# Investigation of Functionality of Vehicle Crumple Zones Recovered after a Traffic Accident
## 2 Experiments and Their Results  
### Determination of Characteristics of Materials and Fabricated Welded Joints  
During a traffic accident, the crumple zones of a vehicle are subject to plastic deformations (plastic deformation waves develop), and the geometry of the entire structure changes. During the post-accident repair of the vehicle, the geometry of the safety elements of its structure must be restored. The present study deals with the effects that may alter the characteristics of these elements, i.e., plastic deformations, when the elements are being straightened back by tensioning, bending, and hammering. An appropriate description of the material is required to be able to design the numerical models. For this purpose, material tension tests were performed to determine the mechanical properties of the materials of the elements investigated and the influence of process-related effects on them. Flat tensioning samples were prepared and the experiments were carried out according to the requirements of standard LST EN 10002-1:2003 [46]. Measurements of the test part of the plates used for the tests were \(L=55\) mm, \(b=20\) mm (Figure 1). The following samples were tested:  
* Six plates produced from the original material;
* Six plates produced from the material hardened by plastic deformation;
* Six plates produced of the thermally treated (annealed) material. The example of the M2O steel tensile diagram obtained during the experiments is presented in Figure 2.  
During design of the numerical model of the thin-walled elements subjected to buckling in the LS-DYNA software package, the material was described by using the two most common models describing the behaviour of the material in the elastoplastic zone. Figure 3 presents tensile diagrams of material M2O (\(\sigma_{ys}=296.7\) MPA, \(\sigma_{u}=430\) MPA) approximated by different laws: by approximating with tangent modulus \(E_{T}=491\) MPA; approximating with exponential hardening function without accounting for the real stress at break values \(k=525\), \(n=0.1123\); and approximating with exponential hardening functions by accounting for the real stress at break value, \(k=580\), \(n=0.184\). Figure 1: Specimens used to determine the mechanical characteristics of the material. Figure 2: Single uniaxial tensile deformation diagram of steel M2O. The first model is based on the law of linear hardening. The linear hardening relationship (Figure 3, curve (2)) between stresses and deformations is expressed in the model as follows:  
\[\sigma=E\cdot\varepsilon,\text{ when }\sigma\leq\sigma_{y} \tag{1}\]  
\[\sigma=E\cdot\varepsilon_{y}+E_{T}\cdot\big{(}\varepsilon-\varepsilon_{y} \big{)},\text{ when }\sigma\geq\sigma_{y} \tag{2}\]  
The \(E_{T}\) module may be determined by the value of ultimate strength:  
\[E_{T}=\frac{\sigma_{u,true}-\sigma_{y}}{\varepsilon_{u,true}-\varepsilon_{y}} \tag{3}\]  
The second model is based on the exponential hardening function (Figure 3, curves (3) and (4)). In this model, the relationship between the stresses and deformations is expressed as follows:  
\[\sigma=k\cdot\varepsilon^{u} \tag{4}\]  
This model provides a more accurate description of the properties of the material, but is more complicated in terms of the determination of the parameters that describe the law. The methodology of two (\(\sigma_{y}\), \(\sigma_{u}\), \(\varepsilon_{y}\), \(\varepsilon_{u}\)) or three (\(\sigma_{y}\), \(\sigma_{u}\), \(\sigma_{f}\), \(\varepsilon_{y}\), \(\varepsilon_{u}\), \(\varepsilon_{f}\)) characteristic points used in the LS-DYNA software package was applied to the determination of the parameters of the second model. The approximation quality was assessed using the mean squared deviation:  
\[SD=\frac{100}{n_{i}}\cdot\sqrt{\sum\!\left(\frac{\sigma_{\varepsilon}-\sigma_{ t}}{\sigma_{\varepsilon}}\right)^{2}} \tag{5}\]  
The obtained results are provided in Table 1.  
Exponential dependence obtained without accounting for the real burst stresses had the best correspondence to the experiment results (Figure 3, curve (3)).