Quantification of constraint effects in elastic-plastic crack front fields

In-plane and out-of-plane constraint effects on crack tip stress fields under both small-scale and large-scale yielding conditions are studied by means of three-dimensional numerical analyses of boundary layer models and of finite size specimens, M(T) and SE(B), respectively. It is shown that the ratio of the plastic zone size over the panel thickness, rpt, plays a key role in formation of the crack-tip fields, particularly the outof-plane stress components. For a vanishingly small plastic zone around the crack tip the stress fields are dominated by the plane strain solution. With increase of the applied loads, i.e. increasing the plastic zone size, the stress fields develop towards the plane stress state. Characterization of “constraint effects” in terms of Q-stress is investigated. The “second term” in the near tip stress field, which is defined as the difference between the full three-dimensional stress fields and the plane strain reference solution, appears to depend on the distance to the tip and to the free surface of the specimen. Hence, the whole three-dimensional crack front fields cannot be correctly described by a two-parameter formulation as the load increases. However, a unique linear relationship between Q and the hydrostatic stress was found in all three-dimensional crack front fields.

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