7.5. SIMULATION OF A HYBRID STRUCTURAL CONNECTION 1 NON-LINEAR FINITE ELEMENT MODELLING
7.5.2 PROGRESSIVE DAMAGE MODELLING
The details of the method used for the progressive damage modelling are given in Chapter 5 and shown schematically in Figure 5.1. In brief the load/displacement is applied incrementally to the structure. At each increment the stress field in the structure is obtained. The stress field is then examined for instances of the Von Mises failure criterion having been exceeded. If failure has been detected the properties of the failed element/integration point are reduced accordingly. The incremental step is recalculated and the stress field examined again, if no failure is detected the next incremental load/displacement step is calculated.
The failure criterion used in this study is Von Mises failure criterion for isotropic materials. This criterion was chosen as the experimental tests showed that failure only occurred in the adhesive layer, which is an isotropic material. Therefore only the adhesive is examined for failure. The degradation of the material properties once failure is detected was based on experimental tests conducted on the adhesive material. As discussed in Section 5.2.2 the material degradation model is not that used in the previous work conducted on this subject (see Chapter 2). The stress in the failed elements is reduced, resulting in a negative Young’s modulus for the material.
7.5.2.1 Progressive damage modelling results
The progressive damage model is a method of predicting failure within the joint to better understand the path of failure and to predict the load-displacement response of the structure. As described in Chapter 5 previous work [48] on damage modelling simulates failure by reducing the stiffness of elements or integration points within the numerical model. In the present research a stress reduction model is used to reduce the stress present in the failed
locations. The results obtained from the numerical model are given in Figure 7.12. This graph shows the experimental load-deflection curve compared with a finite element result and three non-linear results based on damage progression.
The non-linear results have used the three differing stress reduction models as shown in Figure 7.13. The stress reduction models used in this phase were based on the tensile strength results described in Section 4.4. The tensile tests did not capture many data points after the maximum load point. Therefore an estimation of the shape of the post initial failure curve was assumed, the three assumptions are shown in Figure 7.13.
The progressive damage model was run with each of the three material degradation models. As discussed in Section 7.5.1, there is a clear point of divergence between the predicted linear response and experimental observation at 2 mm deflection. The non-linear PDM successfully identifies this point of divergence for all three stress reduction models.
Furthermore, beyond a global displacement of 2 mm the correlation between the presented non-linear numerical results and the experimental result, depending on the choice of post- failure material function (see Figure 7.13), represents a compromise between excellent prediction of failure load with excellent prediction of failure strain.
The progressive damage model clearly indicates the path of failure in the joint as the stresses in the adhesive layer combine to exceed the failure criterion. Figure 7.14 shows the position of the first point of failure of the joint. Its location is at the interface of the steel, balsawood and GRP on the flat side of the hybrid joint. It is in this location that the first experimentally observed crack occurs, subsequently leading to the GRP/steel debond. In the case of the experimentally tested specimens, subsequent increased loading led to crack propagation along the flat side in the steel/GRP interface. Figure 7.15 shows the result obtained from the progressive damage model as a series of snapshots for increasing displacement. Note that when the first integration point in an element exceeds the Von Mises criterion the displacement is less than 1.0 mm. This is considerably earlier than the displacement at which non-linearity occurs in the load deflection curves. However, it is envisaged that it is the collective failure of integration points that results in a loss in global stiffness of the joint. In contrast to what was assumed to have occurred in the experimental testing, failure in the adhesive layer occurs along both the upper and lower adhesive interfaces simultaneously. Experimentally the non-linearity in the load-deflection curve
occurs at approximately 2 mm deflection. Figures 7.15 (c) and (d) span this deflection and exhibit a crack of approximately 20 mm in length on both adhesive interfaces. Figure 7.15 (e) shows that at 3.39 mm deflection a substantial crack had developed. The crack also began to propagate into the interface between the GRP and balsawood.
The material degradation models used thus far are based on an assumption of how the material behaves post initial failure based on the tensile tests conducted in Chapter 4. The approximation involved the consideration of a negative stiffness to ensure a reduction in stress that resulted in zero stress in any failed element when maximum displacement of the model had reached 4.5 mm (Section 7.4.2). However, this assumes that the elemental stress is zero when the global displacement of the specimen is 4.5 mm. In order to increase the accuracy of the prediction of the non-linear behaviour of the joint a better description of the material property degradation curve post-maximum stress should be used.
It could be considered that the area under a stress-strain curve from zero stress to initial failure is the energy required to cause initial failure. If there is further load carrying capability after initial failure then the area under the stress-strain curve from initial failure to complete failure is the energy required to cause complete failure. This latter area could be considered the fracture energy GIC of the material. This assumption was also considered
by De Moura et al. [89] to obtain the relative failure displacement and good correlation between experiment and the model was achieved. This methodology was used in the present research in an attempt to improve the prediction of the non-linear load-deflection curve. The fracture toughness energy values were obtained from double cantilever beam tests as described in Chapter 4. The results showed that the area under the curve was very small and this resulted in a very steep negative stiffness post-maximum stress. When applied to the numerical model this resulted in a large degree of numerical instability, despite efforts to control the numerical stability through the implementation of viscous damping variables the model would not converge. Initial failure load prediction and the on set of non-linearity remain unchanged using the GIc method. However, further research is required on controlling numerical stability with highly negative material stiffness values. The progressive damage modelling approach has been shown to accurately predict the point at which non-linearity occurs and broad assumptions regarding the shape of the post- maximum stress curve resulted in good correlation with experimental results. The new
approach of using fracture toughness values could result in further improvement in the load- displacement prediction when the numerical issues are resolved.
7.6. DISCUSSION
This chapter has examined the numerical simulation of hybrid connections using non-linear finite element analysis and progressive damage analysis. The aim is to develop a method whereby the performance of the joint can be predicted and the knowledge used to aid the design of more efficient hybrid connections.
A numerical model of the hybrid connection was developed which accurately defined the boundary conditions present in the experimental testing. The result of the FEA analysis showed excellent convergence with the linear portion of the experimental joint response. This provided confidence in the validity of the simulation.
A progressive damage methodology was developed for predicting the progression of failure in adhesive connections. The majority of present work with progressive damage modelling concentrates on failure within the composite material [43, 47, 48, 70]. The present work employed a new stress reduction method of failing elements in order to simulate failure within the physical joint. This is contrary to the material degradation models used in the analysis of progressive failure in composites where stiffness is reduced [48]. In addition, a new method of incorporating fracture energy of the adhesive into the progressive model has been developed and a method of applying the method explored.
The information obtained from this chapter will be essential for future structural engineers to examine hybrid joint designs and be able to predict the way in which failure will develop and progress.