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Influence of non-singular higher order terms on the stress field of thin welded lap joints and small inclined cracks in plates
Last modified: 2011-02-25
Abstract
In stress analysis of cracked plates, alongside the stress intensity factor which quantifies the singular
stress component perpendicular to the crack plane, the role played in crack growth by the constant term parallel
to the crack plane, called the T-stress, has been widely investigated by many researchers. There are, however,
cases of practical interest where the influence on the stress field of the higher order terms in the series
expansion for the crack tip stress field, is not negligible. The main aim of the present investigation is to present
and apply a set of equations able to describe more accurately the stress components for those cases where the
mode I and mode II stress intensity factors used in combination with the T-stress are unable to characterise
with sufficient precision the complete stress field ahead the crack tip. The starting point is represented by the
Williams’ solution (Williams, 1957) where stresses as expressed in terms of a power series. An example is
investigated of a thin-thickness welded lap joint characterized by various joint width to thickness ratios, in the
range of d/t ranging from 0.5 to 5. The present paper indicates that the local stresses as well as the strain energy
averaged over a control volume which embraces the slip tip, can be evaluated with satisfactory precision only by
taking into account a further four terms besides KI, KII and T-stress.
stress component perpendicular to the crack plane, the role played in crack growth by the constant term parallel
to the crack plane, called the T-stress, has been widely investigated by many researchers. There are, however,
cases of practical interest where the influence on the stress field of the higher order terms in the series
expansion for the crack tip stress field, is not negligible. The main aim of the present investigation is to present
and apply a set of equations able to describe more accurately the stress components for those cases where the
mode I and mode II stress intensity factors used in combination with the T-stress are unable to characterise
with sufficient precision the complete stress field ahead the crack tip. The starting point is represented by the
Williams’ solution (Williams, 1957) where stresses as expressed in terms of a power series. An example is
investigated of a thin-thickness welded lap joint characterized by various joint width to thickness ratios, in the
range of d/t ranging from 0.5 to 5. The present paper indicates that the local stresses as well as the strain energy
averaged over a control volume which embraces the slip tip, can be evaluated with satisfactory precision only by
taking into account a further four terms besides KI, KII and T-stress.
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