$\mathbf{\epsilon }$	strain tensor	${\sigma }_b$	ultimate strength
${\mathbf{\epsilon }}^{\mathrm{e}}$	elastic strain tensor	$D_{\mathrm{c}}$	critical damage variable
${\mathbf{\epsilon }}^{\mathrm{p}}$	plastic strain tensor	$\theta$	field variable
$\mathbf{\sigma }$	stress tensor	$\psi$	field variable distribution function
$\mathit{D}$	isotropic damage variable	$x$	x coordinate value
$\mathit{C}$	elastic tensor	$y$	y coordinate value
$\dot{\mathbf{\sigma }}$	stress rate	E	elasticity modulus
$\dot{D}$	damage variable rate	μ	Poisson’s ratio
$\dot{\mathbf{\epsilon }}$	strain rate	a0	initial crack length
${\dot{\mathbf{\epsilon }}}^{\mathrm{p}}$	equivalent plastic strain rate	H	width of welded joint
$F_y$	Von Mises yield condition	W	height of welded joint
${\sigma }_y$	radius of yield surface	$\mathsf{\Delta }a$	crack growth increment
$\tilde{\mathit{s}}$	partial stress tensor of damaged materials	σb,316L	ultimate strength of 316L stainless-steel
$\tilde{\mathit{a}}$	back stress tensor of damaged materials	σb,304	ultimate strength of 304 stainless-steel
$\mathit{s}$	stress tensor	J1c	critical fracture toughness
$\mathit{a}$	back stress tensor	dispmax	the max displacement load
$\dot{p}$	equivalent plastic strain rate	disp	displacement load
$\mathit{n}$	unit direction tensor	Gx	gradient factor in x-direction
${\mathbf{\sigma }}_{\max }$	maximum principal stress	Gy	gradient factor in y-direction