**6. Case study**

stress. To obtain the most important information we install the measurement devices at the main stress points. To do this, it is necessary to perform a finite element simulation in order to get the point and the direction of the stresses. **Figure 14** shows the typical process used to

The components evaluated can be from different materials and built with different manufacturing process. In the next figure are shown instrumented components with a point selection from finite element evaluation [7]. Then to find the point and direction of the main stresses, components are instrumented with strain gauges. Its nominal resistance is 120 or 350 ohms. Higher resistance can be used for base material with low heat conductivity and higher voltage excitation than 10 Volts can be mainly used in environments with high electrical noise [18]. **Figure 15** shows chassis components instrumented, **Figure 15a** the rear subframe for a rigid axle, **Figure 15b** a front axle steering knuckle and **Figure 15c** a frontal axle track control

perform this kind of simulation.

264 Contact and Fracture Mechanics

**Figure 14.** General procedure for simulation.

arm.

The accelerated tests are developed to reduce the time and complexity of the test in order to have faster results. **Figure 16** shows a test stand to evaluate a frontal axle track control arm.

The information collected from the strain gauges can be used to evaluate the component, perform a correlation with virtual or analytical tools and build a spectrum. In not all the cases, can we directly measure the microstrain to validate the virtual simulation. The acceleration can be used to validate the finite element model with experimental acceleration results. With this validation, the stresses are found in a virtual way and can be used to perform the real-life prediction [4].

In the next part, the process to develop an accelerated test is shown. The time history in **Figure 17** shows the raw data time history to evaluate a track control arm, its main characteristics is a range of 42,354 N, maximum value of 21,473.6 N and minimum value of −20,880.8 N and the time length is 249.9 s.

After eliminating the amplitudes below 5kN, the new time history has the next characteristics: range of 41,717 N, maximum value of 21,283.5 N and minimum value of −20,433.6 N and the time length is 208.4 s. The pseudodamage has not been modified, while the time has been compressed from 249.9 to 208.4 s (16.6%). This is our target signal to generate the test spec-

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**Figure 18.** Statistical analysis of the raw data compared with the filtered signal (a) cycle counting, (b) cumulative cycle

**Figure 19.** Cutting load damage areas from the raw data time history filtered, (a) 0–249.9 s, (b) zoom between 221.7 and 233.6 s.

**Figure 20.** Statistical analysis after cutting loads below 5000 N, (a) cycle counting, (b) cumulative cycle count, and (c) PSD.

trum, in order to develop the durability test.

count, and (c)PSD.

**Figure 16.** Durability test stand for frontal track control arm.

**Figure 17.** Raw data time history for uniaxial test of track control arm.

The information acquired is then analyzed to eliminate unnecessary information such a noise. To do this, we apply filters, and perform statistical analyses. For a structural analysis it is necessary to have a low pass filter of 100 Hz [19]. To evaluate the changes after applying the filter, it is necessary to perform the statistical analysis using cycle counting tools and evaluate the pseudodamage using the linear damage rule [4]. The results of this evaluation are shown in **Figure 18**.

After applying the filter, the time history obtained has the next characteristics: range of 41,715.3 N, maximum value of 21,283.5 N and minimum of −20,433.6 N; the time length keeps its length of 249.9 s. The pseudodamage was reduced from 4.55 to 4.41, it means a reduction of 3.07% of damage, taking as a reference the raw signal.

There are many ways to accelerate the test. One of them is to eliminate the loads amplitude that do not apply a high amount of damage. To do this, in the time history, we eliminate the amplitude below 5000 N. **Figure 19** shows the process to show the selected areas and the final time history.

The cut signal and the raw data and the filtered raw data were compared using statistical analysis as it is shown in **Figure 20**.

After eliminating the amplitudes below 5kN, the new time history has the next characteristics: range of 41,717 N, maximum value of 21,283.5 N and minimum value of −20,433.6 N and the time length is 208.4 s. The pseudodamage has not been modified, while the time has been compressed from 249.9 to 208.4 s (16.6%). This is our target signal to generate the test spectrum, in order to develop the durability test.

**Figure 18.** Statistical analysis of the raw data compared with the filtered signal (a) cycle counting, (b) cumulative cycle count, and (c)PSD.

The information acquired is then analyzed to eliminate unnecessary information such a noise. To do this, we apply filters, and perform statistical analyses. For a structural analysis it is necessary to have a low pass filter of 100 Hz [19]. To evaluate the changes after applying the filter, it is necessary to perform the statistical analysis using cycle counting tools and evaluate the pseudodamage using the linear damage rule [4]. The results of this evaluation are shown

After applying the filter, the time history obtained has the next characteristics: range of 41,715.3 N, maximum value of 21,283.5 N and minimum of −20,433.6 N; the time length keeps its length of 249.9 s. The pseudodamage was reduced from 4.55 to 4.41, it means a reduction

There are many ways to accelerate the test. One of them is to eliminate the loads amplitude that do not apply a high amount of damage. To do this, in the time history, we eliminate the amplitude below 5000 N. **Figure 19** shows the process to show the selected areas and the final time

The cut signal and the raw data and the filtered raw data were compared using statistical

of 3.07% of damage, taking as a reference the raw signal.

**Figure 17.** Raw data time history for uniaxial test of track control arm.

**Figure 16.** Durability test stand for frontal track control arm.

266 Contact and Fracture Mechanics

analysis as it is shown in **Figure 20**.

in **Figure 18**.

history.

**Figure 19.** Cutting load damage areas from the raw data time history filtered, (a) 0–249.9 s, (b) zoom between 221.7 and 233.6 s.

**Figure 20.** Statistical analysis after cutting loads below 5000 N, (a) cycle counting, (b) cumulative cycle count, and (c) PSD.

To accelerate the test, we can increase the number of repetitions of loads with amplitude high and medium. **Figure 21** shows the statistical analysis increasing the medium loads. The time history obtained has the next characteristics: range of 42,340.9 N, maximum value of 21,906.9 N and minimum value of −20,433.9 N; time length of 135.1 s. The damage was increased from 4.55 to 8.52, which means that it was increased by a factor of 1.87, reducing the time by 45.93% with respect to the raw data.

**Figure 22** shows the statistical analysis increasing the amplitude of high loads and the number of repetitions of high and medium loads. The time history obtained has the next characteristics: range of 59,124.4 N, maximum amplitude of 30,670.6 N and minimum of −28,543.8 N; time length of 167.7 s. The damage was increased from 4.55 to 39.6. This means that it was increased by a factor of 8.7, reducing the time by 32.89% with respect to the raw data.

**Figure 23a** summarizes the spectrums of the all strategies extrapolated to the time histories, the raw filtered data could be cut at below load levels to reduce the time; the medium and high loads in the signal can be increased, reducing the original time and increasing the damage. **Figure 23b** shows the schematic techniques to accelerate the test.

An alternative option to represent the spectrum instead of time history is with Matrix Rainflow. **Figure 24** shows the four analyzed signals: original (**Figure 24a**), filtered (**Figure 24b**), increasing the medium loads (**Figure 24c**), and increasing the number of reversals in high loads inclusive of above the maximum loads of the raw data (**Figure 24d**). The major differences are shown in **Figure 24c** and **d** for medium and high loads, respectively, and the ranges for medium-to-high loads and its number of repetitions have been increased.

**Figure 21.** Statistical analysis increasing medium loads, (a) cycle counting, (b) cumulative cycle count, and (c) PSD.

For variable amplitude loads, this statistical analysis is used to monitor and guarantee that the loads have been applied correctly. Because it is necessary to build a drive used for the actuators to test the applied loads, the feedback through loads are measured and compared with the desired spectrum, and the drive to control the test actuators is developed through an iteration process [20]. Another way to perform an accelerated test based on the spectrum is using two load levels with a constant amplitude load for each load level. Then these results are plotted in an S-N component curve, and the specimen results are evaluated to predict the fatigue strength and different load levels [21]. **Figure 25** shows the experimental results of

**Figure 24.** Rainflow matrix (a) raw data, (b) cut filtered signal, (c) medium loads increased, and (d) high loads increased.

**Figure 23.** Spectrum of the time histories, (a) summary of time test reduction and (b) schematic accelerated test.

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In an S-N curve, the percent replication *(PR)* is found by using the number of stress levels *(L)*

uniaxial constant amplitude loads of steering knuckle.

*)* as is shown in Eq. (8).

and a sample size *(ns*

**Figure 22.** Statistical analysis increasing high loads: (a) cycle counting, (b) cumulative cycle count, and (c) PSD.

To accelerate the test, we can increase the number of repetitions of loads with amplitude high and medium. **Figure 21** shows the statistical analysis increasing the medium loads. The time history obtained has the next characteristics: range of 42,340.9 N, maximum value of 21,906.9 N and minimum value of −20,433.9 N; time length of 135.1 s. The damage was increased from 4.55 to 8.52, which means that it was increased by a factor of 1.87, reducing the time by 45.93% with

**Figure 22** shows the statistical analysis increasing the amplitude of high loads and the number of repetitions of high and medium loads. The time history obtained has the next characteristics: range of 59,124.4 N, maximum amplitude of 30,670.6 N and minimum of −28,543.8 N; time length of 167.7 s. The damage was increased from 4.55 to 39.6. This means that it was

**Figure 23a** summarizes the spectrums of the all strategies extrapolated to the time histories, the raw filtered data could be cut at below load levels to reduce the time; the medium and high loads in the signal can be increased, reducing the original time and increasing the dam-

An alternative option to represent the spectrum instead of time history is with Matrix Rainflow. **Figure 24** shows the four analyzed signals: original (**Figure 24a**), filtered (**Figure 24b**), increasing the medium loads (**Figure 24c**), and increasing the number of reversals in high loads inclusive of above the maximum loads of the raw data (**Figure 24d**). The major differences are shown in **Figure 24c** and **d** for medium and high loads, respectively, and the ranges for

increased by a factor of 8.7, reducing the time by 32.89% with respect to the raw data.

age. **Figure 23b** shows the schematic techniques to accelerate the test.

medium-to-high loads and its number of repetitions have been increased.

**Figure 22.** Statistical analysis increasing high loads: (a) cycle counting, (b) cumulative cycle count, and (c) PSD.

**Figure 21.** Statistical analysis increasing medium loads, (a) cycle counting, (b) cumulative cycle count, and (c) PSD.

respect to the raw data.

268 Contact and Fracture Mechanics

**Figure 23.** Spectrum of the time histories, (a) summary of time test reduction and (b) schematic accelerated test.

**Figure 24.** Rainflow matrix (a) raw data, (b) cut filtered signal, (c) medium loads increased, and (d) high loads increased.

For variable amplitude loads, this statistical analysis is used to monitor and guarantee that the loads have been applied correctly. Because it is necessary to build a drive used for the actuators to test the applied loads, the feedback through loads are measured and compared with the desired spectrum, and the drive to control the test actuators is developed through an iteration process [20]. Another way to perform an accelerated test based on the spectrum is using two load levels with a constant amplitude load for each load level. Then these results are plotted in an S-N component curve, and the specimen results are evaluated to predict the fatigue strength and different load levels [21]. **Figure 25** shows the experimental results of uniaxial constant amplitude loads of steering knuckle.

In an S-N curve, the percent replication *(PR)* is found by using the number of stress levels *(L)* and a sample size *(ns )* as is shown in Eq. (8).

$$P\_n = 100\left(1 - \frac{L}{N\_\*}\right) \tag{8}$$

This value represents the portion of specimens that may be used in the variability to replicate the tests. The recommended values by Lee et al. [18] are as follows:

17–33 for preliminary and exploratory tests,

33–50 for research and development tests,

50–75 for design allowable data tests and

75–88 for reliability tests.

Steering knuckle results shown in **Figure 25** have 7 level of loads, and 90 Specimens using Eq. (4) get a percent replication of 92.2. These high values obtained from these results are evaluated to analyze a proposal to estimate an S-N curve. For a component test, recommended samples used depend on the target, for research and development tests 6–12, and for reliability tests 12–24 samples. The minimum samples for two load levels are three specimens for each load level.

The median is the central value of results at each load level, and the tendency is considered at 50% of reliability and is necessary to evaluate it to know the scatter of the factors described in **Figure 1** (Eq. (8)).

$$\boldsymbol{\mu} = \frac{1}{n} \sum\_{i=1}^{n} \mathbf{x}\_i \tag{9}$$

Results of the slope found in tests are compared with the requirement, and changes on the slope affect the behavior at low or high load levels. **Figure 26** shows the evaluation of the

Accelerated Fatigue Test in Mechanical Components http://dx.doi.org/10.5772/intechopen.72640 271

**Figure 26.** Evaluation results (a) slope test ktest = slope requirement kreq, (b) ktest< kreq, (c) ktest> kreq.

Accelerated tests are used to reduce cost and time in the development process. It can also be used to monitor the quality of the components during its manufacturing life. Experimental evaluation is mandatory prior to final release and start of production to analyze the scatter of the manufacturing process and prevent failures in service life. The importance of performing variable amplitude loads tests is because the prediction of fatigue life under the complex spectrum loads is not possible by any damage hypothesis. The spectrum to evaluate the components in the tests is developed with the loads from different customers and markets and use conditions. Experimental results show discrepancies even within the same batch of production, and the statistical value to evaluate the reliability of the lot under test is the standard deviation that shows the influence of the factors described in **Figure 1**. Although the tests are performed under controlled conditions in a laboratory, in specimens with notches, the batch of production is released if the standard deviation of its fatigue results has a maximum value of 0.2. For samples without notches in uniaxial tests, the maximum scatter allowed is 0.3 and 0.6 for complex test [22]. To evaluate the fatigue strength as well as the scatter, it is necessary to perform durability tests, to prevent failures

results with constant amplitude loads.

**7. Conclusions**

on the service life.

**Author details**

Moises Jimenez1,2\*

\*Address all correspondence to: moisesjimenezmartinez@gmail.com 1 Technical Development, Volkswagen de Mexico, Puebla, México

2 Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Monterrey, Mexico

To evaluate the scatter of the components based on its fatigue results, the standard deviation is evaluated using Eq. (10). To take into consideration, its results have to be between 0.05 and 0.15; for samples without notches, the range is between 0.1 and 0.2, for uniaxial tests the range is between 0.2 and 0.3, while in complex tests, it can reach values between 0.3 and 0.6 [22].

$$\mathbf{s}^2 = \frac{1}{n-1} \sum\_{i=1}^{n} (\mathbf{x}\_i - \boldsymbol{\mu})^2 \tag{10}$$

**Figure 25.** Test results in steering knuckle analysis.

**Figure 26.** Evaluation results (a) slope test ktest = slope requirement kreq, (b) ktest< kreq, (c) ktest> kreq.

Results of the slope found in tests are compared with the requirement, and changes on the slope affect the behavior at low or high load levels. **Figure 26** shows the evaluation of the results with constant amplitude loads.
