TY - JOUR

T1 - Determination of stress intensity factor solutions for cracks in finite-width functionally graded materials

AU - Ravi Chandran, K. S.

AU - Barsoum, I.

N1 - Funding Information:
This research was supported partly by the grant: DAAL 19-99-1-0281 from the Army Research Office, Research Triangle Park, NC. The authors thank the program manager Dr David Stepp of Army Research Office for the support.

PY - 2003/6

Y1 - 2003/6

N2 - A generalized method to determine the stress intensity factor equations for cracks in finite-width specimens of functionally graded materials (FGMs), based on force balance in regions ahead of the crack tip is provided. The method uses the Westergaard's stress distribution ahead of the crack in an infinite plate and is based on the requirement of isostrain deformation of layers of varying moduli ahead of the crack tip. It is shown that the modified Westergaard equation describes the normal stress distribution and the singular stress state ahead of the crack tip in a reasonably accurate manner. Based on this, closed-form analytical equations for the stress intensity factors of cracks in finite-width center cracked specimens were derived. Comparisons of the K values from the analytical equations with that obtained from FEM simulations indicate that the derived stress intensity factor equations for FGMs are reasonably accurate. For the finite-width center-cracked-tension (CCT) specimen, the errors are less than 10% for most of the crack lengths for materials with the outer layer modulus ratios varying from 0.2 to 5. The stress intensity factors were found to be sensitive to the absolute values of moduli of the layers, the modulus ratio of the outer layers as well as the nature of gradation including the increasing and the decreasing functional forms. The stress intensity factor equations are convenient for engineering estimates of stress intensity factors as well as in the experimental determinations of fracture toughness of FGMs.

AB - A generalized method to determine the stress intensity factor equations for cracks in finite-width specimens of functionally graded materials (FGMs), based on force balance in regions ahead of the crack tip is provided. The method uses the Westergaard's stress distribution ahead of the crack in an infinite plate and is based on the requirement of isostrain deformation of layers of varying moduli ahead of the crack tip. It is shown that the modified Westergaard equation describes the normal stress distribution and the singular stress state ahead of the crack tip in a reasonably accurate manner. Based on this, closed-form analytical equations for the stress intensity factors of cracks in finite-width center cracked specimens were derived. Comparisons of the K values from the analytical equations with that obtained from FEM simulations indicate that the derived stress intensity factor equations for FGMs are reasonably accurate. For the finite-width center-cracked-tension (CCT) specimen, the errors are less than 10% for most of the crack lengths for materials with the outer layer modulus ratios varying from 0.2 to 5. The stress intensity factors were found to be sensitive to the absolute values of moduli of the layers, the modulus ratio of the outer layers as well as the nature of gradation including the increasing and the decreasing functional forms. The stress intensity factor equations are convenient for engineering estimates of stress intensity factors as well as in the experimental determinations of fracture toughness of FGMs.

UR - http://www.scopus.com/inward/record.url?scp=0742270456&partnerID=8YFLogxK

U2 - 10.1023/B:FRAC.0000005346.83147.b2

DO - 10.1023/B:FRAC.0000005346.83147.b2

M3 - Article

AN - SCOPUS:0742270456

SN - 0376-9429

VL - 121

SP - 183

EP - 203

JO - International Journal of Fracture

JF - International Journal of Fracture

IS - 3-4

ER -