In subsections 4.5.3 and 4.5.4, the discussion focused on skin and stiffener failures.  A third mode of failure involves the fasteners.  This paragraph will discuss the failure of the fastener system.  Load is transmitted from the skin to the stringers through fasteners.  If the fastener loads become too high, fastener failure may occur by shear.  Fastener failure will reduce the effectivity of the stringer; and therefore, the residual strength of the panel will drop.  The highest loads (F) in the stringer/skin connections will occur in the fasteners adjacent to the crack path.  Fastener failure will occur when the fastener forces F transmitted by the fasteners adjacent to the crack exceed the critical shear load of the fastener.  The fastener failure criterion is given by

where d is the fastener diameter and t_ult is the ultimate shear stress of the fastener material.  It is emphasized that fastener failure need not necessarily cause total failure of the panel.  Once the fastener failure criterion is met, however, the values of L_s and b will change since the loads transferred to the stiffener and skin changes.  Once the fastener fails, the values of b and L_s will be recalculated in order to proceed further with the residual strength analysis.  The load that causes the fasteners to fail by shear can be calculated from Equation 4.5.5; the corresponding nominal stress in the panel then gives the residual strength curve for the fasteners as shown in Figure 4.5.14.  At zero crack length, and for the case where the skin and stringers are made from common materials, the fasteners do not carry any load; the curve therefore tends to increase rapidly for a ®o.  The fastener forces F_i can be computed through the displacement compatibility between the stiffener and the panel.  The necessary steps involved in the computation of F_i are discussed in the example presented in subsection 4.5.7.

Figure 4.5.14.  Residual Strength Diagram for the Fasteners in a Built-Up Structure

In the case of adhesively bonded structures, the adhesive (fastener) failure criterion is based on a maximum adhesive strain value.  The residual strength analysis is fairly complicated (see, for example, reference 24).  Based on the displacement compatibility between the panel and the stiffener, the adhesive segment strain deflection can be numerically computed for different amounts of disbond.  Figure 4.5.15a shows the adhesive strain versus gross stress for various levels of adhesive delamination.  The vertical line AB represents average failure strain of the adhesive.  The intersection points between the line AB and the curves give the critical gross stress versus amount of adhesive failed as shown in Figure 4.5.15b.  The corresponding curve ABC can be used for panel failure analysis.  The area above the curve defines the failure of adhesive.

Figure 4.5.15.  Gross Stress and Critical Stress Diagram for Adhesively Bonded Stringer