Rigid square inclusion embedded within an epoxy disk: asymptotic stress analysis

The asymptotically singular stress state found at the tip of a rigid, squar e inclusion embedded within a thin, linear elastic disk has been determined for both uniform cooling and an externally applied pressure. Since these l oadings are symmetric, the singular stress held is characterized by a singl e stress intensity factor K-a, and the applicable K-a calibration relations hip has been determined for both a fully bonded inclusion and an unbonded i nclusion with frictionless sliding. A lack of interfacial bonding has a pro found effect on inclusion-tip stress fields. When the inclusion is fully bo nded, radial compression dominates in the region directly in front of the i nclusion tip and there is negligible tensile hoop stress. When the inclusio n is unbonded the radial stress at the inclusion tip is again compressive, but now the hoop tensile stress is of equal magnitude. Consequently, an epo xy disk containing an unbonded inclusion appears to be more likely to crack when cooled than a disk containing a fully bonded inclusion. Plastic-plast ic calculations show that when the inclusion is unbonded, encapsulant yield ing has a significant effect on the inclusion-tip stress state. Yielding re lieves stress parallel to the interface and greatly reduces the radial comp ressive stress in front of the inclusion. As a result, the encapsulant is s ubjected to a nearly uniaxial tensile stress at the inclusion tip. For a ty pical high-strength epoxy, the calculated yield zone is embedded within the region dominated by the elastic hoop stress singularity. A limited number of tests have been carried out to determine if encapsulant cracking can be induced by cooling a specimen fabricated by molding a square, steel insert within a thin epoxy disk. Test results are in qualitative agreement with an alysis. Cracks developed only in disks with mold-released inserts, and the tendency for cracking increased with inclusion size. (C) 2001 Published by Elsevier Science Ltd.