J-integral evaluation for an interface crack under thermal load using digital image correlation

Abstract

In this study, a method for evaluating a fracture parameter, J-integral, for an interface crack from the displacement fields under thermal deformation is developed for studying the fracture behavior of an interface crack in an actual electronic component. First, the displacement fields around an interface crack tip are measured using digital image correlation (DIC). Second, the displacement gradient and strain are determined from the displacement fields using a finite element smoothing technique on the domain of integration. Then, the stress components are determined from the strains using the elastic-plastic relations with the incremental strain theory and the each material property. Finally, the J-integral value is determined by the numerical integration on the domain of integration. The effectiveness of this evaluation method is demonstrated by applying this method to the displacement fields obtained from the elastic-plastic finite element analysis.

Investigation by Digital Image Correlation of Mixed-Mode I and II Fracture Behavior of Polymeric IASCB Specimens with Additive Manufactured Crack-Like Notch

“…Following the approach used in [ 23 ], the constitutive relation can be written as shown in Equation (12): where , and are the Poisson’s ratio, Kronecker delta and the stress deviator, respectively. The stress deviator is defined as shown in Equation (13): …”

“…After computing the components of the Cauchy stress tensor by exploiting Equations (10)–(13), the strain energy density W can be computed, according to [ 23 ], as shown in Equation (14): …”

“…Following the approach used in [23], the constitutive relation can be written as shown in Equation ( 12):…”

“…The main advantage of this technique is that it can be performed directly on the structure, without the need of previously knowing neither the geometrical factors nor the loading boundary conditions. The DIC-based methodology consists of numerically computing the J-integral along a rectangular contour of the DIC grid [ 22 , 23 , 24 , 25 , 26 ]. For the J-integral calculation, displacement, strain and stress maps are needed.…”

“…The displacement field is obtained directly from the DIC; the strain field can be computed by numerical differentiation of the former, whereas the stress maps can be computed from the strain maps, given that the constitutive equations of the material are known. The material has thus to be previously characterized, for example, in terms of Ramberg–Osgood parameters, as done for instance in [ 23 ]. The J-integral values calculated by the DIC-based methodology were finally compared to the ones obtained employing the LDC method.…”