that

$$\begin{aligned} G_{{ VRH}}= & {} \frac{1}{2}(G_{{ Voigt}} +G_{{ Reuss}} ), \\ K_{{ VRH}}= & {} \frac{1}{2}(K_{{ Voigt}} +K_{{ Reuss}} ). \end{aligned}$$