## 2 Vehicle Life Cycle Environmental Profile
### Selection of Road Test Sections  
To determine whether the selected test conditions lead to the generation of greater than operating loads and to determine the possible effects of accelerated testing, an appropriate indicator is needed, with values that can be determined at the stage of qualification tests conducted by a designated testing institution when a limited set of operational data concerning the tested vehicle is available. The factor that meets these limitations may be the parameter \(d_{p}\), called pseudo-damage [30]. This is derived from the transformation of the general Basquin formula into the number of permissible load cycles \(N\) of monotonic loading with a range \(S\) of an element made of a material, the properties of which are represented by the coefficients \(\alpha\) (strength of the material to the load equal to half a cycle) and \(\beta\) (slope coefficient of the strength curve of the material in the log-log diagram in the range of the number of load cycles \(N\) from \(10^{3}\) to \(10^{6}\)) [19; 31], as shown in Figure 4.  
\[NS^{-\beta}=\alpha=const \tag{2}\]  
When generalizing Relation (2), the damage value can be included in the Palmgren-Miner linear damage accumulation formula as a quantity, \(D\), which should be \(D\leq 1\):  
\[D=\sum_{i}D_{i}=\sum_{i}\frac{n_{i}}{N_{i}}=\alpha^{-1}\sum_{i}n_{i}S_{i}^{ \beta}\leq 1 \tag{3}\]  
Equation (3) can be expressed in a simplified form as:  
\[D=\alpha^{-1}.d_{p} \tag{4}\]  
where \(d_{p}=\sum_{i}n_{i}S_{i}^{\beta}\). Then, when the purpose of the tests is to compare the effect of selected operating conditions (different road sections) on the damage rate of a vehicle component, the parameters \(\alpha\) and \(\beta\) can be assumed to remain constant during the tests, and Equation (4) is simplified to  
\[D=d_{p}=\sum_{i}n_{i}S_{i}^{\beta} \tag{5}\]  
where: \(d_{p}\) is pseudo-damage. It can be concluded from Relation (5) that for the evaluation of selected road sections (which have an influence on damage to the vehicle component), the load process can be recorded and then the cycles of this load can be counted using various cycle counting methods [19; 32]. Taking into account the length of the road sections and assuming that the test conditions are fixed (i.e., the load, tire pressure, and speed distributions are constant), a normalized value can be determined for each road section \(\widetilde{d}_{pi}\) as follows:  
\[\widetilde{d}_{pi}=\frac{d_{i}}{L_{i}} \tag{6}\]  
where \(d_{i}\) is the value calculated from Relation (4) and \(L_{i}\) is the length of the test section. By performing vehicle mileage tests on various test sections of roads of the same class (e.g., off-road), it is possible to determine which road generates more damage to a component by comparing the normalized values of pseudo damage \(\widetilde{d}_{p1}\) and \(\widetilde{d}_{px}\) under invariable load and comparable speed distributions in the tests:  
\[I_{m}=\frac{\widetilde{d}_{px}}{\widetilde{d}_{p1}}>1\ \rightarrow\text{test truck }x\text{ is }I_{m}-\text{ times more sevier than test truck }1 \tag{7}\]  
In our calculations, a preliminary value of \(\beta=5\) was assumed. This corresponds to a high cycle strength, typical for vehicle components without finishing operations such as grinding or polishing, and without notches, typical for welded joints [31]. Pictures that exemplify the analyzed test road sections are provided in Figure 5. The analyzed roads were of the off-road class only. Equation (5) applies stress-strain history to determine the fatigue life of a component. For preliminary selection of test road sections, this method allows the use of other signals containing data about load cycles, for example, an acceleration signal. However, in order to obtain a direct correlation with the fatigue life of a component, the measurement data should relate directly to the stress-strain history. Then, the choice of \(\alpha\) and \(\beta\) values relates strictly to the fatigue properties of the material.