Lap-shear stress

Key words FRP composites, interfacial adhesive stresses, lap-shear stress distribution, numerical models, theoretical analysis. 

The lap-shear stress distribution, the failure pattern and ultimately the bond strength of FRP joints are also functions of the mechanical properties of the FRP reinforcing fibres. This behavioural dependency is depicted in Fig. 10.3 where lap-shear stress distributions along the bondlength for two identical double-strap CFRP/steel specimens, with different elastic moduli of their reinforcing CF (carbon fibres), are presented. 

This fact is demonstrated in the lap-shear stress distribution for the CFRP/steel double-strap specimen of Fig. 10.3(a) where the outer adherend... 

Lap-shear stress distribution for stiffness-imbalanced double-lap joint (adapted from Hart-Smith, 1973). 

Lap-shear stress variation with exposure temperature for identical double-strap CFRP/steel plate specimens (Al-Shawaf, 2010). 

It is worth mentioning that the lap-shear stress term of equation [10.5], when incrementally calculated, yields an identical form to that of equation [10.3]. In addition, all the simplifying assumptions stated previously for the latter equation are applicable for equation [10.5], as well. 

In this section, two analytical double-lap joint models are briefly introduced, highlighting their strengths and weaknesses in terms of accurate and realistic stress predictions, and finally validating their predicted lap-shear stress distributions for a specific double-strap CFRP/steel joint with experimentally acquired results. 

The analysis includes three mathematically distinct cases addressing all possible interfacial adhesive stress scenarios (1) fully elastic adhesive throughout the bondline, (2) adhesive plastically strained at only one bondline end, and (3) adhesive exhibiting plastic strains at both ends of the joint. For comparison and validation purposes with the second analytical model and the experimental example provided later, only the first scenario is reviewed herein. Bond configuration and notations adopted are shown in Fig. 10.11. It should be noted that the origin of the x-coordinate is the middle of the joint only for the current mathematical lap-shear stress expressions. However, for other contexts in this chapter, the origin is located at the left end of the lap joint (i.e. near the gap of Fig. 10.10). 

The general solution of the basic differential equations (Hart-Smith, 1973) yields equation [10.6] which determines the lap-shear stress along the bondline ( ) ... 

Bond geometry and notations for lap-shear stress mathematical expression. 

The second analytical lap-shear stress model to be discussed in the current context is the TOM model (Tsai et al., 1998). It incorporates adherend shear deformation in the solutions of single- and double-lap joints. In all prior models, shear deformations of the adherends were excluded, possibly due to the relatively small values compared to longitudinal normal deformations (e g. as in metal bonding), or due to the complexity of the formulations. 

Lap-shear stress predictions are successfully achieved with Excel spreadsheets due to the continual iterations of parameters and formulas for each individual CFRP and adherend material, geometrical variations, and environmental preconditioning temperature usually involved in large-scale investigations. Figure 10.13(a) and (b) displays the lap-shear stress predictions... 

Figure 10.18(a) and (b) displays and validates the FE lap-shear stress predictions, with the same experimental double-strap CFRP/steel specimens discussed in Section 10.6.1, along the CFRP/steel joint bondline. The lap-shear stress divergence between the FE predictions and experimental results disclosed in Fig. 10.18(a) close to the x = 0 end is due to erroneous reading of the ERSG in this location, and is discussed in Al-Shawaf (2010). 

Assuming adequate surface preparation, the lap-shear stress of FRP adhesive joints at the critical bond end-zones, and thus the capacities and failure patterns, are functions of the geometrical and thermo-mechanical properties of the interfacial adhesive and both adherends, besides the environmental exposure conditions. 

Adherend stiffness imbalance and thermal mismatch have a substantial effect on the lap-shear stress distribntion along the joint s bondlength. 

The DIG method has great potential in measuring the 2D and 3D surface deformations and strain values of structural components at extreme environmental exposures. It has been adopted in a few interfacial adhesive lap-shear stress analyses of FRP-concrete joints yet the same drawbacks of accurate stress estimation in contact methods persist in the DIG as well. 

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