# Real-Time GPU-Based Digital Image Correlation Sensor for Marker-Free Strain-Controlled Fatigue Testing

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## Abstract

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## Featured Application

**Strain in material testing is defined as relative elongation between two points of interest on the specimen surface. Digital image correlation (DIC) is a non-contact method to measure this deformation without slip and without unwanted normal pressure on the surface of the test specimen—in contrast to mechanical extensometers. However, most DIC sensors require special sample preparation with markers and they are too slow to meet the recommendations of ASTM E606 for strain-controlled low cycle fatigue (LCF) testing, i.e., cyclic fatigue testing in the elastic-plastic range.**

## Abstract

^{−5}relative to the field-of-view. The method is well accepted in material testing for non-contact strain measurement. However, the correlation makes it computationally slow on conventional, CPU-based computers. Recently, there have been DIC implementations based on graphics processing units (GPU) for strain-field evaluations with numerous templates per image at rather low image rates, but there are no real-time implementations for fast strain measurements with sampling rates above 1 kHz. In this article, a GPU-based 2D-DIC system is described achieving a strain sampling rate of 1.2 kHz with a latency of less than 2 milliseconds. In addition, the system uses the incidental, characteristic microstructure of the specimen surface for marker-free correlation, without need for any surface preparation—even on polished hourglass specimen. The system generates an elongation signal for standard PID-controllers of testing machines so that it directly replaces mechanical extensometers. Strain-controlled LCF measurements of steel, aluminum, and nickel-based superalloys at temperatures of up to 1000 °C are reported and the performance is compared to other path-dependent and path-independent DIC systems. According to our knowledge, this is one of the first GPU-based image processing systems for real-time closed-loop applications.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sensor Setup and Integration into Materials Testing Setup

#### 2.2. Real-Time DIC Implementation

## 3. Results

#### 3.1. Processing Time and Latency for Closed-Loop Control

**c**. The final step comprises copying the 3 × 3 pixel neighborhood of ${\mathit{C}}_{\mathit{k},\mathit{m}\mathit{a}\mathit{x}}\left({\mathit{u}}_{\mathbf{0}},{\mathit{v}}_{\mathit{0}}\right)$ back to the CPU and doing the subpixel-evaluation of the peak position according to Equations (5) and (6). The elongation $\mathbf{\Delta}\mathit{l}$ between the two subsets is transformed into an analogue 0–10 V signal for the PID controller. All processing times given in Figure 4 are average processing times measured for 1000 images.

#### 3.2. Comparison to Mechanical Extensometer

^{−5}(1σ) with maximum and minimum in a range of ±3 × 10

^{−5}[32]. So the measurement accuracy can be considered similar to the mechanical extensometer or optical ones based on IC-GN [5].

#### 3.3. Strain-Controlled Testing

#### 3.4. Real-Time Strain-Field Measurement

## 4. Discussion

#### 4.1. Sampling Rate and Processing Speed

#### 4.2. Latency

#### 4.3. Marker-Free Measurement

^{−5}(1σ) and a maximum error of ±3 ×·10

^{−5}measured by a zero-strain-test [32]. It is similar to that of IC-GN based system of Pan et al. [5] quantified by self-consistency using Poisson’s ratio. In our case, the camera resolution is larger (2048 pixel with 61 × 61 pixel per subset instead of 1024 pixel with 41 × 41-pixel subsets in [5]) and the subpixel-resolution lower (0.02 pixel instead of 0.005) which might be an effect of the zero-order shape function. However, these values are not exactly comparable. Nevertheless, they give a hint because other references are hardly available.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References and Notes

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**Figure 1.**Functional diagram of the closed-loop system. The digital image correlation (DIC) system delivers an analogue elongation signal so that it directly replaces a mechanical extensometer.

**Figure 2.**Image of the DIC measurement head and of a polished specimen in a servo-hydraulic testing machine. The red crosses mark the template positions ${\overrightarrow{r}}_{k}$ within the field-of-view.

**Figure 3.**Example images from a nickel-base superalloy (René 80) specimen: reference image (

**a**) with template subsets ${T}_{k}$, measurement image (

**b**) with search subsets ${S}_{k}$, zero-normalized cross-correlation results ${C}_{k}$ (

**c**), and enlarged 3D graph of the right correlation peak (

**d**). The images on the left (full size 2040 × 256 pixel) are split at the broken line.

**Figure 4.**Performance test results processing two subsets per image. The height of the bars gives the total processing time for two subsets per image, the numbers within each field give the processing time for each step in microseconds.

**Figure 5.**Force-controlled test on austenitic steel 1.4550 at room temperature with a 10 Hz triangular force-controlled cycle. The optical system (red curve) resolves the turning points as well as the tactile mechanical extensometer (black curve).

**Figure 6.**Strain-controlled test on nickel-base alloy René 80 at different temperatures from room temperature to 1000 °C. The specimen surface changes with increasing temperature.

**Figure 7.**

**Left**: Strain-controlled stress–strain diagrams of a marker-free and a speckle-painted René80 samples. The inset shows the noise of both measurements.

**Right**: Camera images from the marker-free sample 1 (

**top**) and the speckle-painted sample 2 (

**bottom**).

**Figure 8.**Strain-controlled low cycle fatigue (LCF) tests on AlSi piston alloy for automotive applications. Crack propagation can be observed during the experiment.

**Figure 9.**Real-time strain-field measurement where the local displacement is superimposed by color to the camera image (

**top**).

**Bottom**: The green line shows local displacement with ${l}_{0}=0.2\mathrm{mm}$ with a clear peak at crack 2. For strain-control, mean strain with ${l}_{0}=7.5\mathrm{mm}$ of the green line is measured between the ends (red line in bottom graph).

$\mathit{\epsilon}$ | Mechanical Strain | $\mathit{n}$ | Correlation Size | |
---|---|---|---|---|

${\epsilon}_{o}$ | Strain amplitude | ${n}_{T}$ | Template subset size | |

$\dot{\epsilon}$ | Strain rate | ${n}_{S}$ | Search subset size | |

$\sigma $ | Mechanical stress | $p\left(u,v\right)$ | Polynomial fitting | |

${\sigma}_{row}\left(i\right)$ | Standard deviation of | the correlation peak | ||

row $i$ | $r$ | Subset position in | ||

$I\left(i,j\right)$ | Image intensity | focal plane | ||

$C\left(u,v\right)$ | Correlation amplitude | $S$ | Search subset | |

$d$ | Displacement | $T$ | Template subset | |

${l}_{0}$ | Extensometer base | $u,v$ | Correlation image | |

length | coordinates | |||

$\Delta l$ | Elongation |

**Table 2.**Performance comparison of different real-time 2D-DIC systems. Parameters marked with ‘-‘ are not provided in the corresponding publication.

Pan 2015 [33] | Pan 2016 [5] | Wang 2018 [22] Var. 2 | Wang 2018 [22] Var. 4 | This, Strain-Contr. | This, Full-Field | |
---|---|---|---|---|---|---|

Processor type | CPU | CPU | CPU + GPU | CPU + GPU | CPU + GPU | CPU + GPU |

DIC algorithm | IC-GN | IC-GN | FFT-CC + IC-GN | FFT-CC + IC-GN | FFT-CC | FFT-CC |

Path-dependent | yes | yes | yes | no | no | no |

Maximum displacement | tracking | tracking | tracking | - | 97-pixel | 112-pixel |

No of subsets | 29949 | 4 | 9440 | 100 | 8 | 2500 |

Subset size ${n}_{T}$ | 21-pixel (61-pixel) | 41-pixel | 21-pixel | 21-pixel | 61-pixel | 31-pixel |

Sampling rate | 1.46 Hz (0.24 Hz) | 117 Hz | 30 Hz | 30 Hz | 1200 Hz | 10 Hz |

Processing rate | 44 kHz (7.2 kHz) | 468 Hz | 283 kHz | 3 kHz | 9.6 kHz | 25 kHz |

Latency | - | - | - | - | 2 ms | 100 ms |

Marker-free | no | no | no | no | yes | yes |

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**MDPI and ACS Style**

Blug, A.; Regina, D.J.; Eckmann, S.; Senn, M.; Bertz, A.; Carl, D.; Eberl, C.
Real-Time GPU-Based Digital Image Correlation Sensor for Marker-Free Strain-Controlled Fatigue Testing. *Appl. Sci.* **2019**, *9*, 2025.
https://doi.org/10.3390/app9102025

**AMA Style**

Blug A, Regina DJ, Eckmann S, Senn M, Bertz A, Carl D, Eberl C.
Real-Time GPU-Based Digital Image Correlation Sensor for Marker-Free Strain-Controlled Fatigue Testing. *Applied Sciences*. 2019; 9(10):2025.
https://doi.org/10.3390/app9102025

**Chicago/Turabian Style**

Blug, Andreas, David Joel Regina, Stefan Eckmann, Melanie Senn, Alexander Bertz, Daniel Carl, and Chris Eberl.
2019. "Real-Time GPU-Based Digital Image Correlation Sensor for Marker-Free Strain-Controlled Fatigue Testing" *Applied Sciences* 9, no. 10: 2025.
https://doi.org/10.3390/app9102025