Abstract
The article focuses on the bending problem for a cantilever beam with a straight through-thickness crack, perpendicular to its axis under bending by concentrated force. Depending on the crack location in relation to the axis, crack faces may be in three states: perfect contact, particular contact, or noncontact. Using the theory of functions of complex variable and complex potentials, the considered problem was reduced to a linear conjunction one. An analytical solution of the problem was obtained. In the case of particular contact, the length of the contact area and stress intensity factors were determined. The ultimate force that causes beam destruction was determined. Numerical analyses of the problem were also performed.
Highlights
Beam elements of structures are widely used in engineering practices
Crack faces may be in contact
Parameter d denotes the distance from the left edge of the strip to the crack line (d < L3 )
Summary
Beam elements of structures are widely used in engineering practices. They may contain cracks that are powerful stress concentrators, decreasing the reliability and durability of such structures. Many researchers have studied plane contact problems in crack theory of homogeneous bodies and developed methods for solving this problem. The complex potentials of the problem, the length of the contact area of crack faces, and the ultimate value of the force responsible for beginning of crack propagation were determined. The ultimate value of the force causing beam fracture for contacted crack tip, where sign “+” corresponds to tip A and “–“ to tip B. Q the ultimate force causing beam fracture for non-contacted crack tip, where sign “+” corresponds to tip A and “–“ to tip B
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