TY - JOUR
T1 - Interaction between a crack and a circular inhomogeneity with interface stiffness and tension
AU - Mogilevskaya, Sofia G.
AU - Crouch, Steven L
AU - Ballarini, Roberto
AU - Stolarski, Henryk K.
PY - 2009
Y1 - 2009
N2 - The interaction between a straight crack and a circular inhomogeneity with interface stiffness and energy is considered. The Gurtin and Murdoch model is adopted, wherein the interface between the inhomogeneity and the matrix is regarded as a material surface that possesses its own mechanical properties and surface tension. The elastostatics problem is decomposed into two complimentary problems for (1) a circular disk with unknown distributions of traction and displacements along its boundary and (2) a loaded isotropic plane containing a circular hole with unknown distributions of traction and displacements along its boundary. The unknown distributions are determined through the application of the constitutive relations at the material surface. For selected values of the dimensionless parameters that quantify the geometry, material properties and applied loading, the stress field, stress intensity factors and energy release rates are calculated using a complex boundary integral equation approach. Particular attention is paid to crack-tip shielding and anti-shielding that develops as a result of the stresses introduced by the material surface. An illustrative example involving a perforated plate loaded in tension suggests that the material surface produces a modest level of expected effective toughening.
AB - The interaction between a straight crack and a circular inhomogeneity with interface stiffness and energy is considered. The Gurtin and Murdoch model is adopted, wherein the interface between the inhomogeneity and the matrix is regarded as a material surface that possesses its own mechanical properties and surface tension. The elastostatics problem is decomposed into two complimentary problems for (1) a circular disk with unknown distributions of traction and displacements along its boundary and (2) a loaded isotropic plane containing a circular hole with unknown distributions of traction and displacements along its boundary. The unknown distributions are determined through the application of the constitutive relations at the material surface. For selected values of the dimensionless parameters that quantify the geometry, material properties and applied loading, the stress field, stress intensity factors and energy release rates are calculated using a complex boundary integral equation approach. Particular attention is paid to crack-tip shielding and anti-shielding that develops as a result of the stresses introduced by the material surface. An illustrative example involving a perforated plate loaded in tension suggests that the material surface produces a modest level of expected effective toughening.
KW - Circular inhomogeneity
KW - Complex boundary integral equation
KW - Gurtinand Murdoch model
KW - Straight crack
KW - Surface elasticity
KW - Surface tension
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U2 - 10.1007/s10704-009-9393-9
DO - 10.1007/s10704-009-9393-9
M3 - Article
AN - SCOPUS:70350223427
SN - 0376-9429
VL - 159
SP - 191
EP - 207
JO - International Journal of Fracture
JF - International Journal of Fracture
IS - 2
ER -