Stress ($\sigma$, $\tau$)

Tensile stress (normal to plane) [Pa]$\sigma = \cfrac{\color{rgb(0, 185, 54)}{F_t}}{\color{#29ABE2}{A_0}}$

Shear stress (parallel to plane) [Pa]$\tau = \cfrac{\color{rgb(231, 0, 93)}{F_s}}{\color{#29ABE2}{A_0}}$

Tensile stress (on orange plane) [Pa]${\color{#FF8800}\sigma'} = {\color{#00CCFF}\sigma} \ cos^2\theta$

Shear stress (on orange plane) [Pa]${\color{#FF8800} \tau'} = {\color{#00CCFF} \tau} \ sin\theta \ cos\theta$

Strain ($\epsilon$)

Tensile Strain $\epsilon = \cfrac{\color{#098E2B}\Delta l}{\color{#057AA3}l_0}$

Lateral Strain $\epsilon_l = \cfrac{\color{#098E2B} \Delta w}{\color{#057AA3}w_0}$

Shear Strain $\gamma = \cfrac{\color{#098E2B} \Delta x}{\color{#057AA3}y} = tan{\color{#098E2B} \theta}$

Poisson's Ratio$\nu = -\cfrac{\epsilon_l}{\epsilon}$

Volumetric Change$\cfrac{\Delta V}{V} \approx (1 - 2\nu)\epsilon$

Young’s Modulus [GPa]$E = \cfrac{\sigma}{\epsilon}$

Elastic Shear Modulus$G = \cfrac{\tau}{\gamma}$

True Strain $\epsilon_T = ln(\cfrac{l_i}{l_0}) \ \ \ \ \color{#777} \epsilon_T = ln (1 + \epsilon)^ \ _{\ valid \ before \ necking}$

True Stress $\sigma_T = \cfrac{F}{A_i} \ \ \ \ \color{#777}\sigma_T = \sigma (1 + \epsilon) _{\ valid \ before \ necking}$

Stress Concentration Factor$K_t = 2\sqrt{\cfrac{a}{\rho_t}}$

Mean Stress $\sigma_m = (\sigma_{max} + \sigma_{max})/2$

Stress Range$\sigma_r = \sigma_{max} - \sigma_{min}$

Stress Amplitude$\sigma_a = \sigma_{r}/2$

Stress Ratio$R = \cfrac{\sigma_{min}}{\sigma_{max}}$

Resolved Shear Stress$\tau_R = \sigma cos\lambda \ cos\phi$

Critical Resolved Shear Stress$\tau_{CRSS} = \sigma_Y (cos\lambda \ cos\phi)_{max} = \cfrac{\sigma_Y}{2}$

Condition for Dislocation Motion in Crystal$\tau_R > \tau_{CRSS}$