Figure 3.25 Surface plot showing the change in material response with increasing strain rate (SMC). Figure 3.26 Critical points for compression characterization. Figure 5.11 Simulated tensile response of laminate obtained with different characterizations Figure 5.12 Simulation output compared to experiment, materials 103A and 105C, v= 2 mm/s.
CHAPTERl INTRODUCTION
Progressive damage modelling of laminates
The model accounts for the effects of delamination and was used in the simulation of the low-energy ballistic impact of a unidirectional laminated cylindrical shell. The work presented shows a good correlation between load time histories obtained from simulation and experiment and illustrates how the inclusion of fiber damage improves agreement with experimental results. The two-phase model was introduced for crashworthiness studies of automotive components (Haug and De Rouvray, 1992) and uses the measured elastic properties of a unidirectional layer, together with known fiber properties and fiber volume fraction, to infer orthotropic elastic properties. of matrix material minus fibers. The elementary layer is then described by two components: a one-dimensional phase (fiber) and an orthotropic phase (matrix).
Crashworthiness of thin-walled composite structures
A useful comparison of the energy absorption performance of composite pipes under various boundary conditions (including changes in temperature, humidity level and weather) is provided. The author concludes that braided I-beams can be effectively used for impact energy absorption in side and frontal crashes of vehicles. 1993) consider a combination of cross-sectional, sheet bending, and local buckling effects on the crash energy absorption of a glass fabric/epoxy composite tube. The FE codes LS-DYNA3D and ABAQUS/Explicit were used to model the tube compression, and the authors report good agreement between theory and experiment.
Modelling the crash behaviour of laminated structures
The material models identified in the review of progressive damage models for composites (§ 1.1) adapted for the PAM-CRASH code are the Ladeveze (or global layer) model (Ladeveze and Le Dantec, 1992), the two-phase model (Haug and De Rouvray, 1992) and the extended global investment model used by Johnson and colleagues (Johnson et al., 2001). On the other hand, an extended global embedment model has been developed to model fabric-reinforced composites, but is not yet included in the primary PAM-CRASH code (at the time of design of this study) and is reserved as an option for future research.
CRASHWORTHINESS MODELLING
The PAM-CRASH analysis tool (PAM-Crash Theory Notes, 2000)
The members of the PAM-CRASH code are mainly used for the dynamic analysis of structures and are defined as three-dimensional (3D), Lagrange finite element, explicit vectorized/multi-task codes for the non-linear dynamic analysis of structures. The Lagrangian approach refers to the choice of independent variables for the problem. For this formulation, each particle is characterized by its initial conditions and its actual coordinates are functions of the initial conditions and time. Mesh points coincide with material points in the Lagrange formulation and thus have time-dependent coordinates. This is in contrast to the Eulerian formulation, for which particles 'flow' through a stationary (time-independent) mesh. An Arbitrary Lagrange Euler (ALE) approach has material 'flow' through a mesh (Eulerian) moving according to a user-defined pattern (Lagrangian).
The hi-phase model- PAM-CRASH material 130
Damage for the two-phase model is implemented by reducing the stiffness as given by: . Regarding the material elastic constants, the damage for the two-phase model is defined separately for the tension and compression cases and can propagate independently for the matrix and fibers.
MATERIAL CHARACTERISATION
Tensile characterisation
- Tensile testing oflaminated specimens
- Tensile characterisation parameters
Five specimens were prepared (Fig. 3.3) with strain gauges attached (Fig. 3.4) and tested at a loading rate of 2 mm/min, using a Lloyds tester. The tensile stress-strain curve obtained for the Lam specimen is chosen as representative of the average response of the laminated material and is shown in Fig 3.8, together with the three critical points required for the calculation of the material's modulus of elasticity and damage parameters . From Fig.
Compressive characterisation
- Dynamic testing procedure Apparatus
- Compressive characterisation parameters
By measuring the amplitude and duration of the primary pulse traveling through the bars (using strain gauges attached to the surface of the bars) a dynamic stress-strain curve can be constructed for the material under investigation. An overview of the mean values and sample standard deviations (for the measured and calculated values) can be found at the bottom of the table. Photographs showing a laminated specimen before testing, specimens tested at quasi-static strain rates, and specimens tested at dynamic strain rates are provided in Figs. 3.15 - 3.17. The typical stress-strain plot obtained from Hopkinson testing of the laminated specimens at a strain rate of about 700s-J is compared with the plot obtained from quasi-static testing (Fig. 3.18).
At the bottom of the table is a summary of mean values and sample standard deviations (for measured and calculated values). Tension testing of laminated samples and subsequent calculation of the required material parameters for tensile characterization has already been presented (§ 3.1). Future modeling of the response of the laminated demonstrator will require validation of the compression characterization through compression testing of panel specimens. The required compression characterization parameters are shown in table 3.8.
Calibration of material model
Conclusions
DEMONSTRATOR DESIGN AND TESTING
Laminated demonstrator design .1 Demonstrator geometry
- Layup design and fibre orientation
- Designing for crashworthiness
All these processes require the development of suitable patterns for cutting the fabric reinforcement. Two one-piece patterns for the production of the laminated demonstrator component were subsequently developed. Three-dimensional images of the prototype showing the seam lines of the two patterns (pattern A and pattern B) are provided in Figs.
The dimensional accuracy of the patterns was tested using patterns cut from plain fabric (Fig.). To investigate the effect of varied fiber orientation on the wrinkling performance of the laminated demonstrator component, several layups with different fiber orientations should be selected for experimental investigation. This produces three different constructions for the production of the laminated demonstrator part, namely: LPTl, LPT2 and LPT3.
Laminated demonstrator production
- Hot vacuum bag processing
Manufacturing trials investigating the use of different manufacturing processes (and materials) led to the selection of hot vacuum bags using E-glass cloth 1102 as reinforcement (suppliers AMT, South Africa, see Table 4.3) and Ampreg 20 epoxy resin as matrix material ( SP systems International, see Table 4.1) for the production of laminated demonstrator components.
Demonstrator testing
LPT1
- Conclusions
A further record of the response of the laminated demonstrators to the implemented load cases is provided by photographs showing the failure patterns of the demonstrators recovered after testing (Fig. 4.27). Also shown are line drawings of the particular failure patterns, which provide a schematic representation of the failure. Two deformation modes extracted for LPTl (loaded at 150 mm/s) show how the edge of the demonstrator base plate snaps from one deformation mode (Fig. 4.28, SI=1.9 mm) to another deformation mode (S2= 3.8 mm) .
After the transition, the deformation of the demonstrator is anti-symmetric about the midplane (a reverse symmetry exists). The failure and post-failure behavior of the demonstrator is then influenced by the specific material architecture, as well as the response for higher loading rates. Focusing on the development of the laminated demonstrator, one piece of patterns was developed with the aim of controlling the fiber orientations obtained in the final product.
CHAPTERS
DEMONSTRATOR MODELLING
Finite element model development
- Meshing
- Boundary Conditions
- Material description (layup)
A step-by-step graphic overview of the geometry development (Fig.5.1) shows how the geometry is developed starting with the extrusion of the cylinder sidewall (Fig. As noted, the flat sections of the real prototype consist of 8 layers that are aligned with the global x-axis.Regarding the real laminated component, the modeled layers of the cylinder sidewall are placed alternately at 0° and 45°, relative to the local element coordinate systems of the sidewall elements.
Description of the sidewall layer orientations in terms of the local element coordinate system is made possible by the structure of the sidewall mesh, which is aligned with the global z-axis. Confirmation of the local coordinator orientations for the sidewall elements is provided by viewing the local element directions in the NASTRAN environment (Fig. 5.5). A comparison of the actual component's construction and the construction of the modeled prototype is provided in Fig.5.6.
Numerical simulation
- Simulation of the laminated demonstrator
As the displacement continues, the typical deformation of the real component is seen in the simulated output (S2 = l l mm, S3 = 22mm). A comparison of the simulated stress-strain response (obtained from the different material models) with the experimentally recorded stress-strain diagram is made (Fig. 5.11). Next (Fig. 5.14) is a comparison of the output obtained from a simulation using material 105A with the experimental force displacement history for an SMC prototype tested at 100mm/s.
Finally, the figure shows a comparison of the output obtained by simulation using the 105B material with the experimental results for the 100 mm/s case. Buckling occurs at the same locations as observed during the experiment, and a comparison of the actual and simulated failure patterns (Fig. 5.14) shows good agreement. When the maximum load is exceeded (indicating the initial failure of the prototype component), the parts of the structure showing damage are released (s=2.4 mm).
MODELLING UNDER IMPACT CONDITIONS
Laminated demonstrator crash model
The results obtained from the crash simulation in the form of a force-displacement plot (Fig. 6.2) show how an increase in the initial speed results in an increase in the peak load achieved, as well as more noticeable oscillations in the force-displacement response. New deformation modes are predicted for the crash simulation of the laminated demonstrator LPTI (Fig. 6.2) compared to the simulated deformation obtained at lower speed loading (Fig. 6.3), which takes into account the significantly varied load-displacement behavior. In particular, the transitional deformation mode identified during lower speed loading (Fig. 5.9), which was predominant only at small displacements (up to 1.9 mm during the experiment and up to 3.0 mm during the simulation), is predicted to collision modeling will prevail until failure for the 1 m/2. s crash simulation of LPTl.
For the crash simulation at l m/s complete folding of the base plate occurs which is responsible for the sudden drop in load carrying capacity between 8 and lOmm of displacement. For the 5m/s accident, a high peak load is predicted with a jerk of 14 kN) and folding at the sides of the cylindrical shell, as well as large oscillations in the load transferred to the fixed support are predicted.
Conclusions
CONCLUSIONS
Crash response modeling of the laminated demonstrator LPTI has been completed and the crash simulation results highlight variations in the structure's response at increased impact speed. During the development of the FE mesh, the material structure that needs to be modeled must be taken into account. This influences the selection of individual material areas and careful choice of the spatial orientation of the finite elements can support the description of the layout.
When specifying the boundary conditions of the problem, classifying the boundary elements by group names further helps structure the problem, as the boundary conditions are easily applied and updated for all elements in the group. The meshing process used also demonstrates how mesh grading control along the boundary curves of individual surface segments can be used to manipulate the final finite element mesh structure. Further developments may include consideration of failure initiators and selectively reinforced structural segments during finite element model construction.
