The stress intensity factor at the crack tip of a compact tension specimen is^[4]

${\displaystyle K_{\rm {I}}={\frac {P}{B}}{\sqrt {\frac {\pi }{W}}}\left[16.7\left({\frac {a}{W}}\right)^{1/2}-104.7\left({\frac {a}{W}}\right)^{3/2}+369.9\left({\frac {a}{W}}\right)^{5/2}-573.8\left({\frac {a}{W}}\right)^{7/2}+360.5\left({\frac {a}{W}}\right)^{9/2}\right]}$ 

where ${\displaystyle P}$  is the applied load, ${\displaystyle B}$  is the thickness of the specimen, ${\displaystyle a}$  is the crack length, and ${\displaystyle W}$  is the effective width of the specimen being the distance between the centreline of the holes and the backface of the coupon. The above equation has been fitted using numerical computations for various specimen geometries.

The length of the crack is often measured indirectly during testing by calculating the crack length from the compliance of the coupon. The compliance can be determined from either a crack mouth opening displacement (CMOD) gauge or from strain measurements on the back-face of the coupon.

Crack mouth opening displacement edit

Crack length can be found using a displacement gauge attached to the mouth of the coupon to measure displacements ${\displaystyle v}$  using the equation^[1]

${\displaystyle a/W=1.0010-4.6695{u_{x}}+18.460{u_{x}}^{2}-236.82{u_{x}}^{3}+1214.9{u_{x}}^{4}-2143.6{u_{x}}^{5}}$ 

${\displaystyle u_{x}=\left\{\left[{\frac {EvB}{P}}\right]^{\frac {1}{2}}+1\right\}^{-1}}$ 

This equation is applicable in the range ${\displaystyle 0.2<a/W<0.95}$ .

Back-face strain edit

The crack length can be determined using the back-face strain ${\displaystyle \varepsilon }$  with the following equation^[3]

${\displaystyle a/W=1.0033-2.35U+1.3694U^{2}-15.294U^{3}+63.182U^{4}-74.42U^{5}}$ 

where ${\displaystyle U=1/({\sqrt {A}}+1)}$ , ${\displaystyle A=E(\varepsilon W)B/P}$  and ${\displaystyle E}$  is the Young's modulus of the coupon material. This equation is applicable in the range ${\displaystyle 0.2<a/W<0.95}$ .

Electric Potential Difference edit

The crack length can also be determined from voltage measurements of the electric potential difference (EPD) at points at each side of the mouth of the machined slot at opposite sides of the coupon using^[1]

${\displaystyle a/W=-0.5051+0.8857(V/V_{r})-0.1398(V/V_{r})^{2}+0.0002398(V/V_{r})^{3}}$ 

where ${\displaystyle V}$  is the measured EPD voltage and ${\displaystyle V_{r}}$  is the reference crack voltage corresponding to ${\displaystyle a/W=0.241}$  on an identical specimen. This equation is requires the electrical excitation current is injected along the load line of the specimen. This equation is applicable in the range ${\displaystyle 0.24<a/W<0.7}$ .